Ceramic Materials

Ceramic Materials Ceramic Materials Science and Engineering C. Barry Carter M. Grant Norton C. Barry Carter M. Grant Norton Department of Chemical Engineering School of Mechanical and Materials Engineering and Materials Science Washington State University University of Minnesota Pullman, WA 99164-2920 Minneapolis, MN 55455-0132 Details for Figures and Tables are listed following the index Library of Congress Control Number: 2006938045 ISBN-10: 0-387-46270-8 e-ISBN-10: 0-387-46271-6 ISBN-13: 978-0-387-46270-7 e-ISBN-13: 978-0-387-46271-4 Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC. All rights reserved. This work may not be translated or copied in whole or in part without the written permis- sion of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to pro- prietary rights. 9 8 7 6 5 4 3 2 1 springer.com This text is dedicated to our wives Bryony Carter and Christine Wall Words cannot explain, describe, or say enough Thanks to you both  Preface In today’s materials science curriculum, there is often only time for one course on ceramic materials. Students will usually take courses on mechanical properties, thermodynamics and kinetics, and the structure of materials. Many will also have taken an introductory overview of materials science. In each of these courses, the students will have encountered ceramic materials. The present text assumes back- ground knowledge at this introductory level but still provides a review of such critical topics as bonding, crystal structures, and lattice defects. The text has been divided into seven parts and 37 chapters: we will explain the thinking behind these decisions. Part I examines the history and development of ceramic materials: how they have literally shaped civilization. We include this material in our introductory lectures and then make the two chapters assigned reading. Part II discusses the bonding, structure, and the relationship among phases. Students often find this part of the course to be the most difficult because structures are implicitly 3-dimensional. However, so many properties depend on the structure whether crystalline or amorphous. We have limited the number of structures to what we think the students can manage in one course, we give references to texts that the students can spend a lifetime studying and recommend our favorite software package. Part III consists of two chapters on our tools of the trade. Most ceramics are heated at some stage during processing. Unfortunately heat treatments are rarely exactly what we would like them to be; the heating rate is too slow, the furnace contaminates the sample, the environment is not what we want (or think it is), etc. Techniques for characterizing materials fill books and the students are familiar with many already from their studies on metals. So, the purpose of this chapter is, in part, to encourage the student to find out more about techniques that they might not have heard of or might not have thought of applying to ceramics; you could certainly skip Part III and make it assigned reading especially if the students are taking overlapping courses. Part IV discusses defects in ceramics and aims at providing a comprehensive overview while again not being a dedicated book on the subject. Part IV leads straight into Part V—a basic discus- sion of mechanical properties applied specifically to ceramics. The last two parts contain just over half the chapters. The two topics are Processing (Part VI) and Properties (Part VII) and are, of course, the reason we study ceramic materials. The warning is—these topics form the second half of the book because the student should understand the materials first, but it then becomes too easy to miss them in a one- semester course due to lack of time. We know, we have done this and the students miss the part that they would often appreciate most. Chapter 36 is probably the most fun for half the students and both the authors; Chapter 37 is the most important for all of us. Many modern ceramists will acknowledge their debt to the late David Kingery. His pioneering 1960 text was one of the first to regard ceramics as a serious scientific subject. Both his book and his research papers have been referenced throughout the present text. Our definition of a ceramic material follows directly from Kingery’s definition: a nonmetallic, inorganic solid. Nonmetallic refers to the bonding: in ceramics, it is predominantly covalent and/or ionic. Ceramics are always inorganic solids although they also may be major or minor components of composite materials. P r e fa c e ........................................................................................................................................................................ vii Throughout the text we ask the question “what is special for ceramics?” The answer varies so much that it can be difficult to generalize but that is what we are attempting where possible. Having said that, ceramics are always providing surprises. Indium tin oxide is a transparent conductor of electricity. Yttrium barium copper oxide is a superconductor at 90 K. Doped gallium nitride is revolutionizing home lighting and is becoming a critical component for all traffic lights. Neodynium-doped garnet is the basis of many solid-state lasers. A feature of this text is that we keep in mind that many of today’s high-tech ceramic materials and processing routes have their origin in the potter’s craft or in the jeweler’s art, and materials that are new to the materials scientist may be old friends to the mineralogist and geologist. Throughout the text we will make connec- tions to these related fields. The history of ceramics is as old as civilization and our use of ceramics is a measure of the technological progress of a civilization. The text covers ceramic materials from the fundamentals to industrial applica- tions including a consideration of safety and their impact on the environment. We also include throughout the text links to economics and art. So many choices in ceramics have been determined by economics. We often think of ceramics as being inexpensive materials: bottles, bricks and tiles certainly are. Ceramics are also the most valuable materials we have: per gram, emerald still holds the record. No modern materials text can be complete without considering materials at the nanoscale. Nanoceramics appear throughout this text but we decided not to create a special chapter on the topic. What we have done is to highlight some of these topics as they appear naturally in the text. It is worth noting that nanoscale ceramics have been used for centuries; it is just recently that we have had a name for them. The figures generally contain much more information than is given in the text. We use this fact in some of the homework questions and hope that the extra detail will encourage the students to delve into the literature to learn more about the topic. One place to start this search is, of course, with the original citation if there is one. These citations are grouped together at the end of the text, in part for this purpose, but also to recognize the contributions of our colleagues. On the Web site (http:/web.mac.com/ceramicsbook/iweb), we are developing supplementary material including an extensive list of suggestions for filling any weak or missing areas in the student’s background and will update these suggestions peri- odically. We give annotated references to the original studies that have been quoted in the text. We also include further examples of images that supplement those in the text. The Web site will also house two sets of questions to complement those at the end of each chapter. One set consists of shorter questions that we use in pop quizzes but are also useful for students, especially those working alone, to assess their own progress. The second set includes questions, which we use for homework and take- home exams. After reviewing some history, we consider bonding and structures (Chapters 3–8). Essentially, this set of chapters examines the science that underpins our definition of a ceramic material. The way atoms are connected together by covalent or ionic bonds is illustrated by considering simple and complex structures. We introduce glasses as a natural subsection of complex structures rather than as a separate branch of ceram- ics. Window glass is a ceramic material, just like lithium niobate, mica or silicon. The difference is that glasses are not crystalline: crystalline quartz has more in common with amorphous silica glass than it does with alumina. The final chapter in this sequence is important in most branches of materials science: which ceramics are compatible with other ceramics, which are not, and which of these materials react to form new compounds. We emphasize that these are equilibrium phase diagrams and that ceramics often need high temperatures and long times to attain equilibrium. (Geological times are needed in some cases.) The next two topics (Chapters 9–10) examine two tools (in the broadest sense) that we will use: we need to prepare the ceramic material and this usually involves heating. Then we need to characterize it. viii ........................................................................................................................................................................ P r e fa c e  In Chapters 11 thru 15 we explore the whole topic of defects in ceramics, from point defects to voids, and elaborate on why they are important in the rest of the text. In Chapter 13 the combination of surfaces, nanoparticles and foams builds on the common theme of the surface as a defect but does not treat it in isolation from prop- erties or real ceramic processing. The positioning of the next three chapters (Chapters 16–18) on mechanical properties was decided because of the authors’ bias. This allows us to integrate mechanical behavior into processing, thin films, glass ceramics, and such in the immediately following chapters. We begin the section on processing with a discussion of minerals and then con- sider the different forms and shapes of ceramic powders. The topic of glass is sepa- rated into Chapters 21 and 26 with the use of organic chemistry, the principles of shaping, and the processes that occur during shaping (sintering, grain growth and phase transformations) separating them. In this text we do not want to separate pro- cessing from the science; where we have separated them, this is only done to help the student absorb the concepts serially rather than in parallel! We discuss making films and growing crystals in Chapters 27–29. This group of chapters really gets to the heart of ceramic processing and mixes liquids (whether due to a solvent or to melting) in with the powders. We do not emphasize the mechanical aspects but make it clear that a full understanding requires that we think about them and not just for hot-pressing or for crystalline ceramics. The remaining eight chapters cover the applications of ceramics with the empha- sis on what property is being exploited, how we optimize it, and just how far we can still go with these materials; remember how the development of glass optical fibers has changed society forever in less than 40 years. Again our bias is clear. Ceramics are amazing materials and the underlying physics is fascinating but the subject of physics can easily obscure this excitement. Physicists are often not fully aware of the value of chemistry and all too often underestimate the feel a ceramist has for these materials. Before concluding the text with the most rapidly changing topic of industry and the environment in Chapter 37, we examine two groups of ceramics that affect us all even though we may not think about them—ceramics in biology/medicine and ceramics as gemstones. Whether as objects of beauty or symbols of something more lasting, polished natural single crystals of ceramics have inspired awe for centuries and challenged scientists for nearly as long. We would like to thank our students and postdocs, past and present, who have helped us so much to appreciate and enjoy ceramic materials. The students include Katrien Ostyn, Karen Morrissey, Zvi Elgat, Bruno De Cooman, Yonn Rasmussen (formerly Simpson), David Susnitzky, Scott Summerfelt, Lisa Moore (formerly Tietz), Chris Scarfone, Ian Anderson, Mike Mallamaci, Paul Kotula, Sundar Ramamurthy, Jason Heffelfinger, Matt Johnson, Andrey Zagrebelny, Chris Blanford, Svetlana Yanina, Shelley Gilliss, Chris Perrey, Jeff Farrer, Arzu Altay, Jessica Riesterer, Jonathan Winterstein, Maxime Guinel, Dan Eakins, Joel LeBret, Aaron LaLonde, and Tyler Pounds. The postdocs include John Dodsworth, Monica Backhaus-Ricoult, Hermann Wendt, Werner Skrotski, Thomas Pfeiffer, Mike Bench, Carsten Korte, Joysurya Basu and Divakar Ramachandran and especially Ravi Ravishankar and Stuart McKernan. We thank Carolyn Swanson for carefully drawing so many dia- grams for this text and Janet McKernan for her expert proofreading, continued patience, and rare commonsense. Janet generated the index, negotiated hyphens, and tried to remove all our errors and typos; those that remain that should not or are missing that should be present are solely the responsibility of the authors, We thank our many colleagues for providing figures and understanding on some of the special topics. In particular, we thank Richard Hughes, Rosette Gault, Peter Ilsley, Liz Huffman, and Fred Ward. We thank our colleagues and collaborators. David Kohlstedt who introduced CBC to ceramics. Herman Schmalzried who is not only our guru on solid-state reactions but the model of a truly wonderful Professor and mentor. Gisela Schmalzried who provided meals and company during many visits to Hannover, Göttingen and Bun- tenbock. Paul Hlava has been our guide and guru on everything to do with gems and P r e fa c e ........................................................................................................................................................................ ix minerals: he is one of the world’s natural teachers. MGN thanks Brian Cantor for hosting his sabbatic at Oxford University where parts of this text were written. Like- wise, CBC thanks Eva Olssen at Chalmer’s University, Yoshio Bando at NIMS, and Paul Midgley, Colin Humphreys and the Master and Fellows of Peterhouse at Cambridge University. C. Barry Carter M. Grant Norton x ........................................................................................................................................................................ P r e fa c e  Contents Preface ................................................ vii PART I HISTORY AND INTRODUCTION 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Definitions 3 1.2 General Properties 4 1.3 Types of Ceramic and their Applications 5 1.4 Market 6 1.5 Critical Issues for the Future 7 1.6 Relationship between Microstructure, Processing and Properties 8 1.7 Safety 9 1.8 Ceramics on the Internet 10 1.9 On Units 10 2 Some History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 Earliest Ceramics: The Stone Age 15 2.2 Ceramics in Ancient Civilizations 17 2.3 Clay 19 2.4 Types of Pottery 19 2.5 Glazes 20 2.6 Development of a Ceramics Industry 21 2.7 Plaster and Cement 22 2.8 Brief History of Glass 24 2.9 Brief History of Refractories 25 2.10 Major Landmarks of the Twentieth Century 26 2.11 Museums 28 2.12 Societies 29 2.13 Ceramic Education 29 PART II MATERIALS 3 Background You Need to Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1 The Atom 35 3.2 Energy Levels 36 3.3 Electron Waves 37 3.4 Quantum Numbers 37 3.5 Assigning Quantum Numbers 39 3.6 Ions 42 3.7 Electronegativity 44 3.8 Thermodynamics: The Driving Force for Change 45 3.9 Kinetics: The Speed of Change 47 Contents ..................................................................................................................................................................... xi  4 Bonds and Energy Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.1 Types of Interatomic Bond 51 4.2 Young’s Modulus 51 4.3 Ionic Bonding 53 4.4 Covalent Bonding 58 4.5 Metallic Bonding in Ceramics 63 4.6 Mixed Bonding 64 4.7 Secondary Bonding 64 4.8 Electron Energy Bands in Ceramics 66 5 Models, Crystals, and Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.1 Terms and Definitions 71 5.2 Symmetry and Crystallography 74 5.3 Lattice Points, Directions, and Planes 75 5.4 The Importance of Crystallography 76 5.5 Pauling’s Rules 76 5.6 Close-Packed Arrangements: Interstitial Sites 79 5.7 Notation for Crystal Structures 81 5.8 Structure, Composition, and Temperature 81 5.9 Crystals, Glass, Solids, and Liquid 82 5.10 Defects 83 5.11 Computer Modeling 83 6 Binary Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.1 Background 87 6.2 CsCl 88 6.3 NaCl (MgO, TiC, PbS) 88 6.4 GaAs (β-SiC) 89 6.5 AlN (BeO, ZnO) 90 6.6 CaF2 91 6.7 FeS2 92 6.8 Cu2O 93 6.9 CuO 93 6.10 TiO2 93 6.11 Al2O3 94 6.12 MoS2 and CdI2 95 6.13 Polymorphs, Polytypes, and Polytypoids 96 7 Complex Crystal and Glass Structures . . . . . . . . . . . . . . . . . . . . . . . . 100 7.1 Introduction 100 7.2 Spinel 101 7.3 Perovskite 102 7.4 The Silicates and Structures Based on SiO4 104 7.5 Silica 105 7.6 Olivine 106 7.7 Garnets 107 7.8 Ring Silicates 107 7.9 Micas and Other Layer Materials 108 7.10 Clay Minerals 109 7.11 Pyroxene 109 7.12 β-Aluminas and Related Materials 110 7.13 Calcium Aluminate and Related Materials 111 7.14 Mullite 111 7.15 Monazite 111 xii ..................................................................................................................................................................... C o n t e n t s  7.16 YBa2Cu3O7 and Related High-Temperature Superconductors (HTSCs) 112 7.17 Si3N4, SiAlONs, and Related Materials 113 7.18 Fullerenes and Nanotubes 113 7.19 Zeolites and Microporous Compounds 114 7.20 Zachariasen’s Rules for the Structure of Glass 115 7.21 Revisiting Glass Structures 117 8 Equilibrium Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 8.1 What’s Special about Ceramics? 120 8.2 Determining Phase Diagrams 121 8.3 Phase Diagrams for Ceramists: The Books 124 8.4 Gibbs Phase Rule 124 8.5 One Component (C = 1) 125 8.6 Two Components (C = 2) 126 8.7 Three and More Components 128 8.8 Composition with Variable Oxygen Partial Pressure 130 8.9 Quaternary Diagrams and Temperature 132 8.10 Congruent and Incongruent Melting 132 8.11 Miscibility Gaps in Glass 133 PART III TOOLS 9 Furnaces ................................................ 139 9.1 The Need for High Temperatures 139 9.2 Types of Furnace 139 9.3 Combustion Furnaces 140 9.4 Electrically Heated Furnaces 141 9.5 Batch or Continuous Operation 141 9.6 Indirect Heating 143 9.7 Heating Elements 144 9.8 Refractories 146 9.9 Furniture, Tubes, and Crucibles 147 9.10 Firing Process 148 9.11 Heat Transfer 148 9.12 Measuring Temperature 149 9.13 Safety 151 10 Characterizing Structure, Defects, and Chemistry . . . . . . . . . . . . . . 154 10.1 Characterizing Ceramics 154 10.2 Imaging Using Visible-Light, IR, and UV 155 10.3 Imaging Using X-rays and CT Scans 157 10.4 Imaging in the SEM 158 10.5 Imaging in the TEM 159 10.6 Scanning-Probe Microscopy 161 10.7 Scattering and Diffraction Techniques 162 10.8 Photon Scattering 163 10.9 Raman and IR Spectroscopy 163 10.10 NMR Spectroscopy and Spectrometry 165 10.11 Mössbauer Spectroscopy and Spectrometry 166 10.12 Diffraction in the EM 168 10.13 Ion Scattering (RBS) 168 10.14 X-ray Diffraction and Databases 169 10.15 Neutron Scattering 171 Contents ..................................................................................................................................................................... xiii  10.16 Mass Spectrometry 172 10.17 Spectrometry in the EM 172 10.18 Electron Spectroscopy 174 10.19 Neutron Activation Analysis (NAA) 175 10.20 Thermal Analysis 175 PART IV DEFECTS 11 Point Defects, Charge, and Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . 181 11.1 Are Defects in Ceramics Different? 181 11.2 Types of Point Defects 182 11.3 What Is Special for Ceramics? 183 11.4 What Type of Defects Form? 184 11.5 Equilibrium Defect Concentrations 184 11.6 Writing Equations for Point Defects 186 11.7 Solid Solutions 187 11.8 Association of Point Defects 189 11.9 Color Centers 190 11.10 Creation of Point Defects in Ceramics 191 11.11 Experimental Studies of Point Defects 192 11.12 Diffusion 192 11.13 Diffusion in Impure, or Doped, Ceramics 193 11.14 Movement of Defects 197 11.15 Diffusion and Ionic Conductivity 197 11.16 Computing 199 12 Are Dislocations Unimportant? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 12.1 A Quick Review of Dislocations 202 12.2 Summary of Dislocation Properties 206 12.3 Observation of Dislocations 206 12.4 Dislocations in Ceramics 208 12.5 Structure of the Core 208 12.6 Detailed Geometry 211 12.7 Defects on Dislocations 214 12.8 Dislocations and Diffusion 215 12.9 Movement of Dislocations 216 12.10 Multiplication of Dislocations 216 12.11 Dislocation Interactions 217 12.12 At the Surface 219 12.13 Indentation, Scratching, and Cracks 219 12.14 Dislocations with Different Cores 220 13 Surfaces, Nanoparticles, and Foams . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 13.1 Background to Surfaces 224 13.2 Ceramic Surfaces 225 13.3 Surface Energy 225 13.4 Surface Structure 227 13.5 Curved Surfaces and Pressure 230 13.6 Capillarity 230 13.7 Wetting and Dewetting 231 13.8 Foams 232 13.9 Epitaxy and Film Growth 233 13.10 Film Growth in 2D: Nucleation 233 13.11 Film Growth in 2D: Mechanisms 234 13.12 Characterizing Surfaces 235 xiv ..................................................................................................................................................................... C o n t e n t s  13.13 Steps 239 13.14 In Situ 240 13.15 Surfaces and Nanoparticles 241 13.16 Computer Modeling 241 13.17 Introduction to Properties 242 14 Interfaces in Polycrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 14.1 What Are Grain Boundaries? 246 14.2 For Ceramics 248 14.3 GB Energy 249 14.4 Low-Angle GBs 251 14.5 High-Angle GBs 254 14.6 Twin Boundaries 255 14.7 General Boundaries 258 14.8 GB Films 259 14.9 Triple Junctions and GB Grooves 262 14.10 Characterizing GBs 263 14.11 GBs in Thin Films 264 14.12 Space Charge and Charged Boundaries 265 14.13 Modeling 265 14.14 Some Properties 265 15 Phase Boundaries, Particles, and Pores . . . . . . . . . . . . . . . . . . . . . . . . 269 15.1 The Importance 269 15.2 Different Types 269 15.3 Compared to Other Materials 270 15.4 Energy 270 15.5 The Structure of PBs 271 15.6 Particles 272 15.7 Use of Particles 276 15.8 Nucleation and Growth of Particles 276 15.9 Pores 277 15.10 Measuring Porosity 278 15.11 Porous Ceramics 279 15.12 Glass/Crystal Phase Boundaries 280 15.13 Eutectics 281 15.14 Metal/Ceramic PBs 282 15.15 Forming PBs by Joining 283 PART V MECHANICAL STRENGTH AND WEAKNESS 16 Mechanical Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 16.1 Philosophy 289 16.2 Types of Testing 291 16.3 Elastic Constants and Other “Constants” 292 16.4 Effect of Microstructure on Elastic Moduli 294 16.5 Test Temperature 295 16.6 Test Environment 296 16.7 Testing in Compression and Tension 296 16.8 Three- and Four-Point Bending 297 16.9 K Ic from Bend Test 298 16.10 Indentation 299 16.11 Fracture Toughness from Indentation 300 16.12 Nanoindentation 301 16.13 Ultrasonic Testing 301 Contents ..................................................................................................................................................................... xv  16.14 Design and Statistics 302 16.15 SPT Diagrams 305 17 Deforming: Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 17.1 Plastic Deformation 309 17.2 Dislocation Glide 310 17.3 Slip in Alumina 312 17.4 Plastic Deformation in Single Crystals 313 17.5 Plastic Deformation in Polycrystals 314 17.6 Dislocation Velocity and Pinning 315 17.7 Creep 317 17.8 Dislocation Creep 317 17.9 Diffusion-Controlled Creep 318 17.10 Grain-Boundary Sliding 318 17.11 Tertiary Creep and Cavitation 319 17.12 Creep Deformation Maps 321 17.13 Viscous Flow 321 17.14 Superplasticity 322 18 Fracturing: Brittleness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 18.1 The Importance of Brittleness 325 18.2 Theoretical Strength: The Orowan Equation 326 18.3 The Effect of Flaws: The Griffith Equation 327 18.4 The Crack Tip: The Inglis Equation 329 18.5 Stress Intensity Factor 329 18.6 R Curves 330 18.7 Fatigue and Stress Corrosion Cracking 331 18.8 Failure and Fractography 332 18.9 Toughening and Ceramic Matrix Composites 335 18.10 Machinable Glass-Ceramics 338 18.11 Wear 338 18.12 Grinding and Polishing 339 PART VI PROCESSING 19 Raw Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 19.1 Geology, Minerals, and Ores 345 19.2 Mineral Formation 345 19.3 Beneficiation 347 19.4 Weights and Measures 347 19.5 Silica 348 19.6 Silicates 348 19.7 Oxides 351 19.8 Nonoxides 354 20 Powders, Fibers, Platelets, and Composites . . . . . . . . . . . . . . . . . . . . . 359 20.1 Making Powders 359 20.2 Types of Powders 360 20.3 Mechanical Milling 360 20.4 Spray Drying 362 20.5 Powders by Sol-Gel Processing 363 20.6 Powders by Precipitation 363 20.7 Chemical Routes to Nonoxide Powders 364 20.8 Platelets 365 20.9 Nanopowders by Vapor-Phase Reactions 365 xvi ..................................................................................................................................................................... Contents  20.10 Characterizing Powders 366 20.11 Characterizing Powders by Microscopy 366 20.12 Sieving 366 20.13 Sedimentation 367 20.14 The Coulter Counter 368 20.15 Characterizing Powders by Light Scattering 368 20.16 Characterizing Powders by X-ray Diffraction 369 20.17 Measuring Surface Area (the BET Method) 369 20.18 Determining Particle Composition and Purity 370 20.19 Making Fibers and Whiskers 370 20.20 Oxide Fibers 371 20.21 Whiskers 372 20.22 Glass Fibers 372 20.23 Coating Fibers 373 20.24 Making Ceramic–Matrix Composites 374 20.25 Ceramic–Matrix Composites from Powders and Slurries 374 20.26 Ceramic–Matrix Composites by Infiltration 375 20.27 In Situ Processes 375 21 Glass and Glass-Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 21.1 Definitions 379 21.2 History 380 21.3 Viscosity, η 383 21.4 Glass: A Summary of Its Properties, or Not 385 21.5 Defects in Glass 386 21.6 Heterogeneous Glass 386 21.7 Yttrium–Aluminum Glass 386 21.8 Coloring Glass 386 21.9 Glass Laser 388 21.10 Precipitates in Glass 388 21.11 Crystallizing Glass 388 21.12 Glass as Glaze and Enamel 390 21.13 Corrosion of Glass and Glaze 392 21.14 Types of Ceramic Glasses 393 21.15 Natural Glass 394 21.16 The Physics of Glass 396 22 Sols, Gels, and Organic Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 22.1 Sol-Gel Processing 400 22.2 Structure and Synthesis of Alkoxides 401 22.3 Properties of Alkoxides 402 22.4 The Sol-Gel Process Using Metal Alkoxides 403 22.5 Characterization of the Sol-Gel Process 406 22.6 Powders, Coatings, Fibers, Crystalline, or Glass 407 23 Shaping and Forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 23.1 The Words 412 23.2 Binders and Plasticizers 413 23.3 Slip and Slurry 413 23.4 Dry Pressing 414 23.5 Hot Pressing 414 23.6 Cold Isostatic Pressing 415 23.7 Hot Isostatic Pressing 416 23.8 Slip Casting 417 23.9 Extrusion 418 Contents ..................................................................................................................................................................... xvii  23.10 Injection Molding 419 23.11 Rapid Prototyping 420 23.12 Green Machining 420 23.13 Binder Burnout 421 23.14 Final Machining 421 23.15 Making Porous Ceramics 422 23.16 Shaping Pottery 422 23.17 Shaping Glass 423 24 Sintering and Grain Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 24.1 The Sintering Process 427 24.2 The Terminology of Sintering 429 24.3 Capillary Forces and Surface Forces 429 24.4 Sintering Spheres and Wires 429 24.5 Grain Growth 431 24.6 Sintering and Diffusion 431 24.7 Liquid-Phase Sintering 433 24.8 Hot Pressing 433 24.9 Pinning Grain Boundaries 434 24.10 More Grain Growth 435 24.11 Grain Boundaries, Surfaces, and Sintering 436 24.12 Exaggerated Grain Growth 437 24.13 Fabricating Complex Shapes 438 24.14 Pottery 439 24.15 Pores and Porous Ceramics 439 24.16 Sintering with Two and Three Phases 440 24.17 Examples of Sintering in Action 441 24.18 Computer Modeling 441 25 Solid-State Phase Transformations and Reactions . . . . . . . . . . . . . . . 444 25.1 Transformations and Reactions: The Link 444 25.2 The Terminology 445 25.3 Technology 445 25.4 Phase Transformations without Changing Chemistry 447 25.5 Phase Transformations Changing Chemistry 448 25.6 Methods for Studying Kinetics 449 25.7 Diffusion through a Layer: Slip Casting 450 25.8 Diffusion through a Layer: Solid-State Reactions 451 25.9 The Spinel-Forming Reaction 451 25.10 Inert Markers and Reaction Barriers 452 25.11 Simplified Darken Equation 453 25.12 The Incubation Period 454 25.13 Particle Growth and the Effect of Misfit 454 25.14 Thin-Film Reactions 455 25.15 Reactions in an Electric Field 457 25.16 Phase Transformations Involving Glass 458 25.17 Pottery 459 25.18 Cement 459 25.19 Reactions Involving a Gas Phase 460 25.20 Curved Interfaces 461 26 Processing Glass and Glass-Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . 463 26.1 The Market for Glass and Glass Products 463 26.2 Processing Bulk Glasses 463 26.3 Bubbles 467 xviii ..................................................................................................................................................................... Contents  26.4 Flat Glass 468 26.5 Float-Glass 469 26.6 Glassblowing 470 26.7 Coating Glass 472 26.8 Safety Glass 473 26.9 Foam Glass 473 26.10 Sealing Glass 473 26.11 Enamel 474 26.12 Photochromic Glass 474 26.13 Ceramming: Changing Glass to Glass-Ceramics 474 26.14 Glass for Art and Sculpture 476 26.15 Glass for Science and Engineering 478 27 Coatings and Thick Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 27.1 Defining Thick Film 481 27.2 Tape Casting 481 27.3 Dip Coating 484 27.4 Spin Coating 484 27.5 Spraying 485 27.6 Electrophoretic Deposition 486 27.7 Thick-Film Circuits 488 28 Thin Films and Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 28.1 The Difference between Thin Films and Thick Films 494 28.2 Acronyms, Adjectives, and Hyphens 494 28.3 Requirements for Thin Ceramic Films 495 28.4 Chemical Vapor Deposition 495 28.5 Thermodynamics of Chemical Vapor Deposition 497 28.6 Chemical Vapor Deposition of Ceramic Films for Semiconductor Devices 498 28.7 Types of Chemical Vapor Deposition 499 28.8 Chemical Vapor Deposition Safety 500 28.9 Evaporation 500 28.10 Sputtering 501 28.11 Molecular-Beam Epitaxy 502 28.12 Pulsed-Laser Deposition 503 28.13 Ion-Beam-Assisted Deposition 504 28.14 Substrates 504 29 Growing Single Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 29.1 Why Single Crystals? 507 29.2 A Brief History of Growing Ceramic Single Crystals 507 29.3 Methods for Growing Single Crystals of Ceramics 508 29.4 Melt Technique: Verneuil (Flame-Fusion) 509 29.5 Melt Technique: Arc-Image Growth 511 29.6 Melt Technique: Czochralski 511 29.7 Melt Technique: Skull Melting 514 29.8 Melt Technique: Bridgman–Stockbarger 515 29.9 Melt Technique: Heat-Exchange Method 516 29.10 Applying Phase Diagrams to Single-Crystal Growth 516 29.11 Solution Technique: Hydrothermal 517 29.12 Solution Technique: Hydrothermal Growth at Low Temperature 519 29.13 Solution Technique: Flux Growth 519 29.14 Solution Technique: Growing Diamonds 521 Contents ..................................................................................................................................................................... xix  29.15 Vapor Technique: Vapor–Liquid–Solid 521 29.16 Vapor Technique: Sublimation 522 29.17 Preparing Substrates for Thin-Film Applications 522 29.18 Growing Nanowires and Nanotubes by Vapor–Liquid–Solid and Not 522 PART VII PROPERTIES AND APPLICATIONS 30 Conducting Charge or Not . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 30.1 Ceramics as Electrical Conductors 529 30.2 Conduction Mechanisms in Ceramics 531 30.3 Number of Conduction Electrons 532 30.4 Electron Mobility 533 30.5 Effect of Temperature 533 30.6 Ceramics with Metal-Like Conductivity 534 30.7 Applications for High-σ Ceramics 535 30.8 Semiconducting Ceramics 537 30.9 Examples of Extrinsic Semiconductors 539 30.10 Varistors 540 30.11 Thermistors 541 30.12 Wide-Band-Gap Semiconductors 542 30.13 Ion Conduction 543 30.14 Fast Ion Conductors 543 30.15 Batteries 544 30.16 Fuel Cells 544 30.17 Ceramic Insulators 546 30.18 Substrates and Packages for Integrated Circuits 548 30.19 Insulating Layers in Integrated Circuits 549 30.20 Superconductivity 550 30.21 Ceramic Superconductors 551 31 Locally Redistributing Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 31.1 Background on Dielectrics 556 31.2 Ferroelectricity 560 31.3 BaTiO3: The Prototypical Ferroelectric 562 31.4 Solid Solutions with BaTiO3 565 31.5 Other Ferroelectric Ceramics 565 31.6 Relaxor Dielectrics 565 31.7 Ceramic Capacitors 565 31.8 Ceramic Ferroelectrics for Memory Applications 568 31.9 Piezoelectricity 569 31.10 Lead Zirconate–Lead Titanate (PZT) Solid Solutions 570 31.11 Applications for Piezoelectric Ceramics 571 31.12 Piezoelectric Materials for Microelectromechanical Systems 572 31.13 Pyroelectricity 572 31.14 Applications for Pyroelectric Ceramics 573 32 Interacting with and Generating Light . . . . . . . . . . . . . . . . . . . . . . . . 575 32.1 Some Background for Optical Ceramics 575 32.2 Transparency 577 32.3 The Refractive Index 578 32.4 Reflection from Ceramic Surfaces 579 32.5 Color in Ceramics 580 32.6 Coloring Glass and Glazes 581 32.7 Ceramic Pigments and Stains 581 xx ..................................................................................................................................................................... C o n t e n t s  32.8 Translucent Ceramics 583 32.9 Lamp Envelopes 584 32.10 Fluorescence 585 32.11 The Basics of Optical Fibers 586 32.12 Phosphors and Emitters 588 32.13 Solid-State Lasers 589 32.14 Electrooptic Ceramics for Optical Devices 590 32.15 Reacting to Other Parts of the Spectrum 594 32.16 Optical Ceramics in Nature 595 33 Using Magnetic Fields and Storing Data . . . . . . . . . . . . . . . . . . . . . . . 598 33.1 A Brief History of Magnetic Ceramics 598 33.2 Magnetic Dipoles 599 33.3 The Basic Equations, the Words, and the Units 600 33.4 The Five Classes of Magnetic Material 601 33.5 Diamagnetic Ceramics 601 33.6 Superconducting Magnets 602 33.7 Paramagnetic Ceramics 603 33.8 Measuring χ 604 33.9 Ferromagnetism 604 33.10 Antiferromagnetism and Colossal Magnetoresistance 605 33.11 Ferrimagnetism 606 33.12 Estimating the Magnetization of Ferrimagnets 609 33.13 Magnetic Domains and Bloch Walls 609 33.14 Imaging Magnetic Domains 610 33.15 Motion of Domain Walls and Hysteresis Loops 611 33.16 Hard and Soft Ferrites 612 33.17 Microwave Ferrites 614 33.18 Data Storage and Recording 614 33.19 Magnetic Nanoparticles 616 34 Responding to Temperature Changes . . . . . . . . . . . . . . . . . . . . . . . . . 619 34.1 Summary of Terms and Units 619 34.2 Absorption and Heat Capacity 619 34.3 Melting Temperatures 621 34.4 Vaporization 623 34.5 Thermal Conductivity 624 34.6 Measuring Thermal Conductivity 626 34.7 Microstructure and Thermal Conductivity 626 34.8 Using High Thermal Conductivity 628 34.9 Thermal Expansion 628 34.10 Effect of Crystal Structure on α 630 34.11 Thermal Expansion Measurment 631 34.12 Importance of Matching αs 632 34.13 Applications for Low-α 632 34.14 Thermal Shock 633 35 Ceramics in Biology and Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635 35.1 What Are Bioceramics? 635 35.2 Advantages and Disadvantages of Ceramics 636 35.3 Ceramic Implants and the Structure of Bone 638 35.4 Alumina and Zirconia 639 35.5 Bioactive Glasses 640 35.6 Bioactive Glass-Ceramics 641 35.7 Hydroxyapatite 642 Contents ..................................................................................................................................................................... xxi  35.8 Bioceramics in Composites 644 35.9 Bioceramic Coatings 645 35.10 Radiotherapy Glasses 646 35.11 Pyrolytic Carbon Heart Valves 646 35.12 Nanobioceramics 647 35.13 Dental Ceramics 648 35.14 Biomimetics 648 36 Minerals and Gems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652 36.1 Minerals 652 36.2 What Is a Gem? 653 36.3 In the Rough 653 36.4 Cutting and Polishing 654 36.5 Light and Optics in Gemology 656 36.6 Color in Gems and Minerals 660 36.7 Optical Effects 661 36.8 Identifying Minerals and Gems 663 36.9 Chemical Stability (Durability) 664 36.10 Diamonds, Sapphires, Rubies, and Emeralds 664 36.11 Opal 666 36.12 Other Gems 667 36.13 Minerals with Inclusions 669 36.14 Treatment of Gems 670 36.15 The Mineral and Gem Trade 670 37 Industry and the Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675 37.1 The Beginning of the Modern Ceramics Industry 675 37.2 Growth and Globalization 676 37.3 Types of Market 677 37.4 Case Studies 677 37.5 Emerging Areas 680 37.6 Mining 682 37.7 Recycling 683 37.8 In the Nuclear Industry 685 37.9 Producing and Storing Hydrogen 685 37.10 As Green Materials 687 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691 Details for Figures and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701 xxii ..................................................................................................................................................................... Contents  Part I History and Introduction  1 Introduction CHAPTER PREVIEW In materials science we often divide materials into distinct classes. The primary classes of solid materials are ceramics, metals, and polymers. This classification is based on the types of atoms involved and the bonding between them. The other widely recognized classes are semi- conductors and composites. Composites are combinations of more than one material and often involve ceramics, such as fiberglass. Semiconductors are materials with electrical conductivi- ties that are very sensitive to minute amounts of impurities. As we will see later, most materials that are semiconductors are actually ceramics, for example, gallium nitride, the blue–green laser diode material. In this chapter we will define what we mean by a “ceramic” and will also describe some of the general properties of ceramics. The difficulty when drawing generalizations, particularly in this case, is that it is always possible to find an exception to the rule. It is because of the wide range of properties exhibited by ceramics that they find application in such a variety of areas. A general theme throughout this book is the interrelationship between the way in which a ceramic is processed, its microstructure, and its properties. We give some examples of these interrelationships in this chapter to illustrate their importance. 1.1 DEFINITIONS Most polymers are organic compounds based on carbon, hydrogen, and other nonmetals such as sulfur and chlo- If you look in any introductory materials science book you rine. The bonding between the molecular chains deter- will find that one of the first sections describes the classi- mines many of their properties. Cross-linking of the fication scheme. In classical materials science, materials chains is the key to the vulcanization process that turned are grouped into five categories: metals, polymers, ceram- rubber from an interesting but not very useful material ics, semiconductors, and composites. The first three are into, for example, tires that made traveling by bicycle based primarily on the nature of the interatomic bonding, much more comfortable and were important in the produc- the fourth on the materials conductivity, and the last on tion of the automobile. The terms “polymer” and “plastic” the materials structure—not a very consistent start. are often used interchangeably. However, many of the Metals, both pure and alloyed, consist of atoms held plastics with which we are familiar are actually combina- together by the delocalized electrons that overcome the tions of polymers, and often include fillers and other addi- mutual repulsion between the ion cores. Many main-group tives to give the desired properties and appearance. elements and all the transition and inner transition ele- Ceramics are usually associated with “mixed” ments are metals. They also include alloys—combinations bonding—a combination of covalent, ionic, and some- of metallic elements or metallic and nonmetallic elements times metallic. They consist of arrays of interconnected (such as in steel, which is an alloy of primarily Fe and C). atoms; there are no discrete molecules. This characteristic Some commercial steels, such as many tool steels, contain distinguishes ceramics from molecular solids such as ceramics. These are the carbides (e.g., Fe3C and W6C) that iodine crystals (composed of discrete I2 molecules) and produce the hardening and enhance wear resistance, but paraffin wax (composed of long-chain alkane molecules). also make it more brittle. The delocalized electrons give It also excludes ice, which is composed of discrete H2O metals many of their characteristic properties (e.g., good molecules and often behaves just like many ceramics. The thermal and electrical conductivity). It is because of their majority of ceramics are compounds of metals or metal- bonding that many metals have close packed structures loids and nonmetals. Most frequently they are oxides, and deform plastically at room temperature. nitrides, and carbides. However, we also classify diamond Polymers are macromolecules formed by covalent and graphite as ceramics. These forms of carbon are inor- bonding of many simpler molecular units called mers. ganic in the most basic meaning of the term: they were 1.1 D e f i n i t i o n s .............................................................................................................................................................. 3 not prepared from the living organism. Richerson (2000)  We cannot say “ceramics are insulators” unless we put says “most solid materials that aren’t metal, plastic, or a value on the band gap (Eg) where a material is not a derived from plants or animals are ceramics.” semiconductor. Semiconductors are the only class of material based on  We cannot say “ceramics are poor conductors of heat” a property. They are usually defined as having electrical because diamond has the highest thermal conductivity conductivity between that of a good conductor and an insu- of any known material. lator. The conductivity is strongly dependent upon the pres- ence of small amounts of impurities—the key to making Before we leave this section let us consider a little integrated circuits. Semiconductors with wide band gaps history. The word ceramic is derived from the Greek (greater than about 3 eV) such as silicon carbide and boron keramos, which means “potter’s clay” or “pottery.” Its nitride are becoming of increasing importance for high- origin is a Sanskrit term meaning “to burn.” So the early temperature electronics, for example, SiC diodes are of Greeks used “keramos” when describing products obtained interest for sensors in fuel cells. In the early days of semi- by heating clay-containing materials. The term has long conductor technology such materials would have been included all products made from fired clay, for example, regarded as insulators. Gallium nitride (GaN), a blue–green bricks, fireclay refractories, sanitaryware, and tableware. laser diode material, is another ceramic that has a wide band In 1822, silica refractories were first made. Although gap. they contained no clay the traditional ceramic process of Composites are combinations of more than one mate- shaping, drying, and firing was used to make them. So the rial or phase. Ceramics are used in many composites, term “ceramic,” while retaining its original sense of a often for reinforcement. For example, one of the reasons product made from clay, began to include other products a B-2 stealth bomber is stealthy is that it contains over 22 made by the same manufacturing process. The field of tons of carbon/epoxy composite. In some composites the ceramics (broader than the materials themselves) can be ceramic is acting as the matrix (ceramic matrix compos- defined as the art and science of making and using solid ites or CMCs). An early example of a CMC dating back articles that contain as their essential component a ceramic. over 9000 years is brick. These often consisted of a fired This definition covers the purification of raw materials, clay body reinforced with straw. Clay is an important the study and production of the chemical compounds con- ceramic and the backbone of the traditional ceramic cerned, their formation into components, and the study of industry. In concrete, both the matrix (cement) and the structure, composition, and properties. reinforcement (aggregate) are ceramics. The most widely accepted definition of a ceramic is given by Kingery et al. (1976): “A ceramic is a nonmetal- 1.2 GENERAL PROPERTIES lic, inorganic solid.” Thus all inorganic semiconductors are ceramics. By definition, a material ceases to be a Ceramics generally have specific properties associated ceramic when it is melted. At the opposite extreme, if we with them although, as we just noted, this can be a mis- cool some ceramics enough they become superconductors. leading approach to defining a class of material. However, All the so-called high-temperature superconductors we will look at some properties and see how closely they (HTSC) (ones that lose all electrical resistance at liquid- match our expectations of what constitutes a ceramic. nitrogen temperatures) are ceramics. Trickier is glass such Brittleness. This probably comes from personal expe- as used in windows and optical fibers. Glass fulfills the riences such as dropping a glass beaker or a dinner plate. standard definition of a solid—it has its own fixed shape— The reason that the majority of ceramics are brittle is the but it is usually a supercooled liquid. This property mixed ionic–covalent bonding that holds the constituent becomes evident at high temperatures when it undergoes atoms together. At high temperatures (above the glass viscous deformation. Glasses are clearly special ceramics. transition temperature) glass no longer behaves in a brittle We may crystallize certain glasses to make glass–ceram- manner; it behaves as a viscous liquid. That is why it is ics such as those found in Corningware®. This process is easy to form glass into intricate shapes. So what we can referred to as “ceramming” the glass, i.e., making it into say is that most ceramics are brittle at room temperature a ceramic. We stand by Kingery’s definition and have to but not necessarily at elevated temperatures. live with some confusion. We thus define ceramics in Poor electrical and thermal conduction. The valence terms of what they are not. electrons are tied up in bonds, and are not free as they are It is also not possible to define ceramics, or indeed any in metals. In metals it is the free electrons—the electron class of material, in terms of specific properties. gas—that determines many of their electrical and thermal properties. Diamond, which we classified as a ceramic in Section 1.1, has the highest thermal conductivity of any  We cannot say “ceramics are brittle” because some can known material. The conduction mechanism is due to be superplastically deformed and some metals can be phonons, not electrons, as we describe in Chapter 34. more brittle: a rubber hose or banana at 77 K shatters Ceramics can also have high electrical conductivity: under a hammer. (1) the oxide ceramic, ReO3, has an electrical conductivity 4 ................................................................................................................................................................... I n t r o d u c t i o n at room temperature similar to that of Cu (2) the mixed covers, precious stones, and optical fibers. Glass optical oxide YBa2Cu3O7 is an HTSC; it has zero resistivity below fibers have a percent transmission >96%km−1. Metals are 92 K. These are two examples that contradict the conven- transparent to visible light only when they are very thin, tional wisdom when it comes to ceramics. typically less than 0.1 μm. Compressive strength. Ceramics are stronger in com- Although it is always possible to find at least one pression than in tension, whereas metals have comparable ceramic that shows atypical behavior, the properties we tensile and compressive strengths. This difference is impor- have mentioned here are in many cases different from tant when we use ceramic components for load-bearing those shown by metals and polymers. applications. It is necessary to consider the stress distribu- tions in the ceramic to ensure that they are compressive. An important example is in the design of concrete bridges—the 1.3 TYPES OF CERAMIC AND concrete, a CMC, must be kept in compression. Ceramics THEIR APPLICATIONS generally have low toughness, although combining them in composites can dramatically improve this property. Using the definition given in Section 1.1 you can see that Chemical insensitivity. A large number of ceramics large numbers of materials are ceramics. The applications are stable in both harsh chemical and thermal environ- for these materials are diverse, from bricks and tiles to ments. Pyrex glass is used widely in chemistry laborato- electronic and magnetic components. These applications ries specifically because it is resistant to many corrosive use the wide range of properties exhibited by ceramics. chemicals, stable at high temperatures (it does not soften Some of these properties are listed in Table 1.1 together until 1100 K), and is resistant to thermal shock because of with examples of specific ceramics and applications. Each its low coefficient of thermal expansion (33 × 10−7 K−1). It of these areas will be covered in more detail later. The is also widely used in bakeware. functions of ceramic products are dependent on their Transparent. Many ceramics are transparent because chemical composition and microstructure, which deter- they have a large Eg. Examples include sapphire watch mines their properties. It is the interrelationship between TABLE 1.1 Properties and Applications for Ceramics Property Example Application Electrical Bi2Ru2O7 Conductive component in thick-film resistors Doped ZrO2 Electrolyte in solid-oxide fuel cells Indium tin oxide (ITO) Transparent electrode SiC Furnace elements for resistive heating YBaCuO7 Superconducting quantum interference devices (SQUIDs) SnO2 Electrodes for electric glass melting furnaces Dielectric α-Al2O3 Spark plug insulator PbZr 0.5Ti0.5O3 (PZT) Micropumps SiO2 Furnace bricks (Ba,Sr)TiO3 Dynamic random access memories (DRAMs) Lead magnesium niobate (PMN) Chip capacitors Magnetic γ-Fe2O3 Recording tapes Mn0.4Zn0.6Fe2O4 Transformer cores in touch tone telephones BaFe12O19 Permanent magnets in loudspeakers Y2.66Gd 0.34Fe4.22Al0.68Mn0.09O12 Radar phase shifters Optical Doped SiO2 Optical fibers α-Al2O3 Transparent envelopes in street lamps Doped ZrSiO4 Ceramic colors Doped (Zn,Cd)S Fluorescent screens for electron microscopes Pb1-x La x (ZrzTi1-z )1-x/4O3 (PLZT) Thin-film optical switches Nd doped Y3Al5O12 Solid-state lasers Mechanical TiN Wear-resistant coatings SiC Abrasives for polishing Diamond Cutting tools Si3N4 Engine components Al2O3 Hip implants Thermal SiO2 Space shuttle insulation tiles Al2O3 and AlN Packages for integrated circuits Lithium-aluminosilicate glass ceramics Supports for telescope mirrors Pyrex glass Laboratory glassware and cookware 1. 3 Ty p e s o f C e r a m i c a n d Th e i r A p p l i c at i o n s ...................................................................................................... 5 structure and properties that is a key element of materials and shaping processes, and the methods used for science and engineering. characterization. You may find that in addition to dividing ceramics according to their properties and applications that it is 1.4 MARKET common to class them as traditional or advanced. Traditional ceramics include high-volume items such Ceramics is a multibillion dollar industry. Worldwide bricks and tiles, toilet bowls (whitewares), and pottery. sales are about $100 billion ($1011) per year; the U.S. Advanced ceramics include newer materials such as market alone is over $35 billion ($3.5 × 1010) annually. As laser host materials, piezoelectric ceramics, ceramics for with all economic data there will be variations from year dynamic random access memories (DRAMs), etc., often to year. The Ceramic Industry (CI) is one organization produced in small quantities with higher prices. that provides regular updates of sales through its annual There are other characteristics that separate these Giants in Ceramics survey. categories. The general distribution of industry sales is as Traditional ceramics are usually based on clay and silica. follows: There is sometimes a tendency to equate traditional ceram- ics with low technology, however, advanced manufacturing  55% Glass techniques are often used. Competition among producers  17% Advanced ceramics has caused processing to become more efficient and cost  10% Whiteware effective. Complex tooling and machinery is often used and  9% Porcelain enamel may be coupled with computer-assisted process control.  7% Refractories Advanced ceramics are also referred to as “special,”  2% Structural clay “technical,” or “engineering” ceramics. They exhibit superior mechanical properties, corrosion/oxidation resis- In the United States, sales of structural clay in the form tance, or electrical, optical, and/or magnetic properties. of bricks is valued at $160 M per month. However, finan- While traditional clay-based ceramics have been used for cially, the ceramics market is clearly dominated by glass. over 25,000 years, advanced ceramics have generally been The major application for glass is windows. World demand developed within the last 100 years. for flat glass is about 40 billion square feet—worth over Figure 1.1 compares traditional and advanced ceram- $40 billion. ics in terms of the type of raw materials used, the forming Overall market distribution in the United States is as follows: Advanced Traditional ceramics ceramics  32% Flat glass Raw materials Chemically prepared preparation  18% Lighting Raw minerals  17% Containers powders Clay - Precipitation - Spray dry Silica  17% Fiber glass - Freeze dry  9% TV tubes, CRTs - Vapor phase - Sol-gel  5% Consumer glassware Forming  1% Technical/laboratory Slip casting Potters wheel  1% Other Injection molding Slip casting Sol-gel Hot pressing Advanced ceramics form the second largest sector of the HIPing Rapid prototyping industry. More than half of this sector is electrical and High-temperature processing electronic ceramics and ceramic packages: Electric furnace Hot press Flame kiln  36% Capacitors/substrates/packages Reaction sinter Vapor deposition Plasma spraying  23% Other electrical/electronic ceramics Microwave furnace  13% Other Finishing process  12% Electrical porcelain Erosion  8% Engineering ceramics Laser machining Erosion Plasma spraying Glazing  8% Optical fibers Ion implantation Coating Characterization High-temperature ceramic superconductors, which Light microscopy Visible examination would fall into the category of advanced ceramics, are not X-ray diffraction Electron microscopy Light microscopy presently a major market area. They constitute less than Scanned probe microscopy 1% of the advanced ceramics market. Significant growth Neutron diffraction Surface analytical methods has been predicted because of their increased use in FIGURE 1.1 A comparison of different aspects of traditional and microwave filters and resonators, with particular applica- advanced ceramics. tion in the area of cell phones. 6 ................................................................................................................................................................... I n t r o d u c t i o n  Engineering ceramics, also called structural ceramics, microelectromechanical systems (MEMS), substrates, and include wear-resistant components such as dies, nozzles, packages for integrated circuits. There are many chal- and bearings. Bioceramics such as ceramic and glass- lenges for the future: ceramic implants and dental crowns account for about 20% of this market. Dental crowns are made of porcelain and Integrating with existing semiconductor technology over 30 million are made in the United States each year. Improving processing Whiteware sales, which include sanitaryware (toilet Enhancing compatibility with other materials bowls, basins, etc.) and dinnerware (plates, cups), account for about 10% of the total market for ceramics. The largest Bioceramics are used in the human body. The response segment of the whiteware market, accounting for about of these materials varies from nearly inert to bioactive to 40%, is floor and wall tiles. In the United States we use resorbable. Nearly inert bioceramics include alumina about 2.5 billion (2.5 × 109) square feet of ceramic tiles (Al2O3) and zirconia (ZrO2). Bioactive ceramics include per year. Annual sales of sanitaryware in the United States hydroxyapatite and some special glass and glass–ceramic total more than 30 million pieces. formulations. Tricalcium phosphate is an example of a Porcelain enamel is the ceramic coating applied to resorbable bioceramic; it dissolves in the body. Three many steel appliances such as kitchen stoves, washers, and issues will determine future progress: dryers. Porcelain enamels have much wider applications as both interior and exterior paneling in buildings, for Matching mechanical properties to human tissues example, in subway stations. Because of these widespread Increasing reliability applications it is perhaps not surprising that the porcelain Improving processing methods enameling industry accounts for more than $3 billion per Coatings and films are generally used to modify the year. surface properties of a material, for example, a bioactive More than 50% of refractories are consumed by the coating deposited onto the surface of a bioinert implant. steel industry. The major steelmaking countries are China, They may also be used for economic reasons; we may Japan, and the United States. Structural clay products want to apply a coating of an expensive material to a lower include bricks, sewer pipes, and roofing tiles. These are cost substrate rather than make the component entirely high-volume low-unit-cost items. Each year about 8 billion from the more expensive material. An example of this bricks are produced in the United States with a market situation would be applying a diamond coating on a cutting value of over $1.5 billion. tool. In some cases we use films or coatings simply because the material performs better in this form. An example is 1.5 CRITICAL ISSUES FOR THE FUTURE the transport properties of thin films of HTSCs, which are improved over those of the material in bulk form. Some Although glass dominates the global ceramics market, the issues need to be addressed: most significant growth is in advanced ceramics. There are many key issues that need to be addressed to maintain Understanding film deposition and growth this growth and expand the applications and uses of Improving film/substrate adhesion advanced ceramics. It is in these areas that there will be Increasing reproducibility increasing employment opportunities for ceramic engi- neers and materials scientists. Composites may use ceramics as the matrix phase Structural ceramics include silicon nitride (Si3N4), and/or the reinforcing phase. The purpose of a composite silicon carbide (SiC), zirconia (ZrO2), boron carbide is to display a combination of the preferred characteristics (B4C), and alumina (Al2O3). They are used in applications of each of the components. In CMCs one of the principal such as cutting tools, wear components, heat exchangers, goals has been to increase fracture toughness through and engine parts. Their relevant properties are high hard- reinforcement with whiskers or fibers. When ceramics are ness, low density, high-temperature mechanical strength, the reinforcement phase in, for example, metal matrix creep resistance, corrosion resistance, and chemical inert- composites the result is usually an increase in strength, ness. There are three key issues to solve in order to expand enhanced creep resistance, and greater wear resistance. the use of structural ceramics: Three issues must be solved: Reducing cost of the final product Reducing processing costs Improving reliability Developing compatible combinations of materials (e.g., Improving reproducibility matching coefficients of thermal expansion) Understanding interfaces Electronic ceramics include barium titanate (BaTiO3), zinc oxide (ZnO), lead zirconate titanate [Pb(ZrxTi1−x)O3], Nanoceramics can be either well established or at an aluminum nitride (AlN), and HTSCs. They are used in early stage in their development. They are widely used in applications as diverse as capacitor dielectrics, varistors, cosmetic products such as sunscreens, and we know they 1. 5 C r i t i c a l I s s u e s f o r t h e F u t u r e ........................................................................................................................ 7 are critical in many applications of catalysis, but their use Grain Size (μm) in fuel cells, coatings, and devices, for example, is often 500 100 50 20 10 Fracture quite new. There are three main challenges: Stress MPa Making them 200 Integrating them into devices Ensuring that they do not have a negative impact on σ0 { society 100 1.6 RELATIONSHIP BETWEEN MICROSTRUCTURE, PROCESSING, AND APPLICATIONS The field of materials science and engineering is often defined by the interrelationship between four topics—syn- 0 thesis and processing, structure and composition, proper- 0 0.1 0.2 0.3 ties, and performance. To understand the behavior and (Grain Size)-1/2 (μm-1/2) properties of any material, it is essential to understand its FIGURE 1.2 Dependence of fracture strength of MgO (at 20°C) on the grain size. structure. Structure can be considered on several levels, all of which influence final behavior. At the finest level is the electron configuration, which affects properties such particles and the way in which they were consolidated. as color, electrical conductivity, and magnetic behavior. The grain boundaries in a polycrystalline ceramic are also The arrangement of electrons in an atom influences how important. The strength then depends on whether or not it will bond to another atom and this, in turn, impacts the the material is pure, contains a second phase or pores, or crystal structure. just contains glass at the grain boundaries. The relation- The arrangement of the atoms or ions in the material ship is not always obvious for nanoceramics. also needs to be considered. Crystalline ceramics have a 2. Transparent or translucent ceramics require that we very regular atomic arrangement whereas in noncrystal- limit the scattering of light by pores and second-phase line or amorphous ceramics (e.g., oxide glasses) there is particles. Reduction in porosity may be achieved by hot no long-range order, although locally we may identify pressing to ensure a high-density product. This approach similar polyhedra. Such materials often behave differently has been used to make transparent PLZT ceramics for relative to their crystalline counterparts. Not only perfect electrooptical applications such as the flash-blindness lattices and ideal structures have to be considered but also goggles shown in Figure 1.3, developed during the 1970s the presence of structural defects that are unavoidable in all materials, even the amorphous ones. Examples of such defects include impurity atoms and dislocations. Polycrystalline ceramics have a structure consisting of many grains. The size, shape, and orientation of the grains play a key role in many of the macroscopic properties of these materials, for example, mechanical strength. In most ceramics, more than one phase is present, with each phase having its own structure, composition, and properties. Control of the type, size, distribution, and amount of these phases within the material provides a means to control properties. The microstructure of a ceramic is often a result of the way it was processed. For example, hot- pressed ceramics often have very few pores. This may not be the case in sintered materials. The interrelationship between the structure, process- ing, and properties will be evident throughout this text but are illustrated here by five examples. 1. The strength of polycrystalline ceramics depends on the grain size through the Hall–Petch equation. Figure 1.2 shows strength as a function of grain size for MgO. As the grain size decreases the strength increases. The FIGURE 1.3 Pilot wearing the flash-blindness goggles (in the “off” grain size is determined by the size of the initial powder position). 8 ................................................................................................................................................................... I n t r o d u c t i o n  T (°C) 1000 600 400 200 99.9% 94% 10 log ρ Sapphire 88% Ω m-1 -1 9 Y-rich Y-rich 8 7 6 200 nm 5 8x10-4 1.6x10-3 2.4x10-3 FIGURE 1.4 TEM image of grain boundaries in AlN showing T-1 (K-1) yttria-rich second-phase particles at the triple junctions. FIGURE 1.6 Dependence of resistivity on temperature for different compositions of alumina. by Sandia National Laboratories in the United States for Defects and grain boundaries pin the domain walls use by combat pilots. and make it more difficult to achieve saturation 3. Thermal conductivity of commercially available magnetization. polycrystalline AlN is usually lower than that predicted 5. Alumina ceramics are used as electrical insulators by theory because of the presence of impurities, mainly because of their high electrical resistivity and low dielec- oxygen, which scatter phonons. Adding rare earth or alka- tric constant. For most applications pure alumina is not line metal oxides (such as Y2O3 and CaO, respectively) used. Instead we blend the alumina with silicates to reduce can reduce the oxygen content by acting as a getter. These the sintering temperature. These materials are known as oxides are mixed in with the AlN powder before it is debased aluminas and contain a glassy silicate phase shaped. The second phase, formed between the oxide between alumina grains. Debased aluminas are generally additive and the oxide coating on the AlN grains, segre- more conductive (lower resistivity) than pure aluminas as gates to triple points as shown in Figure 1.4. shown in Figure 1.6. Debased aluminas (containing 95% 4. Soft ferrites such as Mn1−δZnδFe2O4 are used in a Al2O3) are used in spark plugs. range of different devices, for example, as the yoke that moves the electron beam in a television tube. The perme- ability of soft ferrites is a function of grain size as shown 1.7 SAFETY in Figure 1.5. Large defect-free grains are preferred because we need to have very mobile domain walls. When working with any material, safety considerations should be uppermost. There are several important precau- tions to take when working with ceramics. Permeability Toxicity of powders containing, for example, Pb or Cd 0.005 or fluorides should be known. When shipping the material, the manufacturer supplies information on the hazards 0.004 associated with their product. It is important to read this information and keep it accessible. Some standard resources that provide information about the toxicity of 0.003 powders and the “acceptable” exposure levels are given in the References. Small particles should not be inhaled. The effects have 0.002 been well known, documented, and often ignored since the 1860s. Proper ventilation, improved cleanliness, and 0.001 protective clothing have significantly reduced many of the industrial risks. Care should be taken when handling any powders (of both toxic and nontoxic materials). The most injurious response is believed to be when the particle size 0 5 10 15 20 Crystal diameter (μm) is <1 μm; larger particles either do not remain suspended FIGURE 1.5 The variation of permeability with average grain in the air sufficiently long to be inhaled or, if inhaled, diameter of a manganese-zinc ferrite with uncontrolled porosity. cannot negotiate the tortuous passage of the upper 1.7 Sa f e t y ....................................................................................................................................................................... 9  TABLE 1.2 The Color Scale of Temperature using; many states require that they are kept in the laboratory. Color Corresponding T Barely visible red 525°C 1.8 CERAMICS ON THE INTERNET Dark red 700°C Cherry red just beginning to appear 800°C Clear red 900°C There is a great deal of information about ceramics on Bright red, beginning orange 1000°C the Internet. Here are some of the most useful web Orange 1100°C sites. Orange-white 1200°C Dull white 1300°C www.FutureCeramics.com The web site for this text. Bright white 1400°C www.acers.org The American Ceramic Society, membership information, meetings, books. respiratory tract. The toxicity and environmental impact www.acers.org/cic/propertiesdb.asp The Ceramic Proper- of nanopowders have not been clearly addressed, but are ties Database. This database has links to many other the subject of various studies such as a recent report by sources of property information including the NIST the Royal Society (2004). and NASA materials databases. High temperatures are used in much of ceramic pro- www.ceramics.com Links to many technical and indus- cessing. The effects of high temperatures on the human trial sites. body are obvious. What is not so obvious is how hot www.ceramicforum.com A web site for the ceramics something actually is. Table 1.2 gives the color scale for professional. temperature. From this tabulation you can see that an www.ecers.org The European Ceramics Society. alumina tube at 400ºC will not show a change in color but www.ceramicsindustry.com Source of industry data. it will still burn skin. Other safety issues involved with www.porcelainenamel.com The Porcelain Enamel furnaces are given in Chapter 9. Institute. Organics are used as solvents and binders during pro- cessing. Traditionally, organic materials played little role 1.9 ON UNITS in ceramic processing. Now they are widely used in many forms of processing. Again, manufacturers will provide We have attempted to present all data using the Système safety data sheets on any product they ship. This informa- International d’Unités (SI). The basic units in this system tion is important and should always be read carefully. are listed in Table 1.3 together with derived quantities. The As a rule, the material safety data sheets (MSDS) primary exceptions in which non-SI units are encountered should be readily accessible for all the materials you are is in the expression of small distances and wavelengths TABLE 1.3 SI Units SI Base Units Base quantity Name Symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Thermodynamic temperature kelvin K Amount of substance mole mol Luminous intensity candela cd SI-Derived Units Derived quantity Name Symbol Area square meter m2 Volume cubic meter m3 Speed, velocity meter per second m/s Acceleration meter per second squared m/s2 Wave number reciprocal meter m−1 Mass density kilogram per cubic meter kg/m3 Specific volume cubic meter per kilogram m3 /kg Current density ampere per meter A/m2 Magnetic field strength ampere per meter A/m Amount-of-substance concentration mole per cubic meter mol/m3 Luminance candela per square meter cd/m2 Mass fraction kilogram per kilogram kg/kg = 1 10 ................................................................................................................................................................... I n t r o d u c t i o n  TABLE 1.3 Continued SI-Derived Units with Special Names and Symbols Expression in terms Expression in terms Derived quantity Name Symbol of other SI units of SI base units Plane angle radian rad — m·m−1 = 1 Solid angle steradian sr — m2·m−2 = 1 Frequency hertz Hz — s −1 Force Newton N — m·kg·s −2 Pressure, stress pascal Pa N/m2 m−1·kg·s −2 Energy, work, quantity of heat joule J N·m m2·kg·s −2 Power, radiant flux watt W J/s m2·kg·s −3 Electric charge, quantity of coulomb C — s·A electricity Electric potential difference, volt V W/A m2·kg·s −3 ·A−1 electromotive force Capacitance farad F C/V m−2·kg−1·s4 ·A 2 Electric resistance ohm Ω V/A m2·kg·s −3 ·A−2 Electric conductance siemens S A/V m−2·kg−1·s3 ·A 2 Magnetic flux weber Wb V·s m2.kg.s −2A−1 Magnetic flux density tesla T Wb/m2 kg·s −2·A−1 Inductance henry H Wb/A m2·kg·s −2·A−2 Celsius temperature degree Celsius °C — K Luminous flux lumen lm cd·sr m2·m−2·cd = cd Illuminance lux lx l m/m2 m2·m−4 ·cd = m−2 cd Activity (of a radionuclide) becqueral Bq — s −1 Absorbed dose, specific gray Gy J/kg m2·s −2 energy (imparted), kerma Dose equivalent sievert Sv J/kg m2·s −2 Catalytic activity katal kat — s −1 mol SI-Derived Units with Names and Symbols That Include Other SI-Derived Units Derived quantity Name Symbol Dynamic viscosity pascal second Pa·s Moment of force newton meter N·m Surface tension newton per meter N/m Angular velocity radian per second rad/s Angular acceleration radian per second squared rad/s2 Heat flux density, irradiance watt per square meter W/m2 Heat capacity, entropy joule per kelvin J/K Specific heat capacity, specific entropy joule per kilogram kelvin J kg −1 K−1 Specific energy joule per kilogram J/kg Thermal conductivity watt per meter kelvin W m−1 K−1 Energy density joule per cubic meter J/m3 Electric field strength volt per meter V/m Electric charge density coulomb per cubic meter C/m3 Electric flux density coulomb per square meter C/m2 Permittivity farad per meter F/m Permeability henry per meter H/m Molar energy joule per mole J/mol Molar entropy, molar heat capacity joule per mole Kelvin J mol−1 K−1 Exposure (X and γ rays) coulomb per kilogram C/kg Absorbed dose rate gray per second Gy/s Radiant intensity watt per steradian W/sr Radiance watt per square meter steradian Wm−2 sr −1 Catalytic (activity) concentration katal per cubic meter kat/m3 where the Å (angstrom) is used by electron microscopists ture is often quoted in Fahrenheit (ºF) and pressure in and X-ray crystallographers and the eV (electron volt) is pounds per square inch (psi). Conversions between SI used as a unit of energy for band gaps and atomic binding units and some of the special British and U.S. units are energies. We have not used the former but do use the latter provided in Table 1.4. for convenience. In the ceramics industry customary U.S. The SI base unit of temperature is the kelvin, K. We units are commonly encountered. For example, tempera- use both K and ºC in this text. The degree Celsius is equal 1. 9 O n U n i t s ................................................................................................................................................................... 11  TABLE 1.4 Conversion Factors between SI Base Units and SI-Derived Units and Other Systems SI units Related units Special British and U.S. units Length: 1 m 1010 Å 3.28 ft Mass: 1 kg 2.205 lb 1t 0.984 U.K. (long) ton 1.103 U.S. (short) ton Time: 1 s 2.778 × 10 −4 h, 1.667 × 10 −2 min Absolute temperature: yK y − 273.15°C 32 + 1.8(y − 273.15)°F 2 4 2 Area: 1 m 10 cm 10.76 ft 2 Volume: 1 m3 10 6 cm3 35.3 ft3 Density: 1 kg/m3 10 −3 g/cm3 6.24 × 10 −2 lb/ft3 Force: 1 N 105 dyn — 9.807 N 1 kgf (kilogram force) 2.205 lbf Pressure, stress: 105 Pa 1 bar; 14.5 psi 750 mmHg (torr) 0.987 atm Energy, work, quantity of heat 1J 107 erg or 0.239 cal — 105.5 MJ — 105 Btu 0.1602 aJ 1 eV — Power: 1 W 0.86 kcal/h 1.341 × 10 −3 hp Dynamic viscosity: 1 dPa·s 1 P (poise) 102 cP — 3 3 2 Surface tension, surface energy: 1 N/m 10 dyn/cm 10 erg/cm — Magnetic field strength: 1 A/m 4π × 10 −3 oersted — 4 Magnetic flux density: 1 T 10 G (gauss) — in magnitude to the kelvin, which implies that the numeri- TABLE 1.5 Decade Power Notation a cal value of a temperature difference or temperature inter- Factor Prefix Symbol Factor Prefix Symbol val whose value is expressed in ºC is equal to the numerical value of the same temperature difference or interval when 1024 yotta Y 10 −1 deci d its value is expressed in K. 1021 zetta Z 10 −2 centi c 1018 exa E 10 −3 milli m Several of the figures that we have used were obtained 1015 peta P 10 −6 micro μ from sources in which the original data were not in SI 1012 tera T 10 −9 nano n units. In many cases we have converted the units into SI 109 giga G 10 −12 pico p using conversions and rounding in accordance with ASTM 10 6 mega M 10 −15 femto f Standard E 380. Any variations from this procedure are 103 kilo k 10 −18 atto a 102 hecto h 10 −21 zepto z noted in the appropriate place. 101 deca da 10−24 yocto y The decade power notation is a convenient method of representing large and small values within the SI units. a Factors that are not powers of 1000 are discouraged. Examples that you will encounter in this book include nm (10−9 m) and pF (10−12 F). The full decade power notation scheme is given in Table 1.5. CHAPTER SUMMARY We adopted the definition of a ceramic as a nonmetallic, inorganic solid. This definition encompasses a wide range of materials, many of which you might find are described as semi- conductors elsewhere. The definition of ceramics we adopted is not quite complete in that glass—which behaves at room temperature and below like a solid but has the structure of a liquid—is actually a very important ceramic. More than half the ceramic industry is devoted to producing glass. The second largest segment of the ceramics market is in advanced (also called special, engineering, or technical) ceramics. This area is exciting and includes many of the newer materials such as HTSCs, bioceramics, and nanoceramics. These areas are predicted to experience significant growth. 12 ................................................................................................................................................................... I n t r o d u c t i o n  PEOPLE IN HISTORY In most of the chapters we will include a short section relating to the history of the topic, usually one-line biographies of our heroes in the field—some of those who have defined the subject. If the section is a little short in some chapters, the names/events may be listed in another chapter. The purpose of this section is to remind you that although our subject is very old, it is also quite young and many of the innovators never thought of themselves as ceramists. REFERENCES In the reference sections throughout the book we will list general references on the overall theme of the chapter and specific references that are the source of information referenced in the chapter. If a general reference is referred to specifically in the chapter, we will not generally repeat it. CERAMICS TEXTBOOKS Barsoum, M. (2003) Fundamentals of Ceramics, revised edition, CRC Press, Boca Raton, FL. Chiang, Y-M., Birnie, D., III, and Kingery, W.D. (1998) Physical Ceramics: Principles for Ceramic Science and Engineering, Wiley, New York. Kingery, W.D., Bowen, H.K., and Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd edition, Wiley, New York. This has been the ceramics “bible” for 40 years since the publication of the first edition by David Kingery in 1960. Lee, W.E. and Rainforth, W.M. (1994) Ceramic Microstructures: Property Control by Processing, Chapman & Hall, London. Norton, F.H. (1974) Elements of Ceramics, 2nd edition, Addison-Wesley, Reading, MA. Richerson, D.W. (2005) Modern Ceramic Engineering: Properties, Processing, and Use in Design, 3rd edition, CRC Press, Boca Raton, FL. Van Vlack, L.H. (1964) Physical Ceramics for Engineers, Addison-Wesley, Reading, MA. INTRODUCTION TO MATERIALS SCIENCE TEXTBOOKS Askeland, D.R. and Phulé, P.P. (2005) The Science of Engineering Materials, 5th edition, Thompson Engi- neering, Florence, KY. Callister, W.D. (2007) Materials Science and Engineering: An Introduction, 7th edition, Wiley, New York. Schaeffer, J.P., Saxena, A., Antolovich, S.D., Sanders, T.H., Jr., and Warner, S.B. (2000) The Science and Design of Engineering Materials, 2nd edition, McGraw-Hill, Boston. Shackelford, J.F. (2004) Introduction to Materials Science for Engineers, 6th edition, Prentice Hall, Upper Saddle River, NJ. Smith, W.F. and Hashemi, J. (2006) Foundations of Materials Science and Engineering, 4th edition, McGraw- Hill, Boston. JOURNALS Bulletin of the American Ceramic Society, published by the American Ceramic Society (ACerS). News, society information, industry updates, and positions. Free to society members. Ceramic Industry, published by Business News Publishing Co., Troy, MI. Information on manufacturing. Designed mainly for the ceramist in industry. Ceramics International Glass Technology, published by The Society of Glass Technology, Sheffield, UK. Journal of the American Ceramic Society, house journal of the ACerS contains peer-reviewed articles, pub- lished monthly. Journal of the European Ceramics Society, house journal of the European Ceramic Society published by Elsevier. Journal of Non-Crystalline Solids Physics and Chemistry of Glasses Transactions of the British Ceramic Society CONFERENCE PROCEEDINGS American Ceramic Society Transactions Ceramic Engineering and Science Proceedings. Published by the American Ceramic Society; each issue is based on proceedings of a conference. USEFUL SOURCES OF PROPERTIES DATA, TERMINOLOGY, AND CONSTANTS Engineered Materials Handbook, Volume 4, Ceramics and Glasses (1991), volume chairman Samuel J. Schneider, Jr., ASM International, Washington, D.C. CRC Handbook of Chemistry and Physics, 86th edition (2005), edited by D.R. Lide, CRC Press, Boca Raton, FL. The standard resource for property data. Updated and revised each year. C h a p t e r S u m m a ry .......................................................................................................................................................... 13  CRC Handbook of Materials Science (1974), edited by C.T. Lynch, CRC Press, Cleveland, OH. In four volumes. CRC Materials Science and Engineering Handbook, 3rd edition (2000), edited by J.F. Shackelford and W. Alexander, CRC Press, Boca Raton, FL. Dictionary of Ceramic Science and Engineering, 2nd edition (1994), edited by I.J. McColm, Plenum, New York. The Encyclopedia of Advanced Materials (1994), edited by D. Bloor, R.J. Brook, M.C. Flemings, and S. Mahajan, Pergamon, Oxford. In four volumes, covers more than ceramics. Handbook of Advanced Ceramics (2003), edited by S. Somiya, F. Aldinger, N. Claussen, R.M. Spriggs, K. Uchino, K. Koumoto, and M. Kaneno, Elsevier, Amsterdam. Volume I, Materials Science; Volume II, Processing and Their Applications. SAFETY Chemical Properties Handbook (1999), edited by C.L. Yaws, McGraw-Hill, New York. Gives exposure limits for many organic and inorganic compounds, pp. 603–615. Coyne, G.S. (1997) The Laboratory Companion: A Practical Guide to Materials, Equipment, and Technique, Wiley, New York. Useful guide to the proper use of laboratory equipment such as vacuum pumps and compressed gases. Also gives relevant safety information. CRC Handbook of Laboratory Safety, 5th edition (2000), edited by A.K. Furr, CRC Press, Boca Raton, FL. Worthwhile handbook for any ceramics laboratory. Covers many of the possible hazards associated with the laboratory. Hazardous Chemicals Desk Reference, 5th edition (2002), edited by R.J. Lewis, Sr., Van Nostrand Reinhold, New York. Shorter version of the next reference. Sax’s Dangerous Properties of Industrial Materials, 11th edition (2004), edited by R.J. Lewis, Sr., Wiley, New York. A comprehensive resource in several volumes available in most libraries. The Occupational Safety and Health Administration (OSHA) of the U.S. Department of Labor web site on the internet is a comprehensive resource on all safety issues, www.osha.gov. SPECIFIC REFERENCES Nanoscience and Nanotechnologies: Opportunities and Uncertainties, The Royal Society, London, published on 29 July 2004, available at www.nanotec.org.uk/finalReport. Richerson, D.W. (2000) The Magic of Ceramics, The American Ceramic Society, Westerville, OH. A coffee table book about ceramics illustrating their diverse applications and uses. EXERCISES 1.1 Which of the following materials could be classified as a ceramic. Justify your answer. (a) Solid argon (Ar); (b) molybdenum disilicide (MoSi2); (c) NaCl; (d) crystalline sulfur (S); (e) ice; (f) boron carbide (B4C). 1.2 Is silicone rubber (widely used as a caulking material in bathrooms and kitchens) a ceramic or a polymer? Explain your reasoning. 1.3 There are several different phases in the Fe-C system. One phase is the γ-Fe (austenite), which can contain up to about 8 atomic % C. Another phase is cementite, which contains 25 atomic % C. Are either of these two phases a ceramic? Justify your answer. 1.4 The following definition has been proposed: “All ceramics are transparent to visible light.” Is this a good way of defining a ceramic? Explain your reasoning. 1.5 In the distribution of industry sales of advanced ceramics (Section 1.4), 13% was listed as “Other.” Suggest applications that might be included in this group. 1.6 Ceramic tile accounts for about 15% of the floor tile market. (a) What alternatives are available? (b) What advantages/disadvantages do ceramics have over the alternatives? (c) What factors do you think influence the total amount of ceramic floor tiles used? 1.7 Gerber, the baby food manufacturer, is replacing most of its glass baby food jars with plastic. Miller Brewing Co. now sells some of its popular beers in plastic containers. Compare glass and plastics in terms of their application for packaging food and beverages. 1.8 The steel industry is the major consumer of refractories. What other industries might be users of this ceramic product? 1.9 Pearls and garnets are both examples of gems. We classify garnet as a ceramic. Would you classify pearl as a ceramic? Briefly justify your answer. 1.10 Some nuclear reactors use MOX fuel. What is MOX and is it a ceramic? 14 ................................................................................................................................................................... I n t r o d u c t i o n  2 Some History CHAPTER PREVIEW In this chapter we present a brief history of ceramics and glasses. Because of the length of time over which they have been important to human existence it would be possible, indeed it has been done, to fill entire volumes on this one topic. We do not have the luxury of spending so much time on any one topic but history is important. In ceramics, it helps if we understand why certain events/developments occurred and when and how they did. We are really interested in setting the scene for many of the subsequent chapters. The earliest ceramics that were used were flint and obsidian. These exhibit conchoidal fracture like many modern day ceramics, such as cubic zirconia and glasses. This property enabled very sharp edges to be formed, which were necessary for tools and weapons. During the latter period of the Stone Age (the Neolithic period) pottery became important. Clay is relatively abundant. When mixed with water, it can be shaped and then hardened by heating. We will describe the different types of pottery and how the ceramics industry developed in Europe. The Europeans were not responsible for many of the early inventions in pottery; they were mostly trying to copy Chinese and Near East ceramics. Europe’s contribution was to industrialize the process. We are also going to describe some of the major innovations in ceramics that occurred during the twentieth century, such as the float glass process, bioceramics, and the discovery of high-temperature superconductivity. These developments are important in defining the present status of the field and also give some indications of areas in which future innovations may occur. We will conclude the chapter by giving information about museums that have major collections of ceramic materials as well as listing the relevant professional societies. 2.1 EARLIEST CERAMICS: THE based on their color, opacity, banding, and other visible STONE AGE features. Flint is a black variety of chert. Jasper is a red/ brown variety. Certain ancient periods of history are named after the Flint is easily chipped and the fracture of flint is con- material that was predominantly utilized at that time. The choidal (shell-like), so that sharp edges are formed. The Stone Age, which began about 2.5 million years ago, earliest stone tools are remarkably simple, almost unrec- is the earliest of these periods. Stone, more specifically ognizable unless they are found together in groups or with flint, clearly satisfies our definition of a ceramic given in other objects. They were made by a process called per- Chapter 1. cussion flaking, which results in a piece (a flake) being Flint is a variety of chert, which is itself cryptocrystal- removed from the parent cobble (a core) by the blow from line quartz. Cryptocrystalline quartz is simply quartz (a another stone (a hammer-stone) or hard object. Both the polymorph of SiO2) that consists of microscopic crystals. flake and the core have fresh surfaces with sharp edges It is formed from silica that has been removed from sili- and can be used for cutting. While pebble tools do have a cate minerals by chemical weathering and carried by cutting edge, they are extremely simple and unwieldy. water as ultrafine particles in suspension. Eventually, it These basic tools changed, evolved, and improved through settles out as amorphous silica gel containing a large time as early hominids began to remove more flakes from amount of water. Over time, the water is lost and small the core, completely reshaping it and creating longer, crystals form, even at low temperatures. During settling, straighter cutting edges. When a core assumes a distinc- the chemical conditions are changing slowly. As they tive teardrop shape, it is known as a handaxe, the hallmark change, the color, rate of deposition, and texture of the of Homo erectus and early Homo sapiens technology. precipitate can also change. As a result, cryptocrystalline Figure 2.1 shows an example of a stone tool made by per- quartz occurs in many varieties, which are named cussion flaking that was found in Washington State. 2 .1 E a r l i e s t C e r a m i c s : Th e S t o n e A g e .................................................................................................................. 15  FIGURE 2.1 Example of a stone tool made by percussion flaking. Years Before Stone Archaeological Hominid Major Period Present Industry Sites Species Events Neolithic 10,000 Farming Lascaux Pincevent Art Upper Blade tools Paleolithic Dolni Vestonice Homo sapiens Tabun sapiens Middle Mousterian Shanidar Klasies River Homo sapiens Paleolithic flake tools neanderthalensis ¨ ¨ Verteszollos 100,000 Kalambo Falls Archaic Burial of dead Homo sapiens Oldest dwellings 200,000 Torraiba Terra Amata Use of fire Olorgesailie 500,000 Spread Lower Zhoukoudien Trinil out of Africa Paleolithic Clactonian chopping tools 1,000,000 Acheulean Handaxes Homo erectus handaxes Oldowan Koobi Fora 2,000,000 pebble tools Olduvai Homo habilis Large brains Basal Paleolithic Swartkrans First stone tools Hadar 3,000,000 Australopithecus Laetoli Ardipithecus Oldest hominid 6,000,000 fossils FIGURE 2.2 Chronology of the Stone Age. 16 ................................................................................................................................................................... S o m e H i s t o ry  Christian Thomsen first proposed the division of the ages of prehistory into the Stone Age, Bronze Age, and Iron Age for the organization of exhibits in the National Museum of Denmark in 1836. These basic divisions are still used in Europe, the United States, and in many other areas of the world. In 1865 English naturalist John Lubbock further divided the Stone Age. He coined the terms Paleolithic for the Old Stone Age and Neolithic the New Stone Age. Tools of flaked flint characterize the Paleolithic period, while the Neolithic period is represented by polished stone tools and pottery. Because of the age and complexity of the Paleolithic, further divisions were needed. In 1872, the French pre- historian Gabriel de Mortillet proposed subdividing the Paleolithic into Lower, Middle, and Upper. Since then, an even earlier subdivision of the Paleolithic has been desig- nated with the discovery of the earliest stone artifacts in Africa. The Basal Paleolithic includes the period from around 2.5 million years ago until the appearance and spread of handaxes. These different periods are compared in Figure 2.2. Stone tools that were characteristic of a particular period are often named after archeological sites that typi- fied a particular technological stage. FIGURE 2.3 A 25,000-year old baked clay Pavlovian figurine  Oldowan pebble tools were found in the lowest and called the “Venus of Vestonice”; found in 1920 in Dolni Vestonice oldest levels of Olduvai Gorge. in the Czech Republic.  Acheulean handaxes are named after the Paleolithic site of St. Acheul in France, which was discovered in the nineteenth century. remained almost undamaged. It was named the “Venus of  Clactonian chopping tools are named after the British Vestonice” and is believed to have been a fertility charm. site of Clacton-on-sea, where there is also the ear- The absence of facial features on this and other “Venus” liest definitive evidence for wood technology in the figures is causing many anthropologists to rethink the role prehistoric record—the wood was shaped using flint these figures might have played in prehistoric society. The tools. statuette stands about 10 cm tall and has been dated as far  Mousterian flake tools are named after a site in France. back as 23,000 bce. One of the most recent archeological The later blade tools are flakes that are at least twice finds was made in the caves of Tuc d’Audobert in France, as long as they are wide. where beautifully preserved clay bison have been found that are estimated to be 12,000 years old. Another important ceramic during the Stone Age was The earliest archeological evidence of pottery produc- obsidian, a dark gray natural glass precipitated from tion dates back to about 10,000 bce and the discovery volcanic lava. Like other glasses it exhibits conchoidal of fragments from a cave dwelling near Nagasaki, Japan. fracture and was used for tools and weapons back into the This type of pottery is called Jomon pottery because Paleolithic period. of the characteristic surface patterns, which were made with a twisted cord. Jomon means “cord pattern.” The pottery also featured patterns made with sticks, bones, or fingernails. These vessels, like those produced 2.2 CERAMICS IN in the Near East about 10,000 years ago, were fired at ANCIENT CIVILIZATIONS a low temperature compared to modern day pottery production. The oldest samples of baked clay include more than 10,000 By 6400 bce, pottery making was a well-developed fragments of statuettes found in 1920 near Dolní Ves- craft. Subsequent developments in the history of ceramics tonice, Moravia, in the Czech Republic. They portray are shown in Figure 2.4. We will be describing some of wolves, horses, foxes, birds, cats, bears, or women. One these in a little more detail in later sections of this of these prehistoric female figures, shown in Figure 2.3, chapter. 2 . 2 C e r a m i c s i n A n c i e n t C i v i l i z at i o n s .................................................................................................................. 17  about 22000 BCE • Earliest known fired clay figures BCE about 8000 BCE • Fired vessels in Near East Slip coatings, ochre red and black decoration, impressed designs, by about rouletting, incised decoration, control of oxidation-reduction during firing 6000 BCE manganese and spinel black pigments, coil and slab contruction in Near East burnishing, joining, paddle and anvil shaping, carving and trimming clays prepared by decanting suspension about 4000 BCE • Egyptian faience QU EARTHENWARE AR TZ about 1600 BCE • vapor glazing, prefritted glazes wheel throwing earthenware molds craft shops 1500 BCE • glass making alkaline glazes QU AR TZ -F R 10th C • clay-quartz-frit ware in Egypt IT- CL 13th C • enameled minai ware lustre painting 13th C • enamaled minai ware CE about 1000 BCE • glazed AY stoneware in China 14th C • white tile Han Dynasty (206 BCE - 16th C • Isnik tile 221 CE) • white porcelain Blue on white wares TR SO IA FT 1575-1587 • Medici porcelain XI -PA TERRACOTTA about 700 BCE AL 17th C • Gombroon ware Greek black- HA ST on-red ware RD Tang Dynasty (618-906) E about 1695 • soft paste porcelain -P at St. Cloud PO about 100 BCE extensive porcelain AS RC more lead glazes exported from China TE 1742 • soft paste porcelain EL P at Chelsea A Sung Dynasty (960-1279) O IN 1796 • Spode’s English RC 9th C • tin glazed celadon and jun ware bone china EL ware in Baghdad Ming Dynasty (1368-1644) AI lustre painting 1857 • Beleek Blue on white porcelain N frit porcelain 17th C • Arita ware 13th C • rebuilding of Ching-to-Chen TI tin glazed majolica N STONEWAR during Kang Hsi reign -G 15th C • in Spain, Italy LA German 1708 • Bottger porcelain ZE stoneware about 1720 • modern 15th C • salt glazing D polychrome painting European hard porcelain W English slipware AR 16th C • Beginning of opaque “famille-rose”enamels 17th C • fine E E paintings of history 18th C • fine white semi-vitrious terra cotta and stories wares in England Engine turning 17th C • 19th C • Parian porcelain basalte faience in Europe cane ware 1764 • Wedgewood blue and white delft ware JA jasperware SP ER W 20th C • AR Hand-crafted tin-glazed ware E 20th C • Hand-crafted stoneware FIGURE 2.4 The “flow” of ceramic history illustrates the mainstreams of earthenware, terra cotta, and stoneware, of “triaxial” hard-paste porcelain, of quartz-based bodies, and of tin-glazed ware. Some important shaping and decorative techniques are illustrated, but the diagram is far from complete. 18 ................................................................................................................................................................... S o m e H i s t o ry  Abundance in % 52 50 %48 46 44 28 26 24 10 8 6 4 2 0 O Si Al Fe Ca Na K Mg H FIGURE 2.6 Large “grains” of mica clearly show the lamellar Element nature of the mineral. Two orientations are present in this one FIGURE 2.5 Abundance of common elements in the earth’s crust. piece. The clay minerals are layered or sheet silicates with a 2.3 CLAY grain size <2 μm. Chemically they are aluminosilicates. In nature, mica (shown in Figure 2.6) is constructed by Silicate minerals make up the vast majority of the earth’s stacking layers together to form sheets. Kaolinite has a crust, which is not surprising if we consider related structure but tends to have smaller “grains.” Rocks that contain a large amount of kaolinite are known as  The abundance of Si and O (Figure 2.5) kaolin. When the sheets are separated by films of water,  The high strength of the Si–O bond (Table 2.1) the platelets slide over one another to add plasticity to the mixture. This plasticity is the basis of the use of clay for Since silicate and aluminum silicate minerals are widely pottery. Moreover, when the clay–water mixture is dried available, they are inexpensive and form the backbone of it becomes hard and brittle and retains its shape. On firing the traditional high-volume products of the ceramic indus- at temperatures about 950°C, the clay body becomes dense try. Their abundance also explains why earthenware prod- and strong. In Chapter 7 we describe the structures of ucts are found in nearly every part of the world. The some of the important clay minerals, including kaolin. situation is very different with regard to kaolinite, the essential ingredient, along with feldspar and quartz, needed to make porcelain, by far the finest and most 2.4 TYPES OF POTTERY highly prized form of ceramic. Kaolin deposits are more localized. There are excellent deposits, for example, in Pottery is broadly divided into southwest England. In the United States most kaolin comes from the southeast between central Georgia and the Savan-  Vitrified ware nah River area of South Carolina.  Nonvitrified ware Clay minerals remain the most widely used raw mate- rials for producing traditional ceramic products. The total The classification depends upon whether the clay was U.S. production of clays is about 40 million tons per year, melted during the firing process into a glassy (vitreous) valued at $1.5 billion. substance or not. Within these divisions we have the following: TABLE 2.1 Bond Strengths with Oxygen  Earthenware is made from red “earthenware clay” and Bond Strength (kJ/mol) is fired at fairly low temperatures, typically between 950 and 1050°C. It is porous when not glazed, rela- Ti-O 674 Al-O 582 tively coarse, and red or buffcolored, even black after Si-O 464 firing. The term “pottery” is often used to signify Ca-O 423 earthenware. The major earthenware products are Mna-O 389 bricks, tiles, and terra cotta vessels. Earthenware Fea-O 389 dating back to between 7000 and 8000 bce has been Mg-O 377 found, for example, in Catal Hüyük in Anatolia a 2+ state. (today’s Turkey). 2 . 4 Ty p e s o f P o t t e ry .................................................................................................................................................... 19  plastic body. Not being very tough, it is easily scratched and more rare than hard-paste porcelain.  Hard-paste porcelain is porcelain with a relatively high alumina content derived from the clay and feld- spar, which permits good plasticity and formability, but requires a high firing temperature (1300–1400°C). Böttger produced the first successful European hard- paste porcelain in 1707–1708 consisting of a mixture of clay and gypsum. This work laid the foundation for the Meissen porcelain manufacture in Saxony (Germany) in 1710.  Bone China has a similar recipe to hard-paste porce- lain, but with the addition of 50% animal bone ash (calcium phosphate). This formulation improves strength, translucency, and whiteness of the product FIGURE 2.7 Microstructure of a “Masters of Tabriz” tile showing and was perfected by Josiah Spode at the end of the many large grains of crystalline SiO2. eighteenth century. It was then known as “English China” or “Spode China.”  Stoneware is similar to earthenware but is fired to a higher temperature (around 1200–1300°C). It is vitri- 2.5 GLAZES fied, or at least partially vitrified, and so it is nonporous and stronger. Traditional stoneware was gray or buff To hermetically seal the pores of goods made of earthen- colored. But the color can vary from black via red, ware an additional processing step called glazing was brown, and gray to white. Fine white stoneware was introduced around or probably even before 3000 bce by made in China as early as 1400 bce (Shang dynasty). the Egyptians. It involved the coating of the fired objects Johann Friedrich Böttger and E.W. von Tschirnhaus with an aqueous suspension consisting of finely ground produced the first European stoneware in Germany in quartz sand mixed with sodium salts (carbonate, bicar- 1707. This was red stoneware. Later Josiah Wedgwood, bonate, sulfate, chloride) or plant ash. The ware would an Englishman, produced black stoneware called then be refired, usually at a lower temperature, during basalte and white stoneware colored by metal oxides which the particles would fuse into a glassy layer. called jasper. Two other types of glaze, which also date back several  Porcelain was invented by the Chinese and produced millennia, have been applied to earthenware. These are during the T’ang dynasty (618–907 ce). It is a white, the transparent lead glaze and the opaque white tin thin, and translucent ceramic that possesses a metal- glaze. like ringing sound when tapped. Porcelain is made from kaolin (also known as china clay), quartz, and The Lead Glaze feldspar. Fired at 1250–1300°C it is an example of vitreous ware. The microstructure of porcelain is quite The addition of lead reduces the melting or fusion point complicated. Figure 2.7 shows a backscattered electron of the glaze mixture, which allows the second firing to be image obtained using a scanning electron microscope at an even lower temperature. The first lead-rich glazes (SEM) of the microstructure of a “Masters of Tabriz” were probably introduced during the Warring States period tile (1436 ce) showing that it contains many large (475–221 bce). The lead oxide (PbO) content was about grains of quartz immersed in a continuous glass 20%. During the Han dynasty (206 bce–ce 200) higher phase. lead oxide contents were typical, up to 50–60%. Lead  Soft-paste porcelain is porcelain with low clay content glazing was subsequently widely used by many civiliza- that results in a low alumina (Al2O3) content. The most tions. However, lead from the glaze on tableware may be common form of soft-paste porcelain is formed of a leached by food. Table 2.2 shows lead released from two paste of white clay and ground glass. This formulation glazes that were made to match those of two Eastern Han allows a lower firing temperature, but provides a less Dynasty lead glazes. The glaze formulations were remade TABLE 2.2 Composition of Han Lead Glazes (wt%) and Lead Metal Release (ppm) PbO SiO2 Al2O3 Fe2O3 TiO2 CaO MgO K2O Na2O BaO CuO SnO2 Cl S Pb release Glaze 1 59.7 29.5 3.7 1.3 0.2 1.9 0.5 0.9 0.2 0.2 1.2 0.2 2.2 — 42 Glaze 2 43.5 33.4 3.9 2.0 0.6 2.0 0.7 0.5 0.4 7.7 3.0 1.2 — 0.6 120 20 ................................................................................................................................................................... S o m e H i s t o ry and fired by CERAM (formerly the British Ceramic an important and growing export industry that attracted Research Association) in the UK. The amount of lead entrepreneurs and engineers to develop modern produc- released in a standard leach test is determined by filling tion and marketing methods. A leader in this revolution the glazed ceramic item with 4% acetic acid at 20°C for was Josiah Wedgwood. 24 hours; the acid is then analyzed for Pb by flame atomic In 1767 Wedgwood produced improved unglazed black absorption spectrometry. The present U.S. Food and Drug stoneware, which he called “basalte.” The famous Wedg- Administration limit for Pb release from small hollow- wood “jasperware” began production in 1775 and con- ware is 2 ppm. sisted of Some historians believe that lead release from glazes on pitchers and other food and beverage containers and  One part flint utensils poisoned a large number of Roman nobility and  Six parts barium sulfate thus contributed (together with Pb from water pipes) to  Three parts potters’ clay the fall of the Roman Empire (see, for example, Lindsay,  One-quarter part gypsum 1968). Lead poisoning was responsible for the high mor- tality rates in the pottery industry even during the nine- Wedgwood was so excited by this new ceramic body that teenth century. Many countries have now outlawed lead he wrote to his partner: glazing unless fritted (premelted and powdered) glazes are utilized that prevent the lead from being easily leached. The only difficulty I have is the mode of procuring and convey- The possibility of leaching a heavy metal from a glass is ing incog (sic) the raw material. . . . I must have some before I a concern today in the nuclear-waste storage industry. proceed, and I dare not have it in the nearest way nor undisguised. The Tin Glaze Jasper is white but Wedgwood found that it could be The Assyrians who lived in Mesopotamia (today’s North- colored an attractive blue by the addition of cobalt oxide. ern Iraq) probably discovered tin glazing during the (The mechanism for color formation in transition metal second millennium bce. It was utilized for decorating oxides is described in Chapter 32.) The manufacturing bricks, but eventually fell into disuse. It was reinvented process was soon changed (in part because of a sharp again in the ninth century ce and spread into Europe via increase in the cost of the blue pigment) and the white the Spanish island of Majorca, after which it was later jasper was coated with a layer of the colored jasper. Wedg- named (Majolica). Centers of majolica manufacture devel- wood jasper remains sought after and highly collectable. oped in Faenza in Italy (Faience) and in 1584 at the You can visit the Wedgwood factory in England and watch famous production center at Delft in the Netherlands the production process. (Delftware). Tin glazing became industrially important at Wedgwood also was instrumental in changing the way the end of the nineteenth century with the growth of the manufacturing was done. He divided the process into ceramic sanitary ware industry. many separate parts, and allowed each worker to become expert in only one phase of production. This approach was revolutionary at the time and was designed to increase the 2.6 DEVELOPMENT OF A performance of each worker in a particular area and reduce CERAMICS INDUSTRY the requirement for overall skill. He was also concerned with trade secrets; each workshop at his factory had a Quantity production of ceramics began during the fourth separate entrance so workers would not be exposed to millennium bce in the Near East. Transition to a large- more than a limited number of valuable secrets. scale manufacturing industry occurred in Europe during In the increasingly competitive entrepreneurial econ- the eighteenth century. At the beginning of the century, omy of the eighteenth century, Wedgwood was one of the potteries were a craft institution. But this situation was leading figures to have the foresight and the willingness transformed at several important sites: to expend the necessary effort to promote the general interests of the ceramics industry. In the early days of the  Vincennes and Sèvres in France pottery industry in England, transport of raw materials in  Meißen in Germany and product out was done with pack animals. It was clear  Staffordshire in England that quantity production could not be achieved without better transportation. Wedgwood organized a potters’ By the end of the eighteenth century, the impact of greater association to lobby for better roads and, more impor- scientific understanding (such as chemical analysis of raw tantly, a canal system. The opening of the Trent-Mersey materials) had changed the field of ceramics. At the same Canal in 1760 ensured that Staffordshire would remain the time, the ceramic industry played an influential role in the center of English pottery production. industrial revolution and the development of factory As with many industries, the first stage of the indus- systems in England and across Europe. Ceramics became trial revolution did not result in a deterioration of working 2 . 6 D e v e l o p m e n t o f a C e r a m i c s I n d u s t ry ............................................................................................................. 21 conditions. A partly rural craft-based skill, such as pottery  Development of advanced characterization techniques making, became an injurious occupation only as industri- such as X-ray diffraction and electron microscopy, alization progressed, bringing into overcrowded town which provided structural and chemical information centers poor workers from the countryside. Occupational  Developments in ceramic processing technology diseases were prevalent in the potteries. The main pro- blem was diagnosed at an early date—lead poisoning. In 1949 British regulations forbade the use of raw lead 2.7 PLASTER AND CEMENT in glaze compositions. Prior to this there were 400 cases of lead poisoning a year at the end of the nineteenth A special ceramic is hydraulic (or water-cured) cement. century. Although experiments with leadless glazes World production of hydraulic cement is about 1.5 billion were recorded throughout the nineteenth century, lead tons per year. The top three producers are China, Japan, was essential, and the safe solution adopted and approved and the United States. When mixed with sand and gravel, early in the twentieth century was a lead glaze of low we obtain concrete—the most widely utilized construc- solubility, produced by making the glaze suspension out tion material in the industrialized nations. In essence, of fritted lead. concrete is a ceramic matrix composite (CMC) in which Another serious health risk for potters was pneumoco- not just the matrix but also the reinforcing material is niosis: flint dust particles when inhaled caused gradual and ceramic. often fatal damage to the Ancient Romans and lungs. It was a lingering Greeks, 2000 years ago, PORTLAND CEMENTS disease, which took many pioneered the use of Hydraulic materials—water causes setting and decades to diagnose and cement. Its unique chemi- hardening. control. Flint is still used cal and physical properties as a component in the produced a material so bodies of many traditional ceramic wares, but the risk of lasting that it stands today in magnificent structures like pneumoconiosis has been virtually eliminated through the Pantheon in Rome. Roman cement consisted of a proper ventilation, the cleanliness of workshops, and the mixture of powdered lime (CaO) and volcanic ash (a use of protective clothing. mixture of mainly SiO2, Al2O3, and iron oxide)—called In North America the origin of pottery production pozzolana—from Mount Vesuvius, which buried the occurred in regions where there were deposits of earthen- ancient city of Pompeii in 79 ce. This mixture hardens in ware clay and the wood needed for the kilns. The abun- the presence of water. dance of these raw materials were factors in the English Contemporary hydraulic cement, for example, Port- settling in Jamestown, Virginia in 1607. And there is evi- land cement (invented by Joseph Aspdin and named after dence that pottery production began in Jamestown around a natural stone from the island of Portland in England, 1625 (see Guillard, 1971). Similar supplies were available which it resembles), has a composition similar to pozzo- in the Northeast for the English potters accompanying the lanic cement. The chief ingredients of Portland cement are small band of farmers and tradesmen who arrived in di- and tricalcium silicates and tricalcium aluminate. In Plymouth in the 1620s. In New England and in Virginia the reduced nomenclature given in Table 2.3 these ingre- potters used a lead glaze brushed onto the inside of the dients would be expressed as C2S, C3S, and C3A, respec- earthenware vessel to make the porous clay watertight. tively. Portland cement is produced to have a specific The important pottery centers in North America during surface area of ∼300 m2 /kg and grains between 20 and the mid-nineteenth century were Bennington, VT, Trenton, 30 μm. The average composition is given in Table 2.4. In NJ, and East Liverpool, OH. The geographical location of Chapter 8 we will show you on a ternary phase diagram each center formed a right triangle located in the north- the composition range of Portland cements. east. These locations had deposits of fine clay and river The setting reactions for Portland cement are similar transportation, which provided easy access to markets. By to those for the ancient pozzolanic cement. The first reac- 1840 there were more than 50 stoneware potteries in Ohio, tion is the hydration of C3A. This reaction is rapid, occur- earning Akron the tag “Stoneware City.” ring within the first 4 hours, and causes the cement In the past, ceramic production was largely empirical. to set: To maintain uniformity, producers always obtained their raw materials from the same supplier and avoided chang- C3A + 6H → C3AH6 + heat (2.1) ing any detail of their process. The reason was that they were dealing with very complex systems that they did not TABLE 2.3 Reduced Nomenclature for Cement Chemistry understand. Today, as a result of ∼100 years of ceramics research, processing and manufacturing are optimized Lime CaO = C based on an understanding of basic scientific and engi- Alumina Al2O3 = A Silica SiO2 = S neering principles. Research in ceramics was spurred on Water H2O = H by two main factors: 22 ................................................................................................................................................................... S o m e H i s t o ry  TABLE 2.4 Average Overall Composition of Portland Cement Clinker Reduced By element wt% By Phase nomenclature Name wt% CaO 60–67 3CaO·SiO2 C3S Tricalcium silicate 45–70 SiO2 17–25 2CaO·SiO2 C 2S Dicalcium silicate 25–30 Al2O3 3–9 3CaO·Al2O3 C 3A Tricalcium aluminate 5–12 Fe2O3 0.5–6 4CaO·Al2O3 C4AF Tricalcium aluminoferrite 5–12 Fe2O3 MgO 0.1–4 CaSO4 ·2H2O CSH2 Gypsum 3–5 Na 2O, K 2O 0.5–1.3 SO3 1–3 The C3AH6 phase or ettringite is in the form of rods The development of strength with time for Portland and fibers that interlock. The second reaction, which cement is shown in Figure 2.9. The reactions give off a lot causes the cement to harden, is slower. It starts after about of heat (Figure 2.10). In very large concrete structures, 10 hours, and takes more than 100 days to complete. The such as the Hoover Dam at the Nevada–Arizona border in product is tobermorite gel, a hydrated calcium silicate the United States, heat is a potential problem. Cooling (Ca3Si2O7 · 3H2O), which bonds everything together. pipes must be embedded in the concrete to pump the heat out. These pipes are left in place as a sort of reinforce- 2C2S + 4H → C3S2H3 + CH + heat (2.2) ment. In the case of the Hoover Dam, the construction 2C3S + 6H → C3S2H3 + 3CH + heat (2.3) Protuberances grow from the gel coating and form Compressive Strength Reaction complete arrays of interpenetrating spines. Scanning electron (MPa) microscopy (SEM) has been one tool that has been used 40 to examine cement at various stages in the setting and hardening process. Figure 2.8 shows an SEM image recorded 8 days into the hardening process. The plate-like features are calcium hydroxide (CH); the cement (Ct) Hardening reactions 20 grains are already completely surrounded by the tober- Induction morite gel (called CSH in Figure 2.8). period Setting reactions 0 15 min 2.4 hrs 1 day 10 days 100 days t Ct CSH FIGURE 2.9 Increase in compressive strength of Portland cement with time. 10 Heat CH Evolution Setting J (kg-1 s-1) peak 5 Induction Hardening period peak Pore 0 10 μm 15 min 2.4 hrs 1 day 10 days 100 days t FIGURE 2.8 Reaction products in cement after 8 days hardening FIGURE 2.10 Heat evolution during the setting and hardening of (SEM image). Portland cement. 2 .7 P l a s t e r a n d C e m e n t ............................................................................................................................................. 23 consisted of a series of individual concrete columns rather than a single block of concrete. It is estimated that if the dam were built in a single continuous pour, it would have taken 125 years to cool to ambient temperatures. The resulting stresses would have caused the dam to crack and possibly fail. Plaster of Paris is a hydrated calcium sulfate (2CaSO4 · H2O). It is made by heating naturally occurring gypsum (CaSO4 · 2H2O) to drive off some of the water. When mixed with water, plaster of Paris sets within a few minutes by a cementation reaction involving the creation of interlocking crystals: 1 3 CaSO 4 ⋅ H 2 O + H 2 O → CaSO 4 ⋅ 2H 2 O (2.4) 2 2 To increase the setting time a retarding agent (the protein keratin) is added. Plaster of Paris is named after the French city where it was made and where there are abundant gypsum deposits. Following the Great Fire of London in 1666 the walls of all wooden houses in the city of Paris were covered with plaster to provide fire protection. The earliest use of plaster coatings dates back 9000 years and was found in Anatolia and Syria. The Egyptians used plaster made from dehydrated gypsum powder mixed with water as a joining compound in the magnificent pyramids. 2.8 BRIEF HISTORY OF GLASS FIGURE 2.11 Glass workers in Bohemia, from the Travels of Sir John Mandeville, ink and tempera on parchment, Flemish, early fifteenth century. The history of glass dates back as far as the history of ceramics itself. We mentioned in Section 2.1 the use of obsidian during the Paleolithic period. It is not known for certain when the first glass objects were made. Around And beside Acre runs a little river, called the Belyon [Abellin], 3000 bce, Egyptian glassmakers systematically began and near there there is the Fosse of Mynon, all round, roughly making pieces of jewelry and small vessels from glass; a hundred cubits broad; and it is full of gravel. And however pieces of glass jewelry have been found on excavated much be taken out in a day, on the morrow it is as full as ever Egyptian mummies. By about 1500 bce Egyptian glass- it was, and that is a great marvel. And there is always a great wind in that pit, which stirs up all the gravel and makes it eddy makers during the reign of Touthmosis III had developed about. And if any metal be put therein, immediately it turns to a technique to make the first usable hollowware. glass. This gravel is shiny, and men make good clear glass of The glass was made from readily available raw materi- it. The glass that is made of this gravel, if it be put back in the als. In the clay tablet library of the Assyrian King Ashur- gravel, turns back into gravel, as it was at first. And some say banipal (669–626 bce) cuneiform texts give glass formulas. it is an outlet of the Gravelly Sea. People come from far coun- The oldest one calls for 60 parts sand, 180 parts ashes of tries by sea with ships and by land with carts to get some of that sea plants, and 5 parts chalk. This recipe produces an gravel. Na2O–CaO–SiO2 glass. The ingredients are essentially the same as those used today but the proportions are Sand is an important constituent of most oxide glasses. somewhat different. Pliny the Elder (23–79 ce) described Early glassmakers would have made effective use of the composition and manufacture of glass in Naturalis natural resources and set up their workshops near a source Historia. During Roman times glass was a much-prized of raw materials. This practice was also adopted during status symbol. High-quality glassware was valued as much the time of Josiah Wedgwood and was the reason that the as precious metals. ceramic industry developed in the north of England—not Figure 2.11 shows a Flemish drawing from the early in London, the capital. The illustration also shows the fifteenth century depicting glass workers in Bohemia, entire cycle of producing a glass object from obtaining the from the Travels of Sir John Mandeville. It shows the raw materials to testing of the final product. legendary pit of Mynon with its inexhaustible supply of One of the most common methods used to form glass sand. is glassblowing. Although this technique was developed 24 ................................................................................................................................................................... S o m e H i s t o ry over 2000 years ago in Syria the glassblowing pipe has duties were repealed in 1698 because of the reduction in not changed much since then. The main developments are the consumption of coal and the rise in unemployment. In the automated processes used to produce glass containers 1746 duties were again levied, but they were also imposed and light bulbs in the thousands. In Chapter 21 we will on imported glassware. The Act of 1746 required a record summarize the important milestones in glass formation to be kept of all furnaces, pots, pot chambers, and ware- and production. houses, and due notice to be given when pots were to be In this section we consider two specific aspects of the changed. In the same year the regulations were applied for history of glass: the first time to Ireland, as a result of which many of the flourishing glassworks established there to avoid the excise  Lead crystal glass duties began to decline. The duties seriously delayed tech-  Duty on glass nological innovation and in 1845 they were repealed. The industry immediately entered a new period of growth. These events occurred between the very early experimen- The Industrial Revolution started in England during tation with glass in Egyptian and other ancient civiliza- the latter part of the eighteenth century, but this did not tions and more modern developments in glass such as radically affect the glass industry in its early stages optical fibers and glass ceramics. because mechanical power was not required in the glass- The Venetians used pyrolusite (a naturally occurring works. The impact of mechanization is shown best by its form of MnO2) as a decolorizer to make a clear glass. This development in the American glass industry. American addition was essential because the presence of impurities, workers were scarce and wages were much higher than in chiefly iron, in the raw materials caused the glass to have Europe and so means were sought to increase productivity. an undesirable greenish-brown color. The manganese oxi- One of the important developments at this time was a dizes the iron, and is itself reduced. The reduced form of process for making pitchers by first pressing and then manganese is colorless but when oxidized it is purple (Mn free-hand blowing, patented by Gillinder in 1865. This in the +7 oxidation state). Manganese was used until quite patent led to a period in which American container pro- recently as a decolorizer and some old windows may be duction changed from a craft industry to a mechanized seen, particularly in Belgium and the Netherlands, where manufacturing industry. a purple color has developed owing to long exposure to To the early glassmakers the nature of the structure of sunlight, which has oxidized the manganese back to the glass was a mystery. But they did know that the addition purple form. of certain components could modify properties. The most Lead crystal glass is not crystalline. But the addition successful model used to describe the structure of oxide of large amounts of lead oxide to an aluminosilicate glass glasses is the random-network model devised by W.H. formulation produces a heavy glass with a high refractive Zachariasen (1932). This model will be described in some index and excellent transparency. Suitable cutting, exploit- detail in Chapter 21. Although the random-network model ing the relative ease with which lead glass can be cut and is over 60 years old it is still extensively used to explain polished, enhances the brilliance. The lead content, in the the behavior and properties of oxide glasses and is widely form of PbO, in Ravenscroft’s lead crystal glass has been used in industry in developing and modifying glass determined to be about 15%. Now lead crystal glasses formulations. contain between 18 and 38% PbO. For tableware to be sold as “lead crystal” the PbO content must be about 25%. Expansion of the British glass industry followed the 2.9 BRIEF HISTORY OF REFRACTORIES success of lead crystal glass and during the eighteenth century it achieved a leading position that it held for a The development of refractories was important for many hundred years. The beautiful drinking glasses of this industries, most notably for iron and steel making and period are collector items. English production was hin- glass production. The iron and steel industry accounts for dered only by a steady increase of taxation between 1745 almost two-thirds of all refractories used. The discovery and 1787 to pay for the war against France. The tax was by Sidney Gilchrist Thomas and his cousin Percy Gilchrist levied on glass by weight, and as the tendency had been in 1878 that phosphorus could be removed from steel to add more lead oxide, the production was checked. As melted in a dolomite-lined Bessemer converter (and subse- a result, many glassmakers moved to Ireland where glass quently on a dolomite hearth) was an important develop- was free from duty and glassworks were set up in Dublin ment. They solved a problem that had defeated the leading and Waterford. metallurgists of the day. And what is even more remarkable During the eighteenth and nineteenth centuries the is that Thomas, who had originally wanted to be a doctor, British government regarded the glass industry as an inex- was a magistrate’s clerk at Thames police court in London. haustible fund to draw on in times of war and shortage. A Out of interest he attended evening classes in chemistry, glass duty was first imposed by statute in 1695 and made and later metallurgy, at Birkbeck Mechanics Institute (now perpetual the following year, but it was so high as to dis- Birkbeck College, University of London), where he became courage manufacture and was soon reduced by half. The aware of the phosphorus problem. It took three attempts 2 . 9 B r i e f H i s t o ry o f R e f r ac t o r i e s .......................................................................................................................... 25 (over a 1-year period) by Thomas and Gilchrist to report power-producing nuclear reactors. The water-cooled, the successful outcome of their work to the Iron and Steel water-moderated nuclear reactor would not have been pos- Institute. A lesson in perseverance! When their paper was sible without urania. The important properties are finally presented (Thomas and Gilchrist, 1879) the success of their process had become widely known and they 1. Resistance to corrosion by hot water attracted an international audience. 2. Reasonable thermal conductivity, about 0.2–0.1 times Dolomite refractories are made from a calcined natural that of metals mineral of the composition CaCO3 · MgCO3. The produc- 3. Fluorite crystal structure, which allows accommoda- tion of magnesite, a more slag-resistant refractory than tion of fission products (see Section 6.5). dolomite, began in 1880. Magnesite refractories consist mainly of the mineral periclase (MgO); a typical composi- Reactor pellets are often cylinders, about 1 cm high tion will be in the range MgO 83–93% and Fe2O3 2–7%. and 1 cm in diameter, with a theoretical density of about Historically, natural magnesite (MgCO3) that was calcined 95%. Many pellets are loaded into a closely fitting zirco- provided the raw material for this refractory. With nium alloy tube that is hermetically sealed before inser- increased demands for higher temperatures and fewer tion into the reactor. process impurities, higher purity magnesia from seawater Following World War II (and the first use of nuclear and brine has been used. This extraction process is weapons) there was a lot of research in the field of nuclear described in Chapter 19. energy. Many of the people doing this research started In 1931 it was discovered that the tensile strength of with the wartime Manhattan project. Almost all worked mixtures of magnesite and chrome ore was higher than in a few government-supported laboratories, such as that of either material alone, which led to the first chrome– those at Oak Ridge (in Tennessee) or Argonne (in Illinois) magnesite bricks. Chrome refractories are made from or at commercially operated laboratories that were naturally occurring chrome ore, which has a typical com- fully government supported. In other countries most of position in the range Cr2O3 30–45% Al2O3 15–33%, SiO2 the work was also carried out in government laboratories, 11–17%, and FeO 3–6%. Chrome–magnesite refractories for example, Chalk River in Canada and Harwell have a ratio of 70 : 30, chrome : magnesia. Such bricks have in England. The excitement in nuclear energy continued a higher resistance to thermal shock and are less liable to into the 1970s until the Three Mile Island incident. In change size at high temperatures than magnesite, which the United States much of the interest and research they replaced in open-hearth furnaces. The new refracto- in nuclear energy and nuclear materials have passed. ries also replaced silica in the furnace roof, which allowed Work continues in several countries including Japan, higher operating temperatures with the benefits that these France, and Canada and will resume elsewhere as energy furnaces were faster and more economical than furnaces demands grow. with silica roofs. The float-glass process. Flat, distortion-free glass has Finally, not the least important development in refrac- long been valued for windows and mirrors. For centuries, tories was the introduction of carbon blocks to replace the production of plate glass was a labor-intensive process fireclay (compositions similar to kaolinite) refractories in involving casting, rolling, grinding, and polishing. The the hearths of blast furnaces making pig iron. Early expe- process required much handling of the glass and had high rience was so successful that the “all carbon blast furnace” waste glass losses. As a result, plate glass was expensive seemed a possibility. These hopes were not realized and a premium product. Drawing processes were used because later experience showed that there was sufficient extensively for window glass, but were not suitable for oxygen in the upper regions of the furnace to oxidize the producing distortion-free sheets for the more demanding carbon and hence preclude its use there. applications. In 1959 Alastair Pilkington introduced the As in the history of other ceramics, the great progress float-glass process to make large unblemished glass sheets in refractories was partly due to developments in scientific at a reasonable cost. It took 7 years and more than $11 M understanding and the use of new characterization (over $150 M in 2006) to develop the process. We describe methods. Development of phase equilibrium diagrams and the technical details of the float-glass process in Chapter the use of X-ray diffraction and light microscopy increased 21. Float-glass furnaces are among the largest glass- the understanding of the action of slags and fluxes on melting tank furnaces in use today and can produce 800– refractories, and also of the effect of composition on the 1000 tons of finished glass per day. A float-glass production properties of the refractories. line can be 700 feet long, with the tin path over 150 feet in length, and can produce a sheet with a width of 12 feet. 2.10 MAJOR LANDMARKS OF THE The float-glass process dramatically decreased the cost of TWENTIETH CENTURY glass and led to a tremendous increase in the use of glass is modern architecture. Each year the float-glass process Uranium dioxide nuclear fuel. In 1954 and 1955 it was produces billions of dollars worth of glass. decided to abandon metallic fuels and to concentrate upon Pore-free ceramics. During and following World War UO2 (sometimes referred to as urania) as the fuel for II new ceramics became important because of their special 26 ................................................................................................................................................................... S o m e H i s t o ry properties. They were fabricated from single-phase Magnetic ferrites. The development of ceramic mag- powders by sintering. This process differed from the clas- netic materials for commercial applications really started sical silicate ceramic processing in that no liquid phase in the early 1930s. In 1932 two Japanese researchers Kato was formed. In the early stages of their development all and Takei filed a patent describing commercial applica- such ceramics were porous after firing and hence opaque. tions of copper and cobalt ferrites. J.L. Snoeck of N.V. Robert Coble found that the addition of a small amount of Philips Gloeilampenfabrieken in Holland performed a MgO would inhibit discontinuous grain growth in Al2O3 systematic and detailed study of ferrites in 1948. This and permit it to be sintered to a theoretical density to yield work launched the modern age of ceramic magnets. In the a translucent product. The first commercial product using following year, Louis Néel, a French scientist, published this new property was called Lucalox (for transLUCent his theory of ferrimagnetism. This was an important step ALuminum OXide). It is used primarily to contain the in the history of magnetic ceramics because most of the Na vapor in high-pressure Na-vapor lamps, which give ceramics that have useful magnetic properties are ferri- nighttime streets their golden hue. Operating at high magnetic. About 1 million tons of ceramic magnets are temperature, Na-vapor lamps have a luminous efficiency produced each year. >100 l m W−1, the highest of any light source (a 100-W Ferroelectric titanates. These materials are used as tungsten-filament lamp has an efficiency of ∼18 lm W−1). capacitors, transducers, and thermistors, accounting for They have displaced almost all other light sources for about 50% of the sales of electroceramics. The historical outdoor lighting. Na-vapor lamps are produced at an esti- roots leading to the discovery of ferroelectricity can be mated rate of 16 million per year. A new product, the traced to the nineteenth century and the work of famous ceramic-metal halide lamp, utilizes the same ceramic crystal physicists Weiss, Pasteur, Pockels, Hooke, Groth, envelope. It has an intense white light and is just now Voigt, and the brothers Curie. Beginning with the work being introduced. Lumex Ceramic utilizes much of the on Rochelle salt (1920–1930) and potassium dihydrogen same understanding in its preparation. It is based on doped phosphate (1930–1940), the study of ferroelectrics accel- yttrium oxide and is used as a scintillation counter in the erated rapidly during World War II with the discovery of GE computed tomography X-ray scanner. ferroelectricity in barium titanate. There then followed a Nitrogen ceramics. Silicon nitride was first produced period of rapid proliferation of ferroelectric materials in 1857 (Deville and Wöhler, 1857), but remained merely including lead zirconate titanate (PZT), the most widely a chemical curiosity. It wasn’t until much later that it was used piezoelectric transducer. Together with the discovery considered for engineering applications. During the period of new materials there was also an increase in the under- 1948–1952 the Carborundum Company in Niagara Falls, standing of their structure and behavior, which led to new New York, applied for several patents on the manufacture applications for ferroelectric ceramics, including micro- and application of silicon nitride. By 1958 Haynes (Union electromechanical systems(MEMS). Carbide) silicon nitride was in commercial production for Optical fibers. In 1964 Charles K. Kao and George A. thermocouple tubes, rocket nozzles, and boats and cruci- Hockman, at the now defunct Standard Telecommunica- bles for handling molten metal. British work in silicon tions Laboratory (STL) in the UK, suggested sending tele- nitride, which began in 1953, was directed toward the communications signals along glass fibers. These early ceramic gas turbine. It was supposed that sea and land fibers had very high losses—the difference in the amount transport would require turbines with materials capabili- of light that went in versus the light that came out—com- ties beyond those of the existing nickel-based superalloys. pared to the fibers produced today. Robert Maurer, Donald This work led to the development of reaction-bonded Keck, and Peter Schultz at the Corning Glass Works in silicon nitride (RBSN) and hot-pressed silicon nitride New York produced the first low-loss fibers in 1970. They (HPSN). In 1971 the Advanced Research Projects Agency were made by a chemical vapor deposition (CVD) process (ARPA) of the U.S. Department of Defense placed a $17 known as modified CVD (MCVD) and had losses <20 dB/ million contract with Ford and Westinghouse to produce km. Today, losses typically are 0.2–2.0 dB/km. In 1988 two ceramic gas turbines, one a small truck engine and the first transatlantic fiberoptic cable, TAT-8, began car- the other producing 30 MW of electrical power. The goal rying telephone signals from America to Europe. The link was to have ceramic engines in mass production by 1984. is 6500 km long and can carry 40,000 conversations per Despite considerable investment there is still no commer- fiber. Glass fibers are also critical in today’s endoscopes. cial ceramic gas turbine. The feasibility of designing Glass ceramics. S. Donald Stookey made the first true complex engineering components using ceramics has been glass ceramic at Corning Glass Works in 1957. He acci- demonstrated and there has been increasing use of ceram- dentally overheated a piece of Fotoform glass—a photo- ics in engineering applications. Unfortunately there is no sensitive lithium silicate glass. The glass did not melt, viable commercial process for manufacturing complex instead it was converted to a white polycrystalline ceramic silicon nitride shapes with the combination of strength, that had much higher strength than the original glass. The oxidation resistance, and creep resistance required for the conversion from the glass to the crystalline ceramic was gas turbine, together with the necessary reliability, life accomplished without distortion of the articles and with prediction, and reproducibility. only minor changes in dimensions. Small silver crystals 2 .10 M a j o r L a n d m a r k s o f t h e Tw e n t i e t h C e n t u ry ............................................................................................ 27 in the glass acted as nucleation sites for crystallization. started to flow in the reverse direction. The current was The development of this new Pyroceram composition produced by the reaction of the electrolysis products, launched Corning into the consumer products market. In hydrogen and oxygen, which had adsorbed onto the Pt 1958, Corningware® was launched. Stookey went on to electrodes. Grove’s first fuel cell was composed of two Pt develop a number of glass ceramics including one that was electrodes both half immersed in dilute H2SO4: one elec- used as a smooth-top cooking surface for stoves. The trode was fed with O2 and the other with H2. Grove real- invention of glass ceramics is a good example of serendip- ized that this arrangement was not a practical method for ity. But Stookey had to be aware of the significance of energy production. The first practical fuel cell was devel- what he had made. There are many other examples of the oped in the 1950s at Cambridge University in England. role of luck in the invention and development of new The cell used Ni electrodes (which are much cheaper than materials—Teflon, safety glass, and stainless steel. Pt) and an alkaline electrolyte. Pratt and Whitney further Tough ceramics. Ceramics are inherently brittle with modified the alkaline fuel cell in the 1960s for NASA’s low toughness. In 1975 Garvie, Hannink, and Pascoe pub- Apollo program. The cells were used to provide on-board lished a seminal article entitled “Ceramic Steel.” They electrical power and drinking water for the astronauts. were the first to realize the potential of zirconia (ZrO2) for The alkaline fuel cell was successful but too expensive for increasing the strength and toughness of ceramics by uti- terrestrial applications and required pure hydrogen and lizing the tetragonal to monoclinic phase transformation oxygen. There are many different types of fuel cell, but induced by the presence of a stress field ahead of a crack. the one most relevant to ceramics is the solid-oxide fuel A great deal of effort has been expended since to cell (SOFC). The SOFC uses a solid zirconia electrolyte, devise theories and develop mathematical frameworks to which is an example of a fast-ion conductor. We will explain the phenomenon. It is generally recognized that discuss later how fuel cells convert chemical energy into apart from crack deflection, which can occur in two-phase electrical energy. ceramics, the t → m transformation can develop signifi- High-temperature superconductivity. High-tempera- cantly improved properties via two different mechanisms: ture superconductivity was discovered in 1986 by Bednorz microcracking and stress-induced transformation tough- and Müller at the IBM Research Laboratory in Zurich, ening. We describe these mechanisms in Chapter 18. So Switzerland. Art Sleight had shown earlier that oxides far three classes of toughened ZrO2-containing ceramics could be superconductors, but the required temperature have been made: was still very low. The discovery that certain ceramics lose their resistance to the flow of electrical current at  Partially stabilized zirconia (PSZ) temperatures higher than metal alloys may be as impor-  Tetragonal zirconia polycrystals (TZPs) tant as the discovery of superconductivity itself. Because  Zirconia-toughened ceramics (ZTCs) of the significance of their discovery Bednorz and Müller were awarded the Nobel Prize for Physics in 1987, only a Bioceramics. The first suggestion of the application of year after their discovery! The impact of the discovery of alumina (Al2O3) ceramics in medicine came in 1932. But high-temperature superconductivity launched an unprec- the field of bioceramics really did not develop until the edented research effort. The 2-year period after Bednorz 1970s with the first hip implants using alumina balls and and Müller’s discovery was a frenzied time with a host of cups. Studies showed that a ceramic ball was more biocom- new formulations being published. Paul Chu and col- patible than metals and provided a harder, smoother surface leagues at the University of Houston, Texas discovered the that decreased wear. The Food and Drug Administration most significant of these new ceramics, YBa2Cu3O7, in (FDA) in the United States in 1982 approved these for use. 1987. The YBCO or 123 superconductor, as it is known, Each year about 135,000 hips are replaced in the United is superconducting when cooled by relatively inexpensive States; more than a million hip prosthesis operations using liquid nitrogen. This opened up enormous possibilities alumina components have been performed to date. Alumina and led to expansive speculations on a future based on is an example of a nearly inert bioceramic. Bioactive these materials. The original promises have not been ful- ceramics and glasses, materials that form a bond across the filled. However, new applications are being developed and implant-tissue interface, were an important development. the field is still quite young. The current market is less The first and most studied bioactive glass is known as Bio- than 1% of the advanced ceramics market. Predictions glass 45S5 and was developed by Larry Hench and co- indicate that over the next 5 years annual growth rates up workers at the University of Florida. The first successful to 20% might be achieved. use of this material was as a replacement for the ossicles (small bones) in the middle ear. A range of bioactive glass ceramics has also been developed. 2.11 MUSEUMS Fuel cells. The British scientist Sir William Robert Grove (1839) discovered the principle on which fuel cells There are many museums around the world that house are based. Grove observed that after switching off the collections of ceramics. The list that we give here is current that he had used to electrolyze water, a current not exclusive, but it does include some of the major 28 ................................................................................................................................................................... S o m e H i s t o ry collections as well as sites that have important historical St. Helens Crown Glass Company. It contains the Pilk- significance. ington glass collection. www.worldofglass.com.  Ashmolean Museum, Oxford, UK. This is a museum of the University of Oxford. Founded in 1683, it is one of the oldest public museums in the world. Important 2.12 SOCIETIES collections include early Chinese ceramics and Japanese export porcelain. www.ashmol.ox.ac.uk. There are several professional ceramics societies in the  British Museum, London. This is one of the greatest world. In the United States, the American Ceramic Society museums in the world. It contains a large and outstand- (ACerS) founded in 1899 is the principal society for cera- ing collection of antiquities including numerous Stone mists. The society, which is based in Westerville, Ohio, is Age artifacts. www.thebritishmuseum.ac.uk. divided into 10 divisions: Art, Basic Science, Cements,  Corning Museum of Glass in Corning, New York. Electronics, Engineering Ceramics, Glass & Optical This is one of the outstanding glass collections in the Materials, Nuclear & Environmental Technology, Refrac- world. Containing more than 33,000 objects repre- tory Ceramics, Structural Clay Products, and Whitewares senting the entire history of glass and glassmaking. and Materials. The society organizes an annual meeting www.cmog.org. and publishes the Journal of the American Ceramic  Metropolitan Museum of Art in New York City, Society. The journal was created in 1918 and is one of the New York. Ceramic collections include Medici most important peer-reviewed journals in the field: www. porcelain and Böttger porcelain. The museum also acers.org. has one of the finest glass collections in the world. Many other countries have professional societies for www.metmuseum.org. those working in the field of ceramics.  Musée du Louvre, Paris. This is one of the greatest museums of the world. It contains extensive collections  Institute of Materials, Minerals and Mining (IoM3) of antiquities, including many examples of ancient www.iom3.org earthenware vessels, some dating from the Chalco-  Deutsche Keramische Gesellschaft www.dkg.de. lithic period. www.louvre.fr.  European Ceramic Society (ECerS) www.ecers.org  Musée National de Céramique at Sèvres, France. The  Swedish Ceramic Society www.keram.se/sks collection includes examples of early European porce-  Ceramic Society of Japan www.ceramic.or.jp lains including a Medici porcelain bottle made in 1581;  Canadian Ceramics Society www.ceramics.ca the first success in European efforts to produce ware  Chinese Ceramic Society www.ceramsoc.com equivalent to Persian and Chinese porcelain. It also  Society of Glass Technology www.sgt.org contains examples of French soft-paste porcelain as well as earlier ceramics. www.ceramique.com.  Ross Coffin Purdy Museum of Ceramics at the Ameri- can Ceramic Society headquarters in Westerville, 2.13 CERAMIC EDUCATION Ohio. It houses a cross section of traditional and high-tech ceramics produced in the last 150 years. The first formal ceramics program (Clay-Working and www.acers.org/acers/purdymuseum. Ceramics) in the United States was established in 1894 at  Smithsonian Institution. The Freer Gallery of Art and the Ohio State University in Columbus, Ohio. This marked the Arthur M. Sackler Gallery contain collections of a change from on-the-job training that was prevalent in ancient ceramics with important examples from China the traditional North American art potteries and family and the Near East. www.asia.si.edu establishments of earlier years toward a formal university  Victoria and Albert Museum, London. This is the study. Ceramics was also taught at Alfred University in world’s largest museum of the decorative arts. It con- New York, and many other schools across the nation. One tains the National Collections of glass and ceramics. of the most remarkable ceramists of the time was Adelaide The extensive ceramic collection includes Medici Robineau, who taught at Syracuse University in New York. porcelain and early Chinese and Near East ceramics. Robineau was a studio ceramist who devised her own clay www.vam.ac.uk. bodies, concocted her own glazes, threw the forms, and  Wedgwood Museum and Visitors Center in Barlaston, decorated, glazed, and then fired them herself. Few women Stoke-on-Trent, UK. It contains many rare and valu- at the time were involved in the technical aspects of able exhibits tracing the history of the company. It ceramic production. It was considered proper for women is also possible to tour the Wedgwood factory. to be decorators only, rather than be part of more technical www.wedgwood.com. pursuits, or to throw on the wheel, a physically demanding  The World of Glass in St. Helens, UK. This is a new job regarded as better left to men. museum and visitor center in the hometown of Pilk- From 1894 to 1930 a number of universities formed ington glass. Pilkington plc originated in 1826 as the their own ceramic engineering programs: 2 .13 C e r a m i c E d u c at i o n .............................................................................................................................................. 29  New York State School of Clay-Working and Ceramics  University of Alabama: 1928 at Alfred University: 1900  Massachusetts Institute of Technology: 1930  Rutgers University: 1902  University of Illinois: 1905 In the 1960s the first Materials Science departments  Iowa State College: 1906 began to appear in universities. Many of these were  University of Washington: 1919 based on existing Metallurgy departments. In some of  West Virginia University: 1921 the universities that had specific ceramics programs,  North Carolina State University: 1923 these activities were also incorporated into the new  Pennsylvania State College: 1923 materials departments. Now, ceramic science and  Georgia Institute of Technology: 1924 engineering is mostly taught in Materials Science  Missouri School of Mines (now University of Missouri– and Engineering (MS&E) programs in the United Rolla): 1926 States. CHAPTER SUMMARY The history of ceramics is intertwined with human history. From the first use of flint and obsidian during the Stone Age, the formation of vessels from clay, the use of refractories in the iron and steel industry, to the fabrication of optical fibers for high-speed communication ceramics have impacted society and technology in many ways. We mentioned many of the more recent developments in the field of ceramics. The science behind these materials will be described in many of the later chapters. PEOPLE IN HISTORY Aspdin, Joseph was an English mason and invented Portland cement in 1824. It was so named because of its resemblance to white limestone from the island of Portland, England. The first Portland cement made in the United States was produced at Coploy, Pennsylvania in 1872. Bednorz, Johannes Georg (born 1950) and Karl Alexander Müller (born 1927) were scientists at the IBM research laboratory in Zurich, Switzerland, where they discovered the phenomenon of high-temperature superconductivity. They were both awarded the Nobel Prize for Physics in 1987. They began working together in 1982. Böttger, Johann Friedrich was born in 1682. The young Böttger was apprenticed as an apothecary in Berlin where he claimed to have transformed mercury into gold, a feat he apparently demonstrated very convinc- ingly in 1701. When reports of this reached Frederick I, Böttger fled to Saxony, where, in addition to his metallurgical researches, he began his work in ceramics. He used von Tschirnhaus’ mirrors and lenses to produce a dense red stoneware and a European equivalent to white Chinese porcelain. He died in 1719. An authoritative history of Böttger and Meissen has been written by Walcha (1981). Kingery, W. David. Kingery played a key role in creating the field of ceramic science. He was the author of Introduction to Ceramics, first published in 1960, the “bible” for a generation of ceramists. He was well known for his work in the field of sintering. In his later years he worked extensively on the history of ceramics. He died in June 2000. Orton, Edward, Jr. was born in 1863 in Chester, New York. He studied mining engineering at Ohio State University (OSU). He was the founder of the ceramic engineering program at OSU in 1894 and a founder of the American Ceramic Society. He died in 1932. Pilkington, Sir Alastair was born in 1920. He served in the Second World War. In 1942 he was captured on the island of Crete and spent the rest of the war as a POW. After finishing his studies at Cambridge Uni- versity he joined the Pilkington glass company in 1947. By 1959 the float glass process was a success and the production of flat glass was revolutionized. He died in 1995. Ravenscroft, George developed lead crystal glass during the last quarter of the seventeenth century to rival the Venetian cristallo developed during the early sixteenth century. He was granted a patent in March 1674 for a “crystalline glass resembling rock-crystal.” Seger, Hermann A. was the world’s pioneer scientific ceramist. The English translation of Seger’s work, The Collected Writings of Hermann Seger, was published in 1913 by the American Ceramic Society. Simpson, Edward, better known as “Flint Jack,” was an Englishman and one of the earliest experimental stone toolmakers. Using nothing more than a steel hammer he created replicas of ancient stone tools, which he sold in the late nineteenth century to museums and a Victorian public that was very interested in prehistoric times. He was able to make the tools appear old and worn by using chemicals and a lapidary tumbler. In 1867 he was sent to prison for theft. von Tschirnhaus, Count Ehrenfried Walther was born in 1651. He was a physicist famous for his experiments with high temperatures and mineral fusions achieved by focusing sunlight in a solar furnace. He was made a foreign member of the French Royal Academy in 1683. He died in 1708. 30 ................................................................................................................................................................... S o m e H i s t o ry  Wedgwood, Josiah was born in 1730, the last child in a family of 12. He went into business for himself in 1759 in Staffordshire. One of the most remarkable innovators of the eighteenth century he revolutionized the process of manufacturing. He was a member of the Royal Academy and a member of the Lunar Society of Birmingham, which included in its members many of the great innovators of that period such as James Watt, the inventor of the steam engine. Mankowitz (1980) gives a detailed account of the life of Wedg- wood and his pottery. Zachariasen, William Houlder was born in 1906. He was a Norwegian-American physicist who spent most of his career working in X-ray crystallography. His description of the glass structure in the early 1930s became a standard. He died in 1979. GENERAL REFERENCES The American Ceramic Society, 100 Years (1998) The American Ceramic Society, Westerville, OH. A won- derfully illustrated history of the ACerS published to celebrate the societies centennial 1898–1998. For the student with an interest in ceramic history the book by Kingery and Vandiver (1986) and the Ceramics and Civilization series edited by W.D. Kingery (1985, 1986), The American Ceramic Society, Westerville, OH are good resources. Volume I: Ancient Technology to Modern Science (1985). Volume II: Technology and Style (1986). Volume III: High-Technology Ceramics—Past, Present, and Future (1986). Ceramics of the World: From 4000 B.C. to the Present (1991), edited by L. Camusso and S. Burton, Harry N. Abrams, Inc., New York. A beautifully illustrated history of ceramics with lots of historical details. Douglas, R.W. and Frank, S. (1972) A History of Glassmaking, Fouls, Henley-on-Thames, Oxfordshire. The history of glassmaking is described and illustrated extensively. An excellent reference source. Jelínek, J. (1975) The Pictorial Encyclopedia of the Evolution of Man, Hamlyn Pub Grp, Feltham, UK. Beautifully illustrated. Kingery, W.D. and Vandiver, P.B. (1986) Ceramic Masterpieces, The Free Press, New York. Lechtman, H.N. and Hobbs, L.W. (1986) “Roman Concrete and the Roman Architectural Revolution,” in Ceramics and Civilization III: High-Technology Ceramics—Past, Present, and Future, edited by W.D. Kingery, The American Ceramics Society, Westerville, OH, pp. 81–128. This article gives a detailed historical perspective on this topic. Levin, E. (1988) The History of American Ceramics: 1607 to the Present, Harry N. Abrams, Inc., New York. An illustrated history. Schick, K.D. and Toth, N. (1993) Making Silent Stones Speak: Human Evolution and the Dawn of Technol- ogy, Simon & Shuster, New York. SPECIFIC REFERENCES Bednorz, J.G. and Müller, K.A. (1986) “Possible high Tc superconductivity in the Ba-La-Cu-O system,” Z. Phys. B—Condensed Matter 64, 189. The seminal paper describing “possible” high-temperature super- conductivity in an oxide ceramic. Deville, H. Ste.-C and Wöhler, F. (1857) “Erstmalige Erwähnung von Si3N4,” Liebigs Ann. Chem. 104, 256. Report of the first production of silicon nitride. Of historical interest only. Garvie, R.C., Hannink, R.H., and Pascoe, R.T. (1975) “Ceramic steel?” Nature 258, 703. The first description of the use of the tetragonal to monoclinic phase transformation for toughening ceramics. Guillard, H.F. (1971) Early American Folk Pottery, Chilton Book Co., New York. Kao, K.C. and Hockham, G.A. (1966) “Dielectric-fiber surface waveguides for optical frequencies,” Proc. IEE 113, 1151. Lindsay, J. (1968) The Ancient World: Manners and Morals, Putnam, New York. Mankowitz, W. (1980) Wedgwood, 3rd edition, Barrie and Jenkins, London. A standard biography of Josiah Wedgwood. Moseley, C.W.R.D. (translated by) (1983) The Travels of Sir John Mandeville, Penguin Books, London, p. 57. Describes the Fosse of Mynon in Acre, a Syrian seaport on the Mediterranean. Thomas, S.G. and Gilchrist, P.G. (1879) “Elimination of phosphorus in the Bessemer converter,” J. Iron Steel Inst. 20. A landmark paper that led to important changes in the steel making industry and also to the development of new types of refractory. Walcha, O. (1981) Meissen Porcelain, translated by H. Reibig, G.P. Putnam’s Sons, New York. A history of Böttger and Meißen based in large part on archival studies at Meißen. Wood, N. (1999) Chinese Glazes, A&C Black, London. A beautifully illustrated book showing the early Chinese genius for ceramics. Wu, M.K., Ashburn, J.R., Torng, C.J., Hor, P.H., Meng, R.L., Gao, L., Huang, Z.J., Wang, Y.Q., and Chu, C.W. (1987) “Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu-O compound system at ambient pressure,” Phys. Rev. Lett. 58, 908. The first description of superconductivity at liquid-nitrogen temperature. Zachariasen, W.H. (1932) “The atomic arrangement in glass,” J. Am. Chem. Soc. 54, 3841. Describes a model for the structure of oxide glasses that has become a standard for these materials. C h a p t e r S u m m a ry .......................................................................................................................................................... 31  EXERCISES 2.1 Gypsum, the raw material for Plaster of Paris, occurs in several varieties. The Greeks used a form of gypsum as windows for their temples. What particular property would be important for this application? What form of gypsum would be most suitable? 2.2 What do you think might be the role of CuO in the Han lead glaze (Table 2.2)? 2.3 Why do you think it was so important for the early ceramic industries to locate near the source of raw materi- als? Does a similar situation occur today? 2.4 The largest concrete construction project in the world is the Three Gorges Dam in China. How much concrete is used in this project? 2.5 Which company is the largest producer of glass optical fibers? 2.6 Corningware® is a glass ceramic product that was once widely used for cookware, but is rarely used now. What were some of the problems with Corningware® and would these problems be inherent to all glass ceramics? 2.7 Solid oxide fuel cells (SOFC) are not being used in transportation applications (such as automobiles and buses). What fuel cells are being used for these applications and what are their advantages over the ceramic- based SOFCs? 2.8 The transition temperature (Tc) for the YBCO superconductor is 95 K. Higher Tcs are found with other ceramic high-temperature superconductors, but these materials are not being used commercially. What are some of the other materials and what are some of the factors that are limiting their use? 2.9 The Hall of Mirrors (La Galerie des Glaces) at the Palace of Versailles in France was begun in 1678, well before the development of the float glass process. What technology was available in the seventeenth century for producing flat plates of glass? 2.10 Concrete is a mixture of gravel (called aggregate) and cement. The spectacular 142-foot internal diameter dome of the Pantheon in Rome is made of concrete. What material did the Romans use for aggregate in the construction of the Pantheon? Could the material they used be classified as a ceramic? 32 ................................................................................................................................................................... S o m e H i s t o ry Part II Materials  3 Background You Need to Know CHAPTER PREVIEW In this chapter we will summarize three concepts fundamental to all materials science: atomic structure, thermodynamics, and kinetics. You should be familiar with these topics from intro- ductory chemistry, physics, and materials science classes so we give only a brief review here. Books are written on each of these topics. In ceramics, you can often avoid such books, but the details become more critical as you delve deeper into the subject. The properties of a material are determined, to a large extent, by how the constituent atoms bond together. The nature of this bonding is determined by the electron configuration of the atoms. The electron configuration of an atom also determines the properties of the atom and materials that contain it. For example, the ceramic magnetite (Fe3O4) is magnetic due to the presence of unpaired electrons in the 3d level of Fe; you need to know what the 3, the d, and “unpaired” denote. To understand why Mn ions can exist with many different charge states but we invariably find only Al ions with a 3+ charge, you must know the electron configuration of the respective atoms. Knowledge of both thermodynamics and kinetics is necessary to understand how ceramic materials behave and what happens when they are processed. Thermodynamics tells us what is possible while kinetics tells us how long we have to wait for the inevitable. Thus, thermo- dynamics tells us if a specific chemical or physical reaction can occur. In ceramics these changes are often brought about because samples are routinely heated and cooled. Ceramics may be processed at temperatures above 1800°C and then cooled to 25°C. Some processes may occur at 1800°C, but may continue or change as we cool the sample. Conversely, some ceramics change their properties at quite low temperatures: BaTiO3 changes from the paraelectric cubic phase to the ferroelectric tetragonal phase at 120°C. Kinetics tells us how rapidly these reac- tions will proceed. Diamond is thermodynamically unstable at room temperature and atmo- spheric pressure, but the phase change occurs much too slowly to worry jewelers. 3.1 THE ATOM introduction of the spin quantum number. Atoms containing electrons with unpaired spins will have The bases for understanding the structure of the atom are magnetic properties. quantum theory and wave mechanics, which were devel-  It is impossible to know simultaneously the position oped in the early 1900s. The important conclusions of and momentum of an electron with certainty. We use these studies, particularly as they relate to materials, are this property in tunnel diodes. as follows:  Electrons have wavelike properties. This means that they can be diffracted. Electron diffraction, like X-ray  Electrons in atoms can move only in certain stable diffraction, gives us the crystal structure. orbits, that is, only certain energy values are possible. We expand on this fact when we describe energy bands, In the following sections we summarize how these which are used to explain electron conductivity. conclusions lead to our present view of the structure of the  Transition between orbits involves the emission or atom and, in particular, the nature and arrangement of the absorption of energy. These transitions can be the electrons in the atom. We are not attempting to summarize source of color and we use them to analyze chemistry modern physics, but only the concepts that we use in this by spectroscopy. text. You need to understand the main aspects of the  No two electrons in the same atom can have the same nature of the chemical bond in ceramic materials: what is four quantum numbers. This requirement led to the an ionic bond, what is a covalent bond, and why do most 3 .1 Th e At o m .................................................................................................................................................................. 35 bonds show a mixture of the two. In spectroscopy and excess energy is emitted in the form of a photon. Any microscopy we will probe the electronic structure to transition between orbits involves either the emission or determine the local chemistry of the ceramic. absorption of energy. Understanding this concept is neces- sary in, for example, appreciating how a laser works. If the energy emitted is in the visible part of the electro- 3.2 ENERGY THE BOHR ATOM magnetic spectrum (Table LEVELS Quantization of angular momentum 3.1), then we will be able h to observe the emission. The quantization of energy me vr = n Box 3.1 The emission from the is a key aspect in under- 2π ruby laser (ruby is a standing atomic structure. Radius of possible electron orbits ceramic) is at 694 nm (in Bohr’s model involves electrons moving only in ε nh2 2 the red). A frequency r= 0 2 Box 3.2 doubled Nd-doped yttrium certain stable orbits. The πme e aluminum garnet (YAG) angular momentum of the Energy of the electron laser (YAG is another orbiting electrons is quan- me e 4 ceramic) operates in the tized so that only specific E= Box 3.3 2 2 8ε 0 n h green part of the spectrum orbits are allowed and only at 530 nm. certain energy values are Bohr’s model was quite possible. popular at the time because an electron circling the nucleus These orbits are known as stationary states, and the is conceptually similar to the earth circling the sun. The one with the lowest energy is called the ground state. idea that orbiting electrons did not radiate was less easy The quantization of angular momentum is nh/2π, to accept, Bohr simply insisted they did not and that was where n is the principal quantum number. As the principal that! Most importantly, the model explained a number of quantum number increases physical phenomena. Bohr’s assumption that electrons are particles with well-defined orbits was not consistent with 1. The radius, r, of the electron orbit increases, that is, the concept of “simultaneous interdeterminacy” of posi- the electron is further from the nucleus. tion and momentum as propounded in the Heisenberg 2. The energy, E, of that electron is also increased. uncertainty principle. What you should remember from this discussion is the The first five Bohr orbits, that is, n = 1 through 5, are also origin of KLMNO and the terminology. We will use this referred to as shells; we define a shell as a group of states again in Chapter 10. that have the same n. A letter is used to denote each Electron energy levels and the Bohr model are impor- shell: tant for understanding the following: Shell K L M N O...  Atomic radii—as we fill shells going down a particular n 1 2 3 4 5... period the atoms get bigger (r increases).  Ionization energy—as we fill shells going down a par- Charles Barkla, an early X-ray spectroscopist, intro- ticular period it becomes progressively easier to remove duced this terminology for electron shells in 1911. We still the outer electron(s) (E increases with respect to the use it today to designate characteristic X-rays in both X- ground state). ray diffraction and in chemical analysis using electron  Covalent bond formation—ionization energies must be microscopy. Barkla named the two types of characteristic high (E large). X-ray emissions he observed as the K-series and L-series. He later predicted that an M-series and a J-series might exist. An M-series was subsequently discovered, but no J-series. The K shell is hence the first shell. TABLE 3.1 The Visible Part of the Electromagnetic The other aspect of Bohr’s theory is that while an Spectrum electron is in a stationary state, the atom does not radiate. Electrons can be excited into higher energy orbits if the Energy, E (J) Wavelength, λ (nm) Color atom is stimulated (thermally, electrically, or by the 2.84 × 10 −19 700 Red absorption of light). These orbits are the excited states and 3.20 × 10 −19 620 Orange are more distant from the nucleus. The residence time of 3.42 × 10 −19 580 Yellow an electron in the excited state may be very short (∼1 ns) 3.75 × 10 −19 530 Green 4.23 × 10 −19 470 Blue before it spontaneously descends to a lower energy state 4.73 × 10 −19 420 Violet and eventually the ground state. During each transition the 36 ................................................................................................................................ Bac k g r o u n d Yo u N e e d t o K n o w   Magnetic ceramics— experiments that can be THE DE BROGLIE HYPOTHESIS we need to have an M done on a system.” Thus, All matter possesses wave properties. Every moving shell. the Schrödinger wave particle can be associated with a wavelength, λ, given  X-ray spectroscopy— equation includes informa- by we use the Barkla nota- tion about the chemical tion, the energy of the behavior of all atoms and h h characteristic X-rays λ= = compounds and the answer depends on the electron mv p to whether any proposed energy levels involved. chemical reaction will take place or not. Mathematically, Ψ describes the motion of an electron 3.3 ELECTRON WAVES in an orbital. The modulus of the wave function squared, |Ψ(r)|2, is a direct measure of the probability of finding Demonstrating electron diffraction (a property associated the electron at a particular location. The Schrödinger wave with waves) was proof of their wave nature. In 1927 C.J. equation can be solved exactly for hydrogen. To apply it Davisson and L. Germer in the United States and, inde- you must first transform it into polar coordinates (r,θ,φ) pendently, G.P. Thomson and A. Reid in the United and then solve using the method of separation of variables Kingdom showed that electrons could be diffracted in (described in, e.g., Kreyszig, 1999). much the same way as X-rays. We care because we cannot The solution of these equations leads to three quantum explain the properties of electrons and X-rays without this numbers: n, l, and ml. understanding. The Schrödinger wave equation can be set for atoms The wavelike nature of electrons enables electron dif- with more than one electron, but it cannot be solved fraction studies of materials. Most electron diffraction exactly in these cases. The second and subsequent elec- patterns are obtained in a transmission electron micro- trons introduce the complicating feature of electron– scope, which allows us to obtain structural information electron repulsion. Nevertheless, the basic characteristics from very small regions. This is of particular importance of the orbitals do not change and the results obtained for in many new ceramics where we are often dealing with hydrogen are applied to many-electron atoms. thin interface layers (such Methods are now as at grain boundaries) becoming available that and very small grains SCHRÖDINGER WAVE EQUATION allow us to calculate the (nanopowders). The time-independent form is structure of some “bulk” One of the most impor- materials. Generally, this tant consequences of the 2Ψ + 8π2 m/h2 (E − V)Ψ = 0 Box 3.4 is still done only rarely dual nature of electrons is by starting with the 2 is the operator Heisenberg’s uncertainty Schrödinger equation. The principle, which states that ∂2 /∂x2 + ∂2 /∂y2 + ∂2 /∂z2 Box 3.5 calculations are just too it is impossible to know difficult or too time- simultaneously both the In polar coordinates Ψ has the form consuming. Actually, it is momentum and position of worse than it looks because a particle with certainty. Ψ(r,θ,φ) = R(r)Θ(θ)Φ(φ) Box 3.6 we also have to deal with If we are describing the charge. R(r), Θ(θ), Φ(φ) are each only functions of r, θ, and φ. motion of an electron of known energy or momen- tum, we can speak only in terms of the probability of 3.4 QUANTUM NUMBERS finding that electron at a particular position. This leads to the electron-density or electron-cloud representation of Four quantum numbers are necessary to specify the state electron orbitals. of any electron: The Schrödinger equation, as central to quantum mechanics as Newton’s equations are to classical mechan-  n principal quantum number ics, relates the energy of an electron to its wave properties.  l orbital shape, or orbital angular momentum, quantum The equation describes the likelihood that a single elec- number tron will be found in a specific region of space. The wave  m orbital orientation, or orbital magnetic, quantum l function, Ψ, depends on E and V, the total energy and the number potential energy of the electron, respectively.  m spin, or spin magnetic, quantum number s The importance of the wave function has been expressed by Atkins and de Paula (2002): “A wave func- A shell is a group of states that has the same n and tion contains all there is to know about the outcome of corresponds to Bohr’s n. A subshell is a smaller group of 3 . 4 Q ua n t u m N u m b e r s ................................................................................................................................................. 37  Z Z Z Nodal plane – + – + Y Y Y + – X py orbital X px orbital X pz orbital FIGURE 3.1 The 2px , 2py, and 2pz orbitals. The nodal plane represents the area in which the probability of finding the electron is zero. states having both the same QUANTUM NUMBERS  We use transitions for value of n and l. An orbital Li, Na, K and Cs have many common features because chemical analysis of is specified by n, l, and ml, they all have a single electron in an outer s shell: 2s, 3s, ceramics—certain tran- and can contain a maximum 4s and 5s. sitions are allowed of two electrons with oppo- The main difference between MnO, FeO, CoO and (quantum mechanical site spins. NiO is due to the change in the d (l = 3) electrons on selection rules). the transition-metal ion.  n has integer values, 1, 2, 3, . . . and deter- mines the size Y  l has integer values, 0, 1, 2, . . . , n − 1 (for any value of n) and determines shape – +  ml has integer values between −l and +l including 0 (for any value of l) and determines orientation X  ms can have values of ±1/2 and specifies the direction + – of spin dxy orbital The introduction of an external magnetic field provides the most convenient reference axis for ml. The values of Z Z ml are determined by the l quantum number. For each value of l there are (2l + 1) values of ml. For historical + – + reasons the 0, 1, 2, and 3 values of the l quantum number are designated by the letters s, p, d, and f, respectively. X – Y (This choice is a relic of early spectroscopic studies when + – certain spectral series were designated “sharp,” “princi- X + pal,” “diffuse,” or “fundamental.”) dxz orbital dz2 orbital The s orbitals are spherical and the three 2p orbitals have directional properties as shown in Figure 3.1. For Z Z example, the 2pz orbital has regions of greatest concentra- tion or probability along the z-axis and the probability of finding a 2pz electron in the XY plane is zero. The shapes + – + of the five 3d orbitals are more complicated (because there – Y Y are more of them) (Figure 3.2) and we usually do not talk – about f. + – + Are these numbers important for ceramics? The answer, of course, is yes. dyz orbital X dx2–y2 orbital FIGURE 3.2 The 3d atomic orbitals. The 4d, 5d, and 6d orbitals  The color of a ceramic, such as ruby, derives directly are essentially identical to the 3d orbitals except they are bigger. from transitions between energy levels. The energy The sign of the wavefunction changes from one lobe to the next in levels are the result of which orbitals are occupied and a given orbital and is important when we consider the formation of their relative energies. molecular orbitals. 38 ................................................................................................................................ Bac k g r o u n d Yo u N e e d t o K n o w   Magnetism relates di- electron will go: For any SUMMARY OF QUANTUM NUMBERS (QN) rectly to the spin of the set of orbitals of equal Name Symbol Value electrons. If we have energy the electronic more spins up than Principal QN n 1, 2, 3, . . . configuration with the down then we have Orbital-shape QN l 0, 1, 2, . . . (n − 1) maximum number of par- magnetization. Orbital-orientation QN ml Integral values allel spins results in the  Atomic arrangements from −l to +l lowest electron–electron in covalently bonded including zero repulsion. Thus the ground ceramics can be under- Spin QN ms ± 1/2 state for atomic carbon is stood by considering 1s22s22p1x2py1. hybridization of atomic We can build the IONIZATION orbitals. It is the sp3 ground-state electron con- For ceramics, the important feature in all these models hybridization of atomic figuration of atoms of all is which electrons we can move to make the ion and how orbitals in carbon that elements by filling the easy it is going to be. allows the tetrahedral orbitals in order of increas- arrangement of atoms ing energy, making sure in diamond. The s and the p in sp3 refer to the atomic that the Pauli exclusion principle and Hund’s rule are orbitals. obeyed. (Hund’s rules are inviolate in predicting the correct ground state of an atom. There are occasional exceptions when the rules are used to discuss excited states that we encounter, e.g., in spectroscopy.) The total 3.5 ASSIGNING QUANTUM NUMBERS number of electrons that the orbitals can hold is given in Table 3.2. A shorthand notation that expresses the quantum numbers There is no single ordering of orbital energies, but the for each electron represents the electron configuration. following order is a useful guide: The importance of this step is that it allows us, for example, to calculate the magnetic moment of magnetite and determine what happens if we replace the Fe2+ ions with 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s Ni2+ . < 4d < 5p < 6s < 4f ≈ 5d < 6p < 7s < 5f ≈ 6d The key to the building process for many-electron atoms is the Pauli exclusion principle: No two electrons in Figure 3.3 shows a mnemonic diagram that can be used an atom can have the same set of four quantum for determining the filling order. You simply follow the numbers. arrows and numbers from one orbital to the next. Orbital For example, the two electrons in the ground state of energies depend on the atomic number and on the charge atomic He (Z = 2) must possess the following quantum on the atom (ion). numbers: In the sequence of orbital energies shown above the 4s orbitals have a lower energy than the 3d orbitals and so n = 1, l = 0, ml = 0, mS = +1/2 they will be filled first in keeping with the minimum energy principle. For example, the electron configuration n = 1, l = 0, ml = 0, mS = −1/2 of the outer 10 electrons of calcium (atomic number Z = 20) is 3s2 3p6 3d0 4s2. In the filling of the electron orbitals The two electrons in the He atom are placed in the 1s for elements 21 to 29, there are two irregularities, one at orbital with opposite spins, consistent with the Pauli’s 24 (chromium) and one at 29 (copper). Each of these ele- principle. The electron configuration of He is abbreviated ments contains one 4s electron instead of two. The reason as 1s2. The next row in the periodic table is similar; we are just filling the next shell (n = 2 and so on). Lithium (Z = 3) has the electron configuration 1s22s1. We fill the 2s orbital before the 2p because of shielding TABLE 3.2 The s, p, d, and f Orbital Sets effects that lower the energy of the 2s orbital with respect Total number to the 2p orbital. Both the 2s and 2p orbitals in the Li atom Total of electrons are shielded from the +3 nuclear charge by the 1s elec- Type of orbitals that can be orbital Orbital quantum numbers in set accommodated trons. However, the 2s orbital has a larger probability density close to the nucleus and is not shielded as strongly s l = 0, ml = 0 1 2 as the 2p orbital. p l = 1, ml = 1, 0, −1 3 6 For a C atom (Z = 6) there are a number of possible d l = 2, ml = 2, 1, 0, −1, −2 5 10 f l = 3, ml = 3, 2, 1, 0, −1, 7 14 configurations for the second electron in the set of three −2, −3 2p orbitals. We use Hund’s rule to determine where the 3 . 5 A s s i g n i n g Q ua n t u m N u m b e r s ............................................................................................................................. 39  l=0 1 2 3 4 TABLE 3.3 Arrangement of Electrons for the First Row Transition Elements (Z = 21–29) Z Element Electron configuration n=1 1s 1p 1d 1f 1g 21 Sc 1s22s22p 63s23p 63d14s2 22 Ti 1s22s22p 63s23p 63d24s2 2 2s 2p 2d 2f 2g 23 V 1s22s22p 63s23p 63d34s2 24 Cr 1s22s22p 63s23p 63d 54s1 3 3s 3p 3d 3f 3g 25 Mn 1s22s22p 63s23p 63d54s2 26 Fe 1s22s22p 63s23p 63d 64s2 27 Co 1s22s22p 63s23p 63d74s2 4 4s 4p 4d 4f 4g 28 Ni 1s22s22p 63s23p 63d84s2 29 Cu 1s22s22p 63s23p 63d104s1 5 5s 5p 5d 5f 5g 6 6s 6p 6d 6f 6g tion and magnetic behavior of ceramics that contain these 7 7s 7p 7d 7f elements. The electron configurations of all the elements in the 8 8s 8p 8d periodic table are shown in Table 3.4 where we use the shorthand representation for the electron configurations (start with the nearest filled noble gas). FIGURE 3.3 Mnemonic for predicting the filling order of the atomic Examination of the electron configuration of the ele- orbitals. The upper gray block shows imaginary orbitals; orbitals in the lower gray block are not filled in the known elements. ments clearly shows the basis for their periodic behavior. Elements with atomic numbers 2, 10, and 18 are the noble gases. These elements are stable and chemically inert. Inertness is equated with completely filled shells of elec- for this apparent anomaly is that exactly filled and half- trons. Elements with similar outer shell configurations filled 3d orbitals are particularly stable (they have a lower possess many similar properties. Figure 3.4 shows the energy) compared to the neighboring occupancies of four Periodic Table of Elements. It is clearly a good idea to and nine, respectively. The electron configurations of the know where the atoms lie in the periodic table since this first row transition elements are given in Table 3.3. The is going to determine whether they lose or gain electrons electron configurations of the first row transition metals more easily and, thus, how the ion is charged as we will will be of importance when we discuss electrical conduc- now discuss. TABLE 3.4 Electron Configurations of the Elements Z Element Electron configuration Z Element Electron configuration 1 H 1s 53 I [Kr]4d105s25p5 2 He 1s2 54 Xe [Kr]4d105s25p 6 3 Li [He]2s 55 Cs [Xe]6s 4 Be [He]2s2 56 Ba [Xe]6s2 5 B [He]2s22p 57 La [Xe]5d6s2 6 C [He]2s22p2 58 Ce [Xe]4f5d6s2 7 N [He]2s22p3 59 Pr [Xe]4f36s2 8 O [He]2s22p4 60 Nd [Xe]4f46s2 9 F [He]2s22p5 61 Pm [Xe]4f56s2 10 Ne [He]2s22p 6 62 Sm [Xe]4f66s2 11 Na [Ne]3s 63 Eu [Xe]4f 76s2 12 Mg [Ne]3s2 64 Gd [Xe]4f 75d6s2 13 Al [Ne]3s23p 65 Tb [Xe]4f 96s2 14 Si [Ne]3s23p2 66 Dy [Xe]4f106s2 15 P [Ne]3s23p3 67 Ho [Xe]4f116s2 16 S [Ne]3s23p4 68 Er [Xe]4f126s2 17 Cl [Ne]3s23p5 69 Tm [Xe]4f136s2 18 Ar [Ne]3s23p 6 70 Yb [Xe]4f146s2 19 K [Ar]4s 71 Lu [Xe]4f145d6s2 20 Ca [Ar]4s2 72 Hf [Xe]4f145d26s2 40 ................................................................................................................................ Bac k g r o u n d Yo u N e e d t o K n o w  TABLE 3.4 Continued Z Element Electron configuration Z Element Electron configuration 21 Sc [Ar]3d4s2 73 Ta [Xe]4f145d36s2 22 Ti [Ar]3d24s2 74 W [Xe]4f145d46s2 23 V [Ar]3d34s2 75 Re [Xe]4f145d56s2 24 Cr [Ar]3d54s 76 Os [Xe]4f145d 66s2 25 Mn [Ar]3d 54s2 77 Ir [Xe]4f145d76s2 26 Fe [Ar]3d 64s2 78 Pt [Xe]4f145d96s 27 Co [Ar]3d74s2 79 Au [Xe]4f145d106s 28 Ni [Ar]3d 84s2 80 Hg [Xe]4f145d106s2 29 Cu [Ar]3d104s 81 Tl [Xe]4f145d106s26p 30 Zn [Ar]3d104s2 82 Pb [Xe]4f145d106s26p2 31 Ga [Ar]3d104s24p 83 Bi [Xe]4f145d106s26p3 32 Ge [Ar]3d104s24p2 84 Po [Xe]4f145d106s26p4 33 As [Ar]3d104s24p3 85 At [Xe]4f145d106s26p5 34 Se [Ar]3d104s24p4 86 Rn [Xe]4f145d106s26p 6 35 Br [Ar]3d104s24p5 87 Fr [Rn]7s 36 Kr [Ar]3d104s24p 6 88 Ra [Rn]7s2 37 Rb [Kr]5s 89 Ac [Rn]6d7s2 38 Sr [Kr]5s2 90 Th [Rn]6d27s2 39 Y [Kr]4d5s2 91 Pa [Rn]5f 26d7s2 40 Zr [Kr]4d25s2 92 U [Rn]5f36d7s2 41 Nb [Kr]4d45s 93 Np [Rn]5f46d7s2 42 Mo [Kr]4d55s 94 Pu [Rn]5f67s2 43 Tc [Kr]4d 55s2 95 Am [Rn]5f 77s2 44 Ru [Kr]4d75s 96 Cm [Rn]5f 76d7s2 45 Rh [Kr]4d85s 97 Bk [Rn]5f97s2 46 Pd [Kr]4d10 98 Cf [Rn]5f107s2 47 Ag [Kr]4d105s 99 Es [Rn]5f117s2 48 Cd [Kr]4d105s2 100 Fm [Rn]5f127s2 49 In [Kr]4d105s25p 101 Md [Rn]5f137s2 50 Sn [Kr]4d105s25p2 102 No [Rn]5f147s2 51 Sb [Kr]4d105s25p3 103 Lr [Rn]5f146d7s2 52 Te [Kr]4d105s25p4 H 1 He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Na 11 Mg 12 Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 0.9 1.2 1.5 1.8 2.1 2.5 3.0 K 19 Ca 20 Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 0.8 1.0 1.3 1.5 1.6 1.6 1.5 1.8 1.8 1.8 1.9 1.6 1.6 1.8 2.0 2.4 2.8 Rb 37 Sr 38 Y 39 Zr 40 Nb 41 Mo42 Tc 43 Ru 44 Rh 45 Pd 46 Ag47 Cd 48 In 49 Sn 50 Sb 51 Te 52 I 53 Xe 54 0.8 1.0 1.2 1.4 1.8 1.8 1.9 2.2 2.2 2.2 1.9 1.7 1.7 1.8 1.9 2.1 2.5 Cs 55 Ba 56 La 57 Hf 72 Ta 73 W 74 Re 75 Os 76 Ir 77 Pt 78 Au 79 Hg 80 Tl 81 Pb 82 Bi 83 Po 84 At 85 Rm86 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.2 2.2 2.2 1.9 1.9 1.8 1.8 1.9 2.0 2.2 Fr 87 Ra 88 Ac 89 Th 90 Pa 91 U 92 0.7 0.9 1.1 1.3 1.5 1.7 Ce 58 Pr 59 Nd 60 Pm 61 Sm 62 Eu 63 Gd64 Tb 65 Dy 66 Ho 67 Er 68 Tm69 Yb 70 Ly 71 FIGURE 3.4 The Periodic Table of Elements as viewed by a ceramist showing atomic number and electro- negativity. Different shadings show the groupings of some of the most important components of traditional and advanced ceramics. The lighter shading highlights elements used in traditional ceramics. The darker shading shows some of the elements found in advanced ceramics. 3 . 5 A s s i g n i n g Q ua n t u m N u m b e r s ............................................................................................................................. 41 3.6 IONS the energy required to remove one electron from the neutral gaseous atom to produce a gaseous ion with In ceramics we are usually dealing with materials charge +1. that have a significant fraction of ionic character in The noble gases have a complete shell of outer elec- their bonding. The requirements for ionic bonding are trons and have very high ionization energies, whereas the simple: elements in Group I, for example, Na and K, have an outer ns1 orbital and have much lower ionization energies. Second ionization energies, the energy required to remove  One element must be able to lose 1, 2, or 3 electrons. an electron from a gaseous ion with charge +1, are signifi-  The other element must be able to accept 1, 2, or 3 cantly higher than first ionization energies because when electrons. an electron is lost the effective nuclear charge, Z eff, increases. As a result, the In both cases the “3” is effective radius of an atom rare and it must not involve IONIZATION ENERGY or ion de-creases and the too much energy exchange. net attraction between the The ionization energy is Atom (g) + IE1 → Ion + (g) + e− electrons and the nucleus the energy required to increases (Table 3.5). remove an electron from This reaction is always endothermic (IE1 > 0). The sign The electron affinity the gaseous atom. The first is a convention of thermodynamics; some fields use the (EA) of an atom is ionization energy (IE1) is opposite convention. the energy change TABLE 3.5 Ionization Energies of the Elements (MJ/mol) Z Element I II III IV V 1 H 1.3120 2 He 2.3723 5.2504 3 Li 0.5203 7.2981 11.8149 4 Be 0.8995 1.7571 14.8487 21.0065 5 B 0.8006 2.4270 3.6598 25.0257 32.8266 6 C 1.0864 2.3526 4.6205 6.2226 37.8304 7 N 1.4023 2.8561 4.5781 7.4751 9.4449 8 O 1.3140 3.3882 5.3004 7.4693 10.9895 9 F 1.6810 3.3742 6.0504 8.4077 11.0227 10 Ne 2.0807 3.9523 6.122 9.370 12.178 11 Na 0.4958 4.5624 6.912 9.544 13.353 12 Mg 0.7377 1.4507 7.7328 10.540 13.628 13 Al 0.5776 1.8167 2.7448 11.578 14.831 14 Si 0.7865 1.5771 3.2316 4.3555 16.091 15 P 1.0118 1.9032 2.912 4.957 6.2739 16 S 0.9996 2.251 3.361 4.564 7.013 17 Cl 1.2511 2.297 3.822 5.158 6.54 18 Ar 1.5205 2.6658 3.931 5.771 7.238 19 K 0.4189 3.0514 4.411 5.877 7.976 20 Ca 0.5898 1.1454 4.9120 6.474 8.144 21 Sc 0.631 1.235 2.389 7.089 8.844 22 Ti 0.658 1.310 2.6525 4.1746 9.573 23 V 0.650 1.414 2.8280 4.5066 6.294 24 Cr 0.6528 1.496 2.987 4.74 6.69 25 Mn 0.7174 1.5091 2.2484 4.94 6.99 26 Fe 0.7594 1.561 2.9574 5.29 7.24 27 Co 0.758 1.646 3.232 4.95 7.67 28 Ni 0.7367 1.7530 3.393 5.30 7.28 29 Cu 0.7455 1.9579 3.554 5.33 7.71 30 Zn 0.9064 1.7333 3.8327 5.73 7.97 31 Ga 0.5788 1.979 2.963 6.2 32 Ge 0.7622 1.5374 3.302 4.410 9.02 33 As 0.947 1.7978 2.7355 4.837 6.043 34 Se 0.9409 2.045 2.9737 4.1435 6.59 35 Br 1.1399 2.10 3.5 4.56 5.76 36 Kr 1.3507 2.3503 3.565 5.07 6.24 37 Rb 0.4030 2.632 3.9 5.08 6.85 38 Sr 0.5495 1.0643 4.21 5.5 6.91 42 ................................................................................................................................ Bac k g r o u n d Yo u N e e d t o K n o w  TABLE 3.5 Continued Z Element I II III IV V 39 Y 0.616 1.181 1.980 5.96 7.43 40 Zn 0.660 1.267 2.218 3.313 7.86 41 Nb 0.664 1.382 2.416 3.69 4.877 42 Mo 0.6850 1.558 2.621 4.477 5.91 43 Tc 0.702 1.472 2.850 44 Ru 0.711 1.617 2.747 45 Rh 0.720 1.744 2.997 46 Pd 0.805 1.875 3.177 47 Ag 0.7310 2.074 3.361 48 Cd 0.8677 1.6314 3.616 49 In 0.5583 1.8206 2.705 5.2 50 Sn 0.7086 1.4118 2.9431 3.9303 6.974 51 Sb 0.8337 1.595 2.44 4.26 5.4 52 Te 0.8693 1.79 2.698 3.610 5.669 53 I 1.0084 1.8459 3.2 54 Xe 1.1704 2.046 3.10 55 Cs 0.3757 2.23 56 Ba 0.5029 0.96526 57 La 0.5381 1.067 1.8501 58 Ce 0.528 1.047 1.949 3.543 59 Pr 0.523 1.018 2.086 3.758 5.543 60 Nd 0.530 1.034 61 Pm 0.536 1.052 62 Sm 0.543 1.068 63 Eu 0.547 1.085 64 Gd 0.591 1.17 65 Tb 0.564 1.112 66 Dy 0.572 1.126 67 Ho 0.581 1.139 68 Er 0.589 1.151 69 Tm 0.596 1.163 2.288 70 Yb 0.6034 1.174 2.43 71 Lu 0.5235 1.34 72 Hf 0.68 1.44 2.25 3.21 73 Ta 0.761 74 W 0.770 75 Re 0.760 76 Os 0.84 77 Ir 0.88 78 Pt 0.87 1.7911 79 Au 0.8901 1.98 80 Hg 1.0070 1.8097 3.30 81 Tl 0.5893 1.9710 2.878 82 Pb 0.7155 1.4504 2.0815 4.083 6.64 83 Bi 0.7033 1.610 2.466 4.37 5.40 84 Po 0.812 85 At 86 Rn 1.0370 87 Fr 88 Ra 0.5094 0.97906 89 Ac 0.67 1.17 90 Th 1.11 1.93 2.78 91 Pa 92 U 93 Np 94 Pu 0.56 95 Am 0.58 3 . 6 I o n s ............................................................................................................................................................................ 43  TABLE 3.6 Electron Affinities of the Elements (kJ/mol) Element Theory Experimental Element Theory Experimental 1. H 72.766 72.9 27. Co 90.3 2. He <0 28. Ni 123.1 3. Li 59.8 58 29. Cu 173.8 4. Be −18a <0 30. Zn −87c 5. B 29 31. Ga 17c –48d 6. C 113 121 32. Ge 116 c –132d 7. N → N− −58 b 121 33. As 58c –71d N− → N2− −800 b 34. Se →Se − 204d –212c −420 N2− → N3− −1290 b Se − →Se2− 8. O → O− 120 142 35. Br 324.5 O− → O2− −780 b 36. Kr <0 9. F 312–325 328–333 37. Rb 19–39 10. Ne <0 <0 42. Mo 96 11. Na 52 48. Cd −58c 12. Mg −54c <0 49. In 19c –69d 13. Al 48 50. Sn 142d 14. Si 134 51. Sb 59d 15. P 75 52. Te 220 c 16. S → S − 205 200 53. I 296 S − → S2− −590 54. Xe <0 17. Cl 343 348 55. Cs 19–39 18. Ar <0 74. W 48 19. K 45 34–72 75. Re 14 20. Ca <0 81. Tl 117d 22. Ti 37.7 82. Pb 173 d 23. V 90.4 83. Bi −33d 24. Cr 94.6 84. Po 190 d 26. Fe 56.2 Source: Berry, R.S. (1969) Chem. Rev. 69, 533, except a Edlen, B. (1960) J. Chem. Phys. 33, 98; b Baughan, E.C. (1961) Trans. Faraday Soc. 57, 1863; c Ginsberg, A.P. and Miller, J.M. (1958) J. Inorg. Nucl. Chem. 7, 351; d Politzer, P. (1968) Trans. Faraday Soc. 64, 2241. accompanying the addition ELECTRON AFFINITY and very reactive nonmet- of one electron to a neutral als. Two requisites are gaseous atom to produce a Atom (g) + e− → Ion− (g) + EA that the ionization energy negative ion. Values of EA to form the cation and the are shown in Table 3.6. Note: The sign convention used for EA is in contradic- electron affinity to form A positive value indicates tion to that usually found in thermodynamics, an unfor- the anion must be energeti- that the reaction tunate historical artifact. cally favorable. The overall reaction will cost some, but not too much, energy. Atom (g) + e− → Ion− (g) + EA Recap: is exothermic.  Ionization energy, IE: the energy required to remove The values of EA also show a periodic behavior that an electron from the neutral gaseous atom can be explained by examining the electron configurations  Electron affinity, AE: the change in energy when one of the elements. The electron affinity is high for elements electron is added to a neutral gaseous atom in Group VII, for example, F and Cl. The addition of one electron to these atoms forms negative ions with a noble gas electron configuration—a stable arrangement. Atoms that already have full (e.g., He, Ne) or half-full orbitals 3.7 ELECTRONEGATIVITY (e.g., Be, N) often have negative electron affinities. Full and half-full orbitals are more stable. Electronegativity is a measure of the strength with which As we will see in Chapter 4, ionic compounds gener- an atom in a molecule attracts electrons. Like IE and EA, ally form only between very reactive metallic elements the dependence of electronegativity on Z can be explained 44 ................................................................................................................................ Bac k g r o u n d Yo u N e e d t o K n o w by examining electron want to know whether a GIBBS FREE ENERGY configurations. Atoms with process is energetically The change in free energy is defined by almost completely filled favorable, we have to deter- outer energy levels, like F mine the change in free ΔG = ΔH − TΔS Box 3.7 and Cl, are strongly elec- energy (ΔG) associated tronegative and readily with that process. For the The change in enthalpy is given by accept electrons. However, change atoms with nearly empty ΔH = ΔE + PΔV Box 3.8 outer shells, such as Li and A→B Na, readily give up elec- When the process involves no volume change, i.e., PΔV trons and are strongly which may be an oxidation = 0, so ΔH = ΔE we can write electropositive. Higher Z reaction or a phase trans- elements also have a low formation, the change in ΔG = ΔE − TΔS Box 3.9 electronegativity; because free energy is the outer electrons are at a greater distance from the positive nucleus, electrons are ΔG = G B − GA not as strongly attracted to the atom. The electronegativity where G B is the free energy scale of the elements is CONVENIENT FORMS OF DG of the final state and GA is included in Figure 3.4 Mixing A and B to form a solution (important in con- the free energy of the using Pauling’s classifica- structing phase diagrams) initial state. tion: F is assigned the  ΔG < 0 for a favor- largest electronegativity, 4, ΔG = RT(XA lnaA + XB lnaB) able process. There is and the other elements are a natural tendency to then based on this value. Oxidation of a metal to form a ceramic move spontaneously The differences in the elec- from A to B. tronegativities of two atoms ΔG = RT lnpO2  ΔG > 0 for an unfavor- in a molecule can be used able process. The reac- to estimate bond strengths Electrochemical process (such as in a fuel cell) tion as written will not and bond ionicities (i.e., proceed spontaneously; the percentage of ionic ΔG = −zFE ΔG = RT lnpO2 the reverse reaction will character in the bond—the be the spontaneous extent of “mixed” bonding; one. see Section 4.6 for numerical examples).  ΔG = 0 for a process at equilibrium. 3.8 THERMODYNAMICS: THE DRIVING In many processes, particularly those that occur in FORCE FOR CHANGE ceramics, there is little if any volume change and so PΔV = 0. Because the sign of ΔG is dependent upon Thermodynamic principles are important in all aspects of temperature and pressure, a particular system, such as materials science. In this section we introduce some of the a crystal structure, can be stable only within a certain fundamentals, but thermodynamics will be used in several range of P and T. By varying P and/or T, ΔG will eventu- other chapters (e.g., point defects, Chapter 11, and sur- ally become negative relative to some other structure faces, Chapter 13). The primary role of thermodynamics in ceramics is to indicate whether a system is stable and TABLE 3.7 Important Thermodynamic Parameters what conditions (usually changes in temperature or pres- Parameter Definition Units sure) will cause it to change. Our system may be a crystal structure, a phase, a grain boundary, an aggregate of CP Heat capacity at constant pressure J/K powder particles, or a concentration of defects. Table 3.7 cP Molar heat capacity at constant pressure J K−1 mol−1 lists some of the important thermodynamic parameters we CV Heat capacity at constant volume J/K cV Molar heat capacity at constant volume J K−1 mol−1 meet in ceramics together with their units. E Energy J G Gibbs free energy J H Enthalpy J Thermodynamic Stability μi Chemical potential J The Gibbs free energy (G) is a property that provides a P Pressure Pa S Entropy J/K convenient measure of the driving force of a reaction and T Temperature K may be used to define thermodynamic stability. When we 3 . 8 Th e r m o dy n a m i c s : Th e D r i v i n g F o r c e f o r C h a n g e ....................................................................................... 45 and a phase transition will occur. This may be a transition from one crystal structure to another (e.g., the phase trans- G g formation in quartz), or it may be a transition from one aggregate state to another state (e.g., during sintering when we get grain growth and reduction in total grain Entropy of boundary area), or it could be when we melt a solid to vaporization g+L form a liquid. The Gibbs free energy is a function of temperature, pressure, and the numbers of moles of all the species L present in the system. Entropy of fusion s+L Effect of Temperature Many of the processes of interest in ceramics occur at high s temperature. At absolute zero, T = 0 K, the term contain- ing the entropy change, TΔS, is zero and ΔG depends only MPt BPt on ΔE. However, as T increases the TΔS term becomes T FIGURE 3.5 Variation in the Gibbs free energy as a function of increasingly important and at some temperature a process temperature. The vertical segments are associated with phase can occur spontaneously even though ΔE is positive. The transformations. values of ΔE and ΔS depend on temperature and we can rewrite Box 3.9: ΔGT = ΔET − TΔST (3.1) When the signs of ΔET and ΔST are the same, some reactions that are not favorable at one temperature become The subscript indicates that the values are given at a tem- favorable at another, and vice versa. It is often useful to perature, T. To obtain values of ΔET and ΔST we need to know the temperature at which a reaction becomes favor- use the heat capacities of the material. able. This is the temperature at which a positive ΔGT The molar heat capacities are switches to a negative ΔGT due to the −TΔST term. We find this crossover temperature by setting ΔGT in Eq. 3.1 equal cP = dH/dT (3.2) to 0 and solving for T cV = dE/dT (3.3) ΔET T= (3.7) In many solids, particularly ceramics, with low coeffi- ΔST cients of expansion cp ∼ cv. It is easier to obtain values of cp and the variation with temperature is normally fitted to Figure 3.6 shows the effect of temperature on reaction an analytical expression of the form favorability. The slopes of the two lines and the crossover temperature will depend on the specific system. cP = a + bT + cT −2 (3.4) We use Eq. 3.4 in Chapter 34 (Eq. 34.3) to determine cP for various ceramics. Using cP we can obtain expressions for ΔET and ΔST ΔG > 0 ΔG < 0 TΔS ΔE T ΔHT = ΔH 298 + ∫ Δc dT P (3.5) 298 T cP ST = S0 + ∫ dT (3.6) 0 T ΔE If the external work of expansion due to heating is zero, TΔS as it is when a material is heated at constant volume, or if it is negligible, as it is when solids are heated at atmo- spheric pressure, all the heat supplied goes into internal T energy and we can approximate ΔHT by ΔET. It is values FIGURE 3.6 Effect of temperature on reaction spontaneity. The of ΔH298 that you will find tabulated. The variation of ΔG two lines cross when the energy contribution becomes less than with temperature is illustrated in Figure 3.5. the entropy contribution. 46 ................................................................................................................................ Bac k g r o u n d Yo u N e e d t o K n o w  We can combine Eq. 3.9 with our definition of Gibbs G298 – H298 free energy and produce a differential form of the Gibbs (kJ/mol) equation: 4 C (diamond) ∂G = V ∂P − S ∂T + ∑ μ i ∂ni (3.10) C (graphite) The importance of Eq. 3.10 is that it links the free energy of the system to our usual experimental variables (T and 0 P) and the observable properties (V and concentration). 3.9 KINETICS: THE SPEED OF CHANGE -4 Thermodynamics tells us whether a process can happen. 0 0.5 1.0 1.5 2.0 P (GPa) Kinetics tells us whether that process will happen at a FIGURE 3.7 Pressure dependence of the Gibbs free energies of reasonable, or measurable, rate. The rates of chemical carbon in graphite and diamond. Diamond becomes more stable at reactions have been found to depend very strongly on the high pressures. temperature. A useful rule of thumb is that the rate doubles for every 10 K increase in temperature. The rate, k, of Effect of Pressure many reactions follows the Arrhenius rate law Higher pressures favor structures that have a higher k = A exp −(Ea /RT) (3.11) density. Their formation involves a decrease in volume (negative ΔV). For instance, diamond (ρ = 3.51 g cm−3) is where R is the gas constant (8.314 J K−1 mol−1), A is a more stable than graphite (ρ = 2.26 g cm−3) at very high temperature-independent preexponential constant, and Ea pressures. At room temperature graphite will transform is the activation energy. A plot of k versus T gives a curve to diamond at pressures greater than about 1.5 GPa that increases exponentially. The activation energy repre- (14,400 atm) as shown in Figure 3.7. Graphite is the stable sents the minimum energy required for a reaction to phase at room temperature and pressure. The influence of happen. The value of Ea may be determined from the pressure, at constant T, on the Gibbs free energies of two logarithmic form of the Arrhenius equation: phases, α and β, is given by Ea (∂G (α→β)/∂P) T = ΔV(α→β) (3.8) ln K = + ln A (3.12) RT A plot of ln k against 1/T yields a straight line with slope Effect of Composition −Ea /R, as shown in Figure 3.8. This type of plot is called an Arrhenius plot and a reaction giving such a straight line In ceramics we are often dealing with multicomponent is said to show Arrhenius behavior. systems such as the ternary quartz, clay, and feldspar used Most reactions that proceed at a moderate rate, that is, in the formation of porcelains or the binary NiO, Al2O3 occur appreciably in minutes or hours, have values of Ea that react to form a spinel. Equilibrium, at constant T and between 50 and 100 kJ. For such reactions you can use Eq. P, is reached in these systems when the chemical potential, 3.11 to verify the photographer’s guide that reactions go μi, of a component is the same in all of the phases in which two or three times as fast when the temperature increases it is present. The chemical potential, or the partial molar by 10°C. free energy of a component in a given phase, is defined An important example of a process that exhibits Arrhe- as nius behavior is diffusion. The diffusion coefficient D (units of cm2 /s) is a strong function of temperature. μi = (∂G/∂ni) T,P,nj (3.9) D = D 0 exp(−Ea /RT) (3.13) where ni is the number of moles of component i and nj is the number of moles of component j. For ceramics the value of Ea varies over quite a wide range Deduction of the phase rule (Chapter 8), which defines from about 50 kJ/mol to 800 kJ/mol (∼0.5 eV per atom the conditions of equilibrium in terms of the number of to 8 eV per atom). The activation energy represents the phases and the components of a system, follows directly energy necessary for an atom to jump from one atomic from the requirement that μi of each constituent i be the position to another. same in every phase at equilibrium. If μi is different then The diffusion coefficient also depends on chemical we will get a reaction, the rate of which will be deter- potential and time. These changes are represented in mined by kinetics. Fick’s laws, which we will describe in Chapter 11. 3 . 9 K i n e t i c s : Th e S p e e d o f C h a n g e ......................................................................................................................... 47  T [°C] At sufficiently low temperatures any structure can be 1500 1400 1300 1200 stabilized kinetically. Kinetic stability is not a well-defined k term because the limit below which a conversion rate (g-eq·cm–1 s–1) is considered to be negligible is arbitrary. There are many examples of kinetically stabilized materials. Two examples in ceramics are 10-10  Glasses. At room temperature a glass is a kinetically stabilized material. Given enough time all glasses will transform to their crystalline counterpart.  Tridymite (a high-temperature polymorph of SiO2). Transformation of quartz at 867°C should lead to the 10-11 formation of tridymite. However, the transformation is very slow (it involves a complete alteration of the crystal structure) and direct conversion by heating alone has not been proved. All natural tridymite con- tains other oxides, which it is believed stabilize the structure; pure tridymite cannot be obtained at room temperature. 10-12 5.5 6.0 6.5 1/T [10-4 K-1] Notice that we have not considered the environment of the FIGURE 3.8 An Arrhenius plot. The slope of the line gives the combining atoms/ions, so we have not actually used the activation energy for the process. crystal/amorphous nature of the ceramic. CHAPTER SUMMARY We reviewed some of the fundamentals that underlie all aspects of materials science. Knowing the electron configuration of an atom allows us to understand some of the properties of materi- als that contain that atom. It also helps us to determine the type of bonding that occurs between different atoms. In ceramics the bonding is important because it is not straightforward. It often involves ionic and covalent contributions and sometimes also a metallic component. Thermodynamics and kinetics enable us to explain why and how chemical reactions take place. This type of information is important in many areas of ceramics, but particularly in ceramic processing. Traditional processing of ceramic components is carried out at high tem- peratures because the kinetics would be too slow otherwise. Kinetics is often closely linked to economics. Processes that are slow are usually expensive. PEOPLE IN HISTORY Arrhenius, Svante August won the 1903 Nobel Prize in Chemistry for his work on the electrical conductivity of salt solutions (he was also nominated for the Physics Prize). He is often hailed as a pioneer of modern environmentalism for his work on the greenhouse effect. One of his predictions was that the United States might pump its last barrel of oil in 1935. Fortunately he was proved wrong, but his concern about the world’s natural mineral resources and the need for alternative sources of energy was prescient. He died in 1927 at age 68. Barkla, Charles Glover (1877–1944) was born in Widnes, Lancashire, England. After obtaining his master’s degree in physics he went to work in the Cavendish Laboratory with J.J. Thomson. In 1913 he accepted the position of Chair in Natural Philosophy in the University of Edinburgh in Scotland and he remained there until he died. He was awarded the 1917 Nobel Prize in Physics for his discovery of the characteristic Röntgen radiation of the elements. Bohr, Neils (Denmark) in 1913 proposed an atomic model where electrons could move only in certain stable orbits. He won the Nobel Prize in Physics in 1922 and died in 1962 at age 77. Boltzmann, Ludwig Eduard was born in Vienna in 1844 and died at age 62. His constant is inscribed on his tomb in Vienna. Many argued strongly against his ideas and he committed suicide shortly before experi- ments justified them. Davisson, Clinton Davis and Germer, Lester Halbert were working at Bell Labs at the time of their discovery of electron diffraction. Davisson died in 1958 at age 76 (born 1881) and Germer died in 1971 at age 75 (born 1896). 48 ................................................................................................................................ Bac k g r o u n d Yo u N e e d t o K n o w  de Broglie, Louis in 1924 hypothesized that all matter possesses wave properties. A French Duke, he won the Nobel Prize in Physics in 1929. He died in 1987 at age 94. Heisenberg, Werner (1901–1976) was born in Würzburg in Germany. He obtained his PhD in 1923 at the University of Munich. He published his theory of quantum mechanics when he was 23 and for this theory he was awarded the 1932 Nobel Prize in Physics. At the end of World War II he was taken prisoner by American troops and sent to England. He returned to Germany in 1946. He was Director of the famous Max Planck Institute for Physics and in 1953 became President of the Alexander von Humboldt Founda- tion. He died in 1976 at age 74. Pauli, Wolfgang (1900–1958) was born in Vienna, Austria. He obtained his doctoral degree in 1921 from the University of Munich. After that he worked with Max Born and then with Neils Bohr. He held various appointments in the United States during World War II, including the Institute of Advanced Study in Princeton. After the war he returned to the Federal Institute of Technology in Zurich as Professor of Theoretical Physics. He won the 1945 Nobel Prize in Physics for developing the eponymous exclusion principle. Pauling, Linus Carl won the Noble Prize for Chemistry in 1954 and in 1962 for Peace. He died in 1994 at age 93. Schrödinger, Erwin was born in Vienna, Austria in 1887. His great discovery, Schrödinger’s wave equation, was made in 1926, and for that he won the Nobel Prize in Physics in 1933. When Hitler came to power in Germany (1933) Schrödinger moved to England. He then moved back to Austria but had to escape when his native country became annexed in 1938. He eventually moved to the Institute for Advanced Studies in Dublin where he remained until he retired. He died in 1961 at age 73. Thomson, Joseph John and Thomson, George Paget were father and son. Rutherford was J.J. Thomson’s student at Cambridge. J.J. Thomson discovered the electron in 1897 and won the Nobel Prize in Physics in 1906. G.P. Thomson won the Nobel Prize in 1937 together with Davisson; he died in 1976 (born 1892). So, the father “proved” that electrons were particles and the son “proved” they were waves. GENERAL REFERENCES Atkins, P.W. and de Paula, J. (2002) Atkins’ Physical Chemistry, 7th edition, Oxford University Press, Oxford. A physical chemistry text often used at the sophomore/junior level. DeHoff, R. (2006) Thermodynamics in Materials Science, 2nd edition, CRC, Boca Raton, FL. A standard thermodyanamic text for materials science. Gaskell, D.R. (2003) Introduction to the Thermodynamics of Materials, 4th edition, Taylor & Francis, New York. Thermodynamic text for undergraduate courses in materials science. Huheey, J.E., Keiter, E.A., and Keiter, R.L. (1993) Inorganic Chemistry: Principles of Structure and Reactiv- ity, 4th edition, Cummings, San Francisco. A standard inorganic chemistry textbook. Much of this should be background material. Kreyszig, E. (1999) Advanced Engineering Mathematics, 8th edition, Wiley, New York. Senior level under- graduate/graduate-level engineering mathematics text that describes the method for transforming Carte- sian coordinates into polar coordinates and the method of separation of variables. Pauling, L. (1960) The Nature of the Chemical Bond, 3rd edition, Cornell University Press, Ithaca, NY. A classic, and one of the most frequently cited of all scientific texts. Gives a detailed description of his scale of electronegativity. Planck, Max (1922) Treatise on Thermodynamics, Dover Publications. Winner of the 1918 Nobel Prize for Physics SPECIFIC REFERENCES Arrhenius, S. (1889) “Ober die Reacktionsgeschwindigkeit bei der Inversionvon Rohrzucker durch Säuren,” Z. Phys. Chem. 4, 226–248. Bohr, N. (1913) “The constitution of atoms and molecules,” Phil. Mag. 26, 1, 476. Bohr, N. (1913) “Constitution of atoms and molecules III,” Phil. Mag. 26, 1, 857. Davisson, C. and Germer, L.H. (1927) “Diffraction of electrons by a nickel Crystal,” Phys. Rev. 30, 705. DeBroglie. L. (1925) “Recherches sur la théorie des quanta,” Ann. Phys., Paris 3, 22. Heisenberg, W. (1927) “The problem of several bodies and resonance in quantum mechanics. II,” Z. Phys. 41, 239. Hund, F (1925) “Interpretation of spectra,” Z. Phys. 33, 345. Thomson, G.P. and Reid, A. (1927) “Diffraction of cathode rays by a thin film,” Nature 119, 890. EXERCISES 3.1 Explain the trend in the first ionization energies of elements in the second row (Na to Cl) of the periodic table. C h a p t e r S u m m a ry .......................................................................................................................................................... 49  3.2 Explain the trend in ionization energies of singly charged ions of the halogens. 3.3 Explain the trend in electron affinities of elements in the second row (Na to Cl) of the periodic table. 3.4 What is the ionization energy of F−? Would you expect the process of ionization to be endothermic or exothermic? 3.5 Calculate the energy of the Na 3s1 electron. The value of the first ionization energy for Na is 0.50 MJ/mol. Explain the difference, if any, between these two numbers. 3.6 Explain the trend in Pauling electronegativities of elements in the second row (Na to Cl) of the periodic table. 3.7 An electron has the principal quantum number four. What are the possible values of l, ml, and ms for this electron? 3.8 Determine the activation energy for the reaction shown in Figure 3.8. 3.9 Even though glasses are not thermodynamically stable, we know they exist at room temperature. Explain this phenomenon and describe briefly how you could increase the rate at which a glass would crystallize. 3.10 Show that the volume change for the transformation graphite → diamond is negative. 50 ................................................................................................................................ Bac k g r o u n d Yo u N e e d t o K n o w  4 Bonds and Energy Bands CHAPTER PREVIEW Bonding in ceramic materials may be quite complicated. It will be primarily covalent and/or ionic, but it may also have a metallic component, a van der Waals component, etc. In this chapter we will review the basic types of primary and secondary bonds and see how they apply to ceramics. We will also review the concept of energy bands, which we use in discussing electrical properties later. The purpose of this chapter is to review the concepts that we will use throughout the text. If it is not a review for you, suggestions are given for suitable texts that will give you the details. Important topics include the type of bonding, the origin of hybridization, mixed bonding, and energy bands. 4.1 TYPES OF INTERATOMIC BOND dE nA mB F= = − (4.2) dr r n + 1 r m + 1 We can divide interatomic bonds into two categories: The force will be zero at the equilibrium separation.  Primary (strong) bonds The sign conventions for force: In Figure 4.1a the force  Secondary (weak) bonds is attractive when F is positive. This is the usual conven- tion in materials science (and in Newton’s law of universal The types of primary and secondary bonds and their gravitation). The force is attractive if A > 0 and negative energy ranges are given in Table 4.1. In the next few sec- if A < 0. Beware: in electrostatics, the convention is that tions we will briefly review the general characteristics of a negative force is attractive. these bonds. All interatomic forces are electrostatic in origin. The simplest expression for the bond energy is 4.2 YOUNG’S MODULUS A B E=− n + m (4.1) We can change the equilibrium spacing (r 0) of the r r atoms in a solid by applying a force. We can push the where r is the interatomic distance and A, B, n, and m are atoms closer together (compression), r < r0, or pull them constants characteristic of the type of bonding. The first further apart (tension), r > r 0. Young’s modulus (E) is a term is the attractive component the second is due to measure of the resistance to small changes in the repulsion. Only when m > n will a minimum (equilibrium) separation of adjacent atoms (modulus is Latin for value of E be possible. Equation 4.1 indicates that attrac- “a small measure”). It is the same for both tension and tive forces predominate when atoms are far apart and compression. repulsive interactions predominate when the atoms are Young’s modulus is related to the interatomic bonding close together. The bond–energy curve can be plotted as forces and, as you might expect, its magnitude depends on shown in Figure 4.1a. When the energy is a minimum the the slope of the force–distance curve at r0. atoms are at their equilibrium separation (r = r 0); the Close to r 0 the force–distance curve approximates a lowest energy state defines the equilibrium condition. In tangent; when the applied forces are small the displace- discussing ceramics, we usually think of the material in ment of the atoms is small and proportional to the force. terms of ions; ions with the same sign always repel one We can define the stiffness of the bond, S 0, as the slope another due to the Coulomb force. of this line: If we differentiate Eq. 4.1 with respect to r, we obtain ⎛ d E⎞ 2 S0 = ⎛ ⎞ an equation that describes the resultant force F between a dF =⎜ 2 ⎟ (4.3) pair of atoms ⎝ dr ⎠ r = r ⎝ dr ⎠ r = r 0 0 4 . 2 Yo u n g’s M o d u l u s ................................................................................................................................................... 51  TABLE 4.1 Typical Bond Strengths If we consider pulling two planes of atoms apart then the total force per unit area can be obtained by dividing F Type of bond Bond energy (kJ/mol) by r 02 Ionic 50–1000 Covalent 200–1000 F S (r − r ) S ⎛ r − r0 ⎞ Metallic 50–1000 =σ= 0 2 0 = 0 ⎜⎝ ⎟ = Eε (4.5) van der Waals 0.1–10 2 r0 r0 r0 r0 ⎠ Hydrogen 10–40 where σ and ε should be familiar to you already, they are stress and strain, respectively. Moduli obtained from this The stiffness is analogous to the spring constant or elastic approach are approximate because they relate to two force constant of a spring and is the physical origin of atoms only, ignoring the effects of neighboring atoms. Hooke’s law. Close to r0 we can assume that the force (Although we only discussed Young’s modulus here the between two atoms that have been stretched apart a small conclusions are applicable to the other elastic moduli we distance r is describe in Chapter 16.) As the interatomic spacing, and in some cases the bonding, varies with direction in a single F = S 0 (r − r 0) (4.4) crystal, Young’s modulus is dependent upon the direction of stress in relation to the crystal axes. Single crystals are elastically anisotropic. Figure 4.1b shows force–distance plots for two materi- als; one having weakly bonded atoms and the other having strongly bonded atoms. With reference to bond–energy curves a material with a high modulus will have a narrow, steep potential energy well; a broad, shallow energy well would be characteristic of a low modulus. Table 4.2 lists values of Young’s moduli for different materials as a func- tion of melting temperature. You can see the general trend: the higher the melting temperature, the higher the modulus. Melting temperatures are also indicative of bond strengths, which are determined mainly by the depth of the energy well. The modulus is determined by the curvature at the bottom of the well. It is this difference that accounts for deviations from the general trend. As the temperature of a material is increased it is generally found that Young’s modulus slowly decreases as shown for single-crystal aluminum oxide (corundum) in TABLE 4.2 Young’s Moduli as a Function of Melting Temperature Average Young’s Melting temperature, Compound modulus (GPa) (°C) Titanium carbide 310 3180 Tungsten 414 2996 Silicon carbide 345 Sublimes > 2800 Periclase (MgO) 207 2800 Beryllia (BeO) 310 2585 Spinel (MgAl2O4) 241 2160 Corundum (Al2O3) 366 2050 Iron 207 1539 Copper 110 1083 Halite (NaCl) 34 801 Aluminum 69 660 Magnesium 41 650 FIGURE 4.1 (a) Bond-energy curve for KCl. At infinite separation, Polystyrene 2.8 <300 the energy is that required to form K + and Cl− from the correspond- Nylon 2.8 <300 ing atoms. (b) Force-distance curves for two materials: one where Rubber 0.07 <300 the bonding is strong and one where it is weak. 52 ............................................................................................................................................. B o n d s a n d E n e r g y Ba n d s Young’s The requirement for ionic bonding is that the ioniza- Modulus tion energy to form the cation and the electron affinity to (GPa) form the anion must both favor it energetically. The forma- 460 tion of isolated ions from isolated atoms requires energy and, thus, the formation of the pair of ions would not produce a stable situation. However, the pair of ions will 450 have a strong mutual attraction that leads to a strong binding in the molecule. Because the Coulomb force is strong and long range, many ionic compounds have high melting and high boiling temperatures. Ionic bonds do not 440 favor particular directions. This is very different from covalent bonding. 430 0 200 400 600 800 1000 Energy of an Ion Pair T (K) Before considering a lattice of ions, we will consider a FIGURE 4.2 Temperature dependence of Young’s modulus for corundum. single pair of oppositely charged ions separated by a dis- tance r. The electrostatic attractive energy E is Z M Z X e2 E=− (4.7) ( 4πε 0 r ) Figure 4.2. As we approach absolute zero, the slope of the curve approaches zero as required by the third law of thermodynamics. (The entropy of any pure substance in complete internal equilibrium is zero.) An empirical rela- tionship that fits the data for several ceramics is 300 −T E = E 0 −bT exp ⎛ 0 ⎞ (4.6) Young’s ⎝ T ⎠ Modulus (GPa) E 0 is Young’s modulus at absolute zero and b and T0 are empirical constants; T0 is about half the Debye tempera- ture. (The Debye temperature is the temperature at which the elastic vibration frequency of the atoms in a solid is the maximum.) As the temperature is increased the sepa- ration between the atoms is increased and the force neces- sary for further increases is slightly decreased. For polycrystalline ceramics there is an additional 250 Al2O3 effect due to grain boundaries. At high temperatures there is a rapid decrease in the measured values of Young’s moduli as shown in Figure 4.3. This has been attributed to nonelastic effects such as grain boundary sliding and grain boundary softening. So Young’s modulus of a bulk ceramic is continuing to change as described by Eq. 4.6, but we are measuring changes due to the grain boundaries. MgO The importance of grain boundaries in the mechanical behavior of ceramics will become very apparent in later chapters. 200 4.3 IONIC BONDING ThO2 In a pure ionic bond there is complete transfer of electrons from one atom to another. Pure ionic compounds do not exist. Although compounds such as NaCl and LiF are 400 800 T (°C) 1200 often thought of as being ionic, in general, all such “ionic” FIGURE 4.3 Temperature dependence of Young’s modulus of solids have a covalent component. several polycrystalline ceramics. 4 . 3 I o n i c B o n d i n g ......................................................................................................................................................... 53 Z M and ZX are the charges on the cation and anion, respec- tively. The negative sign in Eq. 4.7 means that as r becomes - + - + - + - + - + smaller, the energy becomes increasingly more negative. To obtain equilibrium separation there must be repulsion Reference to balance the attraction. Strong repulsive forces arise r0 ion when the full electron orbitals of both ions overlap, because FIGURE 4.4 Linear array of ions of alternate sign separated by r0. some electrons must then go into higher energy states in accordance with the Pauli exclusion principle. The repul- sion energy rises rapidly with decreasing distance between interactions is known as the Madelung constant, A (Mad- the ions. elung, 1918). The energy per ion pair in the crystal is The repulsive energy is often given by an equation of then the form A Z M Z X e2 B E=− (4.10) Er = n (4.8) ( 4πε 0 r0 ) r The Madelung constant is defined as the ratio of the B is a constant and n is known as the Born exponent. Coulomb energy of an ion pair in a crystal to the Coulomb Information about the Born exponent may be obtained energy of an isolated ion pair at the same separation (the from compressibility data since we are measuring the equilibrium separation of the ions in the crystal not in an resistance of the ions to be closer together than r 0. The isolated pair). Born exponent depends on the type of ion involved. Larger Zi Z j ions have higher electron densities and hence larger values A= ∑− (4.11) of n (Table 4.3). i Z1 Z 2 rij The total energy of the ion pair is given by summing Eqs. 4.7 and 4.8 The distance rij is the separation between ions at equilibrium. Z Z e 2 B In three dimensions the series presents greater diffi- E=− M X + n (4.9) culty than the linear example. It is not possible to write ( 4πε 0 r ) r down the successive terms by quick inspection. More importantly, the series converges slowly and keeps revers- The inset in Figure 4.1a ing in sign so you have to shows how when r is large MADELUNG CONSTANT FOR LINEAR ARRAY consider the whole infinite the bond energy is >0, For the infinite linear array of ions shown in Figure 4.4 crystal. because of the net energy we obtain An approach we can involved in forming the use to obtain A for a three- ion pair. A = 2[1 − 1/2 + 1/3 − 1/4 + . . .] dimensional crystal struc- ture is illustrated for NaCl Madelung Constant The factor 2 occurs because there are two ions, one to (Figure 4.5). We want to the right and one to the left of our reference ion, at equal consider the interactions In a crystal lattice, all the distances rij. We sum this series using the expansion between the central cation ions will interact. The and all the other ions in the interaction between ions with opposite charge will ln(1 + x) = x − x /2 + x /3 − x /4 + . . . 2 3 4 cell. Due to electroneutral- ity requirements in the unit be attractive, but will Thus the linear Madelung constant cell, ions located on the be repulsive between ions cube faces count 1/2, those of like charge. The summation of all these A = 2 ln 2. on the cell edges count 1/4, and the corner ions count 1/8. (This is the same approach that you use when determining the number of TABLE 4.3 Values of the Born Exponent, n atoms per cell.) Using Eq. 4.11 we obtain Ion configuration n He 5 A = − (6 / 2 ) ( −1) / 1 − (12 / 4 )(1) / 2 − (8 / 8) ( −1) / 3 Ne 7 Ar, Cu + 9 Hence Kr, Ag + 10 Xe, Au + 12 A = 3 − 2.1212 + 0.5774 = 1.456 54 ............................................................................................................................................. B o n d s a n d E n e r g y Ba n d s  - + - than 1. The implication is that the crystal is more stable + - + than an isolated ion pair. The fact that the Madelung con- - + - stant for the NaCl structure, which has six nearest neigh- bors, is close to the Madelung constant of the CsCl structure, which has eight nearest neighbors, indicates that r0 3  The number of neighbors does not significantly influ- + - + ence the lattice energy. - + -  The Coulomb energy does not depend on the type of + - + crystal structure. r0 2 In Chapter 5 we will see that packing is the most r0 important consideration in determining the structure - + - adopted by predominantly ionically bonded crystals. The difference in A between some crystal structures is very + - + Na+ Cl- small. In such cases, for example, the zinc blende and - + - + - wurtzite structures (named after the two crystalline forms of ZnS), the difference in the resulting electrostatic energy FIGURE 4.5 NaCl structure showing distances between ions in is small. For zinc blende and wurtzite it is ∼0.2%. When multiples of r0. the energy difference between structure types of the same stoichiometry is small, we often encounter polymorphism: the compound can form with more than one structure. We If we consider a larger cell size the value we obtain for will examine this useful complication in Chapter 7. the Madelung constant is closer to that determined for the NaCl structure using computer calculations. Doubling the Lattice Energy length of the cell edge gives A = 1.75. These simple cal- culations are a little misleading because the sum is really With knowledge of the Madelung constant we write the infinite. There are two important points: total energy for 1 mol of the crystal lattice containing an Avogadro’s number (N) of ion pairs:  A is well defined for a particular crystal structure, it is usually ∼2. A N Z M Z X e2 NB E=− + n (4.12)  A is unique for a particular crystal structure and is ( 4πε 0 r ) r the same for NaCl and MgO. The minimum energy, E 0, at r 0 is obtained by differentiat- Table 4.4 lists Madelung constants for some common ing Eq. 4.12 with respect to r: crystal structures. The value of the Madelung constant is determined only by the geometry of the lattice and is dE A N Z M Z X e2 nBN =0= − n +1 independent of the ionic radius and charge. Unfortunately, dr ( 4πε 0 r02 ) r some tables incorporate ionic charge, so care is necessary when looking up and comparing values. For example, the The constant B is then Madelung constant for fluorite may be given as 5.038 and that of Al2O3 as 25.031; the constant for MgO may then A N Z M Z X e2 r0n −1 be given as different from that for NaCl. B= 4πε 0 Table 4.4 confirms that the value of the Madelung constant for all these different crystal structures is greater Rewriting Eq. 4.12 gives the Born–Landé equation, which is quite successful in predicting accurate values of the lattice energy of an ionic compound: TABLE 4.4 Madelung Constants of Some Common Crystal Structures A N Z M Z X e2 ⎛ 1− ⎞ 1 E0 = − (4.13) Structure Coordination number Geometric factor, A 4πε 0 r0 ⎝ n⎠ Sodium chloride 6:6 1.74756 Cesium chloride 8:8 1.76267 It requires only knowledge of the crystal structure (in Zinc blende 4:4 1.63806 order to choose A correctly) and r0. Both parameters are Wurtzite 4:4 1.64132 readily available from X-ray diffraction data. Fluorite 8:4 2.51939 As an example of using Eq. 4.13 we will calculate the Rutile 6:3 2.408a value of E 0 for MgO. We need to substitute the following Corundum 6:4 4.1719a values: 4 . 3 I o n i c B o n d i n g ......................................................................................................................................................... 55 A = 1.748 (from Table 4.4) TABLE 4.5 Lattice Energies of Some Alkali and Alkaline n = 8 (an average value based on Table 4.3) Earth Metal Halides at 0 K (kJ/mol) r 0 = 210 pm (from X-ray diffraction data) Compound Born–Haber cycle Born–Landé equation This gives E 0 = −4046.8 kJ/mol. NaF −910 −904 The terms in Eq. 4.1 are modified in other models NaCl −772 −757 NaBr −736 −720 since it would be surprising for one value of n to fit all NaI −701 −674 atoms when we have no physical justification for any par- KCl −704 −690 ticular number. For example, the repulsion term may be KI −646 −623 represented by CsF −741 −724 CsCl −652 −623 CsI −611 −569 Er = be− ( r /r ) (4.14) MgF2 −2922 −2883 CaF2 −2597 −2594 Where b and ρ are constants determined from compressi- bility measurements. This gives the Born–Mayer equation (Born and Mayer, 1932) for lattice energy: For gaseous diatomic molecules ΔHA is the enthalpy of dissociation (bond energy plus RT) of the diatomic A N Z M Z X e2 ⎛ r⎞ molecule. For metals that vaporize to form monatomic E0 = − ⎜⎝ 1 − ⎟⎠ (4.15) 4πε 0 r0 r0 gases ΔHA is identical to the enthalpy of sublimation. If a diatomic molecule M2 sublimes, then the dissociation The Born–Mayer equation emphasizes the fact that enthalpy of the reaction (M2 → 2M) must also be included. Eq. 4.1 is designed only to match the observed phenome- As defined earlier, E is the lattice energy of the crystal non. It is not a fundamental “truth” like the Coulomb and represents the heat of formation per mole of a crystal + − interaction. MX from M(g) and X(g) . As an example of using the Born–Haber cycle we will calculate the lattice energy of MgO. The values of the The Born–Haber Cycle various thermodynamic parameters can be found in The Born–Haber (Born, 1919; Haber, 1919) cycle shows Kubaschewski et al. (1993), Johnson (1982), and in the the relationship between lattice energy and other thermo- NIST-JANAF tables (Chase, 1998). dynamic quantities. It also allows the lattice energy to be For MgO: calculated. The background of the Born–Haber cycle is Hess’s law, which states that the enthalpy of a reaction is ΔHf −601.7 kJ/mol the same whether the reaction proceeds in one or several ΔHAM 147.7 kJ/mol steps. The Born–Haber cycle for the formation of an ionic ΔHAX 249 kJ/mol [the actual value for the dissociation compound is shown in Figure 4.6. It is a necessary condi- enthalpy is 498 kJ/mol, but we need to take half tion that this value because we are considering the reac- tion ½O2 (g) → O (g)] ΔHf = ΔHAM + ΔHAX + ΔHIE + ΔHEA + E (4.16) ΔHIE 2188 kJ/mol ΔHEA −638 kJ/mol or in terms of the lattice energy By substitution into Eq. 4.17 we get E = −2548.4 kJ/mol. E = ΔHf − ΔHAM − ΔHAX − ΔHIE − ΔHEA (4.17) If we compare this value with that calculated using the Born–Landé equation we see that they are quite different. ΔHAM and ΔHAX are the enthalpies of atomization of the The Born–Haber cycle gives a lattice energy about 60% metal and the nonmetal, respectively. higher than the Born–Landé value. The reason for this difference is that although we often regard MgO as essen- tially an ionic ceramic, it does have an appreciable cova- ΔHIE lent character. If similar calculations, using the Born–Landé M(g) M+(g) equation and the Born–Haber cycle, are performed for + NaCl or one of the other alkali halides the values obtained ΔHEA using the two methods agree to within 1% or 2% as shown ΔHAM X(g) X-(g) in Table 4.5. The differences in the above calculations are sometimes used as a means of defining an ionic com- ΔHAX E pound—if the results are similar, it must be ionic. Although ΔHf M(s) + 12X2(g) MX(s) this definition is not too useful within the context of ceramics, it does serve as an illustration that the bonding FIGURE 4.6 The Born–Haber cycle. in most ceramics is not simply ionic. 56 ............................................................................................................................................. B o n d s a n d E n e r g y Ba n d s Ionic Radii Many mineralogists use Goldschmidt’s values. The most comprehensive set of ionic radii is that compiled by Shannon We know from quantum mechanics that atoms and ions and Prewitt (1969) and revised by Shannon (1976). Table 4.6 do not have precisely defined radii. However, the concept lists Shannon’s ionic radii. Although there are several differ- of an ion as a hard sphere with a fixed radius is very useful ent tabulations they are, for the most part, internally consis- when predicting crystal structures. Experimental evidence tent. So it is important to use radii from only one data set. shows that such a model has some justification: the model Never mix values from different tabulations. often “works.” Nevertheless, always bear in mind that There are several important trends in the sizes of atoms and ions are not rigid spheres and their size will be ions: affected by their local environment. We cannot measure ionic radii directly. What we can  The radii of ions within a group in the periodic table measure rather easily, and with high accuracy using X-ray increase with increasing Z (this is for main group ele- crystallography, in most crystals is r0. ments; the transition metals often behave differently).  The radius of a cation is smaller than the correspond- r0 = r M + r X (4.18) ing atom.  The radius of an anion is larger than the corresponding r M is the radius of the cation (usually a metal) and r X is atom. the radius of the anion.  In a particular row of the periodic table the anions are To obtain ionic radii it is necessary to fix the radius of larger than the cations. one of the ions in Eq. 4.18. Historically, the radius of the I− ion was fixed and the other radii calculated with respect to Using X-ray methods, it is possible to obtain accurate it (Landé, 1920). Later, Pauling (1960) produced a consistent electron density maps for ionic crystals; NaCl and LiF set of ionic radii that has been used widely for many years. are shown in Figure 4.7. It has been suggested that the TABLE 4.6 Ionic Crystal Radii (in pm) Coordination Number = 6 Ag + Al3+ As5+ Au + B3+ Ba 2+ Be2+ Bi3+ Bi5+ Br− C4+ Ca 2+ Cd2+ 115 54 46 137 27 135 45 103 76 196 16 100 95 Ce4+ Cl− Co2+ Co3+ Cr 2+ Cr 3+ Cr4+ Cs + Cu + Cu2+ Cu3+ Dy3+ Er 3+ 87 181 75 55 80 62 55 167 77 73 54 91 89 Eu3+ F− Fe2+ Fe3+ Ga3+ Gd3+ Ge4+ Hf4+ Hg2+ Ho3+ I− In3+ K+ 95 133 78 65 62 94 53 71 102 90 220 80 138 La3+ Li + Mg2+ Mn2+ Mn4+ Mo3+ Mo4+ Mo 6+ N5+ Na + Nb5+ Nd3+ Ni2+ 103 76 72 83 53 69 65 59 13 102 64 98 69 Ni3+ O2− OH− P5+ Pb2+ Pb4+ Rb + Ru4+ S2− S6+ Sb3+ Sb5+ Sc3+ 56 140 137 38 119 78 152 62 184 29 76 60 75 Se2− Se6+ Si4+ Sm3+ Sn4+ Sr 2+ Ta5+ Te2− Te6+ Th4+ Ti2+ Ti3+ Ti4+ 198 42 40 96 69 118 64 221 56 94 86 67 61 Tl + Tl3+ U4+ U5+ U6+ V2+ V5+ W4+ W6+ Y3+ Yb3+ Zn2+ Zr4+ 150 89 89 76 73 79 54 66 60 90 87 74 72 Coordination Number = 4 Ag + Al3+ As5+ B3+ Be2+ C4+ Cd2+ Co2+ Cr4+ Cu + Cu2+ F− Fe2+ 100 39 34 11 27 15 78 58 41 60 57 131 63 Fe3+ Ga3+ Ge4+ Hg2+ In3+ Li + Mg2+ Mn2+ Mn4+ Na + Nb5+ Ni2+ O2− 49 47 39 96 62 59 57 66 39 99 48 55 138 OH− P5+ Pb2+ S6+ Se6+ Sn4+ Si4+ Ti4+ V5+ W6+ Zn2+ 135 17 98 12 28 55 26 42 36 42 60 Coordination Number = 8 Bi3+ Ce4+ Ca 2+ Ba 2+ Dy3+ Gd3+ Hf4+ Ho3+ In3+ Na + Nd3+ O2− Pb2+ 117 97 112 142 103 105 83 102 92 118 111 142 129 Rb + Sr 2+ Th4+ U4+ Y3+ Zr4+ 161 126 105 100 102 84 Coordination Number = 12 2+ 2+ 3+ 2+ 2+ Ba Ca La Pb Sr 161 134 136 149 144 4 . 3 I o n i c B o n d i n g ......................................................................................................................................................... 57  Cl- 100 50 10 Li+ F- 2 1 0.5 0.1 0.15 0.1 0.3 0.5 0.5 0.3 0.5 0.05 1 1 1 2 2 0.15 2 10 5 5 10 50 20 10 100 15 50 Na+ 0.1 nm FIGURE 4.7 Electron density maps for (a) NaCl and (b) LiF. minimum in the electron density contours between the Molecular Orbitals nuclei could be taken as the radius position for each ion. The ionic radii values obtained by this method differ One way to consider covalent bond formation is to look at somewhat from those obtained by other methods and tend what happens to the individual atomic orbitals (AOs) on to make the anions smaller and the cations larger. Notice adjacent atoms as they overlap at short distances to form that the electron density does not go to zero in the region molecular orbitals (MOs). The simplest case is that of two between nuclei even for “ionic” crystals. 1s orbitals. At relatively large separations (≥1 nm) the electron orbital on one atom is not influenced significantly by the presence of the other atom. As the two atoms 4.4 COVALENT BONDING approach each other the orbitals overlap and the electron density between the nuclei increases. At r 0, the individual A pure covalent bond forms when atoms that have the AOs become a single MO—called a bonding MO—with same electronegativity combine; the electrons are shared the electron density concentrated between the nuclei. equally. Such a bond occurs only between identical atoms. A bonding MO can be described as the sum of the Examples of pure covalent bonds are the C—C bond in wave functions of the contributing AOs: diamond and the Si—Si bond in silicon. If the atoms have similar electronegativities, then a bond can form that has ΨBond = ΨA + ΨB (4.19) a large covalent component. The most important such bonds for ceramics are the Si—O bond found in silicates The probability of finding an electron at a given point in and the Al—O bond in alumina. the MO is proportional to Ψ2Bond: The bond-energy curve for a covalent bond has the same general shape as that shown in Figure 4.1a. The main (ΨBond) 2 = (ΨA + ΨB) 2 (4.20) difference is that we do not have the additional energy term associated with the formation of ions. The forces Equation 4.20 is shown as a function of internuclear involved are still electrostatic: distance in Figure 4.8. We can represent an MO pictorially in a manner  Attractive forces are forces between the electrons of similar to the way we do for AOs by outlining a shape that one atom and the nucleus of the neighboring atom. encloses most of the electron density and, consequently, is  Repulsive forces are forces between electrons on given by the molecular wave function. Figure 4.9 repre- neighboring atoms. sents the bonding MO formed by the combination of two 58 ............................................................................................................................................. B o n d s a n d E n e r g y Ba n d s  ψ2 Antibonding 1sA + 1sB MO σ* E 1sA 1sB AO AO 1s 1s A B r Bonding FIGURE 4.8 Distribution showing the probability of finding an MO electron at a given point in an MO as a function of distance. σb Atom A Molecule Atom B FIGURE 4.11 Energy level diagram for the H2 MOs and the 1sB corresponding AOs. + + + and antibonding MOs are referred to as σb and σ*, respec- 1sA tively. Figure 4.11 shows the relative energies of these MOs at r 0. From two 1s AOs, which have the same energy, FIGURE 4.9 Pictorial representation of a bonding MO obtained by summing two AOs. In this case the example is H2. we can construct two MOs. The bonding MO is lower in energy than the AOs and the antibonding MO is higher in energy. We can also form MOs from the overlap of p orbitals. There are three p orbitals that are equivalent in shape and 1s AOs. Because regions of high electron density lie volume but point along different coordinate axes. Figure between the atoms, covalent bonds are directional. The 4.12 shows six different kinds of MO formed from overlap directional nature greatly influences the atomic arrange- of the px, py, and pz orbitals. ments in covalently bonded solids and their mechanical properties. Diamond, a purely covalently bonded ceramic, On the convention of assigning coordinate axes: The line that is the hardest known material. connects the nuclei in a diatomic molecule is designated the We can also form an MO—called an antibonding z-axis and is thus common to both nuclei. The two sets of cor- MO—by subtracting the wave functions of the contribut- responding x- and y-axes are parallel. ing orbitals: The overlap of the pz orbitals is qualitatively similar to Ψ* = ΨA − ΨB (4.21) the overlap of s orbitals and the bonding MO is designated In the antibonding MO, illustrated in Figure 4.10, the electron density is greatly reduced in the overlap region – + + – – + – + and is zero midway between the nuclei. The antibonding 0 0 0 0 0 MO is less stable than the isolated AOs from which it is – + – – + – + derived and consequently is higher in energy. A(a) A(b) z A(a) A(b) z MOs that are symmetrical when rotated around a line joining the nuclei are called sigma (σ) MOs. The bonding σ zb σ z* + + + – X X – – X X – + 0 Nodal plane + + – z z A(a) A(b) 0 A(a) A(b) 0 + – + – σz b – – + πz * πzb FIGURE 4.12 MOs formed from the pz (top figure) and px (bottom FIGURE 4.10 Pictorial representation of the formation of an figure) AOs. The original AOs are shown at the upper right of each antibonding MO. An appropriate example would again be H2. MO. 4 . 4 C ova l e n t B o n d i n g ................................................................................................................................................. 59  AO MO AO AO MO AO σz* E σz* E πx* πy* 2p πx* πy* 2p 2p 2p σzb πxb πyb πxb πyb σzb σs* 2s 2s σs* σsb 2s 2s FIGURE 4.14 Energy level diagram for homonuclear diatomic molecule where s-p hybridization has occurred. σsb FIGURE 4.13 Energy level diagram for homonuclear diatomic molecule where there is negligible s-p hybridization. neglect mixing. However, in the case of elements to the left of F in the periodic table mixing between the 2s and 2p AOs is important and results in a change in the order of the levels as shown in Figure 4.14. An sp hybrid orbital formed from one s orbital and a σbz. The two px orbitals and the two py orbitals do not single p orbital is illustrated in Figure 4.15. A combination overlap along the z-axis, rather they overlap above and below it. This type of MO is called a π orbital. The π MOs that concentrate electron density in the region between the two nuclei are known as π bonding MOs. The combination + of px orbitals produces a bonding MO πbx, while the com- bination of py orbitals produces a bonding MO πby. These two MOs have the same shape and energy, but are – orthogonal. Following the convention used for the antibonding σ MOs, the π antibonding MOs are denoted by π*x and π*. y Assuming no mixing of the s and p orbitals, the relative energies of the MOs are s+p σbs < σ*s < σzb < πbx = πby < π*x = π*y < σ*z A diagram of these energy levels is shown in Figure 4.13. It was constructed by allowing only those interac- tions between those orbitals on atom A and atom B, which – + have the same energy. Actually interactions can occur between AOs on the same atom provided that the energy between the orbitals is not too large. This new arrange- s-p ment of the electrons is called hybridization. Hybridization of Atomic Orbitals + In atoms containing AOs that are close in energy different – orbitals can mix to give so-called hybrid orbitals. Mixing between 1s and 2s orbitals will not occur. For example, in Na the energy difference between these orbitals is 9 MJ/mol. The energy difference between the 2s and 2p orbitals is less and varies with Z. In F, the energy differ- FIGURE 4.15 Two sp hybrid orbitals formed by adding and ence between the s and p orbitals is large enough that we subtracting the corresponding wave functions. 60 ............................................................................................................................................. B o n d s a n d E n e r g y Ba n d s of s and p orbitals causes reinforcement in the region in Z which the sign of the wave function is the same and can- cellation where the signs are opposite. 2s (all +) We can represent these situations mathematically: Y Ψsp1 = Ψs + Ψp (4.22) sp3 Ψsp2 = Ψs − Ψp (4.23) + sp3 X + where Ψs and Ψp are the wave functions of an s and p Mixing orbital and Ψsp1 and Ψsp2 represent the new sp orbitals. This Z sp3 process is very similar to the formation of MOs. Keep in + 2pz + sp3 mind, however, that in the present case we are combining + two or more orbitals on the same atom to form a new set – of hybrid AOs. – 2py sp3 hybrid orbitals Y + + Hybridized Orbitals in Ceramics – X 2px A very important example of hybridization occurrs between one s orbital and three p orbitals to form sp3 FIGURE 4.16 Formation of sp3 hybrid orbitals. hybrid orbitals. In carbon, the ground state electron con- figuration is 1s22s22p1x2p1y; in this state carbon would be divalent because only the unpaired electrons in the px and py orbitals are available for bonding. To form four bonds, carbon must be raised to its valence state. This requires the promotion of one of the s electrons from the 2s orbital from each neighboring carbon, forming four bonds. The to the formerly empty 2pz orbital. The electron configura- four electrons from the central carbon and one from each tion now becomes 1s22s12p1x2p1y2p1z. This promotion costs neighboring carbon are just sufficient to fill the bonding 406 kJ/mol, but is more than compensated for by the for- MOs. The four antibonding orbitals are empty. In diamond, mation of two extra C–C bonds. The C–C bond energy is the bonding and antibonding MOs are separated by a large 348 kJ/mol. energy as shown in Figure 4.17. This energy gap is the Hybridization between the 2s, 2px, 2py, and 2pz orbitals reason diamond is an electrical insulator at room tempera- occurs to form four equivalent sp3 hybrid orbitals, as ture. (We will discuss the energy gap again in Section 4.8 shown for carbon in Figure 4.16. Each sp3 hybrid orbital and Chapter 30.) has 25% s and 75% p character. The four sp3 orbitals are Several other important ceramic materials in which directed toward the corners of a regular tetrahedron. Thus, the bonding is predominantly covalent have tetrahedral in diamond each carbon atom has four localized tetrahe- dral sp3 hybrid orbitals. A C–C MO is formed when orbit- als from neighboring carbon atoms combine. The angle between three carbon bonds is 109°28′. For covalently bonded materials that show tetrahedral coordination, sp3 E σ* hybridization must occur. π* Points to Note: σ* πo  Promotion of electrons to form an excited state can p occur independently of hybridization. 2p π  Hybridization prohibits certain configurations and sp3 sp2 allows others (C hybridizes sp3 in diamond and sp2 in 2s graphite). σ  The local atomic order depends upon mutual repulsion σ of the valence electrons and space requirements.  The structure a material adopts is the one that has the lowest energy. s 1s 1s 1s s In diamond, for each tetrahedral group there are four Diamond CC4 C(sp3) C C (sp2) CC3 Graphite 3 sp orbitals associated with the central carbon and one FIGURE 4.17 Energy level diagram for diamond and graphite. 4 . 4 C ova l e n t B o n d i n g ................................................................................................................................................. 61 coordination of nearest-neighbor atoms, for example, The spatial arrangement of atoms around each N atom silicon carbide (SiC) and aluminum nitride (AlN). In these is the same as that around each B atom. Structurally there materials sp3 hybridization has occurred but, because of are many similarities between h-BN and graphite and both the different electronegativities of the constituent atoms, can be converted under high temperature and pressure into the electron density will not be symmetrical in a plane a cubic form. The crystal structures of cubic boron nitride drawn between the atoms. The crystal structure of these (c-BN) and diamond are similar. However, unlike graph- materials is described in Chapter 6. ite, h-BN is an electrical insulator. The reason for this In graphite, the carbon atoms are in a trigonal planar difference is that the pz orbitals in h-BN, which lie per- arrangement with each carbon bonded to three nearest pendicular to the plane of the network, are either empty neighbors. The carbon is sp2 hybridized. Hybridization in the case of B or filled in the case of N. Because the occurs between the C 2s orbital and the 2px and 2py orbit- energies of the p orbitals on B and N are quite different, als producing three hybrid orbitals lying in a plane at 120° there is little interaction, with no delocalization as was the to each other. Overlap of the sp2 hybrid orbitals to produce case in graphite. localized bonds between carbon atoms results in a hexago- nal network.  h-BN is a white or colorless insulator. The strong bonding between carbon atoms causes  Graphite is a shiny black or gray electrical overlap of adjacent 2pz orbitals, which are aligned perpen- conductor. dicular to the plane of the hybrid orbitals. This overlap is termed π-type overlap. Since the 2pz orbital is half-filled Hybridization can also involve d orbitals (for atoms the π band will only be half full as shown in Figure 4.17. with Z > 21). The shapes produced are more complicated This half-filled band is why graphite has a high electrical than those for hybridization only between s and p conductivity. orbitals. Table 4.7 lists some hybrid orbitals containing s, In hexagonal boron nitride (h-BN), which has a struc- p, and d orbitals and these are illustrated in Figure 4.18. ture similar to graphite, the bonding between the B and Hybridization involving s, p, and d orbitals occurs in N atoms is predominantly covalent and the trigonal planar MoS2. Mo (Z = 42) has the electron configuration [Kr] structure in the layers is a result of sp2 hybridization of the 4d5 5s1. One of the 4d electrons is promoted into the empty atomic orbitals of the B and N atoms. The ground state px orbital to give the following electron configuration: electronic configuration of B is 1s22s22p1x; one 2s electron [Kr] 4d4 5s1 5p1x. Hybridization occurs to produce d4sp is promoted to the 2py orbital giving the electron configu- hybrid orbitals on each Mo atom, resulting in trigonal ration 1s22s12p1x 2p1y. The unfilled 2s and 2p orbitals hybrid- prismatic coordination with each Mo being surrounded by ize to form three equivalent sp2 hybrid orbitals. Nitrogen six sulfur atoms. has the electronic configuration 1s22s22pxpypz. Promotion For most ceramic materials we will not need to con- of one of the 2s electrons gives the following electron sider hybridization involving d orbitals. However, even configuration to the atom 1s22s2px2py2p2z . The three half- when they are not involved in bonding the d orbitals can filled orbitals combine to give three sp2 hybrids in the xy be extremely important in determining the properties of plane. materials (particularly magnetism). TABLE 4.7 Orbital Geometries for Hybridization Number of bonds Representation Shape Example 2 sp Linear BeH2, HgCl2 2 3 sp Trigonal B2O3, BN, graphite 4 sp3, Tetrahedral SiO2, diamond dsp2 Square planar AuBr4 5 dsp3, d3sp, Trigonal bipyramid PCl5 d2sp2, d4s Square pyramid IF5 6 d2sp3, Octahedral MoO3 d4sp Trigonal prism MoS6 in MoS2 8 d4sp3, Dodecahedral — d 5p3 Square antiprism — 62 ............................................................................................................................................. B o n d s a n d E n e r g y Ba n d s  180° 120° 90° sp sp2 dsp2 1 109 2° 90° 90° 120° sp3 dsp3 d 2sp3 FIGURE 4.18 Geometric arrangements of some hybrid orbitals involving s, p, and d AOs. 4.5 METALLIC BONDING IN CERAMICS  TiN is gold in color and is an electrical conductor.  TiN has a very high melting point (2949°C) and is Metallic bonding is the primary bond in metals and can brittle at 25°C. be thought of as an electrostatic interaction between the delocalized valence electrons and the positively charged The former suggests it is a metal; the latter properties are ion cores. It is the delocalized electron gas that gives rise associated with ceramics. The bonding in transition metal to many of the characteristic properties of metals such as carbides and nitrides is very complex. It consists of a high electrical and high thermal conductivities. Metallic combination of metal-to-metal and metal-to-nonmetal bonds do not require a balance of the electric charge interactions and involves simultaneous contributions of between the elements; the electrostatic equilibrium is metallic, covalent, and ionic bonding. between the metal ions and the electron gas. For this The exact details of the bonding mechanisms in these reason different elements can mix in metallic alloys in ceramics are still controversial, and several different arbitrary ratios. approaches to explain the wide range of observed proper- Metallic bonding is traditionally neglected because of ties have been suggested. One common feature to all the the definition of a ceramic. However, some compounds proposed mechanisms is that of orbital hybridization. that are thought of as ceramics can, under certain condi- Hybridization of the s, p, and d orbitals of the transition tions, show metallic behavior. Others can even be super- metal as well as hybridization of the s and p orbitals of conducting. (Superconductivity is a property associated the nonmetal has been proposed. with both metals and ceramics.) So it helps to keep a more The transition metal borides also show characteristics open view of ceramics. of covalent and metallic materials. The bonding in the In addition to bonds showing mixed covalent and ionic borides is also complicated by the fact that there are inter- character, the bonding in some ceramics shows partial actions between the B atoms to form chains, layers, or metallic character. Transition metal carbides (e.g., TiC and three-dimensional networks. In the carbides and nitrides Mo2C) and nitrides (e.g., TiN and NbN) have properties there are no C–C or N–N interactions. Despite these com- that suggest both metallic and covalent bonding occurs in plexities we can still use some of the same approaches that the crystal. we use for simple oxides (Chapter 6) to predict the crystal 4 . 5 M e ta l l i c B o n d i n g i n C e r a m i c s .......................................................................................................................... 63 structure of these ceramics. The point to remember is that the bonding in ceramics is usually mixed and is occasion- ally very complex. Many of the new ceramics are interest- ing because of their special properties and these often occur because the bonding is mixed. 4.6 MIXED BONDING LiH From the preceding sections it should be clear that in ceramics we do not usually have pure ionic bonds or pure covalent bonds but rather a mixture of two, or more, dif- ferent types of bonding. Even so it is still often convenient and a frequent practice to call predominantly ionically BeH BH bonded ceramics “ionic ceramics” and predominantly covalently bonded ceramics “covalent ceramics.” From the series of electronegativity values we can form some general rules about bonding.  Two atoms of similar electronegativity will from either a metallic bond or a covalent bond, according CH NH to whether they can release or accept electrons, respectively.  When the electronegativities differ the bond is partially ionic. The ionic character of a bond increases with the dif- ference in electronegativity of the two atoms as shown by OH FH Eq. 4.24: FIGURE 4.19 Contours of constant electron density in the first row hydrides. Fraction of ionic character = 1 − exp[−0.25 (XM − XX) 2] (4.24) 4.7 SECONDARY BONDING XM and XX represent the electronegativities of M and X Secondary bonds are so called because the compound (keeping the cation/anion labeling). Using Eq. 4.26 and involved invariably also has ionic or covalent bonding. electronegativity values in Table 3.6 we can see that B4C, Secondary bonds are generally much weaker than primary SiC, and BN are highly covalent (6%, 12%, and 22% ionic bonds, although they can be critical in determining both character, respectively). Oxides of the alkali metals and the existence of a particular crystal structure and the prop- alkaline-earth metals are predominantly ionic. The metal– erties of a material. oxygen bond in MgO has 73% ionic character and 82% van der Waals Bonding ionic character in BaO. Some important ceramics fall in between these limits, for example, GaN (38% ionic char- The origin of van der Waals bonding (known also as the acter), SiO2 (51% ionic character), ZnO (59% ionic char- London interaction) is weak electrostatic attraction between acter), and Al2O3 (63% ionic character). In bonding that closely spaced neutral atoms and molecules. The explana- shows mixed ionic-covalent characteristics, the electrons tion for this universally attractive force is that even a neutral are located closer to the electronegative atom (compare atom has a charge distribution that fluctuates very rapidly. the electron densities around the Li + and F− ions in When two atoms are brought together the fluctuations in Figure 4.19). one can induce a field around the other and this coupling Since the covalent bond is directional, while the ionic results in the attractive force. Although van der Waals bond is not, the degree of directionality changes with bond bonding is present in all crystalline solids it is important character. Such changes can have a marked influence on only when not overwhelmed by strong bonding forces. crystal structure. Both ionic and covalent bonds can be The energy of a crystal bound by van der Waals forces very strong, but since covalent bonds are directional, can be expressed by the Lennard–Jones potential with two covalent materials respond differently to deformation. The constants, ALJ and BLJ fraction of covalent character can thus influence the A B E = − LJ + 12LJ (4.25) mechanical properties of the ceramic. r6 r 64 ............................................................................................................................................. B o n d s a n d E n e r g y Ba n d s  Again, the potential is empirical: it provides a good fit over one another easily so that MoS2 has mechanical prop- to the experimental data. Both the repulsive and attractive erties that are similar to those of graphite. terms decrease rapidly with increasing r. The attractive van der Waals forces are proportional to 1/r 7 and are, Hamaker Constant therefore, of much shorter range than the ionic (Coulom- van der Waals interactions are just as important at the bic) forces, which are proportional to 1/r 2. macroscopic level, where they can influence behavior such In ceramics, van der Waals bonding is important in as wetting and fracture, as they are at the atomic and layered structures. In pyrophyllite, a layered silicate, van molecular level. The interaction energies between differ- der Waals bonds between the oxygen ions in adjacent ent macroscopic geometries can be described in terms of layers allow easy slip parallel to the layers. In the mineral the Hamaker constant, as shown in Figure 4.20. talc, van der Waals bonds between the layers are even weaker than in pyrophyllite. You can cleave talc with your = π2 ALJρ1ρ2 (4.26) fingernail. In graphite and hexag- where ALJ is the coefficient onal boron nitride there is TYPICAL VALUES IN CALCULATING in Eq. 4.25 and ρ1 and ρ2 are strong covalent bonding the number of atoms per within each layer. Between ALJ ∼ 10−77 J m6 unit volume in the two the layers the bonding is ρ ∼ 3 × 1028 m−3 (for r ∼ 0.2 nm) bodies. Typical values for van der Waals. These Hamaker constants are materials show highly about 10−19 J for interactions anisotropic properties, for example, in their mechanical across vacuum (or air); values for some ceramics are listed strength. Little effort is required to separate the sheets, but in Table 4.8. We can use these values to estimate the strength much more effort is required to break them. of the van der Waals interactions between, for example, two MoS2 has a structure built of MoS6 units where each spherical particles using the equations in Figure 4.20. Mo is surrounded by six S atoms. The layers are joined Remember that the forces are obtained by differentiating the by van der Waals bonds between the S atoms and can slip energies with respect to distance. Two spheres R1 R2 Two crossed cylinders p2 R2 p1 D -A R1R2 W= 6D (R1+R2) R1 Sphere–surface W = -A R1R2/6D D R Two cylinders R1 R2 D W = -AR/6D L Two surfaces 1/2 AL D W= 12 2 D3/2 ( R1R2 R1+R2 ) W = -A/12πD2 per unit area FIGURE 4.20 Interaction energies for macroscopic geometries. The key is the Hamaker constant, . 4 .7 S e c o n da ry B o n d i n g ............................................................................................................................................... 65  TABLE 4.8 Hamaker Constant 4.8 ELECTRON ENERGY BANDS IN CERAMICS Material (zJ) Al2O3 The energy levels for electrons in a single isolated 140 Fe3O4 atom are highly discrete and given by Box 3.6 in 210 ZrO2 Chapter 3. When a number of atoms are brought 270 TiO2 430 together to form a solid the Pauli exclusion principle SiC 440 does not allow any two electrons to have the same set Fused quartz 63 Mica of four quantum numbers. The energies that were 100 CaF2 identical in the isolated atoms shift relative to one 70 another in the formation of a molecule and subsequently a solid. The sharply defined electronic energy levels TABLE 4.9 Hamaker Constants for Fused Quartz Interact- broaden into an allowed band of energies when a ing with Air across Another Medium large number of atoms are brought together to form a Medium (zJ) solid. We illustrated how this happens in diamond and graphite in Figure 4.17. Water −8.7 If we think of a solid as just a very large molecule then Octane −7 Tetradecane −4 we can view the formation of electron energy bands as arising from a combination of a large number of MOs. As the molecule becomes larger, the number of MOs increases Things, as you might expect, are actually a little more and they become more closely spaced in energy. In a solid complicated than Eq. 4.26 implies. We need, as in the the number of MOs is so large that we can regard them calculation of the Madelung constant, to consider the simply as a continuous band of energy levels. influence of neighboring atoms on the interaction between If we consider the case of diamond, the highest occu- any pair of atoms. An alternative method developed by pied band, referred to by chemists as the highest occupied Lifshitz (1956) for determining uses bulk properties of molecular orbital (HOMO), is σb. The lowest unoccupied a material such as dielectric constants and refractive band, referred to as the lowest unoccupied molecular indices. The values given in Table 4.8 were calculated orbital (LUMO), is the σ*. Although the bands themselves using this approach. In general, materials with high dielec- are important, the most significant aspect of these dia- tric constants and refractive indices have higher values of grams is the energy gap between bands. Knowledge of the . If the interactions occur across a medium then the band gap energy, which is related to chemical bonding, value and sign of may change as shown in Table 4.9. will allow us to draw important conclusions about the electrical conductivity of a material. The effect of distance on the formation of energy Hydrogen Bonding bands is illustrated in Figure 4.21. The closer the atoms Hydrogen bonds are usually stronger than van der Waals are together the more marked is the shift in available bonds but still considerably weaker than primary bonds. energy states. The higher energy states broaden first. Hydrogen bonds occur when a hydrogen atom that is in an Broadening of the lower energy states, which are closer to ordinary covalent bond joins another, usually highly elec- the nucleus, is less marked. tronegative atom. The classic example in which such bonds In materials science we usually define the highest are important is, of course, water. The H–O bonds in the filled electron energy band when the material is in its H2O molecule are fully saturated, yet the bonds between ground state as the valence band. The lowest energy band the molecules can be so strong that ice forms with a well- containing unoccupied states when the material is in its defined crystal lattice. ground state is the conduction band. At absolute zero the In kaolinite, hydrogen bonds can form between basal electrons occupy the lowest available energy states; the oxygen atoms of one plane and the upper hydroxyl groups energy of the highest occupied state is the Fermi energy, of the next. The weak EF. This energy level sepa- hydrogen bonding be- rates the occupied from the tween each octahedral– DENSITY OF STATES unoccupied electron levels 3 tetrahedral double layer only when the electron π 8m 2 1 makes the materials very N (E ) = ⎛ 2 ⎞ E 2 configuration is in its anisotropic. Layers easily 4⎝ h ⎠ ground state (i.e., at 0 K). slip over one another giving A solid behaves as an Fermi–Dirac distribution: the material a greasy feel insulator if the allowed and making it excellent for 1 energy bands are either molding, particularly when P (E ) = filled or empty, for then no exp [( E − EF ) / kT ] + 1 water is present. electrons can move in an 66 ............................................................................................................................................. B o n d s a n d E n e r g y Ba n d s  0 3d 4s 3p N (E) Density E (eV) of 3s States E -10 1.0 P (E) Fermi Ro = 0.367 nm Function E EF -20 F (E) Electron Distribution Function E EF FIGURE 4.22 Electron distribution functions. -30 2p In this book we will primarily represent the energy levels 0 0.5 1.0 R (nm) 1.5 of a solid as the familiar and simple block diagrams showing the band gaps. This approach is straightforward, FIGURE 4.21 Formation of electron “bands” as the interatomic but the question that is often asked is what are we plotting spacing is reduced. on the x-axis? A more satisfactory form is illustrated in Figure 4.23 where we plot the density of states versus energy. Either description allows the prediction of the electric field. Metals always have a partially filled valence electrical properties of a material based on the size of Eg. band; the Fermi energy is in the middle of the band and So we can determine whether a material will behave as a this makes the metals electrical conductors. In semicon- conductor or an insulator. ductors and insulators we always have completely filled or It is possible to convert an insulator to a metal under completely empty electron bands; the Fermi energy lies very high pressures as a result of the broadening of the between the bands, and consequently they are not good energy bands that occurs when the atomic cores are moved electrical conductors at ambient temperatures. closer together as shown in Figure 4.24. If we assume that Classically, the valence and conduction bands in the Fermi level does not change, then the material will ceramics are well separated, so they are insulators. In undergo a transition from insulator to metal at the point perfect insulators the gap between bands is so large that at which the valence and conduction bands begin to thermal excitation is insufficient to change the electron overlap. Very high pressures are required to cause this energy states, and at all temperatures the conduction band type of transition. For example, germanium is usually a contains essentially zero electrons and the next lower band of energy is completely full, with no vacant states. In models of electrons in solids we usually introduce two functions: P(E) T = finite T = 0° K I  Density of states, N(E), defines the number of energy N (E) II and N(E) states available to electrons. There are no available P (E) N(E) energy states in the band gap and so N(E) is zero in this region.  Fermi function, P(E), defines the probability of finding Valance band Conduction band an electron at a particular energy state. These functions are shown graphically in Figure 4.22 E Eg > 2-3 eV together with the electron distribution function F(E): EF FIGURE 4.23 Plot of the density of states function and Fermi F(E) = 2N(E)P(E) (4.27) function versus energy. 4 . 8 E l e c t r o n E n e r g y Ba n d s i n C e r a m i c s ............................................................................................................... 67  Conduction Insulator/Semiconductor Metal Ε Ε Band E hν+ Conduction band hν EF Valence Eg Band Valence band k k FIGURE 4.25 Illustration of direct and indirect band gap transi- P tions. Energy is plotted versus wave vector. FIGURE 4.24 Plot of energy versus pressure illustrating how an insulator-to-metal transition can occur at high pressures. Atom Molecule Nanoparticle Solid E TABLE 4.10 Critical Pressure for Metal–Insulator Transfor- mation at 300 K Material P (GPa) C 168 BN 211 SiC 64 AlN 90 GaN 87 FIGURE 4.26 Illustration of how the energy band gap arises in a nanoparticle. semiconductor with a band gap of 0.7 eV. It becomes a metal under a pressure of 12 GPa. Examples of critical indirect band gap. It is direct band gap materials that are pressures for insulator–metal transitions at 300 K in some of most interest for optoelectronic applications. ceramics are given in Table 4.10. The probability of electronic transitions across the To understand some of the optical properties of ceram- band gap is higher in materials with a direct band gap and ics and why certain materials may be favored for solar cell this results in higher efficiency in devices such as lasers or laser applications, we need to know whether the band and LEDs. gap is direct or indirect. The two situations are illustrated Before we leave this chapter a word must be given in Figure 4.25. The electrons in a band have both energy about nanomaterials. The value of Eg for nano-sized and momentum (they are not bound) expressed as a wave crystals is often significantly larger than for the bulk form vector, k, with units of reciprocal length (usually cm−1). of the material. This is associated with how the bands Energy diagrams can be plotted for different broaden as the number of atoms in the solid increases as wave vectors. illustrated in Figure 4.26. In direct band gap materials the top of the valence As an example, bulk silicon has Eg = 1.1 eV. For nano- band and the bottom of the conduction band are located crystalline silicon Eg varies with the size of the crystals at the same point in k space. This is not the case for an and for sizes less than 2 nm Eg > 2 eV. CHAPTER SUMMARY This chapter was a review of things that you already knew. There are three types of primary bonds that are used to hold atoms together. In introductory materials science classes we tend to think of each type of bond as being a distinct form, with materials adopting one type or another. At a qualitative level this approach might work, and in the cases of many metals, semiconductors, and polymers it is usually quite close to the actual situation we encounter. However, in ceramics almost every bond has a mixture of covalent, ionic, and, in some cases, metallic character. The type of interatomic bond affects the crystal structure that a material adopts. The influence of mixed bonding can mean that the type of structure predicted, based 68 ............................................................................................................................................. B o n d s a n d E n e r g y Ba n d s  on either purely ionic or purely covalent bonding, is incorrect. The role of hybridization, or mixing, of atomic orbitals is very important in ceramics, which are predominantly covalently bonded. For example, the tetrahedral coordination of carbon atoms in diamond requires the sp3 hybridization. We discussed the concept of energy bands here, both in terms of the broadening of electron energy states and also from the MO approach. Knowledge of electron energy band diagrams is essential in understanding the electrical properties of materials. The most important feature of the energy band diagram is the band gap. There are no available states in this region. Secondary bonding is also important in many ceramics. The most familiar properties of graphite, hexagonal-BN, and clay minerals are determined by the presence of weak secondary bonds. PEOPLE IN HISTORY Born, Max was born in Breslau in 1882. He graduated from the University of Göttingen in 1907 where he worked on the stability of elastic wires and tapes. During the World War I he had to join the German Armed Forces where in a scientific office he worked on the theory of sound ranging. After the war he was appointed Professor at the University of Frankfurt-on-Main. In 1933 he was forced to emigrate from Germany and came first to Cambridge University in England, then to the Indian Institute of Science in Bangalore, and finally to the University of Edinburgh in Scotland, where he worked until his retirement in 1953. He won the 1954 Nobel Prize in Physics and died in 1970. Haber, Fritz was born in Breslau, Germany in 1868. He completed his studies at the University of Heidelberg, the University of Berlin, and the Technical School at Charlottenberg. The Haber process for the synthesis of ammonia was patented in 1908 and by 1914 the process was into quantity production. Ammonia was important in Germany’s war efforts as a source of nitric acid, which is essential for the manufacture of explosives. It is clear that this prolonged the war. Haber was given the 1918 Nobel Prize in Chemistry (actually awarded in 1919) for his work on nitrogen fixation. In 1933 Haber resigned from his post as Director of the Institute for Physical and Electrochemistry at Berlin-Dahlem. He died in exile in Switzerland in 1934. Madelung, Erwin was born in 1881 in Bonn, Germany. From 1921 to 1949 he was Professor of Theoretical Physics at Frankfurt University. He died in 1972. van der Waals, Johannes Diderik was a Dutch physicist, born in Leyde in 1837; he died in Amsterdam in 1923. He was awarded the Nobel Prize for physics in 1910 for his work on the equation of state for gases and liquids. Young, Thomas was born in 1773. His accomplishments include his introduction of the Modulus of Elasticity. He is best known for his work in optics. He died in 1829. GENERAL REFERENCES Huheey, J.E. (1993) Inorganic Chemistry: Principles of Structure and Reactivity, 4th edition, Harper & Row, London. If the different interactions are not familiar to you from introductory chemistry or materials science classes, this text covers the material in some detail. Kittel, C. (2004) Introduction to Solid State Physics, 8th edition, Wiley, New York. A more rigorous and mathematical treatment of energy bands than we give in this chapter. Pauling, L. (1960) The Nature of the Chemical Bond, Cornell University Press, Ithaca, NY. Often referenced and well worth seeing. SPECIFIC REFERENCES Born, M. (1919) “A thermo-chemical application of the lattice theory,” Verhandl. Deut. Phys. Ges. 21, 13. Born, M. and Mayer, J.E. (1932) “Lattice theory of ionic crystals,” Z. Phys. 75, 1. Chase, M.W., Jr. (1998) NIST-JANAF Thermochemical Tables, 4th edition, American Chemical Society, Washington D.C.; American Institute of Physics for the National Institute of Standards and Technology, New York. Haber, F. (1919) “Theory of the heat of reaction,” Verhandl. Deut. Phys. Ges. 21, 750. Hamaker, H.C. (1937) “London-van der Waals attraction between spherical particles,” Physica 4, 1058. The original. Johnson, D.A. (1982) Some Thermodynamic Aspects of Inorganic Chemistry, 2nd edition, Cambridge University Press, Cambridge, UK. Kubaschewski, O., Alcock, C.B., and Spencer, P.J. (1993) Materials Thermochemistry, 6th edition, Elsevier, Oxford, UK. Lande, A. (1920) “Size of atoms,” Z. Phys. 1, 191. C h a p t e r S u m m a ry .......................................................................................................................................................... 69  Lifshitz, E.M. (1956) “The theory of molecular attractive forces between solids,” Soviet Phys. JETP–USSR 2, 73. Madelung, E. (1918) “The electric field in systems of regularly arranged point charges,” Phys. Z. 19, 524. Shannon, R.D. and Prewitt, C.T. (1969) “Effective ionic radii in oxides and fluorides,” Acta Crystallogr B25, 925. Gives the alternatives to Pauling’s radii. Shannon, R.D. (1976) “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,” Acta Crystallogr. A32, 751. van Vechten, J.A. (1973) “Quantum dielectric theory of electronegativity in covalent systems. III. Pressure- temperature phase diagrams, heats of mixing, and distribution coefficients,” Phys. Rev. B7, 1479. WWW http://www.lrsm.upenn.edu/~frenchrh/hamaker_software.htm. Roger French’s site for calculating the Hamaker constant. www.deconvolution.com/Overview/170.htm. More on Hamaker. EXERCISES 4.1 By considering the hybridization of orbitals in diamond explain why it is (a) an electrical insulator at room temperature and (b) extremely hard. 4.2 Why are covalently bonded materials in general less dense than metallically or ionically bonded ones? 4.3 Calculate the force of attraction between a Na + and a Cl− ion the centers of which are separated by 1.5 nm. 4.4 Calculate Born–Landé lattice energies of the following compounds: NaCl, KCl, and CsCl. Compare the values you obtain to those given in Table 4.5 and discuss any differences. 4.5 Sketch bond-energy curves for two ceramics, one with a high Young’s modulus and one with a low Young’s modulus. 4.6 Rank the following ceramics in terms of increasing fraction of ionic character in their bonds: SiC, AlN, Si3N4, B4C, GaN, Al2O3, and SiO2. 4.7 Sketch a bond-energy curve for two atoms held together by van der Waals forces. Describe how this curve differs from the one shown in Figure 4.1, which is for ionic bonding. 4.8 What do we mean by the term “insulator–metal transition.” Are there any practical applications for such a transition? 4.9 Estimate the force of adhesion between two spherical Al2O3 particles of radius 1 mm separated by a distance of 10 nm. How does the force change as the separation increases? 4.10 Estimate the surface energy of Al2O3. Assume that for two surfaces in contact D ∼ 0.2 nm. 70 ............................................................................................................................................. B o n d s a n d E n e r g y Ba n d s  5 Models, Crystals, and Chemistry CHAPTER PREVIEW Most ceramics are crystalline. The exception is glass, which we usually discuss separately. Not only do the properties of ceramic crystals depend on how the atoms or ions are arranged, but the type and nature of defects also depend on crystal structure. You probably first encountered crystallography when discussing metals. Sixty-five (almost 90%) of the metallic elements are either cubic or hexagonal. In ceramics, many of the most important materials are neither cubic nor hexagonal, so we need to be more familiar with the rest of the subject. It is recommended that you memorize the main structures described in Chapters 6 and 7. In this chapter we provide the means to make this study more systematic. To understand why ceramics have particular structures and why certain defects form in these structures, it is really important to understand Pauling’s rules. These rules require you to visualize a tetrahedron and an octahedron and to see how they fit together. To understand properties such as piezoelectricity or the mechanisms of phase transformations, you must be able to visualize the crystal structure of the material. This is particularly important when we want to predict the properties of single crystals. We summarize the features of crystallography that we use throughout the text and give references to more specialized resources for rigorous proof of theorems and more detailed discussion. An important point to keep in mind is that the term “ceramic” generally refers to materials that have been processed in the laboratory or the factory plant but that often do exist in nature. Sometimes the natural minerals are rare such as moissanite, which is now being manufactured as a gemstone. There are far more materials and structures in nature than are used in tech- nology. Understanding the basic principles and knowing where to learn more about minerals may help you find the next monazite or at least to know why it might be useful. A great source for further reading lies in the mineralogical literature. 5.1 TERMS AND DEFINITIONS 1. The unit cell should have the same symmetry as the crystal—the base vectors are parallel to symmetry We will begin by defining the vocabulary of the subject. axes or perpendicular to symmetry planes. Most of this section should be familiar to you from other 2. The origin of the unit cell is usually a center of courses. symmetry. Crystal Lattice: A three-dimensional array of 3. The base vectors should be as short as possible and the points related by translational symmetry. The translation cell volume should be as small as possible. The excep- can occur in three independent directions giving tions arise when choosing a longer vector and a larger three independent base vectors. We can fully describe cell makes the symmetry more obvious. such a lattice by three vectors, a, b, c, and three 4. The angles between the axes should be as close as angles, α, β, γ. The special property of a crystal lattice possible to 90°, or if not then >90°. is that the lattice points are identical: if we have an 5. A unit cell having the smallest possible volume is atom at or near one point, there must be an identical called a primitive cell. atom at the same position relative to every other lattice point. Lattice Parameters: The vectors a, b, c and the angles Unit Cell: The vectors a, b, c define a cell. There is, α, β, γ are called the lattice parameters of the unit cell. in principle, an infinite number of ways to define a unit Tabulated lattice parameters are, unless otherwise stated, cell in any crystal lattice. But, as in many areas of crystallo- values at room temperature and pressure. They vary with graphy, there is a convention: changes in temperature or pressure. 5 .1 Te r m s a n d D e f i n i t i o n s ......................................................................................................................................... 71  Crystal System: There CRYSTAL SYSTEMS N N are seven unique shapes N = Ni + f + c (5.1) All crystals belong to one of the seven crystal systems. 2 8 that can each be used to fill three-dimensional space. Basis: Group of atoms These are the seven crystal systems into which all crystals associated with each and every lattice point. We can are classified. They are listed in order of increasing sym- describe crystal structures in terms of a Bravais lattice and metry in Table 5.1. a Basis: Bravais Lattices: There are 14 different ways to arrange lattice points. These are constructed as three separate types: Bravais Lattice + Basis = Crystal Structure (5.2)  Primitive (P) lattices—one lattice point per unit cell This approach is often used by solid-state physicists and  Body-centered (I) lattices—a lattice point at the corners is particularly useful when we want to determine the and one in the center of the cell structure factor of a crystal. Crystal structures are formed  A-, B-, C-, or F-centered lattices—a lattice point at the by placing a basis of atoms either on the points of a corners and others at one (A, B, C) or all three (F) of Bravais lattice or in some fixed relation to those points. the faces There may be no atoms actually located on the lattice points. The 14 Bravais lattices are shown in Figure 5.1. For reasons Coordination Number (CN): Number of nearest of symmetry (Rule 1 above) we do not always choose a neighbors. primitive cell. The face-centered cubic cell may be referred Symmetry Elements: These symmetry elements are to the rhombohedral cell (which is primitive), but the easy to understand because you can see them by handling cubic cell reflects the higher symmetry of the lattice. real crystals or crystal shapes. For example, crystals of Lattice Points Per Cell: Primitive cells have only one MgO are cubic and calcite (CaCO3) is trigonal as shown lattice point per cell whereas nonprimitive cells have more in Figure 5.2. They apply to macroscopic shapes, but we than one. A lattice point in the interior of a cell (Ni) can limit our choice by ignoring those in which the shape be thought of as belonging entirely to that cell; one in a could not correspond to the unit cell of a crystal. cell face (Nf ) is shared by two cells and a corner one (Nc) is shared by eight. The number of lattice points (N) per  Rotation Axis. Clockwise rotation of 360°/n about the cell is given by axis. Crystals may have 2-fold (diad), 3-fold (triad), 4-fold (tetrad), or 6-fold (hexad) rotation axes; the 1- fold axis is always present. Any other rotation, such as a 5-fold axis, is not consistent with the requirement TABLE 5.1 The Seven Crystal Systems that a crystal lattice must have translational Relationship between symmetry. System lattice parameters Example  Mirror Plane. When a plane can be chosen such that all features on one side of the plane appear, as if in a Triclinic a≠b≠c Turquoise α ≠ β ≠ γ ≠ 90° Kyanite mirror, on the other side of the plane, then the crystal Albite feldspar has a mirror plane (also known as a plane of sym- Monoclinic a≠b≠c Monazite metry). We call this an m plane. α = γ = 90°; β ≠ 90° Titanite  Center of Symmetry. If every feature in or on the object Orthoclase can be joined by an imaginary line through the center Orthorhombic a≠b≠c Olivine of the object to an identical feature, then we say the α = β = γ = 90° Brookite object has a center of symmetry. Stibnite  Inversion Axis. If when any point is rotated about an Tetragonal a=b≠c Zircon axis and then moved through the center of symmetry α = β = γ = 90° Rutile it arrives at an identical point, then the object has an Hausmannite inversion axis. Hexagonal a=b≠c High quartz α = β = 90°; γ = 120° Wurtzite We refer to such axes as 1̄, 2̄, 3̄, 4̄, or 6̄ axes. Notice Beryl that the 1̄ axis is, in fact, describing a center of symmetry. Rhombohedral a=b=c Ilmenite The 2̄ axis is an alternative description of an m plane. (or Trigonal) α = β = γ ≠ 90° Calcite There are other symmetry elements such as screw axes Corundum that are meaningful for crystals but not for our macro- Cubic a=b=c Halite scopic crystal shapes. Figure 5.3 illustrates some of the α = β = γ = 90° Magnetite symmetry elements for a cube. The most important are the Garnet four 3-fold axes along the <111> diagonals. 72 ............................................................................................................................ M o d e l s , C ry s ta l s , a n d C h e m i s t ry  c β α β β y γ a b x Triclinic Monoclinic P Monoclinic C c b a Orthorhombic P C I F c c a a a´ α a y a a a 120° αα Tetragonal P Tetragonal I x Hexagonal Rhombohedral a a a Cubic P Cubic F Cubic I FIGURE 5.1 The fourteen Bravais lattices. 5 .1 Te r m s a n d D e f i n i t i o n s ......................................................................................................................................... 73  AR43 AR42 AM A AR41 A Mirror Rotation A A AR41 Ai AR41i (A) Inversion Inversion + rotation FIGURE 5.3 Symmetry elements for a simple cube. of symmetry elements produce the same answer. For example, m is the same as 2̄ while 2̄3 and 2m3 are both the same as 2/m3, which is written as m3. So, as with any convention, the only way to get it right is to memorize it. Table 5.3 lists the symmetry operations associated with each of the seven crystal systems. The final column in Table 5.3 has the maximum possible symmetry and is called the holosymmetric point group. For example, NaCl is m3m while FeS2 is m3. Both crystals are cubic, but they have different symmetries; we will show the reasons for this in Chapter 6. The notation is not always the same as indicated at the top of the column. The symbols given here are known as the international convention. Actually we could write them out fully, but the reduced description contains the essentials; for example, m3m is actually 4̄/ m3m and 43 is actually 432. (B) FIGURE 5.2 Crystals with faceted surfaces illustrating macro- scopic symmetry elements; (a) MgO, (b) calcite. TABLE 5.2 Symmetry Operators (Hermann–Mauguin Notation) a 5.2 SYMMETRY AND X Rotation axis alone CRYSTALLOGRAPHY X̄ Inversion axis alone X/m Rotation axis with a symmetry plane normal to it Xm Rotation axis with a symmetry plane that is not normal Describing the symmetry of crystals is often more com- to it (usually a vertical symmetry plane) plicated than that of solid shapes such as the cube in X̄m Inversion axis with a symmetry plane not normal to it Figure 5.3. For example, the crystal may have a cubic X2 Rotation axis with a diad normal to it shape and belong to the cubic crystal system but not have X/mm Rotation axis with a symmetry plane normal to it and the maximum internal symmetry. another not so Table 5.2 lists the Hermann–Mauguin notation for a In writing the symbol, the principal symmetry axis is placed first. For cubic, expressing the symmetry operators. Some combinations 3 is always second. 74 ............................................................................................................................ M o d e l s , C ry s ta l s , a n d C h e m i s t ry  TABLE 5.3 The 7 Crystal Systems and the 32 Crystal Point Groups Crystal system Essential symmetry X X̄ X/m Xm X̄m X2 X/mm Triclinic 1-fold axis 1 1̄ — — — — — Monoclinic 2-fold axis (parallel to y) 2 m 2/m — — — — Orthorhombic — — — mm — 222 mmm Trigonal 3-fold axis (parallel to z) 3 3̄ — 3m 3̄m 32 — Cubic Four 3-fold axes 23 — m3 — 4̄3m 43 m3m Tetragonal 4-fold axis (parallel to z) 4 4̄ 4/m 4mm 4̄32 42 4/mmm Hexagonal 6-fold axis (parallel to z) 6 6̄ 6/m 6mm 6̄m2 62 6/mmm You can find the full details of the international conven- [UV̄W]. Some low-index directions in the orthorhombic tion in the International Tables for Crystallography (1983). system are illustrated in Figure 5.5. These symmetry operations A special direction, or elements can be com- CONVERTING NOTATION: known as the zone axis, is bined to provide 32 differ- MILLER AND MILLER-BRAVAIS the one that is common to ent crystal classes. The two planes h1k1l1 and h2 k2 l2. crystal classes are often U = u − t u = (2U − V)/3 The directions [h1k1l1] and called the crystal point V = v − t v = (2V − U)/3 [h2 k2 l2] are the normals to groups. They are the point W=w t = −(u + v) the two planes and the zone groups that are consistent = −(U + V)/3 axis [UVW] is then given with the translational sym- w=W by the vector cross-product. metry of a crystal. The zone axis has particu- lar significance in electron microscopy because it represents the direction of the inci- 5.3 LATTICE POINTS, DIRECTIONS, dent electron beam with respect to the sample. AND PLANES When discussing crystals with hexagonal symmetry, it is helpful to use Miller– The notation used for iden- Bravais indices because MILLER INDICES tifying planes and faces of these clarify the symmet- Low-index planes have small values of h, k, and l (and crystals is that of W.H. rically equivalent planes. i). All are integers. Miller and is referred to as In this scheme, a fourth the Miller indices of a index, i, is introduced such plane. The lengths of the unit cell are a, b, and c. A that i = −(h + k). Figure 5.6 shows some planes and direc- family of planes cuts these axes at the origin and at tions in the hexagonal system. The advantage of the four- –ah, –bk , –lc . The plane is then defined by the indices h, index Miller–Bravais system, and the main reason for its k, and l. If these indices are not all integers use, is that similar planes have similar indices (as we saw we multiply by the quotient to make them integers. Thus in the case of the Miller system). For example, the planes the intercepts –32 a, 4b, and 1c give h, k, and l values of –23 , –14 , (101̄0), (011̄0), (1̄100), (1̄010), (01̄10), and (11̄00) are the and 1 and this hkl is 8.3.12. We use periods to separate six sides (called prism planes) of the hexagonal lattice; the numbers only if one of them is greater than 9. If these clearly are of similar type. In the Miller system, the intercept is negative we write h̄ (bar h, sometimes read however, these will be (100), (010), (1̄10), (1̄00), (01̄0), as h bar). and (11̄0), and they are Figure 5.4 illustrates FINDING THE ZONE AXIS definitely not of a similar some of the low-index type. planes in the orthorhombic [UVW] = [h1k1l1] × [h2 k2 l2] To transform directions, crystal system. Since there U = k1l2 − l1k2 it is helpful to remember may be different combina- V = l1h2 − h1l2 from Figure 5.6 that the tions of hkl that give sym- W = h1k2 − k1h2 vector [1 1 1 0] is a null metry-equivalent planes we vector: it has no length! use (hkl) to denote a partic- Thus we can change the ular plane and {hkl} to denote an equivalent set of planes. three-index direction [1 1 0] in Figure 5.6 to its four- The faces of the cube form the set of {100} planes. index form as follows [1 1 0] → [1 1 0 0] → [1+f 1+f f 0]. Directions are easier to define. The vector Ua + Vb + So that our four-index notation for directions is the same Wc is simply written as [UVW]. We can then write <UVW> as for planes (i.e., U + V + W = 0), we want 2 + 3f to be to denote all the equivalent directions formed by permut- zero. Thus f = − –23 and the direction is [–31 –31 − –23 0] or ing U, V and W. The vector Ua − Vb + Wc is denoted by [112̄0]. 5 . 3 L at t i c e P o i n t s , D i r e c t i o n s , a n d P l a n e s ......................................................................................................... 75  d200 [001] d100 (0001) [011] c z (100) (200) y (110) (1011) (1210) x (1100) [110] a3 a2 [010] (110) (111) (102) FIGURE 5.4 Miller indices of some lattice planes. The lattice- [100] a1 [210] plane spacing is given by dhkl . FIGURE 5.6 Indices of planes (using Miller–Bravais notation) and directions (using three-index Miller notation) in the hexagonal unit The two notations are related and it is straightforward cell. to convert between them. The Miller–Bravais system is widely used in ceramics because alumina (sapphire) often juxtaposition. Twin planes are usually special low- behaves as if it were hexagonal, although it is actually index planes. trigonal.  Piezoelectricity. Crystals must be noncentrosym- metric.  Thermal conductivity. Phonon conductivity is most 5.4 THE IMPORTANCE OF efficient in simple crystal structures formed by small CRYSTALLOGRAPHY atoms.  Fracture. Often crystallographic, but not always (e.g., Understanding the crystalline structure of ceramics is glass and cubic zirconia). critical to understanding many of their properties.  Cleavage. Always crystallographic. Cleavage planes have high atomic density, but we also need to consider  Diffusion. Often depends on the size and number of charge. interstitial sites, both functions of the crystal  Ferrimagnetism. In ferrimagnets the coordination structure. number of the magnetic cation (usually an Fe ion)  Deformation by slip or twinning. In ceramics there are determines its behavior in an applied magnetic field. both crystallographic and electrostatic considerations. The slip direction is usually along a close packed To really appreciate the importance, and complexities, of direction. The slip plane will usually be a closely the relationships between crystallography and properties, packed plane or one that does not put like charges in see Nye (1985). [233] 2 11 [100] 3 5.5 PAULING’S RULES [111] [001] Ceramic materials are often thought of as being ionically bonded and ions thought of as being charged spheres. Many important ceramics are oxides in which the oxygen [100] anion is much larger than the cation. The crystal structure [010] adopted by the material is based on a balance between the c attractive and repulsive forces in the crystal. The electro- b [120] static attractive force between ions of unlike charge implies [210] that an ion with a high CN would be more stable than an 1 1 0 2 ion with a low CN, that is, the electrostatic attraction is O a [100] maximized. However, if too many ions of the same charge [120] are clustered around an individual ion of the opposite FIGURE 5.5 Indices of directions in an orthorhombic unit cell with charge, they begin to interfere with one another, that is, examples of vectors included. the electrostatic repulsion is maximized. There exists a 76 ............................................................................................................................ M o d e l s , C ry s ta l s , a n d C h e m i s t ry CN where the attraction is A MNEMONIC r maximized and the repul- 2+ Radius ratio = M (5.3) Ca is a cation. rX sion is minimized. This number is determined by A given CN is stable only the ratio of the radii of the two ions. Questions then arise when the ratio of cation to anion radius is greater than as to why certain oxides have the structure they do and some critical value. These limits are given in Table 5.4. how this affects mixing or doping of oxides. The derivation of these limits is strictly geometric as Pauling proposed a set of rules to use when discussing shown in Figure 5.7. such topics. These rules Why are the radius work so well that they are MX ratio and CN related? sometimes regarded as M is the cation and is often a metal. Coulomb interactions laws, which they are not. X is the anion and is never a metal. mean that like signs should We will discuss the origin You will sometimes see CA or +− instead of MX. be as far apart as possible of the rules and then the and opposite signs as close rules themselves. together as possible. The idea is simply that ions of opposite sign pack Crystal structures are thus at their most stable when the together in such a way as to keep ions of like sign apart. cations have the maximum CN allowed by r . In many X well-known ceramics, the cation coordination polyhedron Rule 1: A coordinated polyhedron of anions is formed is the basic building block. about each cation. The cation–anion distance is deter- On Rule 2: In a stable structure, the total electrostatic mined by the sum of the two radii and the CN is deter- strength of the bonds, S, reaching an anion in a coordina- mined by the radius ratio. tion polyhedron from all neighboring cations should be equal to the charge of the anion Rule 2: In a stable structure, the total strength of the bonds that reach an anion in a coordination polyhedron ZM from all neighboring cations should be equal to the S= (5.4) CN charge of the anion. where CN is the coordination number and Z M = charge on Rule 3: The polyhedra in a structure tend not to share the cation. The fundamental idea is that the crystal must edges or faces. If the edges are shared, the shared edges be electrically neutral. are shortened. Shared faces are the least favorable. We can illustrate this idea for the oxygen anion. Each Rule 4: Crystals containing different cations of high O2− might bond to a combination of cations: valence and small CN tend not to share polyhedron ele- ments with each other.  Si4+ ions, S = 4/4 = 1. Two bonds of strength 1 reach Rule 5: The number of essentially different kinds of the shared oxygen ion from the surrounding silicon constituents in a crystal tends to be small. ions. This is the case in, for example, cristobalite (a polymorph of SiO2). The Si4+ are surrounded by four When reading the discussion of these rules, keep in O2− ions in a tetrahedral arrangement. mind the following questions and remember that all rules  Al3+ ions, S = 3/6 = 1/2. Each O2− ion is surrounded have exceptions. by four Al3+ , each with a bond strength of 1/2. The Al3+ is surrounded by six O2− ions in an octahedral  Why do CsCl and NaCl have different structures? arrangement. This is the case in, for example,  Why do Mg2+ ions tend to occupy tetrahedral sites corundum. while Al3+ ions occupy octahedral sites in spinel, when  In the mineral kyanite, Al2SiO5, we have one Si4+ plus both ions occupy octahedral sites in MgO and two Al3+ ions surrounding each O2− ion. There are six Al2O3? O2− around each octahedral Al3+ ion.  Why do zinc blende and wurzite have different struc-  In forsterite, Mg2SiO4, we have one Si4+ ion plus three tures when both are ZnS? Why does GaAs have one octahedral Mg2+ ions (S = 2/6). We need three Mg2+ structure and AlN have the other? ions to balance the charge.  What determines the structure of silicates? Are any other structures like this? TABLE 5.4 Pauling’s Critical Radius Ratios  Is the structure of BaTiO3 important regarding its properties? Polyhedron CN Minimum (= rM /rX) On Rule 1: A coordinated polyhedron of anions is Cube 8 0.732 formed about each cation. The cation–anion distance is Octahedron 6 0.414 Tetrahedron 4 0.225 determined by the sum of the two radii. CN is determined Triangle 3 0.155 by the radius ratio: 5 . 5 Pau l i n g’s R u l e s ...................................................................................................................................................... 77  CsCl NaCl Sphalerite a 2 1 2a 2 1 8 a 3 unit a Face of cell unit cell 1a 2 2rx rx 3 1r 6 1a = 1r 2 2 x 4 2 x 1a 2 = rx 1a 1a 2 = rx 2 1a = r 2 2 = rx 2 2 x 4 rM + rX = rX 3 rM + rX = rX 2 rM + rX = rX • 1 6 2 rM/rX = 3-1 rM/rX = 2-1 rM/rX =1 6-1 2 = 0.732 = 0.414 = 0.225 FIGURE 5.7 Geometric method for calculating limiting radius ratios. In silicates, the Si atoms are each surrounded by four limit of stability of the polyhedron. Thus, if two anion O2− anions, so each O ion has an additional charge of −1 polyhedra have an edge or face in common, then the that must be used to bond to another ion. Thus, for an cations are being brought too close together. We can aluminosilicate, we need a large cation with a charge of provide an alternative statement of the rule. The existence +1 or +2 so it can be surrounded by eight or more oxygen of edges, and particularly faces, common to two anion ions. Calcium (with CN = 8) fits this requirement to give polyhedra in a coordinated structure decreases its calcium aluminosilicate. Table 5.5 shows values of pre- stability. dicted CN and S for various cations. Examples: On Rule 3: Polyhedra in a structure prefer not to share edges or faces. Clearly, if the faces are shared, then at least CsCl: the anions sit at the corners of cube and share three edges are also shared. faces. This effect is large for cations with a high valence and NaCl: the anions sit at the corners of octahedra and share small coordination number. In the first case, the charge on edges. the cation is large increasing the Coulomb repulsion. It is ZnS: The anions sit at the corners of tetrahedra and share especially large when the radius approaches the lower vertices. If polyhedra share edges, these edges tend to be shortened. TABLE 5.5 Predicted Coordination and Strength of the We can think of this shortening as concentrating more Bond “anion” between cations, which are too close together! Predicted The converse of the rule is that if you find an apparent Ion rM /rX coordination Strength of bond violation it is likely that the bonding is not ionic. However, Si4+ 0.29 4 1 many materials with the ZnS structure, which does the Al3+ 0.39 4 or 6 ¾ or ½ (¾ or 3/ 6 ) best job of separating like ions, have predominantly cova- Mg2+ 0.51 6 1/ 3 ( 2/ 6 2/ 6 ) lent bonding. Determination of the fraction of ionic char- Ti4+ 0.44 6 2/ 3 ( 4/ 6 ) acter in a bond can be made using Eq. 4.24. K1+ 0.99 8 / 18 Some examples: 78 ............................................................................................................................ M o d e l s , C ry s ta l s , a n d C h e m i s t ry   In FeS2 (iron pyrites, fool’s gold and a ceramic) the seen in grocery stores in which oranges in adjacent layers [FeS6] octahedra are linked by shared edges that are sit off-center, resting within the pocket created by the longer than expected. oranges sitting side by side below. Materials scientists and  Silicates contain [SiO4] 4− tetrahedra; in all cases, they crystallographers (as well as greengrocers) have known share corners due only to strong mutual repulsion that this is the most efficient way to stack a bunch of round between Si4+ . Again there is actually a large covalent objects, but mathematicians took a long time to be con- component to the bonding. vinced (see the interesting book on this topic and other  It is thus a geometric rule again, but is, nonetheless, mathematical riddles by Singh, 1997). A mathematical important. For example, the edges of the occupied octa- proof for what is known as the Kepler conjecture was hedra in Al2O3 are 0.25 nm long, not 0.28 nm long. announced in 1998 and the manuscript was published 7 years later (Hales, 2005). On Rule 4: Crystals containing different cations of Crystal structures having an APF of 0.74 are called high valence and small CN tend not to share polyhedron close-packed structures. There are only two close-packed elements with each other. Sharing parts of polyhedra structures: decreases the stability of the structure, so this rule is really a corollary to rule 3.  Face-centered cubic (fcc) As an example, in CaTiO3, [CaO12] polyhedra share  Hexagonal close-packed (hcp) edges and [TiO6] polyhedra share corners. The Ti4+ cation is more highly charged than the Ca2+ cation, so the CN is smaller; the Coulombic repulsion between cations is pro- We will consider the fcc and hcp structures in some detail portional to the product of the charges. because they are so common. For the fcc structure all the On Rule 5: The number points are actually lattice of essentially different GARNET points. In the hcp structure kinds of constituents in a Ca3Al2Si3O12 is not only a gemstone but also a ceramic. this is not the case. Thus crystal tends to be small. Other garnets such as yttrium aluminum garnet (YAG) we should never say the As far as possible, the and gallium gadolinium garnet (GGG) are technologi- “hcp lattice” but we do. environment of chemically cally much more important materials. The hcp structure describes similar atoms will be a particular arrangement similar (and Pauling’s Ion: Ca 2+ Al 3+ Si4+ of similar atoms, but it is analysis assumes that the 2− O coordination 8 6 4 not a lattice of identical bonding is all ionic). O bond strength, S –8 = –4 2 1 –6 = –2 3 1 –4 = 1 4 points. If all types of bonding The relationship are possible, it is difficult between the fcc and hcp to predict what will happen, but if every oxygen has the structures is illustrated in Figure 5.8a. The atoms on the same environment then there is only one possibility. The (111) planes of the fcc structure are arranged in a hexago- result is actually found in garnet. This rule only requires nal pattern just like the atoms on the (0002) planes of the the ions to be similarly coordinated. Their actual geo- hcp structure. The only difference between the two struc- metric positions need not be equivalent. They are not tures is the way in which these hexagonal sheets of atoms structurally indistinguishable. The rule actually has are arranged above one another. In the hcp structure, the limited value because in a majority of silicates, the oxygen atoms in the second layer are above the hollows in the first ions do not have like environments. layer and the atoms in the third layer are above the atoms in the first layer, so the stacking sequence can be sum- 5.6 CLOSE-PACKED ARRANGEMENTS: marized as A B A B A B. . . . The stacking in the hcp INTERSTITIAL SITES structure is illustrated in Figure 5.8b. The first two atom layers in the fcc structure are put down in the same way, A close-packed structure is one that has the maximum but the atoms of the third layer are placed in the hollows volume of the unit cell occupied by atoms. The occupied of the second layer; not until the fourth layer does a posi- fraction of the unit cell can be determined by calculating tion repeat. The stacking sequence for fcc is therefore A the atomic packing factor (APF): B C A B C A. . . . This sequence is illustrated in Figure 5.8c. In predominantly ionically bonded oxide ceramics, the number of atoms per cell × volume of one atom O 2− ion approximates a sphere. So we can view these APF = volume of unit cell structures as based on a close-packed arrangement of (5.5) spheres and then filling the remaining space. We must remember that the anions are not necessarily touching, but The maximum possible APF for packing of spheres all they are merely arranged in a way that is the same as that having the same size is 0.74. This arrangement is the one in the close-packed structures. 5 . 6 C l o s e - pa c k e d A r r a n g e m e n t s : I n t e r s t i t i a l S i t e s ......................................................................................... 79  A A A A C B B B B A A A A A A C C (0002) B (111) B A A A A Planes Planes [001] (111) A A (0002) [111] B B y C 1 1 1 1 x 3 3 3 3 2 2 2 2 A 3 3 3 3 A fcc hcp 1 1 1 1 (A) 3 3 3 3 2 2 2 2 3 3 3 3 y A layer 1 1 1 1 1 1 1 1 3 3 3 3 B layer x 2 2 2 2 2 2 2 2 3 3 3 3 C layer (C) 1 1 1 1 2 2 2 2 A layer 1 1 1 1 2 2 2 2 B layer FIGURE 5.8 (a) Comparison of fcc and hcp structures using the stacking of close-packed rafts of atoms (spheres); (b) the stacking (B) sequence in hcp; (c) the stacking sequence in fcc. So we now need to answer the following questions: rahedral sites or just the octahedral sites. The fcc lattice can be stabilized by filling a combination of tetrahedral  Where are the interstitial sites? and octahedral sites. In the fcc arrangement there are eight  What is their CN? tetrahedral sites and four octahedral sites per cell. The  How many sites are there? location of these sites is shown in Figure 5.9a.There are four tetrahedral sites and two octahedral sites per cell in The fcc and hcp arrangements offer both octahedral and the hcp arrangement. The location of these sites is shown tetrahedral interstices, making them good hosts for cations, in Figure 5.9b. since two size ranges can be incorporated. Both fcc and In ceramics the APF is always <0.74, even though we hcp arrangements can be stabilized by filling just the tet- have increased the number of atoms per cell. As an (A) (B) FIGURE 5.9 (a) Interstitial sites in the fcc structure; (b) interstitial sites in the hcp structure. 80 ............................................................................................................................ M o d e l s , C ry s ta l s , a n d C h e m i s t ry  TABLE 5.6 The Strukturbericht Notation TABLE 5.8 Notation for Different Crystal Structures Symbol Definition Symbol Definition Strukturbericht Prototype Pearson Space group A Element E-K Complex A1 Cu cF4 Fm3̄m B AB compounds L Alloys A2 W cI2 Im3̄m C AB2 O Organic A3 Mg hP2 P63 /mmc D AmBn S Silicates A9 Graphite hP4 P63 /mmc Bh WC hP2 P6̄m2 Bk BN hP4 P63 /mmc B1 NaCl cF8 Fm3̄m example, if we fill all the octahedral sites in an fcc arrange- B2 CsCl cP2 Pm3̄m ment of O2− with cations (e.g., Mg2+) as we’ll see in Chapter B3 Sphalerite cF8 F43̄m 6, the APF is 0.69. In other words, 69% of the cell volume B4 Wurtzite hP4 P63mc is occupied by ions. B10 PbO tP4 P4/nmm B26 CuO mC8 C2/c C2 FeS2 (pyrite) cP12 Pa3 C3 Ag2O cP6 Pn3̄m 5.7 NOTATION FOR CRYSTAL C4 TiO2 (rutile) tP6 P42 /mnm STRUCTURES C6 CdI2 hP3 P3̄ml C7 MoS2 hP6 P63 /mmc One of the things you will notice is that many crystal C8 High quartz hP9 P6222 C9 β Cristobalite cF24 Fd3̄m structures are named after particular materials (often a C10 β Tridymite hP12 P63 /mmc naturally occurring mineral) that exhibit the structure. C18 FeS2 (marcasite) oP6 Pnnm There are no systematic names for crystal structures, as C21 TiO2 (brookite) oP24 Pbca there are, for example, for organic compounds, which are C43 ZrO2 mP12 P21/c named using a system recommended by the International D09 ReO3 cP4 Pm3̄m D011 Fe3C oP16 Pnma Union of Pure and Applied Chemistry (IUPAC). This D51 α-Al2O3 hR10 R3̄c system provides us with a systematic way of naming many D52 La 2O3 hP5 P3̄c1 organic compounds on sight and the name indicates the D53 Mn2O3 cI80 Ia3̄ structure of the compound. A similar system is not used E21 CaTiO3 cP5 Pm3̄m for naming crystal structures. However, there are several H11 MgAl2O4 cF56 Fd3̄m L10 AuCu tP2 P4/mmm different notations for specifying crystal structures that L11 CuPt hR32 R3̄m can be very useful. L12 AuCu3 cP4 Pm3̄m  Strukturbericht. The symbol consists of a letter that characterizes the type of structure and a number des- ignating a specific type within a letter category. The Table 5.7. Even though you will be able to find out the rules are given in Table 5.6. crystal system, the Bravais lattice, and the number of  Pearson. The symbols give, successively, the crystal atoms from this notation, you will not be able to dif- system, the Bravais lattice symbol, and the number of ferentiate among different structures with similar atoms per unit cell. The notation is summarized in notations. For example, cF8 refers to sodium chloride, diamond cubic, and zinc blende structures, which are different from one another. TABLE 5.7 Symbols Used in The Pearson Notation Examples of Strukturbericht and Pearson symbols are given in Table 5.8. Symbol System Lattice aP Triclinic (anorthic) P mP Simple monoclinic P 5.8 STRUCTURE, COMPOSITION, mC Base-centered monoclinic C AND TEMPERATURE oP Simple orthorhombic P oC Base-centered orthorhombic C Many ceramics exist in different structures at different oF Face-centered orthorhombic F temperatures. These structures are known as polymorphs oI Body-centered orthorhombic I and we will give some examples in Chapter 6. The most tP Simple tetragonal P tI Body-centered tetragonal I stable structure at any particular temperature is governed hP Hexagonal P by its free energy, G. The polymorph with the lowest free hR Rhombohedral R energy is the most stable. Expressions for the free energy cP Simple cubic P and internal energy were given in Chapter 3. Both the cF Face-centered cubic F internal energy, E, and the entropy, S, depend on crystal cI Body-centered cubic I structure. 5 . 8 S t ru c t u r e , C o m p o s i t i o n , a n d Te m p e r at u r e ................................................................................................... 81  The following rules can be given for the temperature 60 and pressure dependence of thermodynamically stable Enthapy α-Al2O3 structures: Relative to bulk Al2O3  At T = 0, G = E, that is, the free energy is fixed by the (kJ/mol) internal energy.  At T > 0, the TS term becomes increasingly important γ-Al2O3 40 and structures with a low degree of order are favored.  At a sufficiently high temperature a polymorph with a larger S may achieve a lower G in spite of its larger E, as illustrated in Figure 5.10. The increased values of E and S of the high-temperature forms correspond to 20 more open structures (larger specific volumes) with higher symmetry.  There are two components to entropy (both increase as T increases)—thermal entropy and configurational entropy.  In the liquid state, the order is even lower and it is the lowest in the gaseous state. Raising the temperature 0 0 100 200 300 will lead to melting and finally to evaporation. Surface Area (m2/g)  Higher pressures favor structures that occupy a lower FIGURE 5.11 Calculated enthalpy of alumina (γ- and α-) poly- volume, that is, that have a higher density. morphs as it varies with the surface area. The calculation is an MD simulation using data for small surface areas. A large surface area per gm implies small particles. The crystal structure of a ceramic also depends on composition. As an example, consider three oxides of iron: There is another factor that can influence the equilib- 1. Wüstite (FeO): Cubic rocksalt structure. Iron is in the rium structure of a material and that is surface energy. The 2+ oxidation state. effect of surface energy has become of increasing impor- 2. Hematite (Fe 2O3): Rhombohedral corundum structure. tance with the interest in nano-sized particles of ceramics. Iron is in the 3+ oxidation state. When particle size becomes very small the fraction of 3. Magnetite (Fe3O4): Cubic spinel structure. Iron is in atoms on the surface becomes very large. Surface energy 3+ and 2+ oxidation states. effects can then dominate as illustrated in Figure 5.11, which shows that γ-Al2O3, rather than α-Al2O3, can become The reasons for these differences are explained by Paul- the thermodynamically stable phase of aluminum oxide ing’s rules. when the surface area exceeds ∼175 m2 /g. The key thing to remember is that nanomaterials do not always behave the same as the bulk material. E E3 E2 E1 5.9 CRYSTALS, GLASS, SOLIDS, AND LIQUID Classically, there are three distinct states of matter: gas, liquid, and solid. (The newer two, plasma and Bose– Einstein condensates, are not applicable to our discussion so we omit them.) In the previous section we noted how G1 as temperature increases it is thermodynamically favor- G2 able for transitions to occur from a more ordered form to a less ordered one. The atoms or molecules that make up G3 a gas are randomly arranged (E and S are high) and widely separated. A gas will fill all the available space inside a T container. The atoms or molecules that make up a liquid FIGURE 5.10 Schematic showing the relationship between internal energy E and free energy G of three polymorphic forms: are also randomly arranged, but they are closer together E3 > E2 > E1 and S 3 > S 2 > S1. The form with the lowest G will be than those in a gas and they move relative to one another. the one usually found at a specific temperature. The characteristic of a liquid is that it will fill a container 82 ............................................................................................................................ M o d e l s , C ry s ta l s , a n d C h e m i s t ry to the extent of its own volume. The third state of matter TABLE 5.9 Hierarchy of Crystal Lattice Defects is solid, which can be defined as having a fixed shape. “Dimension” Defect Some topics Solids can be classified as either crystalline or noncrystalline. 0 Point defects Geometry, strain energy, When we discuss crystals we are concerned with inter- charge atomic bonding, interatomic distances, the environment of 1 Line defects Geometry, energy the ions and long-range ordering. All of these concepts, 2 Surfaces Thermodynamics except for long-range ordering, are relevant to noncrystal- Grain boundaries Structure, chemistry, wetting line materials such as glass. In fact, when we discuss Phase boundaries Phase distribution silica-based glasses, the main point is how we do or do 3 Volume defects Precipitates, particles, and not link SiO4 tetrahedra together. The concept of order voids that is important is separating the different classes of condensed matter. The basic differences are summarized below: discuss are three-dimensional defects. Ceramics usually Crystal Ordering on lattice—long-range order have mixed bonding, that is, a combination of ionic and Glass Short-range order covalent bonding. So, when we introduce defects, we Liquid No order to short-range order usually change the local distribution of charge or break There are many amorphous ceramics (glasses). There are bonds, depending on which type of bond predominates. fewer amorphous semiconductors and some amorphous Any change in charge distribution can produce long-range metal alloys. The main consideration, as you will see in effects. A broken covalent bond is known as a dangling Chapter 21, is the rate of cooling necessary to avoid crys- (unpaired electron) bond that also behaves like a localized tallization. In many oxides the critical rate of cooling is charge. very easy to achieve because the number of components We have discussed the packing of ions in terms of is large and we have directional (covalent) bonding. The coordination polyhedra. When we create defects in a latter consideration also holds for the semiconductors, but crystal we can create new polyhedra that are not found in for metal alloys we usually can rely only on frustrating the perfect crystal. Pauling’s rules were developed for crystallization using complex compositions and rapid perfect crystals, but the principles still apply when we quenching. examine defects. One complication is that as we introduce grain boundaries, for example, new sites are produced that depend on the detailed nature of the grain boundary. 5.10 DEFECTS Amorphous materials present a new challenge when describing point defects. Two amorphous materials can One reason that we need to understand the structure of have different structures that depend on the processing perfect crystals is so that we can begin to understand history even if the chemistry is the same. imperfect crystals. The topic is not just specific to cera- mics. The interaction of defects is often most important to us. For ceramics, a special example of such interactions 5.11 COMPUTER MODELING occurs in grain growth. Grain-boundary movement in ceramics usually involves the movement of point defects. Computer modeling of oxide structures and of defects in Understanding atomic bonding helps us understand the oxides is becoming more important, in part because the structures of crystals and glass. When we think of crys- code is improving, but mainly because faster computers tals, we think of atoms arranged in a perfect way. We can make more realistic calculations. The problems for traditionally think in terms of crystal defects, but we will ceramic materials are those discussed in Chapters 3 and also consider how these ideas apply to defects in glass. 4. If the bonding is ionic, then the ion–ion interactions are One question to keep in mind is “how is this feature both strong and long-range. If there is a covalent compo- different from metals?” The answer is not always as nent to the bonding, then the bonds have a directional obvious as it might seem at first, because we often compare character. (Glasses exist in a metastable state so their ceramic materials to particularly simple (usually fcc) structure is, by definition, not the equilibrium one.) The metals. Apart from carbon and the elemental semiconduc- problem is 2-fold. We need a computer code that can tors, Si and Ge, all ceramics contain two or more different handle the long-range interactions. Even simple ceramics atoms, so we should at least compare them with metal can have large unit cells, which means that the computer alloys not pure metals. The next question is “how do must be able to handle a large number of atoms. defects influence the properties of the ceramic?” For that We will summarize the approaches being used by dif- we need to understand defects first. ferent researchers to calculate properties of ceramics. This We classify defects as having 0, 1, 2, or 3 dimensions, discussion is very brief and incomplete, but it should as shown in Table 5.9. Actually all of the defects we will provide an idea of how the subject is developing. One 5 .11 C o m p u t e r M o d e l i n g ............................................................................................................................................ 83 encouraging feature is that software packages that are  Ceramics usually contain charged species. This means suitable for the knowledgeable researcher who is not an that the interionic forces extend over very large dis- expert programmer are becoming available commercially. tances (remember the Madelung constant). To model These packages fall into two categories that can be linked. such materials we need large unit cells. This problem In one the atomic structure of a ceramic crystal can be becomes more difficult when we model defects. displayed after inputting the appropriate crystal parame-  When the ceramic is covalent or has a large covalent ters. Such programs are simply using the rules of crystal- component to the bonding, directions are important. Si lography to generate the structures. The other, and far is the classic example of a covalent material and can more complex, programs also use the interatomic poten- be modeled, but only because enormous effort could tials to deduce features of the structure and are performed be justified by its commercial importance. Modeling using molecular dynamic (MD) approaches. silicates, which also have a large covalent component, is less developed. Terms Used in Modeling Ceramics lag behind metals for two reasons. First, We will begin by listing some of the terms you will most ceramics contain more than one component so we encounter: Pseudo-potential is an expression that is being need to have potentials for each ion. (FeO contains three used to represent a real crystal potential. An equation like ions for this purpose.) Second, the potentials have to be Eq. 4.1 is chosen and the parameters changed until a cal- used to predict known quantities and these are not usually culated value is obtained that agrees well with the known as well known as they are for metals. value of a physical parameter. This process will be carried A number of software packages are now available as out simultaneously for several parameters that are chosen shareware or commercially. One such program is GULP: to have some relevance to what you would like to calcu- the acronym stands for Generalized Utility Lattice late. Electronic structure calculation: Although ceramics Program. GULP can be used to perform different types of are thought of as insulators, the electrons are important in simulation on three-dimensional periodic solids and on understanding optical properties, for example. isolated defects in such materials. GULP simulates struc- tures of ionically bonded materials using a shell model and uses the crystal symmetry to accelerate the calculations Computer Modeling of Structures: and to simplify the input. These two factors can make it The Need for Potentials faster and more efficient than other programs. If you use Most ceramics cannot be modeled from first principles GULP, for example, you will have access to at least 23 dif- simply because we do not know the potentials well enough. ferent potentials or models, including Buckingham, Morse, So the challenge with modeling crystals is that we have to Coulomb, and Stilinger-Weber. Examples of the uses of use a model for the potential. These are available for Si GULP are modeling Al2O3, defects in garnets, zeolites, and are quite good for Al2O3 and MgO. and molecular sieves, and the structure of Al2SiO5 poly- We can summarize the problems for modeling cera- morphs. CeriusTM, another software package for simulating mics as follows: structures, also includes diffraction modules. CHAPTER SUMMARY This is the chapter in which we introduce crystallography. Some students object to having to learn this material. Our view is that you cannot understand point defects, piezoelectricity, grain boundaries, elasticity of noncubic crystalline materials, etc., unless you understand the differ- ences between the different crystal structures, and for this you must understand the principles of crystallography. Pauling’s rules for ionic ceramics give us a set of tools to allow us to predict the coordination of ions and even to guess the structure of a crystal that may be new to us. The exceptions to these rules often result from the presence of a covalent component to the bonding, which itself gives clues to the coordination. Once we know the crystal structure, we can predict what point defects might occur and even guess at the energies involved—just from counting broken bonds, for example. The best-known examples of such point defect sites are the octohedra and tetrahedral in the close packed (fcc or hcp) lattices, but we find these poly- hedra in many different crystal structures, though they may be more difficult to recognize elsewhere. So just by considering Pauling’s rules, we are introduced to one of the most useful concepts of solid-state chemistry—the concept of crystals being constructed by arranging polyhedra. The polyhedra are clusters of atoms that behave in quite systematic ways. As we will see in the following chapters, the most important of these polyhedra will be the tetrahedron formed by four oxygen ions with an Si ion at the center, but it is certainly not the only polyhe- dron of interest to us. 84 ............................................................................................................................ M o d e l s , C ry s ta l s , a n d C h e m i s t ry  PEOPLE IN HISTORY Bravais, Auguste (1811–1863) presented his ideas on crystallography to the French Academy of Sciences in 1849. He was interested in a number of fields including botany, astronomy, and physics. It is for his work in crystallography that he is best remembered. Goldschmidt, Victor Moritz was born in Zurich, but spent his scientific career in Norway (1888–1947). Like Pauling, he derived rules for ionic radii. Haüy, René-Just (1743–1822) published his essay in 1784 on a theory of the structure of crystals; the story is that his interest in crystals began when he examined a specimen of calcite that he had accidentally just dropped. Hooke, Robert (1635–1703) published Micrographica in 1665 showing images taken with his microscope. A genius. Miller, William Hallowes (1801–1880) was born in South Wales and was Professor of Mineralogy at Cam- bridge University from 1832 until he died. He wrote the book that explained the notation developed by William Whewell (who also coined the word scientist); he gave full credit to the pioneering work of his mentor, Whewell, but we still refer to Miller indices. Wulff, Georgii (Yurii) Viktorovich was a Russian crystallographer born in 1863. The initial G was used in translations of his papers rather than the Y. He died in 1925 in Moscow. Wyckoff, Ralph Walter Graystone was born in 1897 and died in 1994. He was the author of the classic book, The Stucutre of Crystals, 1931. GENERAL REFERENCES A great source for further reading lies in the mineralogical literature. The books by Putnis (1992), Deer, Howie, and Zussman (1992), etc. provide great insight, as does the literature from solid-state chemistry such as the books of Wells (1970), Hyde and Anderson (1989), etc. These references are given in Chapters 6 and 7. Barrett, C.S. and Massalski, T.B. (1980) Structure of Metals, 3rd edition, Pergamon, New York. Together with Pearson (below) gives more on the Strukturbericht notation. Buerger, M. (1978) Elementary Crystallography, The MIT Press, Cambridge, MA. One of the best introduc- tions to the subject. At the level of this text. Burdett, J.K. (1995) Chemical Bonding in Solids, Oxford University Press, Oxford. Crystal modeling on a Macintosh or using Windows XP is easy using CrystalMaker. http://www. crystalmaker.co.uk. Gale, J.D. (1996) Empirical potential derivation for ionic materials, Phil. Mag. B, 73, 3. Giacovazzo, C. et al. Fundamentals of Crystallography, 2nd edition, IUCr/Oxford University Press, Oxford. Comprehensive. International Tables for Crystallography, Vol. A, 5th edition (2002), edited by T. Hahn, D. Reidel, Boston. Molecular Simulations Inc. (MSI) produces CeriusTM. The corresponding structure modeling package is CASTEP. http://www.msi.com/materials/cerius2/castep.html#info. Nyberg, M., Nygren, M.A., Pettersson, L.G.M., Gay, D.H., and Rohl, A.L. (1996) “Hydrogen dissociation on reconstructed ZnO surfaces,” J. Phys. Chem. 100, 9054. Phillips, F.C. (1972) An Introduction to Crystallography, 4th edition, Wiley, New York. Includes a clear description of the Herman–Mauguin notation and the 32 classes of crystal symmetry. First published in 1946. SPECIFIC REFERENCES Gale, J.D. (1997) “GULP—a computer program for the symmetry adapted simulation of solids,” JCS Faraday Trans. 93, 629. Hales, T.C. (2005) “A proof of the Kepler conjecture,” Ann. Math. 162, 1065. The paper is 121 pages long! Twelve reviewers spent more than 4 years reviewing it. Nye, J.F. (1985) Physical Properties of Crystals, Clarendon Press, Oxford. Pearson, W.B. (1972) The Crystal Chemistry and Physics of Metals and Alloys, Wiley, New York. Gives many more details on crystal notation (see also Villars and Calvert below). Singh, S. (1997) Fermat’s Last Theorem, Fourth Estate, London. Villars, P. and Calvert, L.D. (1985) Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, Vols. 1, 2, 3, ASM International, Metals Park, OH. EXERCISES 5.1 Calculate the percentage of free space in an fcc stacking of spheres and a cubic stacking of spheres. Relate the result to two important different ceramic structures. 5.2 Based on Pauling’s radii, how do you expect the lattice parameters of Si and SiO2 (high cristobalite) to compare? How does this fit with experiment? Discuss. C h a p t e r S u m m a ry .......................................................................................................................................................... 85  5.3 When the {111} planes of SiC stack with the sequence ABABAB, the SiC has hexagonal symmetry. When they stack with the sequence ABCABC, it has cubic symmetry. What symmetry does it have when it stacks ABCBABCBABCBA? Explain your reasoning. 5.4 The face-centered cubic cell may be referred to the rhombohedral cell. Using a sketch show the relationship between the two cells. 5.5 Are there any intersticies in hcp that are not present in fcc? 5.6 Why is there no Bravais lattice called orthorhombic A, monoclinic B, or tetragonal C? 5.7 If a sapphire crystal showed only one type of rhombohedral plane and the two basal planes, what would the shape of the crystal be? 5.8 FeS is a more complicated structure than FeO. Why would you not be surprised at this result? 5.9 In calcite (CaCO3) the Ca2+ ion has a CN 6. Using the appropriate Pauling rule determine the ion environment around each O2− ion. 5.10 From the ionic radii given, estimate the coordination numbers for the following oxides: (a) MgO, (b) Al2O3, (c) Li2O; Li + 76 pm; O2− 140 pm; Mg2+ 72 pm; Al3+ 54 pm. 86 ............................................................................................................................ M o d e l s , C ry s ta l s , a n d C h e m i s t ry  6 Binary Compounds CHAPTER PREVIEW In this and the following chapter, we will describe the most important simple (binary) crystal structures found in ceramic materials. You need to know the structures we have chosen because many other important materials have the same structures and because much of our discussion of point defects, interfaces, and processing will use these materials as illustrations. Some, namely FeS2, TiO2, CuO, and Cu2O, are themselves less important materials and you would not be the only ceramist not to know their structure. We include these oxides in this discussion because each one illustrates a special feature that we find in oxides. These structures are just the tip of the topic known as crystal chemistry (or solid-state chemistry); the mineralogist would have to learn these, those in Chapter 7, and many more by heart. In most examples we will mention some applications of the chosen material. In traditional ceramic oxides, the anion is usually the larger ion, so we often think of a ceramic crystal structure as a three-dimensional (3D) array of anions with cations inserted in the interstices. Whether or not a particular structure is stable depends on Pauling’s rules. We first review some of the important lattices, paying particular attention to the polyhedra that are formed by groups of anions. As the variety of ceramics being used in today’s high-technology environment increases, some of the above assumptions cease to be valid. In certain oxides, the cation is larger than the anion and covalently bonded oxides and nonoxides cannot be treated as arrays of hard spheres. So we learn the rules and try to understand the exceptions. The concept of crystals being arrays of polyhedra will still work whether the bonding is ionic or covalent and whether the anion or the cation is larger. In this and the following chapter, the xyz-axes in the schematics of cubic crystal structures lie along the cube edges; the length of the cube edge is the lattice parameter. 6.1 BACKGROUND nent, beware. Similarly, if the cation is large (e.g., in UO2), we should not (though we sometimes do) consider the Using Pauling’s rules, we can think of all crystal struc- structure as a close-packed stacking of anions even if they tures in terms of filling polyhedra. The polyhedra are do appear to lie on an fcc lattice. those we discussed in Chapter 5. Particularly simple cases Although we will examine only a few materials here, are the simple-cubic (sc), the hexagonal close-packed each one has the same structure as other important materi- (hcp), and the face-centered cubic (fcc) lattices. In oxides als; we will list a few of these isomorphous materials. The like Al2O3 and MgO, the anion is the larger ion, which we examples chosen are also important because other crystal consider to form a scaffold so that the cations fill the structures can be related to them with only a small distor- interstices between the anions. This thinking has a histori- tion added to change the symmetry. cal bias to it. It comes from the days when ceramics were The logic of this chapter is summarized as follows: light-element oxides. Such compounds automatically have smallish cations. CsCl sc lattice with a two-atom basis With the growing importance of ternary and tertiary NaCl, GaAs fcc lattice with a two-atom basis oxides and the nonoxide ceramics, we have to be careful CaF2, FeS2 fcc lattice with a three-atom basis when making such assumptions. You must also remember AlN Hexagonal “close-packed” structure with that Pauling’s rules apply to compounds in which the a two-atom basis bonding is primarily ionic. In some compounds, the struc- Cu2O More complex but still cubic ture is the one predicted by Pauling’s rules, but the reason TiO2, CuO Much more complex may not be the one we gave when deriving the rules! In Al2O3, CdI2 “hcp” anions but not hcp structures other words, if the bonding has a large covalent compo- MoS2 Layered material 6 .1 Bac k g r o u n d ............................................................................................................................................................. 87 6.2 CsCl CsCl structure 0.3 55 CsBr We start with the CsCl structure because it is the simplest 0.25 80 CsI 0.42 35 TlCl possible, not because of its importance. The Bravais lattice 0.42 40 TlBr of the CsCl structure is sc. We can view this structure in Rutile structure two ways: 0.11 7.5 MgF2 Rocksalt structure 0.12 9.0 LiF  Two interpenetrating sc lattices, one of Cs + and one of 0.19 15 NaF Cl−. The two sublattices are displaced by −12 <111> 0.21 26 NaCl  One sc lattice with a two-atom basis (Cs + at 0,0,0 and 0.21 30 KCl Cl− at −12 , −12 , −12 ) 0.25 40 KBr 0.25 45 KI 0.4 28 AgCl The concept of a sublattice is helpful when visualizing Fluorite structure 0.13 12 CaF2 structures, but the phrase is sometimes used when the 0.25 15 BaF2 atoms do not really lie on a lattice. In this example, the UV IR lattice could be based on the positions of either the Cs + ions or the Cl− ions. 0.1 1.0 10 100 We can check this structure against Pauling’s rules. Transmitting Wavelength, in μm The ratio of the ionic radii (in pm) is FIGURE 6.2 Range of transmittance for halide samples grouped by structure. (Each sample is 2 mm thick; 10% cut off.) The vertical band shows the visible range. rCs /rCl = 170/181 = 0.94 + − As the ratio is >0.732 the Cs + should be 8-fold coordi- 6.3 NaCl (MgO, TiC, PbS) nated. It is clear from Figure 6.1 that the coordination number is indeed 8. This structure does not appear to The NaCl (rocksalt or halite) structure is quite simple and occur for oxides since the (divalent) cation radius would is found for sulfides and carbides and some oxides, includ- need to be >102.5 pm (O2− is 140 pm). It is not directional ing MgO, CaO, SrO, BaO, CdO, FeO, and NiO. The anions bonding that causes the structure to be adopted, just the are in an fcc arrangement and all the octahedral interstices packing requirements. This structure is the model B2 are occupied by cations, as shown by Figure 6.3. The CN structure found in some important intermetallics like is 6 for both anions and cations. NiAl. It is also adopted by a number of halides having The NaCl structure can be represented as follows: useful optical properties: as shown in Figure 6.2, CsBr, CsI, TlCl, and TlBr transmit in part of the ultraviolet  Two interpenetrating fcc lattices: one of anions and the (UV), all of the visible (the shaded region), and the near other of cations displaced by −12 <001> or by −12 <111> infrared (IR).  An fcc lattice with a two-atom (Na-Cl) basis (Na + at 0,0,0 and Cl− at −12 ,0,0 or alternatively Na + at 0,0,0 and Cl− at −12 , −12 , −12 ) Of course, this structure is actually not close packed even though we have an fcc arrangement of anions. In the fcc metals each atom has 12 nearest neighbors (CN is 12); in NaCl each ion has six nearest neighbors (CN is 6), so the packing of the anions must be less dense than fcc. (By Pauling’s rules, the octahedral interstice between the Cl− ions must be larger than the minimum or the structure will be unstable.) For MgO (magnesia or periclase), r Mg /rO = 0.6 so that 2+ 2− the Mg must be surrounded by oxygen ions in an octahe- dral configuration. The bond strength (valence/coordina- tion), SMg = + −26 = + −13 so each O2− must also be surrounded by 6 Mg ions. There is not a lot of choice on how to join them. Notice that rNa /rCl = 0.56, which is also >0.414 but + − FIGURE 6.1 CsCl crystal structure. The polyhedron is the cube. less than 0.732. 88 ......................................................................................................................................................... B i n a ry C o m p o u n d s  TABLE 6.1 Atomic Radius and Radius Ratios for Some Carbides and Nitrides Metal (M) Ti Zr Atomic radius (nm) 0.147 0.160 C/M ratio 0.525 0.482 N/M ratio 0.511 0.470 Table 6.1. The radius-ratio values given in Table 6.1 are consistent with a CN of 6 based on the critical radius ratios given earlier in Table 5.4. The interstitial atoms are located either in an octahedral site or in the center of a trigonal prism. For the transition metals, the tetrahedral interstices in the close-packed structures are too small for C or N. All the octahedral interstitial sites are occupied in the NaCl structure. In general, when the radius ratio is less than 0.59 the metal atoms form very simple structures. The interstitial atom and its nearest metal neighbors com- prise a structural unit. We can consider the structure of these materials as a metal structure with occupied inter- stitial sites. In the carbides and nitrides there are no C–C or N–N interactions. FIGURE 6.3 The NaCl crystal structure with Cl at 000. (Top) Ion Some of the nitrides and carbides such as NbC, TaC, positions; (bottom) an edge-sharing Cl octahedron. and ZrN, which adopt the NaCl structure, are low- temperature superconductors. Although there is no evidence that this property is a direct consequence of the crystal structure, the crystal structure may play an impor- FeO, CoO, MnO, and NiO are similar. NiO has the tant role. NaCl structure above its Néel temperature (523 K). Below Carbides with the NaCl structure have high hardness, this temperature magnetic ordering makes it rhombohe- are chemically inert, and have high melting temperature. dral. MnO and FeO behave similarly, but CoO undergoes The best-known example is TiC. It melts at 3147°C, has a a tetragonal distortion when the spins align; the Neél Knoop hardness of 2470 kg/mm2, a Young’s modulus of temperatures are 122, 198, and 293 K, respectively. Stoi- 310 GPa, and is resistant to oxidation up to 1200°C (for chiometric NiO is pale green. When heated in air it oxi- more discussion of this see Chapters 16–18). dizes and becomes a semiconductor. Many of the oxides, carbides, and nitrides with the NaCl structure tend to be nonstoichiometric. Titanium 6.4 GaAs (b-SiC) monoxide exists over the range Ti0.85O to TiO, while FeO never occurs; it is always nonstoichiometric with a com- We can represent this structure as follows: position ranging from Fe0.90O to Fe0.96O. As a consequence of these vacancies, the transition metal exists in two  Two interpenetrating fcc lattices one of anions and the valence states, causing the oxide to exhibit semiconductor other of cations displaced by −41 <111> properties (as for NiO).  An fcc lattice with a two-atom basis (one atom at 0,0,0 In the transition metal carbides and nitrides, think of and the other at −41 ,−41 ,−41 ) the metal as being in the close-packed arrangement with the carbon or nitrogen atoms located in interstices. The This structure is rather open: the atomic packing factor coordination number can again be determined by the (APF) for GaAs is only 0.41. In the GaAs structure each radius ratio, which in this case is given by rx/rm where rx atom has only four nearest neighbors; the coordination is the radius of the intersti- number (CN) for both Ga tial atom and rm is the and As is 4. The structure radius of the metal atom. II–VI, III–V, AND IV–IV is shown in Figure 6.4 in Some values of atomic The classical name for this structure is zinc blende or 3D. The (110) projection radius and radius ratios for sphalerite (ZnS). is important because it transition metal carbides GaAs, InP, InSb, etc. are not minerals. clearly shows the tunnels and nitrides are given in Cubic SiC is known as carborundum or moissanite. along the <110> direction 6 . 4 G a A s ( β - S i C ) ............................................................................................................................................................ 89  TABLE 6.2 Relationship between Band Gap Energies and Bonding in III–V Semiconductors Compound Eg (eV) Ionic character in bond (%) AlP 3.0 9 GaP 2.35 6 AlAs 2.1 6 AlSb 1.55 4 GaAs 1.35 4 InP 1.30 4 GaSb 0.70 2 InAs 0.33 2 InSb 0.17 1 (% ionic character was calculated using Eq. 4.24) We could have chosen to stack the cations and then fill the interstices with anions, but the anions are usually larger. Other isomorphous materials include InP, InSb, GaP (known collectively as the III–Vs), and cubic SiC. Materials with a GaAs structure are usually semi- conductors; this property is a direct consequence of the covalent bonding. In the III–Vs the band gap increases as FIGURE 6.4 The zinc-blende crystal structure. (Top) Ion positions; the ionic component to the bonding increases, as shown (bottom) corner-sharing tetrahedra. in Table 6.2. If we replace all the Ga and all the As by C, Si, or Ge, we have the diamond-cubic (dc) structure of diamond, Si and Ge. Now the bonding is entirely covalent (and Pauling’s rules would not work). We consider the (remember that there are six equivalent <110> GaAs structure again in comparison to AlN. directions). You will see many high-resolution transmis- sion electron microscope (TEM) images recorded with this sample orientation 6.5 AlN (BeO, ZnO) since it optimizes the detail seen in the image. APPLY PAULING’S RULES A second polymorph of An example is shown in ZnS is wurtzite (with a “t” Figure 6.5. BeO r Be /r O = 0.25 2+ in English but würzite in 2− We can form the struc- ZnS r Zn /r S = 0.34 2+ German). Many AB com- 2− ture by stacking the anions pounds such as AlN, GaN, in an fcc sequence and BeO, and ZnO form in the then filling half the tetrahedral interstices with cations. wurtzite and zinc-blende structures under different condi- tions. We can form the wurtzite structure by arranging the anions with hcp stacking and then filling half the tetrahe- dral interstices with cations. The structure is illustrated in Figure 6.6. The CN for both anions and cations is 4. The first nearest-neighbor environment in AlN is identical to that in GaAs but in GaAs there are four identical <111> directions whereas AlN only has one [0001] direction. Consider BeO: the bond strength is SBe = + –24 = + –21 . Each 2+ O2− must be surround by four Be2+ . So the structure has to be created by stacking tetrahedra.  For wurtzite we stack the tetrahedra ABABAB  For zinc blende we stack the tetrahedra ABCABC Although the theory clearly works beautifully, the catch FIGURE 6.5 HRTEM image of GaAs showing the Ga-As 0.14-nm is that the bonding between the Be2+ ions and the O2− ions, dumbbell. or the Zn2+ ions and the S2− ions, actually has a large 90 ......................................................................................................................................................... B i n a ry C o m p o u n d s covalent component; PACKING IN ZnS relies on the properties of sulfides in particular do 2− We have hcp packing of S ions for wurtzite and fcc its grain boundaries as will tend to be covalently 2− packing of S for zinc blende. In both structures Zn 2+ be seen in Chapter 14. GaN bonded. So it is not really ions are located in half the tetrahedral interstices to is of great interest for correct to apply Pauling’s maximize their separation. manufacturing blue-green rules that were developed laser diodes and blue and for ionic materials! green LEDs. In the future Another material that can be grown in either the wur- it will be ubiquitous in solid-state white lighting for tzite or zinc blende forms is SiC. The bonding here is energy-efficient domestic use and is already the best mainly covalent (∼88%) since both Si and C are group IV material available for green traffic lights. elements. SiC is special in that it is very difficult to produce in a single structure. It always has the chemical composi- tion SiC, but tends to be a mixture of the two stacking 6.6 CaF2 sequences. The two struc- tures are two of the poly- The mineral CaF2 is known types of SiC. The cubic FLUORITE-STRUCTURE OXIDES as fluorite, fluorspar, and form of SiC is being pro- c-ZrO2, CeO2, UO2 Blue John. The ionic duced as a diamond simu- radii are rCa = 100 pm and 2+ lant known as moissanite. r F = 130 pm, so rCa /r F is − 2+ − BeO and AlN have both been used for electronic pack- ∼0.8. By Pauling’s rules; the Ca2+ ions should have CN = aging because of their high thermal conductivity. BeO has 8 and the F − ions should have CN = 4. Since the fluoride the higher thermal conductivity, but its powder is highly ions are larger, we should think of the structure as a simple toxic. cubic stacking of the F − ions with the Ca2+ ions filling ZnO is a semiconductor where the conductivity every other cube interstice. However, you may remember depends on an excess of zinc atoms; its use in varistors the structure better by arranging the Ca2+ ions on an fcc lattice and then placing the F − anions on the –14 , –14 , –14 sites. These are the sites occupied by the Ga in GaAs, but now we occupy all such sites not just half of them. There is a large unoccupied cube interstice in the middle of the cell α at –21 , –21 , –21 (the unoccupied site in the other description). The fluorite structure is shown in Figure 6.7. Cubic zirconia (CZ) is stable only at high temperatures A or when stabilized by the addition of a dopant. CZ is a β [0001] well-known diamond simulant in jewelry. Ceria and urania are both stable in the fluorite structure. In UO2, our alter- [1100] B nate description of the structure is now clearly the better α one: the U 4+ ion is large. The unoccupied cube interstice A FIGURE 6.6 The wurtzite crystal structure viewed along [1120]. (Top) Ion positions showing the AαBβ stacking; (bottom) two FIGURE 6.7 The fluorite crystal structure. The fluorine ions occupy interpenetrating arrays of corner-sharing tetrahedra. (Only one set the eight tetrahedral sites (or the Ca ions occupy half the cube is needed to construct the crystal.) sites with an empty one at the center of the unit cell). 6 . 6 C a F 2 ............................................................................................................................................................................ 91 at –21 , –21 , –21 (in the center of the cell) in UO2 is very important; it can accommodate nuclear fission products (like He) without straining the lattice. The oxides Li2O, Na2O, and K2O are said to have an antifluorite structure because the location of the anions and cations is reversed relative to fluorite. There is a great deal of interest in fluorides with the CaF2 structure for optical applications. State-of-the-art production processes for semiconductor devices use deep- UV lasers to produce circuits with features as small as 130 nm. CaF2 will then be the material of choice for semi- conductor lithography. It is one of only a few materials that are transparent at the shorter wavelengths of deep-UV light (refer to Figure 6.2, CaF2 is transparent down to FIGURE 6.8 The FeS2 crystal structure. The Fe ions occupy the fcc positions; the cubic cell also contains four S-S dumbells. 0.13 μm). The next major steps for lithography are expected to be systems using even shorter wavelength light, ulti- mately achieving feature sizes down to 70 nm when even CaF2 will not suffice. You will also see top-of-the-line cameras using fluorite lenses so optical-quality CaF2 will retain its value. along different directions for each of the edges. The result is that NaCl belongs to the m3m class but pyrite belongs to the m3 class (still cubic but with a lower symmetry). 6.7 FeS2 Hence, NaCl has a 4-fold axis along [001] while FeS2 does not, but you can find large (>4 cm on the side) single- The structure of pyrite (fool’s gold) is complicated but crystal cubes of pyrite. Many binary metal chalcogenides interesting. The Fe cations sit inside a sulfur octahedron. (compounds containing S, Se, or Te) have an FeS2 struc- Three such octahedra then share a common vertex and ture, as do a few oxides (CdO2, α-K 2O, β-Na2O). Note that there is no edge sharing. The S–S bond length within the S is below O in the periodic table—so we might ask what octahedron is 0.307 nm or 0.332 nm, but the S–S bond that is the charge on Fe in FeS2? joins the octahedra together is only 0.218 nm long. The Some relationships between the NaCl structure and space group is Pa3̄ with a = 0.542 nm. It is instructive to materials with related structures such as pyrite are shown compare pyrite and NaCl. The pyrite structure is shown in Figure 6.9. This schematic is one illustration of how a in Figure 6.8. Both appear to have an fcc cell with the Cl simple structure can be systematically distorted to produce being replaced by an S2 dumbbell, but the dumbbells point a host of new crystal structures. PdS2 AX2 structures Pyrites Random pyrites Substitution structures { CdCl2 atacamite anatase NaCl structure {random (Li2TiO3) regular { (LiNiO2 rhombohedral) alkali halides and hydrides (LiInO2 tetragonal) Rhombohedral variants alkaline-earth oxides, Subtraction and addition (FeO, low-NaSH) sulfides structures Mg3NF3, Mn2SnS4 interstitial MO, MC, MN (Mg6MnO8, Li2V4O7) intermetallic, SnSb, PbSe Structures with complex ions Na(SbF6), [Co(NH3)6][TlCl6] calcite high-temperature forms with randomly oriented Tetragonal variants or rotating nonspherical GeS, (SnS) structure ions CaC2, KOH, KSH (3 + 3 coordination) (NH3R)X Orthorhombic TII structure (InBr, InI) low-KCN (5 : 5 coordination) FIGURE 6.9 Schematic showing how two simple structures (NaCl and FeS2) can be related to more complicated crystal structures. 92 ......................................................................................................................................................... B i n a ry C o m p o u n d s 6.8 Cu2O 6.9 CuO There are two main oxides of copper, Cu2O and CuO. You might think CuO would have a simple structure Cuprite, Cu2O, is cubic with the m3m crystal group. It (following CoO, NiO, and ZnO). Actually, tenorite (also takes a little effort to imagine the structure. Start with the known as melaconite) is monoclinic with the 2/m crystal Si structure (dc) and replace all of the Si atoms with O2− class. The Cu atoms lie approximately in the middle of anions. Each anion is now surrounded by four other anions. a square plane of four anions. Each anion is surrounded Place a Cu + cation between every pair of anions. Then, by four cations in what resembles a distorted tetrahe- where there is no tetrahedron in the dc structure, insert a dron. The square-plane coordination is the special new filled tetrahedron. We could alternatively have just feature of the cupric, Cu2+ , ion. Knowing the complex created the tetrahedra of anions with cations between each structure of these oxides can help in understanding the one, and then stacked the maximum number (without oxidation mechanisms of Cu. The square-plane coordi- changing their rotation) into the cube. This structure is nation seen in this binary oxide will be relevant when difficult to visualize! we later think about complex copper-based oxides, such A simpler way of remembering the structure is shown as YBCO. in Figure 6.10. Four Cu ions form an fcc unit cell and the two O ions occupy two of the tetrahedral sites. The O2− ions are much larger than the Cu + ions. (Remember how we think about the fluorite structure.) 6.10 TiO2 This structure is particularly interesting because it consists of two linkages of tetrahedra that are rotated TiO2 exists as rutile, anatase, and brookite. These struc- 90° to one another. The upper tetrahedron in Figure 6.10 tures are different and we cannot think in terms of simply is linked to another along the [11̄0] direction at the packing oxygen anions and filling the interstices. Each top and along the [110] direction at the bottom (A of the TiO2 structures consists of Ti4+ cations in the connects to B). The second tetrahedron has the reverse center of oxygen octahedra. In rutile, which has tetrago- arrangement. nal symmetry, the structure is constructed by linking Isomorphous oxides are Ag2O and Pb2O. Cu2O and octahedra. An octahedron is placed at each of the eight Ag2O are p-type semiconductors because they contain corners such that two are actually sharing an apex (e.g., excess oxygen atoms. The energy gap in Cu2O is ∼1.5 eV, at T). The six points on these octahedra are then con- and the impurity levels (acceptors) are about 0.3–0.6 eV nected by one rotated octahedron sitting in the center of above the valence band edge. Cuprite occurs naturally as the unit cell. The edges of the octahedra thus link a transparent red mineral. together to give chains along the z-axis, as shown in Figure 6.11. Each Ti4+ is thus surrounded by six O2− ions and each O2− anion is surrounded by three Ti4+ ions. The structure is primitive tetragonal with a = 0.459 nm, c = 0.296 nm, and two formula units per unit cell. The easiest projection is (001) where we are looking along the 4-fold axis. In anatase, the arrangement of the anions and cations is similar and the crystal is again tetragonal, but now each octahedron is somewhat distorted and shares four of its edges with other octahedra. In brookite, the structure is even more complicated with octahedra sharing both edges and corners. So the trend rutile–anatase–brookite is to ever decreasing symmetry. Rutile is the simplest compound of a family of titanates that has high dielectric constants ranging from κ ∼ 100 for rutile to several thousand for BaTiO3. Of B the other oxides that share the rutile structure, CrO2 A is ferromagnetic with a Curie temperature of 389 K, and VO2 and MnO2 are antiferromagnetic with Néel temperatures of 343 K and 84 K, respectively. SnO2 (cassiterite) and several binary fluorides such as MgF2 FIGURE 6.10 The Cu2O crystal structure. (Top) Ion positions; are isomorphous. A lesser known isomorphous com- (bottom) two “occupied” tetrahedra. The Cu ions sit at the fcc pound is stishovite, which is a high-pressure form of sites; two O ions “occupy” tetrahedral sites. SiO2. 6 .10 T i O 2 .......................................................................................................................................................................... 93  stacking), which is why we see the Al3+ ions when looking down the c-axis. It is instructive to consider this structure in some detail. We can build it by stacking occupied octahedra (shown on the right). Each octahedron shares a face with the one above and the one below, but these are not regular octahedra. Pauling’s rules say that it is not favorable to share faces of polyhedra. To compensate, the Al3+ cations move away from each other and toward the unoccupied octahedron (e.g., P1 and P2) as can be seen in Figure 6.12; the oxygen anions move close together (e.g., the boxed group labeled S) to shield the nearby positive charges. The result is that the (0001) “plane” of Al3+ cations actually lies on two distinct (0001) planes. This also means that there are two different oxygen–oxygen ion distances in the octahedra. We saw a similar effect in Section 6.7. Specific letters are used to designate several of the common crystallographic planes in corundum (Table 6.3). P1 P2 These different orientations are shown schematically in T Figure 6.13. It is useful to know this convention, especially P1 FIGURE 6.11 Rutile crystal structure viewed nearly parallel to the z-axis. Each of the pairs of overlapping octahedra (e.g., P1/P2) S shares an edge. The two octahedra in the lower right thus have point T in common. The central octahedron touches each of the eight at the corners. P2 6.11 Al2O3 Alumina (the ceramic) or corundum (the mineral) refers to α-Al2O3. When it is doped with Cr3+ the mineral is called ruby; when doped with Ti ions we call it sapphire. [1120] Natural sapphire actually contains a combination of Ti4+ and Fe2+ , which compensate the charge difference. Some [0001] of the Fe2+ can be replaced by Ti2+ so that the Fe : Ti ratio can vary. (We may also have Ti3+ present.) Hematite, Fe2O3, is isomorphous with alumina; it actually has almost exactly the same c/a ratio. Ilmenite is closely related, but with Fe + Ti instead of Al + Al. Cr2O3 and Ga2O3 have a related structure. (In2O3 is completely different!) The crystal structure of Al2O3 is trigonal with a 3̄m crystal class, and has a pseudohexagonal oxygen sublattice (which is why we usually use a hexagonal cell and four- index Miller–Bravais notation) but the symmetry really is 3-fold, not 6-fold. In Al2O3 the oxygen ions have what can be thought of as hcp stacking with the Al3+ ions occupying two-thirds of the octahedral interstices (balancing the charge). The corundum structure is shown from two direc- FIGURE 6.12 The sapphire crystal structure. (Top) [112̄0] view; tions in Figure 6.12. Six parallel (0001) planes of oxygen (bottom) [0001] view; (left) atomic models; (right) stacking octahedra. P1 and P2 are two unoccupied octahedra. S is a triangle ions are required to build the Al2O3 rhombohedral cell of more closely spaced O2− ions. Open circles in the lower left because the stacking is AαBβAγBαAβBγ; the Al3+ ions show the AB stacking of the anions. The unit cell is outlined for always sit in the C positions (thinking of the ABC fcc both projections. 94 ......................................................................................................................................................... B i n a ry C o m p o u n d s  TABLE 6.3 Common Crystallographic Planes in Sapphire Plane “name” Miller–Bravais index d spacing (nm) a (112̄0) 0.2379 Mo c or basal plane (0001) 0.2165 m (101̄0) 0.1375 n (112̄3) 0.1147 S r (11̄02) 0.1740 if you want to order or use single-crystal sapphire substrates. Aluminum oxide is by far the most widely used com- 25 63, 87 pound with this structure. As a single crystal it is used in watch bearings and pressure-resistant windows. Hot- 13, 37 75 pressed powders are employed as electrical insulators, windows or radomes transparent to microwaves, envelopes a=0.3 16 nm for lamps, and electrical devices. In polycrystalline form it is also the basis of refractory bricks, crucibles, and spark-plug insulators. 6.12 MoS2 AND CdI2 FIGURE 6.14 The crystal structure of molybdenite. The S ions MoS2 and CdI2 are based on the hcp structure. In molyb- stack AABB while the Mo ions occupy half the trigonal prisms in denite, the Mo atoms are located in the positions corre- each S “sandwich”. sponding to the unit cell of the hcp structure. An S–S pair is centered along the c-direction directly opposite the Mo atoms, giving the structure shown in Figure 6.14. The expect that phases with r M/r X between 0.41 and 0.73 would stacking sequence can be written as AbA BaB, where the form any of these structures. However, the more ionic capital letters denote the S atoms and the lowercase letters compounds form the rutile structure, while the more cova- the Mo atoms. The coordination number of the metal atom lent compounds have the CdI2 structure. Those in which is 6, as it is in the TiO2 and CdI2 structures. Thus, we would the bonding is intermediate adopt the MoS2 structure. Several of the Mo and W chalcogenides adopt the molybdenite structure, but MoS2 is the most interesting (a) 30° (m) phase and is an excellent (dry) lubricant. It is instructive to compare the MoS2 structure to the structure of graphite, 30° which is shown for comparison in Figure 6.15. The unit (m) r n n n n c r r n n (c) 61° 57.6° c (r) (n) n r n n r 32.4° a (m) a a n n n r FIGURE 6.15 The crystal structure of graphite. The C atoms form hexagonal rings as seen on the left. A unit cell is outlined and is FIGURE 6.13 The location of important planes in sapphire. shown alone on the right. 6 .1 2 M o S 2 a n d C d I 2 ....................................................................................................................................................... 95 cell of graphite is clearly hexagonal and has lattice param- Reconstructive Reconstructive eters a = 0.2456 nm and c = 0.6696 nm. The C–C bond High High High length is 0.142 nm in the sheets and 0.335 nm between quartz 867°C tridymite 1470°C cristobalite sheets. The six-membered rings are stacked to give an Displacive 160°C ABAB stacking sequence. It is the long bond distance in the c-direction that gives graphite similar properties as a Middle Displacive 573°C tridymite Displacive 200±35°C solid lubricant. (Actually, it is the weak bonds between pairs of basal planes that cause the bonds to be long, which Displacive 105°C is the underlying reason.) As expected, graphite has highly anisotropic properties. The properties of graphite within Low Low Low the sheets are similar to those of a metal, whereas the quartz tridymite cristobalite properties perpendicular to the sheets are more like those of semiconductors. FIGURE 6.16 Schematic of how the polymeric forms of silica can be converted into one another by displacive or reconstructive Since in MoS2 and graphite the interlayer, van der structural transformations. Waals, bonding is very weak, the structures can also exist in a rhombohedral form with a stacking sequence AbA BaB CcC; other layer materials naturally adopt this structure. assumed by a compound differ only in the order in which The crystal structure of BN is closely related to that of a two-dimensional layer is stacked. The effect is common graphite except that the atoms in one layer lie directly in layer structures (e.g., MoS2, graphite, and layer sili- above those in the next and the six-membered rings are cates). Silicon carbide (SiC), a ceramic material of con- made up of alternating B and N atoms. siderable importance, displays the richest collection of This structure can also be derived from the hcp struc- polytypic forms. More than 200 SiC polytypes have been ture by replacing the metal atoms in the unit cell by I determined. Figure 6.17 shows the structural relationship atoms and by adding Cd atoms at the corners of the unit between five of the different polytypes. Table 6.4 gives cell. Thus, the I− ions sit in an hcp arrangement with the the stacking sequence and lattice parameters for the Cd2+ ions between them. The more covalent AB2 phases polytypes. tend to form the CdI2 structure. Thus, the larger polariza- You will notice in Figure 6.17 that we have translated ble iodides and bromides form this structure with highly the usual cubic representation of the zinc blende cell into polarizing cations, while the fluorides favor the rutile a rhombohedral one, which can be compared directly with structure. the unit cells of the other SiC polytypes. A way of viewing the cubic (3C) cell as a rhombohedral cell is shown in Figure 6.18. The former cubic-cell diagonal has now 6.13 POLYMORPHS, POLYTYPES, become the c-axis of the corresponding rhombohedral AND POLYTYPOIDS cell. Of course, the arrangement of the atoms remains unchanged. Polymorphs are materials that have the same chemical You will also notice that we introduced a new notation composition but different crystal structures. Many ceramic scheme in Table 6.4. The Ramsdell notation is frequently materials show this behavior, including SiO2, BN, BaTiO3, used when referring to different polytypic forms and ZrO2, and BeO. Transitions between the different poly- describes the stacking sequence in these complex morphs may occur as a result of changes in temperature structures. The notation consists of a number and a letter. or pressure. The relationships between the polymorphic The number indicates the number of layers in the sequence. forms of silica are shown in Figure 6.16 with the corre- The letter indicates the structure type (C = cubic, H = sponding transformation temperatures. These are not the hexagonal, R = rhombohedral). At one extreme we have only known phases of SiO2. At pressures around 2 GPa, the zinc blende SiC (3C) with pure cubic stacking in the quartz transforms into coesite. At even higher pressures, [111] direction. At the other extreme we have wurtzite SiC around 7.5 GPa, coesite transforms to stishovite. The high- (2H) with pure hexagonal stacking in the [0001] direction. pressure forms have been prepared experimentally and are The other polytypes have either H or R stacking sequences. also found at the famous Cañon Diablo Meteor site in For example, the carborundum III (B5) structure in Figure Arizona. (We will examine these structures further in 6.17 has the Ramsdell symbol 4H—the sequence consists Chapter 7.) of four layers, then repeats, and the structure is When an element exists in different solid phases we hexagonal. refer to the phases as allotropes. Graphite and diamond This chapter discusses the structure of a series of are two allotropes of carbon. binary compounds that are also used as models for other Polytypism is a special—one-dimensional—type of compounds. All ceramics students must learn some of polymorphism in which the different crystal structures these structures by heart, but it is equally important to 96 ......................................................................................................................................................... B i n a ry C o m p o u n d s  TABLE 6.4 Relationship between Polytypes in Silicon Carbide Lattice parameters Ramsdell Structure Strukturbericht Stacking sequence a (nm) c (nm) notation Wurtzite B4 AB 0.3076 0.5048 2H Zinc blende B3 ABC 0.308 0.755 3C Carborundum III B5 ABAC 0.3076 1.004 4H Carborundum II B6 ABCACB 0.3080 1.509 6H Carborundum I B7 ABACBCACBABCBAC 0.3080 3.781 15R a 2 3 c=15 a a 2 3 2 3 a c=6 2 3 c=4 a 2 3 c=3 c=2 B4 B3 B5 B6 B7 Wurtzite Zincblende SiC III SiC II SiC I FIGURE 6.17 The stacking sequence for five SiC polytypes. know the reason we chose these structures and how they relate to Pauling’s rule (Chapter 5). Also remember that Pauling’s rules were developed for ionic materials, so any covalent component may compromise the predictions. The polyhedra found in these simple structures reappear in much more complex structures as will be seen in Chapter 7. Each of the compounds has an application as illustrated γ here, but we concentrate more on those in later chapters. As an example, CaF2 used to be known as an interesting C structure and a semiprecious stone. That it would today C β β be grown as 200-mm-diameter crystals for 135-μm UV ch lithography would not have been imagined a few years B B ago. Although it is used for its optical properties, the ori- α α entation of the crystal must be controlled because the ac optical properties depend on the crystal orientation. The A A best large sapphire windows (with minimum birefrin- ah gence) are cut from (0001) crystals. The crystal structure FIGURE 6.18 Relating the cubic and rhombohedral unit cells for of crystalline materials controls most of the properties of zinc blende. these materials. 6 .13 P o ly m o r p h s , P o ly t y p e s , a n d P o ly t y p o i d s ..................................................................................................... 97  CHAPTER SUMMARY To really understand ceramic materials, you must know their basic crystal structures. Then you can picture the polyhedra such as the tetrahedron and the octahedron and know what we mean when we talk about linking them, distorting them, substituting them, etc. Always keep in mind Pauling’s rules. We have discussed the most important of the structures of the binary compounds: you must know CsCl, NaCl, GaAs, AlN, CaF2, MoS2, and Al2O3 by heart. We have also included FeS2, Cu2O, CuO, CdI2, and TiO2 in part because these materials are becom- ing more important in their own right, but also because they provide insight into many related binary compounds. Throughout this chapter and in Chapter 7 we have drawn many of the dia- grams using CrystalMaker. This is an affordable program for the Mac and PC and should be available to every student taking any ceramics or mineralogy course. It is today’s equivalent of the real (wooden) ball-and-(steel) stick models that used to be passed around the class but rarely were taken home to your dorm-room. It allows you to switch from ball-and-stick to poly- hedra at the click of a mouse. PEOPLE IN HISTORY Bragg, W.H. and son W.L. Bragg did not discover X-ray diffraction, but they realized that it could be used to determine the structure of crystals. The first structure they solved was that of NaCl. They won the 1915 Nobel Prize in Physics “for their services in the analysis of crystal structure by means of X-rays.” Aside from the Braggs, the other father and son tandem of Nobel laureates is the Thomsons (Sir Joseph Thomson, Physics 1906, and his son George Paget Thomson, Physics 1937) and the Siegbahns (Karl Manne Siegbahn, Physics 1924, and his son Kai Siegbahn, Physics 1981). Coes, Loring, a high-pressure scientist, gave his name to the high-pressure form of quartz. He first synthesized coesite in 1953 in the Norton Laboratories. Moissan, Ferdinand Frédéric-Henri began researching diamond synthesis in 1889. His idea was to produce diamonds by passing an electrical current through a sample of iron and sugar charcoal, then rapidly quenching it in cold water. However, after one experiment Moissan did isolate very small diamond octa- hedral crystals. After his death in 1907 it was revealed that one of Moissan’s assistants had planted natural diamonds to make Moissan feel better. Moissan did actually make SiC, which was later given the name moissanite. IUCr is the International Union of Crystallography. The Society publishes the journal Acta Crystallographica. IUCr recorded: “the very first specialized X-ray diffraction meeting with international representation was an informal one and was held at Ewald’s mother’s house on the Ammersee, Germany, in 1925. In addition to Ewald, the small group included W. L. Bragg, L. Brillouin, C. G. Darwin, P. J. W. Debye, R. W. James, M. von Laue, I. Waller and R. W. G. Wyckoff.” GENERAL REFERENCES Bragg, W.L. and Claringbull, G.F. (1965) Crystal Structure of Minerals, Cornell University Press, Ithaca, Volume IV of the series The Crystalline State. If you have time to look at the original work, see this in your library. CrystalMaker. www.crystalmaker.co.uk We repeat this information: you should try it. Deer, W.A., Howie, R.A., and Zussman, J. (1996) An Introduction to the Rock-Forming Minerals. 2nd edition, Prentice-Hall, Englewood Cliffs, NJ. This is a classic for good reason. Galasso, F.S. (1970) Structure and Properties of Inorganic Solids, Pergamon, Oxford. A useful reference that surveys a wide range of structures. Not as complete as Wells. Hyde, B.G. and Anderson, S. (1989) Inorganic Crystal Structures, Wiley, New York. The structures of many crystals are beautifully described and related in this book. Megaw, H. (1973) Crystal Structures: A Working Approach, W.B. Saunders Co., Philadelphia. This is such a nice text. O’Keeffe, M. and Hyde, B.G. (1996) Crystal Structures, I. Patterns and Symmetry, Mineralogical Society of America, Washington, D.C. Another treasure. Putnis, A. (1992) Introduction to Mineral Sciences, Cambridge University Press, Cambridge. Wells, A.F. (1984) Structural Inorganic Chemistry, 5th edition, Oxford University Press, Oxford. This is the book that you go to first when you want to learn about a new structure. The price may mean that you consult it in the library rather than buying your own copy. SPECIFIC REFERENCES Ramsdell, R.S. (1947) “Studies on silicon carbide,” Am. Mineral. 32, 64. The original description of the notation. 98 ......................................................................................................................................................... B i n a ry C o m p o u n d s  Xu, X., Beckman, S.P., Specht, P., Weber, E.R., Chrzan, D.C., Erni, R.P., Arslan, I., Browning, N., Bleloch, A., and Kisielowski, C. (2005) “Distortion and segregation in a dislocation core region at atomic resolu- tion,” Phys. Rev. Lett. 95, 145501. EXERCISES 6.1 Draw and label (the ions and at least three directions) the [100], [111], and [110] projections for rocksalt, GaAs, CsCl, and fluorite. 6.2 Draw and label (the ions and at least three directions) the [0001], [11̄00], and [112̄0] projections for hematite. 6.3 Draw and label (the ions and at least three directions) the [0001], [11̄00], and [112̄0] projections for ZnO. 6.4 Estimate the radius of the cubic interstice in UO2. Discuss this result using Pauling’s rules. 6.5 You know the crystal class of FeS2 and its space group. Explain the relationship. 6.6 Prove that the APF for GaAs is 0.41. The atomic radii for Ga and As are 0.135 and 0.125 nm, respectively. The lattice parameter is 0.565 nm. 6.7 The coordination number for silver and copper ions in Ag2O and Cu2O is four. This is quite unusual for these ions. What would you expect the coordination number to be based on the sizes of the ions and how might you explain the observed differences, if any. The ionic radii of the ions are given in Table 4.6. 6.8 Does rutile obey Pauling’s rules? 6.9 How do the densities of high cristobalite and silica glass compare? You will need to dig for the data on this one—the library or the Internet. 6.10 NaCl, TiC, and PbS all have the same structure. Are they all good examples of Pauling’s rules in action? C h a p t e r S u m m a ry .......................................................................................................................................................... 99  7 Complex Crystal and Glass Structures CHAPTER PREVIEW This chapter is separated from the previous one just to make it less overwhelming. We have demonstrated the principles in Chapter 5 and considered some of the simpler ceramic structures in Chapter 6. Now we are considering structures that have more than two chemically different atoms in the unit cell (like YBa2Cu3O7), although some will still only have two components. We will include materials (like SiO2) in which covalent bonds are particularly important and encounter materials involving secondary bonds such as van der Waals interactions (especially in the clay minerals). It is a little difficult to learn these structures by heart but some, like cristobalite and per- ovskite, you should know. For others, you may survive by just knowing the basic ideas involved. This emphasizes the reason for this chapter (and Chapter 6)—if you understand the building blocks, you can better appreciate the properties of more complex structures that are composed of combinations of such building blocks. The logic behind the order in which these are dis- cussed is first cubic, then the silicates (starting with silica), then the complicated ones, and finally some new materials that challenge our perception of what a ceramic is. Glass has often been treated separately from ceramics, but today few programs in materials science have the time for a specialized course on glass. We include a discussion of glass struc- tures in this chapter since they link so closely with the crystal structure of crystalline silicates and the general concept of coordination polyhedra. We will discuss the properties of glass later. Remember that the structure of glass is not random; it just lacks long-range order. We have point defects and other defects in glass just as we do in crystals; the challenge is to define the nondefective structure to which we can relate them. What makes a point defect in glass a defect and not just part of the glass? A common mantra throughout this chapter is that diagrams are essential. A difficulty is that you generally need more than one diagram (view) to appreciate a three-dimensional (3D) structure. Computer programs can make the 3D aspects much more apparent. In this and the previous chapter, the xyz-axes in the schematics of cubic crystal structures lie along the cube edges; the length of the cube edge is the lattice parameter. 7.1 INTRODUCTION Al3+ ion (rAl3+ /rO2− = 0.38), which sits inside oxygen tetra- hedra in many aluminosilicates but inside octahedra in In most simple metal-oxide structures, r M << r X and the others (as is the case for Al2O3). The Al3+ ion has a CN structures can be built up by considering a nearly close- of both 4 and 6 in sillimanite, both 5 and 6 in andalusite, packed arrangement of oxygen ions with cations located but only 6 in kyanite, even though all three are stable in interstices. The ionic radius ratios given earlier are minerals and all have the composition Al2SiO5. Another useful and provide a means of predicting the coordination example is the Zr4+ ion (r Zr 4+ /rO2− = 0.51), which is octahe- number (CN) of a particular compound and often the drally coordinated in several crystals, e.g., CaZrO3 (iso- predictions are in good agreement with observed values. morphous with perovskite), but has a CN of 8 in zircon, In cases in which the observed CN differs greatly from ZrSiO4. As Pauling said, the size of the ion depends on the expected value, such as 12 for K+ in mica, the site that it occupies. KAl3Si3O10 (OH) 2, it is probable that the other ions present Table 7.1 lists some deviations from the CN predicted play the most important part in determining the by radius ratios. Where the observed CN is larger than arrangement. predicted there is a gain in electrostatic energy by increas- The ions that are close to the transition values of the ing the number of nearest neighbors. This gain is larger radius ratio can show variations in CN. An example is the than the energy expended in deforming the surrounding 100 ................................................................................................................ C o m p l e x C ry s ta l a n d G l a s s S t ru c t u r e s  TABLE 7.1 CN and Bond Strength, S, of Various Cations In spinel we often think of the O2− ions as sitting on with Oxygen the fcc lattice sites. Actually, they are generally slightly Ion rM (pm) CNtheory CNobs S displaced from these exact positions. Considering the cations and thinking of MgAl2O4, the Al3+ ions now B3+ 27 3 3, 4 1 or −34 occupy some of the octahedral sites with the Mg2+ ions Li + 76 6 4 −14 being located on tetrahedral sites. This arrangement is the Si4+ 40 4 4, 6 1 “normal” as opposed to “inverse” spinel structure; most Al3+ 54 4 or 6 4, 5, 6 −34 or −12 spinels are not exactly normal! Note that the arrangement Ge4+ 53 4 4, 6 1 or −32 of the oxygen ions is essentially the same as in MgO, but Na + 102 6 4, 6, 8 −16 Zr4+ 72 6 6, 8 −32 or −12 now some of the octahedral and some of the tetrahedral Ca 2+ 100 6, 8 6, 7, 8, 9 −14 interstices are occupied instead of only the octahedral Ce4+ 87 6 8 −12 ones. K+ 138 8, 12 6, 7, 8, 9, 10, 12 −19 Normal spinel: the A2+ ions occupy only tetrahedral  sites and the B3+ ions occupy only octahedral sites.  Inverse spinel: all the A 2+ ions and half the B3+ ions sit on the octahedral sites; the tetrahedral sites are occu- pied now by the other half ions. Remember that the of the B3+ ions. ions are not rigid spheres. SOME IMPORTANT SPINELS Where the observed CN is γ-Fe2O3 Maghemite The arrangement of the smaller than predicted MgAl O 2 4 “Real” spinel cations is such that the there is often an appre- NiFe2O4 A classic ferrite lattice parameter of ciable amount of covalent Fe3O4 Magnetite the spinel MgAl2O4 is close character to the bonding. to twice that of the corre- Covalent bonds are strongly sponding MgO. If we think directional. of the spinel cubic unit cell as divided into eight cubes, Why so much about silicates? Effort is devoted to sili- these smaller cubes would be almost exactly the size of cates not just because they are the main constituents of the MgO unit cell. This means that six parallel {111} the earth’s upper mantle (and therefore the geological planes of oxygen ions are required to construct the rhom- materials we most readily see), but because they are really bohedral cell rather than three. ubiquitous (even when you do not at first realize it) and Looking at some ionic radii, we can understand why therefore provide many of our raw materials. We suspect the same structure can be formed with Ni or Co substitu- that silicates also have an enormous range of unexplored ting for Mg. Similarly Fe or Cr can substitute for Al. applications. Silicates also link in with the second unusual topic for such a chapter, namely glass: many glasses are O2−, 140 pm; Mg 2+ , 72 pm; Ni2+ , 69 pm; Co2+ , 75 pm silicates that lack long-range order. O2−, 140 pm; Al3+ , 54 pm; Fe3+ , 65 pm; Cr 3+ , 62 pm If we look at this structure along a [110] direction 7.2 SPINEL (Figure 7.1a and b), we can see the tetrahedra and octa- hedra. Remember that the anions are in an fcc stacking The mineral spinel is MgAl2O4. Spinels have the general sequence, so this is a close-packed direction for the O ions. formula AB2O4 although later we will also write it as Spinel thus shows particularly clearly how a structure can AO · nB2O3, where n describes the nonequimolarity. Bragg be built up by systematically filling some of the octahedral and Nishikawa actually solved the spinel structure inde- (O) sites and some of the tetrahedral (T) sites. The appar- pendently in 1915. The spinel structure is so important ently touching tetrahedra are actually at different heights because the magnetic ferrites are spinels. For the ferrites in this projection, so they do not share an edge. The lines P1 we express the chemical formula as MO · Fe2O3, where M and P2 remind you where the edge-on {111} planes lie. If we is a divalent metal ion like Mn, Ni, Fe, or Co (or a mixture rotate the structure through 90° about the horizontal [11̄0] of such ions). axis, we reach the [001] projection shown in Figure 7.1c. Although structurally quite simple, spinel has a large We can look at the structure in several ways. In Figure number of atoms or ions associated with each lattice point 7.1b, the cell has been divided into eight distinct layers of in its Bravais lattice. The Bravais lattice is face-centered ions. This sequence is PqRsTuVw, where the upper case cubic (fcc), and the unit cell contains a total of 56 ions (32 refers to mixed O2− plus octahedral cation layers and oxygen ions). There are four lattice points per fcc unit cell the lower case refers to the tetrahedral cations. This and thus 14 ions associated (two formula units) with each method of building the structure emphasizes that there are lattice point. only two different “planes” of ions to stack! The row of 7. 2 S p i n e l ........................................................................................................................................................................ 101  OF OF nates of atoms in the unit cell. Since the structure factor, T F, depends on xn, yn, and zn, the value of Fnormal ≠ Finverse. O O O O In γ-Fe2O3, the other cation is a “vacancy”; maghemite T T is known as a defect spinel and is related to the other P1 important defect spinel γ-Al2O3 (although there may be OF P2 T T other complications involving H + ions in this case). The O O O O Fe ions in magnetite occupy both tetrahedral and octahe- T dral sites so it is FeFe2O4, but we have not specified which (A) OF OF ion (Fe2+ or Fe3+) sits where. Spinels are notorious for being nonequimolar (n ≠ 1, which does not mean the same w as nonstoichiometric). When the formula is written V as AO · nB2O3, the value of n can vary from 1 to 3.5 u depending on A, B, and T (temperature). T s R 7.3 PEROVSKITE q P With a general formula ABO3, the A cation and the anions (B) effectively form an fcc array with a large octahedron in the center of the cell but no available tetrahedra (because of the charge). The ideal perovskite structure is simple cubic, and this is what we generally imply when we refer to the perovskite structure. The mineral perovskite is CaTiO3 and is actually orthorhombic at room temperature, becoming cubic only at temperatures above 900°C. Other ceramics with the perovskite structure include BaTiO3, SrTiO3, and KNbO3, each being written in the general form ABO3. Do not confuse the structure with that of ilmenite, FeTiO3, which is related to the alumina structure. (C) The perovskite structure is shown in Figure 7.2a. FIGURE 7.1 (a–c) The spinel crystal structure. The 32 anions in Looking at the ionic radii, we can see a trend. The O2− the unit cell form eight slightly distorted fcc oxygen lattices. The anion and the larger cation (A2+) have similar radii, so that cations are then distributed with one tetrahedron occupied in each the structure is not just determined by O2−. The larger “subcell” (rather like Cu2O). The 16 octahedral sites are then cation and the anion combine to form a “close-packed” distributed in rows along one <110> direction or the orthogonal one depending on the layer [V,R or T,P in (b)]. arrangement with the smaller cation, B4+ , sitting in the oxygen octahedral interstices. The octahedra then link together by sharing corners as shown in Figure 7.2b. The bond strength is given as octahedral sites actually rotates 90° every 1/4 cell (i.e., every two layers). Hence layers P and T are shifted relative 4 2 2 1 to one another, but are rotated 90° relative to R and V. The Ti − O = + = ; Ca − O = + = 6 3 12 6 structure is effectively shifted by 1/4 [11̄ 10] every four layers (half way up the cell). Each O2− anion coordi- (We will return to this stack- BaTiO3 AND KNbO3 nates with two Ti4+ and ing in Chapter 14.) four Ca2+ cations so that How did Bragg deter- A B O the total bond strength is mine the spinel structure r Ba = 135 pm r Ti = 61 rO = 140 pm 2+ 4+ 2− 2 1 and how can you distinguish r K = 138 pm + r Nb = 64 rO = 140 pm 5+ 2− 2× + 4 × = +2 normal and inverse? X-ray 3 6 diffraction measures the Barium titanate (BaTiO3) distribution of electrons CaCO3 AND CaTiO3 is the prototype ferroe- and, hence, allows us to The carbonate is an inorganic salt. The anion is CO3 , 2− lectric material. It has the deduce atom position by which is quite like a sphere, although it actually has 3- ideal perovskite structure measuring the structure fold symmetry and is shown as a triangle in Figure 7.3. above 120°C. At temper- factor. The positions xn, yn, This anion and the Ca2+ are arranged in a similar way atures below 120°C the and zn are fractional coordi- to NaCl but with a 3-fold distortion. small cation (Ti4+) shifts 102 ................................................................................................................ C o m p l e x C ry s ta l a n d G l a s s S t ru c t u r e s  off its ideal symmetric position at the center of each octa- hedral interstice. This shift creates an electric dipole; it polarizes the structure electrically, which in turn causes the material to become noncubic; this changes the cell dimensions. Spontaneous electrical polarization in the absence of an applied electric field is termed ferroelectri- city. The link between electric field and mechanical defor- mation of the unit cell is known as the piezoelectric effect: it allows us to convert an electrical signal to a mechanical one and vice versa. This shift actually has the same origin as the flexibility of this structure: many ions can fit in the central ocahedron. (A) The perovskite structure is particularly important for several reasons:  Many perovskites are ferroelectric  Many perovskites are piezoelectric  Many perovskites have a high dielectric constant The perovskite structure is also of interest to mineralo- gists. A mineral with the perovskite structure of composi- tion close to MgSiO3 is believed to be the predominant mineral in the lower mantle (depths of about 600 km) of the earth. The perovskite structure of MgSiO3 is stable (B) only at very high pressures. FIGURE 7.2 The perovskite crystal structure. The lattice is simple cubic with several cations able to occupy the central octahedron. (a) Atomic model; (b) the polyhedron. (A) (B) FIGURE 7.3 The crystal structure of calcite. The Ca cations sit in an octahedral site; the CO2− ions are 2+ represented as a triangle that each links six octahedra. The octahedra have one of two orientations each and “stack” in an ApBqCr sequence giving the 3̄ symmetry producing the c lattice parameter of 1.71 nm (a is 0.50 nm). 7. 3 P e r ov s k i t e ................................................................................................................................................................ 103  Tetrahedron 3-, 4-, 6-T rings Single chain Double chain Sheet End View Olivine Beryl (Si6O18)12- Pyroxene Amphibole Mica (SiO4)4- Zeolite (Si4O12)8- (SiO3)2- (Si4O11)6- (Si2O5)2- Bentonite? (Si3O9)6- FIGURE 7.4 Arranging SiO4 tetrahedra in different silicates. The exception is the sheet that extends indefi- nitely in all directions in the plane. These are the best known ways of combining (or not) the SiO4 tetrahedra. Perovskites have also received much attention since To give you an idea of the variety of structures that are 1986 because the superconducting oxide YBCO contains then possible, a discussion of just the structures (not prop- perovskite structural elements. The importance of this erties—just structures) of rock-forming minerals consist- structure was again realized in 1993 when the phenome- ing of isolated SiO4 tetrahedra is the subject of a 900-page non of colossal magnetoresistance (CMR) was discovered text. Table 7.3 lists some examples of the classes of sili- in a range of manganate ceramics with a layered per- cates with special structures; Table 7.4 gives an idea of the ovskite structure similar to that found in YBCO and other complex crystallography involved. Clearly, we cannot go high-temperature superconductors. through all the ideas of silicates since this is an enormous field. You should know the general principles, the bonding, etc., and the language! 7.4 THE SILICATES AND STRUCTURES A special feature of the silicates is that it is often quite BASED ON SiO4 easy to replace the cations that are outside the SiO4 tetra- hedra. This leads to the idea of isomorphous replacement. We can start by considering ionic radii and Pauling’s We can even replace the Si 4+ in the SiO4 tetrahedron with rules. other similar sized ions such as Al3+ having the same oxygen coordination. The idea is that rAl /rO = 0.39, 3+ 2− rSi /rO = 0.40/1.40 = 0.29 < 0.41 4+ 2− which is close to 0.41. Al3+ can have six or four coordina- tion. To balance the charge we also need to replace some Thus, tetrahedral coordination is expected and the bond strength, S, is +1 (= + –44 ). The (SiO4) 4− units are the build- ing blocks for all silicates; each O2− ion is coordinated with two Si4+ ions, so the tetrahedra join at corners. Actu- ally there is a very large covalent component too so that TABLE 7.2 Linking SiO4 Tetrahedra to Make Silicates the Si–O bond is very strong (it is only ∼40% ionic); Number of therefore Pauling’s rules do not really apply and we just shared vertices Structure unit Structure formula talk about the SiO4 unit and take account of the charge separately. 0 [SiO4] 4− Orthosilicates 1 [Si2O7] n6− Pyrosilicates Some possible linkages of SiO4 tetrahedra are illus- 2 [SiO3 ] n2n− Pyroxene chain trated in Figure 7.4. This is a key idea in understanding 2.5 [Si4O11] n6n− Amphibole silicates. We can either keep the SiO4 tetrahedra separate Note the difference between or link them to one another. If we link them, then we can this and infinite-sheet clays form chains or rings. Then we can join rings to make (Si2O5) 3 [Si2O5] n2n− sheets or join chains to make double chains. Units formed 4 [SiO2] n0 3D network by these combinations are listed in Table 7.2. 104 ................................................................................................................ C o m p l e x C ry s ta l a n d G l a s s S t ru c t u r e s  TABLE 7.3 Examples of Silicate Structures TABLE 7.5 Some Densities Orthosilicates Forsterite Olivine and garnet refer to Oxide a (nm) c (nm) Density (g/cm 3) Fayalite groups containing many Monticellite well-known minerals High quartz 0.501 0.547 2.65 Grossular High tridymite 0.503 0.822 2.26 Ring silicates Beryl Rings of SiO 4 tetrahedra High cristobalite 0.713 2.32 Cordierite connected at a corner MgO 3.59 Chain silicates Enstatite Pyroxenes are single-chain Al2O3 3.96 Diopside compounds Sheet silicates Muscovite Mica and kaolinite refer to Biotite groups of sheet silicates Talc Framework silicates Anorthite Groups include the quartz minerals, feldspars, and zeolites involves a displacive phase transformation; the atoms need to move only slightly relative to one another. However, to change from one form to another requires breaking bonds. This process is much more difficult and is known as a reconstructive phase transformation. Na + (say) by Ca2+ . The following are two well-known The Si–O–Si arrangement of ions does not always examples: lie exactly on a straight line, especially for the low- temperature forms. If the bonding were purely ionic, the  Forsterite and fayalite are structurally almost identical line would be straight and the O2− should lie exactly in the and thus form a continuous solid solution with Mg2+ middle: the reason in each case is that we want to maxi- gradually being replaced by Fe2+ across the series (as mize the electrostatic attractive forces and minimize the we go to fayalite). electrostatic repulsion. However, the Si–O bond is ∼60%  The feldspar minerals fall into two main series, the covalent, so there is a strong tendency toward directional alkali (K–Na) feldspars, where we gradually replace bonding. The different forms of silica have different densi- Na + by K+ across the series, and the plagioclase ties, each being much less dense than the more ionic (Ca–Na) feldspars, where there is a continuous varia- oxides as shown in Table 7.5. tion in composition by substituting Ca2+ + Al3+ for Na + The structure of high cristobalite, showing the highest + Si4+ . symmetry, is illustrated in Figure 7.5 as arrangements of atoms and as a stacking of tetrahedra. The Si4+ cations sit in the same positions as the Si atoms in the diamond-cubic 7.5 SILICA (dc) Si structure. An O2− anion is located between each pair of Si4+ cations! In high tridymite the Si4+ cations sit Silica has many different polymorphic forms (see Section on wurtzite sites instead of zinc blende and the O2− anion 6.13). We will discuss three forms of SiO2, namely quartz, again sits between the cations! You can appreciate the tridymite, and cristobalite (note the spelling). For each movement that is needed to transform tridymite to cristo- form, at low temperatures (the α phase) we find a structure balite. When tridymite is found, it always contains small that is a distortion of the high-temperature form (the β amounts of impurities. It is possible that these impurities phase). In each case, changing from the α to β structure are necessary to stabilize the structure. TABLE 7.4 Some Silicates Olivine P mmm Orthorhombic Island silicate Zircon I 4/mmm Tetragonal Island silicate Beryl C 6/mmm Hexagonal Island silicate Cordierite C mmm Orthorhombic Ring silicate Tourmaline R 3m Trigonal Ring silicate Enstatite P mmm Orthorhombic Chain silicate Talc C 2/m Monoclinic Layer silicate Mica C 2/m Monoclinic Layer silicate Cristobalite F m3m Cubic Framework silicate Albite C -1 Triclinic Framework silicate Anorthite P -1 Triclinic Framework silicate 7. 5 S i l i c a ......................................................................................................................................................................... 105  of tetrahedra are not actually sharing edges, as appears to be the case in Figure 7.6a. The result of this distribution of cations is that the crystal structure is orthorhombic with the b lattice parameter by far the longest at 1.02 nm; the a and c lattice parameters are 0.48 nm and 0.60 nm, respec- tively. The O2− anions at the corners of the tetrahedra are linked by O–A–O bonds (A being Mg or similar); some tetrahedra point up and others point down. In forsterite, this Mg2+ ion is located at the center of an octahedron just as it is in MgO. The best-known composition of olivine, the light green gemstone peridote, is (Mg0.9Fe0.1) 2SiO4. The oliv- ines are a group of minerals showing isomorphous replacement.  Forsterite, Mg2SiO4: up to 10% Fe replaces Mg.  Fayalite, Fe2SiO4: up to 10% Mg replaces Fe.  Monticellite, Ca(Mg,Fe)SiO4: the Ca and Mg/Fe give an ordered stacking.  Tephroite, Mn2SiO4: this is a rare mineral that may (A) contain Zn, Fe, or Mg substituting for Mn. Olivine is one of the most important materials in the earth sciences. (A) (B) FIGURE 7.5 The crystal structure of cristobalite. The most symmetric of SiO2 having cubic symmetry (m3m) and a lattice parameter of 0.72 nm. 7.6 OLIVINE The olivine minerals are orthosilicates: the SiO4 tetra- hedra are isolated from one another, meaning that the tetrahedra do not share oxygen ions. The structure is seen from two directions in Figure 7.6, which shows that the structure can be envisioned in a way that relates it to spinel and alumina. The hexagonal ABAB stacking of the anions seen in Figure 7.6a is just like alumina as is the view from normal to these close-packed layers shown in Figure 7.6b. (B) Unlike alumina, some of the cations are in tetrahedral FIGURE 7.6 The crystal structure of olivine, an orthosilicate. sites while others are in octahedral sites, like spinel; but (a) View along [001]; (b) view along [100]. Examples of octahedra unlike spinel, the two types of site are present between and tetrahedra are outlined in both figures. Typified by forsterite, every close-packed layer of anions. Like spinel, the pairs Mg2SiO4. 106 ................................................................................................................ C o m p l e x C ry s ta l a n d G l a s s S t ru c t u r e s  TABLE 7.6 Examples of Garnets Garnet Formula Alternate a (nm) Pyrope Mg3Al2Si3O12 Mg3Al2 (SiO4) 3 1.146 Alamandine Fe(II) 3Al2Si3O12 Fe(II) 3Al2 (SiO4) 3 1.153 Spessartine Mn3Al2Si3O12 Mn3Al2 (SiO4) 3 1.162 Grossular Ca3Al2Si3O12 Ca3Al2 (SiO4) 3 1.185 Andradite Ca3 (Fe(II),Ti) 2Si3O12 Ca3Fe(III) 2 (SiO4) 3 1.205 Uvarovite Ca3Cr 2Si3O12 Ca3Cr 2 (SiO4) 3 1.202 Hydrogrossular Ca3Al2Si2O8 (SiO4)1−m (OH) 4m YAG Al3Al2Y3O12 Al5Y3O12 YIG (I: iron) Fe3Fe2Y3O12 Fe5Y3O12 GGG Ga3Ga 2Gd3O12 Ga5Gd3O12 tions of garnets are summarized in Table 7.6. The garnets have the general formula A3B2 (DO4)3, where A and B refer to divalent and trivalent cations; D is Si in the case of silicates. In the nonsilicates, the structure is interesting because the same trivalent ion can sit in two very dif- ferent sites, the A site and the B site. Important nonsili- cate garnets include YAG (a laser host material) and YIG (a magnetic garnet) It may help to remember the composition of YAG, say, by remembering that it is 4(X2O3), where X is a com- bination of trivalent cations. The structure is formed by combining DO4 tetrahedra and BO6 octahedra (at the corners). The 3D framework thus formed contains cavi- (A) ties that can be viewed as distorted cubes of a triangular dodecahedron as shown in Figure 7.7. The A cation sits in the large dodecahedral site (CN = 8). This is a very fle- xible crystal structure that has certainly not been fully exploited due to its complexity. However, many new garnets are now being produced such as the erbium-doped yttrium scandium gallium garnet [(Y,Er)3Sc2Ga3O12, or Er:YSGG] single crystals. These materials are being used for diode-pumped solid-state lasers that radiate in the 3-μm range. 7.8 RING SILICATES (B) The ring silicates are also known as the metasilicates. FIGURE 7.7 The crystal structure of garnet. The general formula is Well-known ring silicates are beryl, tourmaline, and A3B3 (CO4) 3 where C is Si for the silicates. The B cation sits in an cordierite. The first two are mainly thought of as gem- octahedral site while the largest cation A is located in a dodecahe- stones; all have interesting properties and cordierite has dron. The bcc unit cell has a lattice parameter of ∼1.1 nm. With 20 atoms in the chemical formula there are 160 atoms in the unit cell. already found a special application. Its low coefficient of thermal expansion means that it does not fracture easily during rapid heating or cooling and thus finds use in 7.7 GARNETS refractories. In fact, it is the material used to form the honeycomb structure of catalytic converters. Garnet refers to both the The structures of beryl garnet group of silicates and cordierite are closely and the garnet structure, RING SILICATES related: to change from which is also adopted by Beryl Be3Al2Si6O18 one to the other replace nonsilicates. Some names Cordierite Al3Mg2 (Si5Al)O18 3Be2+ + 2Al3+ (= 12+) by and chemical composi- Tourmaline XY3Z6B3Si6 (O,OH)30 (OH,F) 3Al3+ + 2Mg2+ (= 13+). 7. 8 R i n g S i l i c at e s ......................................................................................................................................................... 107  strong, but those between the layers are weak; hence they are known as layer materials. Before window glass was available, mica sheets were used as window material. We can easily cleave the sheets to produce a thin transparent ceramic. Figure 7.9 shows the structure of mica. The van der Waals bonding between the sheets is not usually shown since it is so weak. Mica comes in several forms including muscovite, biotite, and the lesser-known phlogopite variety. Micas are used to provide easy paths for crack propagation in some commercial machinable ceramics. FIGURE 7.8 The crystal structure of tourmaline. The 3-fold axis can be seen. The lattice parameters are a = 1.58 and c = 0.71 nm. Most of the nominal 140 atoms in the cell sit in tetrahedral or octahedral sites, but the important boron ion sits at the center of three planar anions. Then maintain overall neutrality by replacing one Si4+ ion by an Al3+ ion. Tourmaline is quite complex, with one end member having the formula NaAl3Al6B3Si6O30 (OH). The structure shown in Figure 7.8 is interesting because it exhibits tri- gonal not hexagonal symmetry. Since it is piezoelectric, tourmaline was used in the 1940s as a pressure-sensing component in the A-bomb. It is now used by some to “attract inspiration and to promote understanding.” 7.9 MICAS AND OTHER LAYER MATERIALS FIGURE 7.9 The crystal structure of mica showing the large K + ions forming a sheet of octahedral sites. The c lattice parameter Micas have very special properties: they are very rigid, normal to this sheet is 2.0 nm with a and b being much smaller, but cleave very easily along one plane. The crystal struc- 0.52 and 0.90, respectively. The polyhedron model emphasizes the ture is well defined; the bonds within the layers are very layer nature of the structure. 108 ................................................................................................................ C o m p l e x C ry s ta l a n d G l a s s S t ru c t u r e s 7.10 CLAY CLAY MINERAL GROUP In the  tetrahedral MINERALS Kaolinites Smectites Illites Vermiculites sheet each [SiO4] 4− tet- rahedron shares three Clay minerals are among cor ners, forming a con- the most important materials we know or have ever known tinuous sheet with the general formula (Si2O5)n2n−. since they form the basis of pottery and building bricks.  The nonbonded tetrahedral apices of the sheet all point The properties of clays are determined by the fact that in the same direction. they are layer materials. They are a subgroup of the layer  These apices connect the tetrahedral sheet to the octa- silicates. In general, the clay minerals are hydrated alumi- hedral sheet. num silicates based on (Si2O5)n sheets.  The O atoms at the apex of each tetrahedron are shared Kaolinite [Al2Si2O5(OH) 4] is the most common clay with an octahedral sheet. mineral; it is a 1:1 layer silicate, meaning that the structure  The octahedral sheet is made up of an array of edge- consists of alternating layers of [SiO4] 4− tetrahedra com- sharing octahedra with either (OH) groups or O atoms bined with octahedrally coordinated aluminum ions as at the corners. shown schematically in Figure 7.10. Because the charge must be balanced, Al3+ ions occupy only two-thirds of the octahedral sites in kaolinite. The linkage between the tetrahedral and the octahedral sheets imposes restrictions on their relative sizes. If the fit between the sheets is not ideal then the resultant misfit leads to the formation of small crystals, as the strain imposed by any misfit will increase with the area of the layer. There is strong primary (covalent/ionic) bonding within each of the layers. However, the bonding between the layers is the weaker van der Waals type. Because the bonding is weak between the sheets, these silicates exhibit perfect one-directional cleavage. Another member of the illite group is hydrous mica, in which the principal interlayer cation is K. A smectite you might encounter is montmorillonite; smectites can expand by incorporating water or organics between the structural layers. Vermiculite is derived from the Latin vermiculare, which means to breed worms, and describes what appears to happen when the material is heated rapidly. Otherwise it is very similar to phlogopite mica. As you would guess, most of these minerals have complex chemical compositions. 7.11 PYROXENE The pyroxene group of minerals contains ferromagne- sium silicates that occur in almost all types of igneous rock, so they are very important in mineralogy. Names you might encounter include enstatite, diopside, augite, jadeite, and spodumene; there are 20 accepted names of minerals in the group. The Si–O tetrahedra are linked at two corners and form an infinite chain parallel to the z-axis. The base of each tetrahedron is nearly parallel to the (001) plane. The chains are then linked laterally by layers of octahedra that contain six- or eight-coordinated cations such as Ca, Mg, Fe, or Na. The octahedra share FIGURE 7.10 In the crystal structure of kaolinite, the SiO4 tetrahedra form one side of the sheet while the octahedra contain edges and thus form continuous sheets on the (100) OH− on the outer layer attached to the Al3+ ions. The sheets are plane. A projection of the pyroxene structure in given in held together only by van der Waals bonds. Figure 7.11. 7.11 P y r ox e n e ................................................................................................................................................................. 109  ture and that the c lattice parameter is large (2.12 nm for CA6): it is a very anisotropic structure. The Na + ions can move quite freely within the “twin” plane between the spinel layers; as a result the cation conductivity is high within these planes but negligible in the perpendicular direction. The high ion conductivity makes these ceramics of interest for battery applications, and this has been exploited in the Na–S cell. This cell was developed around 1965 by Ford Motor Co., but has not been used in production. The main difficulty is that the cell must be kept at an operating temperature of 350°C to keep the electrode molten. The mineral barium magnetoplumbite has the chemical formula BaFe12O19 or BaO · 6Fe2O3 and is per- haps the most important of the hexagonal ferrite since FIGURE 7.11 The crystal structure of a pyroxene (spodumene) it is a hard magnet with the spins all aligned along the shows layers of Li + (larger) and Al3+ (smaller) ions in octahedra c-axis. This oxide is used in the magnetic stripe on credit alternating with layers of Si4+ in tetrahedra giving a nominal formula of LiAlSi2O6. cards. Diopside monoclinic Ca(Mg,Fe)Si2O6 (a = 0.975 nm, b = 0.892 nm, c = 0.525 nm, β = 105.83°) Enstatite orthorhombic (Mg,Fe) 2Si2O6 (a = 1.822 nm, b = 0.881 nm, c = 0.517 nm) Jadeite monoclinic NaAlSi2O6 Spodumene monoclinic LiAlSi2O6 c/2 You can guess the complexity of the structure from the lattice parameters! While these materials are extremely Spinel important in mineralogy, they are not yet exploited much in ceramics. 7.12 b-ALUMINAS AND RELATED MATERIALS The β-aluminas are a family of nonstoichiometric alumi- nates of which the most important have the approximate formulas Na2O · 11Al2O3 (β-alumina), Na2O · 8Al2O3 (β′- alumina), and Na2O · 5Al2O3 (β″-alumina). There are actually quite a few important ceramics that can be thought of as being constructed with layers of spinel separated by less dense arrays of cations. These include not only the β-aluminas, but also the magnetop- lumbites and CaAl12O19 (CA6: see Section 7.13). A model of the β-alumina structure is shown in Figure 7.12. We can think of this structure as being two twin-related blocks FIGURE 7.12 The crystal structure of β-alumina. The main of spinel separated by a plane containing the large Na + features are the large value of c, the twinned spinel blocks, and ions. The result is that this “twin” plane is an open struc- the mirror plane containing the Na + (or K + or Ca + ) ion. 110 ................................................................................................................ C o m p l e x C ry s ta l a n d G l a s s S t ru c t u r e s 7.13 CALCIUM ALUMINATE AND RELATED MATERIALS In Chapter 2 we mentioned cement and the reactions that occur during the setting and hardening of this material. There is a class of cements known as calcium aluminate cements (CACs) or high-alumina cements (HACs). These ceramics are not used as widely as Portland cement, but their attraction is the rapid hardening reactions. In 1 day CAC achieves the same strength as Portland cement achieves in a month. The principal component present in CAC is calcium monoaluminate (CA in cement chemistry nomenclature, see Table 2.3). Its structure resembles that of β-tridymite, one of the polymorphs of SiO2. Rather than having [SiO4] 4− tetrahedral sharing corners in CA we have [AlO4]5− tetra- hedra. The large Ca2+ ion distorts the tridymite network and the structure is monoclinic. The [AlO4]5− tetrahedron is about the same size as the FIGURE 7.13 The crystal structure of mullite viewed along the [SiO4] 4− tetrahedron and can form rings, chains, two- short z-axis (a = 0.76 nm, b = 0.77 nm, c = 0.29 nm). The sites dimensional sheets, or three-dimensional networks in the Oc and T are never fully occupied so this is an idealized schematic same way by sharing oxygen corners. Other related calcium of this orthorhombic orthosilicate. The chains of octahedra at the aluminates are also important in the chemistry of high corners and center lie along z. alumina cements. The common feature of the structures of grossite (CA2) and mayenite (C12A7) is that they too contain corner-sharing AlO4 tetrahedra. This causes problems when determining Burgers vectors of dislocations—the details of the crystal structure can be  Grossite, calcium dialuminate, is monoclinic. It is less different in different mullites. 2Al2O3 · 2SiO2 has been reactive than CA. produced synthetically. Fe3+ and Ti3+ can replace Al3+; it  Mayenite, dodecacalcium heptaaluminate is cubic. It is is a very accommodating structure. the most reactive species in HACs. Mullite has many important high-tech applications.  Hibonite, CA6, is found in Ca-rich aluminas and has a We use mullite for coatings and for fibers. One use of magnetoplumbite structure (see Section 7.12). mullite is in ceramic–matrix composites or CMCs; it has useful mechanical strength and has promise as the matrix for oxide-reinforcing fibers. Above all, when we heat a 7.14 MULLITE clay containing Al2O3 and SiO2 we form mullite. Hence the claim that mullite is the most important ceramic and Mullite is thought by some to be the most important certainly the most important silicate for the ceramist. ceramic, although (like spinel) the name now refers to a group of ceramic materials. It is an orthorhombic silicate made up of chains of AlO6 octahedra running parallel to 7.15 MONAZITE the z-axis and cross-linked by tetrahedra containing Si and Al. In Figure 7.13 these chains of octahedra (Oc) are The mineral monazite has the composition LnPO4; the seen at the corners and center of the unit cell and run into anion is effectively (PO4)3−. In nature, the mineral actually the paper; the two parallel chains are rotated relative to consists of a mixture of several slightly different minerals one another. The polyhedron labeled C is not a tetrahe- since Ln (representing a lanthanide) can easily be replaced dron, although it looks like one in this projection; T is a by one or more rare earths, such as Ce, La, Nd, etc., and tetrahedron though. Sometimes the structure is rather dif- usually also contains thorium. There is some disagree- ferent (it is a derivative), but the material is still called ment on the lattice parameters for monazite in the litera- mullite (or a mullite). Mullite, the mineral was originally ture, which may, in part, depend on its purity. There are from the Isle of Mull in Scotland, is 3Al2O3 · 2SiO2 or also two unit cells in use: simply 3/2-mullite The composition actually varies over a wide range corresponding to Al2 [Al2+2x Si2−2x]O10−x, quite a 1. Monoclinic, P21/n, with a = 0.6782 nm, b = 0.7057 nm, solid-solution range. The crystal structure can be related c = 0.6482 nm, and β = 103.21° to that of sillimanite (Al2SiO5, i.e., x = 0 in the general 2. Monoclinic, P21/c, with a = same, b = same, but formula or Al2O3 · SiO2), but is much more complicated! c = 0.6269 nm (a + c of “1”), and β = 126.53° 7.1 5 M o n a z i t e ................................................................................................................................................................ 111 The latter is correct by today’s crystallographic conven- ture. The structure consists of a sequence of oxide layers tions, but the former is found to be useful in describing perpendicular to the c-axis as follows: defects such as twin boundaries, so you may encounter both. Monazite is the primary ore for Th, Ce, and La; the 1. A Cu–O layer has two oxygen vacancies as com- first of these means that it is often radioactive. Mineral pared with the “fully oxidized” YBCO perovskite. The engineers have long known that it is a principal source of Cu(1) site in this oxygen layer has CN = 4 and is sur- Ce, but even then it often contains significant concentra- rounded by four oxygen ions in a square arrangement (as tions of ThO2. Until the mid-1990s, few ceramists had found in CuO). In YBa2Cu3O7 this is the plane made by heard of it. Then it was found to be a potential coating the CuO “chains.” material for fibers to be used in ceramic composites. In 2. A Ba–O layer. this application, the composition is usually chosen to be 3. A Cu–O layer in which the Cu(2) has a CN = 5 and LaPO4. is surrounded by five oxygen ions that form a square-based pyramid. This is the plane we call CuO2 plane. 7.16 YBa2Cu3O7 AND RELATED 4. A Y layer that has four oxygen vacancies as com- HIGH-TEMPERATURE pared with the fully oxidized perovskite. SUPERCONDUCTORS (HTSCs) You will see in the literature that the chemical formula YBa2Cu3O7 (YBCO) has an orthorhombic layered- of YBCO is alternatively written as YBa2Cu3O6+x or perovskite structure, with c ∼ 3a and a ∼ b, as shown in YBa2Cu3O7−δ. The reason is that the material is almost Figure 7.14a. The Cu and O ions are arranged as chains always oxygen deficient. So which form is correct? along the b direction between the Ba–O layers and as YBa2Cu3O6 is an insulator. It has to be doped to gradually planes between the Ba–O and Y layers. Figure 7.14b shows become a metallic-like conductor and a superconductor how the YBCO structure is related to the perovskite struc- below Tc. The doping is achieved by adding additional X Y X Ba Cu Cu (B) (C) (A) FIGURE 7.14 Models for YBCO. (a) The unit cell; the shaded region shows the perovskite unit with Y in the center and Cu at the corners, X points to the location of oxygen ions in the fully oxygenated orthorhombic (a ≠ b) compound (with . . . O7). The structure is more readily appreciated from (b) [100] and (c) [110] views, each showing six unit cells. Note how the perovskite “unit cell” is rotated 45° relative to the unit cell of the YBCO. 112 ................................................................................................................ C o m p l e x C ry s ta l a n d G l a s s S t ru c t u r e s oxygen-forming CuO “chains.” These oxygen ions attract 7.17 Si3N4, SiAlONs, AND electrons from the CuO2 planes that then become metallic. RELATED MATERIALS So the “correct” formula for YBCO is YBa2Cu3O6+x where x corresponds to partial oxygen content: Most of the materials discussed so far in this chapter have been oxides, and, in general, ceramists have neglected For 0.0 < x < 0.4, YBa2Cu3O6+x is an insulator. nonoxides. Part of the reason is that materials are often For ∼0.4 < x < 1.0, YBa2Cu3O6+x is a superconductor. processed, in a partial pressure of O2. In what follows we will briefly introduce some of the exceptions that have not The oxygen content can be changed reversibly from 6.0 to been mentioned previously. 7.0 simply by pumping oxygen in and out of the parallel Silicon nitride, Si3N4, exists in two forms designated chains of CuO running along the b-axis. Careful studies as α and β. The structures and lattice parameters of these indicate that the maximum Tc is reached for x ∼ 0.93 forms were determined by X-ray diffraction data. (Tc = 94 K) and that for x = 1.0 Tc = 92 K. (The important point is that liquid N2 boils at 77 K.) α-Si3N4; hexagonal: a = 0.7748 nm; c = 0.5617 nm. Space It is thought that superconductivity essentially takes group P63/m. place within the quasi-two-dimensional CuO2 planes. The β-Si3N4; hexagonal: a = 0.7608 nm; c = 0.29107 nm. Space Cu–O chains can be considered as a “charge-reservoir” group P31c. that is needed to transfer charge into the CuO2 planes. This means we can consider this HTSC as CuO2 planes sepa- Each Si is at the center of a slightly irregular tetrahedron rated by a charge reservoir. Charge carriers are added by of nitrogen atoms. The SiN4 units then share corners; each doping: adding oxygen to YBa2Cu3O6, which enters the N is common to three tetrahedra. The structures differ in compound as O2− and forms CuO chains. To maintain the arrangement of the tetrahedral units. Planes of atoms charge balance, electrons are removed from the copper in the β form are linked along the [001] direction in a oxide planes and the remaining holes are mobile (hence sequence ABAB . . . , whereas in the α form the sequence conduction). The properties are anisotropic (i.e., different is ABCDABCD. . . . along different directions). Therefore, the orientation of The SiN4 and SiO4 tetrahedra are similar, except that the individual grains is essential in the fabrication of poly- whereas each oxygen atom in SiO4 is common to two tet- crystals or epitactic thin films. rahedra, each nitrogen atom in SiN4 is common to three The other high-temperature superconductors— tetrahedra. bismuthates and thallates—are all layered structures with By substituting O2− for N3− and Al3+ for Si4+ we can Cu–O planes present. The different phases are formed by form a family of compounds known as “SiAlONs.” These stacking the same building-block layers in different can be produced by high-temperature reactions between, sequences as shown in Figure 7.15 producing, e.g., Bi2Sr2- for example, Si3N4 and Al2O3. The general formula for the CaCu2O8 (known as the Bi 2212 phase). SiAlONs is (Si,Al)3 (O,N) 4. Other metal atoms can be incorporated into the structure giving (Si,M)(O,N) 4; pos- sibilities for M include Mg+Al, Li+Al, and Y. The interest in β-C3N4 is that it is predicted to have a • • bulk elastic modulus comparable to diamond. Several • • • • attempts have been made, with varying degrees of success, • Ca • Ca • • to produce it in bulk and as a thin film. The structure of CuO2 CuO2 • • β-C3N4 is related to the β-Si3N4 structure. The CN4 tetra- • Ca SrO • Ca BaO • • hedra link by sharing N atoms. Each C atom has four CuO2 Bi2O2 CuO2 Tl2O2 • CaO SrO SrO BaO • BaO BaO nearest neighbors forming an almost regular tetrahedron, CuO2 Bi2O2 CuO2 CuO2 Tl2O2 CuO2 whereas each N atom has three nearest-neighbor C atoms SrO SrO Ca BaO BaO Ca forming 120° bond angles. Bi2O2 CuO2 CuO2 Tl2O2 CuO2 CuO2 CaO Ca Ca BaO Ca Ca CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 7.18 FULLERENES AND NANOTUBES SrO SrO SrO BaO BaO BaO Bi2O2 Bi2O2 Bi2O2 Tl2O2 Tl2O2 Tl2O2 In Chapter 6, we discussed the structure of diamond and CaO SrO SrO BaO BaO BaO graphite—allotropes of carbon. The discovery of the C60 CuO2 CuO2 CuO2 CuO2 CuO2 CuO2 molecule in 1985 introduced a new, third, ordered form of • • • • • • • • • • • • carbon—the fullerenes. The special new feature of C60 • • • • • • (shown in Figure 7.16a) is the regular incorporation 2111 2122 2223 2021 2122 2223 of five-sided rings of C atoms that allows the formation FIGURE 7.15 Schematic of the different building-block layers that of curved sheets of carbon atoms. C60 has 12 pen- produce the biphase oxide superconductors. tagonal (five-sided) and 20 hexagonal (six-sided) faces 7.18 F u l l e r e n e s a n d N a n o t u b e s ............................................................................................................................... 113  A wide variety of fullerene structures have been pro- duced with the general formula Cn, where n can take on small (70) or very large values (240 and 540). In each case, the structure consists of 12 uniformly distributed pentagons connecting an array of hexagons. Although pentagons are necessary to give an approxi- mately spherical shape, by simply rolling a hexagonal graphite sheet we can produce carbon nanotubes. These objects can be considered as a new source of mesoporous ceramics. They are dimensionally confined in two direc- tions. If the ends are closed, as shown in Figure 7.16b, we again need to incorporate the pentagon. Just as graphite grows as sheets, the single-walled nanotube (SWNT) can grow as a multiwalled nanotube as can be seen in Figure 7.16c. The “layer” spacing of the walls is usually what we (A) expect from graphite except at the closed ends. It is an interesting exercise to take a single sheet of graphite (drawn on paper), roll it, and rejoin the bonds; you imme- diately realize that you can introduce a shear or chirality (like a screw dislocation along the tube). The chirality determines the electrical conduction along the nanotube. (B) Many variations on the C nanotube can be produced using other layer materials, such as MoS2. Tubes built from other oxides that are not layer materials might some- times be better described as pipes. 7.19 ZEOLITES AND MICROPOROUS COMPOUNDS Zeolites are aluminosilicates that have a framework struc- ture with large cavities built in. The general formula of the zeolites is (Na2,K2,Ca,Ba)[(Al,Si)O2] n · xH2O, which means that they are chemically related to the feldspars. They are found in nature as crystals with large mineral specimens coming from Pune (near Mumbai in India). (C) They are becoming much more important as synthetic minerals when they are used as molecular sieves or cata- FIGURE 7.16 The structure of (a) C60 and (b) carbon nanotubes. (c) Image of the end of a six-layer carbon nanotube. lyst supports. The atlas of zeolite types lists 98 tetrahedral frameworks that are structurally distinct and are known symmetrically arrayed to form a molecular ball; in fact, a as the TO4 frameworks where T (at the center of the O soccer ball uses the same geometric configuration as tetrahedron) is usually either Si or Al, but could be P, Ga, fullerene. B, or other components. The International Zeolite Asso- In the solid state, the C60 molecules bind with each ciation (IZA) has compiled a list of the different structural other though weak van der Waals forces and can self- types and has given each one a three-letter code, which is assemble to form an fcc arrangement. At room tempera- called, the Structural Type Code. The 3D frameworks are ture the size of the cubic unit cell is 1.4 nm, and the then assembled using secondary building units (SBUs) nearest-neighbor C60 –C60 distance is 1.0 nm. At lower tem- that consist of four, five, and six rings. This can be illus- peratures the arrangement of the fullerenes may become trated by examining the example shown in Figure 7.17. simple cubic with a larger unit cell. In the fcc arrange- This figure represents sodalite, which is actually cubic ments there are, of course, intersticies with either an octa- with a lattice parameter of 0.887 nm. hedral or tetrahedral character. Alkali metal atoms such Microporous ceramics are being designed to extend as K or Rb can be incorporated into the interstitial sites the concept of zeolites by building structures that do not to give a molecular formula of K3C60 or Rb3C60. The necessarily have the well-defined walls of a zeolite crystal interest in these doped fullerenes is that they are super- but still have the large cavities; an ordered alignment of conductors. The highest Tc in the series of alkali metal- the cavities can make it appear that the material is crystal- doped C60 is 33 K for Cs2RbC60. line. The IUPAC definition is that a microporous material 114 ................................................................................................................ C o m p l e x C ry s ta l a n d G l a s s S t ru c t u r e s  Studying the structure of glass is difficult because of the lack of translational symmetry. X-ray diffraction spectra from glasses show diffuse maxima not sharp spots or even sharp rings. These diffuse rings can be interpreted in terms of a radial distribution function [RDF; the quantity is ρ(r)]. ρ(r) = atom density in a spherical shell of radius r from the center of any selected atom. An illustration of such a function is shown in Figure 7.18. The peaks in this figure correspond to the broad (A) bands seen in the diffraction pattern. The corresponding plot for the crystalline material is also shown. The func- tion is equally applicable for a crystal, but the peaks are then delta functions. What is less clear is whether a par- ticular (or any) glass is truly amorphous or if “crystallites” at the nanometer scale are present. The structure of an oxide glass can be modeled in terms of coordination polyhedra of cations surrounded by a variable number of oxygen ions. In crystalline oxides, the polyhedra cannot share only corners but must also share edges and/or faces; in glasses the polyhedra can share only corners. Silica glass is then pictured as a dis- ordered version of the crystal with all oxygen ions brid- (B) ging terahedra as shown in Figure 7.19. Zachariasen summarized his findings as four rules and FIGURE 7.17 The structure of sodalite, a zeolite. The tetrahedra emphasized how the structure of SiO2 glass differs from shown in (a) link together to form large “cages”; the most important features are the channels between the cages, which are seen in the crystalline form shown here as the (111) plane of (b). In (a) the corner and body-centering ions are Cl− ; the others cristobalite. are Na + ions. The tetrahedra contain either Si + or Al + . 1. An oxygen ion will link to two or fewer glass-forming atoms. contains micropores (free diameter < 2 nm); mesoporous 2. CN of the glass-forming atoms is small (usually it materials contain mesopores (free diameter 2–50 nm). is 4). 3. Oxygen polyhedra share only corners. 4. The polyhedra form a 3D network. 7.20 ZACHARIASEN’S RULES FOR These rules have been used since the 1930s and have THE STRUCTURE OF GLASS become almost folklore. Remember that they were Many compounds can form glasses. Silicate glasses are what we usually think of as “glass.” However, the topic 30 actually includes many other materials that are thought of 4πr 2ρ(r) as amorphous, although even that terminology can be misleading. In this section, we will discuss the aspects of 20 structure only as they relate to the theme of polyhedra. We leave the question of “what is a glass”? to Chapter 21. In 1932 W.H. Zachariasen proposed a set of rules that is usually satisfied when an oxide forms a glass. His ana- 10 lysis was based on the following considerations: The interatomic bonding forces in glasses and crystals 0 must be similar given the similar elastic modulus of 2 3 4 5 6 7 8 the two types of solids. r, Å Like crystals, glasses consist of an extended three- FIGURE 7.18 RDF of a glass showing a sharp first-neighbor peak, dimensional network, but the network does not have a broader second-neighbor peak, and then a gradual increase with translational periodicity. increasing r. 7. 2 0 Z ac h a r i a s e n ’s R u l e s f o r t h e S t ru c t u r e o f G l a s s .................................................................................... 115  (A) (B) FIGURE 7.19 Comparing the structure of (a) crystalline silica and (b) glass. proposed when the main glasses studied were silicates, TABLE 7.7 CN for Formers, Modifiers, and Intermediates although borate and phosphate glasses were known. Formers Intermediates Modifiers Further tendencies for glass formers have been listed: Dopant CN Dopant CN Dopant CN 1. The valence of the cation is 3 or greater. Si 4 Li 1 2. As the size of the cation decreases so does its glass- Ge 4 Na 1 forming tendency. B 3 K 1 3. The cation’s electronegativity is between 1.5 and 2.5. Al 3 Al 3 Cs 1 P 5 Rb 1 In a general way, the role of the cations depends on the V 5 Be 2 Be 2 As 5 Mg 2 valence, CN, and the related values of the single-bond Sb 5 Ca 2 strength. Cations of higher valence and lower coordination Zr 4 Zr 4 Ba 2 than the alkalis and alkaline earth oxides may also con- Sr 2 tribute, in part, to the network structure. We can list the Zn 2 Zn 2 cations in three groups. The different types of ion present Cd 2 Cd 2 Hg 2 in oxide glasses are summarized in Table 7.7. Ga 3 Sn 4 1. Network formers are cations that form coordination Pb 2 Pb 4 polyhedra in glass (like Si). 2. Network modifiers are oxides that do not participate directly in the network (like Na). 3. Intermediate ions can sometimes act in either role (like Al). 116 ................................................................................................................ C o m p l e x C ry s ta l a n d G l a s s S t ru c t u r e s  Si4+ bridge-rupture mechanism leads to a loosened network Na+ structure with two types of oxygens: Bridging oxygens are bonded to two Si. Nonbridging oxygens (NBOs) are bonded to one Si. To summarize, Zachariasen’s model has dominated glass science for several decades and is still extremely useful. However, diffraction methods do not actually provide definite proof for such a model; they can only confirm that the results do not contradict this hypothesis. Remember also that the model was developed specifically for oxide glasses and is not necessarily applicable to other types of glasses. O2– 7.21 REVISITING GLASS STRUCTURES FIGURE 7.20 Schematic of how network modifiers in glass cause The Zachariasen model began to be reexamined in the nonbridging O ions. 1990s. The important point is that silicate glass is, in many ways, just like the other silicates that do have long-range order. In particular, they are all 3D solids. In practice, in oxide glasses, the polyhedra are triangles Figure 7.21 shows the same information as Figure 7.19b and tetrahedra. When a network modifier such as Na2O is but redrawn to show different ways of looking at this added to silica glass (SiO2), a specific number of Si–O structure. A crystal composed of corner-sharing SiO4 tetra- bonds is broken. This process is represented schematically hedra has orientational and translational symmetry. We in Figure 7.20. Si–O bonds are broken and the added can then call such a network “topologically ordered.” A oxygen saturates the unsatisfied bond of one Si and two silica glass is then topologically disordered—we cannot Si–O− bonds are formed. The excess negative charge on describe it by symmetry operations but it looks very the oxygen is compensated by the nearby Na + cations similar to the crystalline form otherwise. The tetrahedron (adding an ionic character to the glass). The Si–O–Si is an example of a rigid structuring element called a (A) (B) (C) (D) FIGURE 7.21 Different ways (a–d) of representing the same array of ions in a silica glass. 7. 21 R e v i s i t i n g G l a s s S t ru c t u r e s ........................................................................................................................... 117 polytope (i.e., our polyhedra). The connectivity of a 3D it is {3,2}). The Si atoms define a point (which can be structure can be described by the parameter {V,C}, where called a node) in each triangle. If we join these nodes, as V is the number of vertices per polytope and C is the in Figure 7.21a, we have an array of primitive rings; now number of polytopes sharing a vertex. Incidentally, the this network of nodes is a {2,3} set because we are just polytope for the glass former B2O3 is the BO3 triangle, so joining lines and three join at each junction. This new the tetrahedron is not the essential polytope. A network of network is said to tile or tessellate the 2D space. The set triangles on a plane joined at the vertices is a {3,2} of tetrahedra associated with this ring is then called a local arrangement. cluster and can be compared to the unit cell in a crystal. For our (SiO4) tetrahedron V is 4 but the diagram Alternative tiling schemes are shown in Figure 7.21b and shown in Figure 7.19b is actually a 2D continuous random c. The challenge is to describe the 3D structure. Our usual network of triangular polytopes with V = 3 and C = 2 (so way of looking at it is shown in Figure 7.21d. CHAPTER SUMMARY This chapter examined some crystal structures that students must learn, including spinel and perovskite. Students should also know the different arrangements of the SiO4 tetrahedra. Most of the other structures are looked up as needed, but the idea of how to build micas and clays really should be known. The structures of materials like the β-aluminas, YBCO, the SiAlONs, and the fullerenes all use concepts that we examined in Chapter 6, but in a more complicated form. The special feature in the fullerenes is the five-sided ring; in Chapters 12 and 14 we will see five-sided rings in dislocation cores and grain boundaries in Si and Ge where they have been known since before 1960. These structural features were well known years before they were discovered. You can look up the complex structures, but you should be able to recognize the special features of each one and how they are constructed from simple atomic groupings. Zeolites are endlessly fascinating and are like enormous 3D crossword puzzles. These materials are often left to inorganic chemists to synthesize or chemical engineers to use, which is unfor- tunate since their applications in materials science and engineering are far reaching. Three pages on glass is not an adequate treatment, but hopefully will indicate some of the potential for discovery in these noncrystalline solids. PEOPLE IN HISTORY Curl, Robert F. Jr. (1933–), Richard E. Smalley (1943–2005), and Sir Harold W. Kroto (1939–) shared the 1996 Nobel Prize in Chemistry for their discovery of fullerenes. In 1999, buckyballs were found to exist naturally in a meteor. Fuller, Richard Buckminster (1895–1983) is the architect and inventor of the geodesic dome, which resembles the structure of C60 shown in Figure 7.16a. C60 is often referred to as the buckyball. Megaw, Helen Dick died in 2002 aged 94. She reported the crystal structure of BaTiO3 in Nature 155, 484 (1945). She spent most of her academic career in Cambridge. Zachariasen, William Houlder (1906–1979). The Norwegian-American physicist spent most of his career working in X-ray crystallography. But he is best remembered for his description of the glass structure in the early 1930s. He wrote only one paper on glass and was surprised to see it become the work that he is remembered for (information courtesy of J.C. Phillips). GENERAL REFERENCES In addition to the references given in Chapter 6, the following are recommended. Baerlocher, Ch., Meier W.M. and Olson, D.H. (2001) Atlas of Zeolite Framework Types, 5th edition, Elsevier, Amsterdam. This requires a good understanding of crystallography but includes lots of sources for future exploration. You can download the atlas from the site for the International Zeolite Association: http:// www.iza-structure.org/databases. Deer, W.A., Howie, R.A., and Zussman, J. (1992) An Introduction to the Rock-Forming Minerals, 2nd edition, Longman, London. This book (680+ pages) contains a wealth of data on the subject. Olivines, garnets, and pyroxenes abound. Doremus, R.H. (1994) Glass Science, 2nd edition, John Wiley & Sons, New York. This is the first book to go to when you continue your study of glass. Griffen, Dana T. (1992) Silicate Crystal Chemistry, Oxford University Press, Oxford. Clear diagrams but does not include mullite. Hobbs, L.W. (1995) “The role of topology and geometry in the irradiation-induced amorphization of network structures,” J. Non-Cryst. Solids 182, 27. Polyhedra as polytopes and much, much more. 118 ................................................................................................................ C o m p l e x C ry s ta l a n d G l a s s S t ru c t u r e s  Hobbs, L.W., Jesurum, C.E., Pulim, V., and Berger, B. (1998) “Local topology of silica networks,” Phil. Mag. A78, 679. Liebau, F. (1985) Structural Chemistry of Silicates, Springer, Berlin. Great reading but not easy. Melody, J.G. (1995) Love Is in the Earth: A Kaleidoscope of Crystals, Earth-Love Publishing, Wheat Ridge, CO. If you are interested in an entirely different assessment of ceramics. Parthé, E. (1964) Crystal Chemistry of Tetrahedral Structures, Gordon and Breach, New York, Chapter IV and Appendix A. Schneider, H. and Komarneni, S., Eds. (2005) Mullite, Wiley-VCH, Weinheim, Germany. The definitive text on this important though structurally complex group, of materials. Sosman, R.B. (1965) The Phases of Silica, Rutgers University Press, New Brunswick, NJ. The classic, though now a little neglected, text on silica. Stanworth, J.E. (1971) “Oxide glass formation from the melt,” J. Am. Ceram. Soc. 54, 61. Wells, A.F. (1984) Structural Inorganic Chemistry, 5th edition, Oxford University Press, Oxford. Repeated here because this book is so important. Wenk, H.-R. and Bilakh, A. (2004) Minerals Their Constitution and Origin, Cambridge University Press, Cambridge. Concentrates on the materials—a super resource. SPECIFIC REFERENCES Fenner, C.N. (1913) “The stability relations of the silica minerals” Am. J. Sci. 36, 331. Gave the original version of the silica phase diagram. Hardie, D. and Jack, K.H. (1957) “Crystal structures of silicon nitride”, Nature 180, 332. Initial report of the structures of Si3N4. Hay, R.S. and Marshall, D.B. (2003) “Deformation twinning in monazite,” Acta Mater. 51, 5235. [And Hahn T. ed. (1985) Space Group Symmetry, International Tables for Crystallography, Brief Teaching Edition, D. Reidel Publishing Co., Dordrecht.] Jack, K.H. (1976) “SiAlONs and related nitrogen ceramics,” J. Mater. Sci. 11, 1135. A review article by the pioneer in the field. The most cited article in Journal of Materials Science. Liu, A.Y. and Cohen, M.L. (1989) “Predication of new low compressibility solids,” Science 245, 841. Proposes a compound, β-C3N4, which should have outstanding mechanical properties but is not widely available (it is rare). This paper has over 1200 citations. Zachariasen, W.H. (1932) “The atomic arrangement in glass,” J. Am. Chem. Soc. 54, 3841. The random network model for glass structure has been the dominant factor in developing glass formulations for 70 years. This is the classic reference for that model. EXERCISES 7.1 Compare the ionic sizes in CaZrO4 and CaSiO4 and discuss how well they fit Pauling’s rules and if they should. 7.2 Discuss for Mg2TiO4 and Mn-Zn ferrite, which is preferred, normal or inverse spinel, on the basis of Pauling’s rules. 7.3 In spinel, other than <110>, is there a low-index direction where only like cations project on one another? 7.4 How many ions do you expect to find in a unit cell of grossular? 7.5 Discuss whether we should write the formula for superconducting YBCO as YBa 2Cu3O7 − δ or YBa2Cu3O6+x. 7.6 We often say that the structure of YBCO is related to the perovskite structure. Draw diagrams of the two crystal structures and then explain this relationship. 7.7 By delving into the literature, explain which three materials you think are the next (after those discussed in the chapter) most important in each of these categories: silicates, oxides, nonoxides. Then summarize how they are processed. 7.8 In silicon oxynitride, Si2N2O, we have SiN3O tetrahedra. Sketch the possible structure of this ceramic. 7.9 Consider the fcc arrangement of doped solid C60 that we described in Section 7.18. Explain why we get only Cs1C60 when we dope with Cs and why for sodium doping we can get Na6C60 and Na10C60. 7.10 By examining the literature, discuss how niobates and titanates can be combined and how the perovskite structure facilitates this. C h a p t e r S u m m a ry .......................................................................................................................................................... 119  8 Equilibrium Phase Diagrams CHAPTER PREVIEW Most ceramics are multicomponent materials and the most stable phase at any temperature will be the one with the lowest free energy, G. One use of phase diagrams is to represent the phase or phases we might expect to be present as a function of temperature. There are a large number of books just concerned with this one topic. Much work was carried out in the 1950s and 1960s, but many systems have remained almost completely unexplored and it is not a well-funded area in the United States now. The lack of effort is in spite of the demonstration that new complex ceramics, such as the high-temperature superconductors YBCO and BiSCCO and the magnetic manganates, possess extraordinary, and potentially very useful, properties. Much of the classical work on phase equilibria has actually been concerned with processing metals. Thus the Fe–O phase diagram is perhaps the most thoroughly characterized because of its importance to the iron and steel industry. A word to keep in mind throughout our discussion is equilibrium: we are talking about equilibrium phase diagrams. Often we use a phase diagram as a guide to processing. If the process is in progress then it is not in equilibrium. And, by definition, a chemical reaction is not an equilibrium process. If a reaction is exothermic then a rise in temperature favors the reactants. Although most of the phase diagrams we use in ceramics are for a pressure of 1 atmosphere, in one-component systems such as carbon, pressure is a very important variable. It tells us what pressure we need for direct synthesis of diamond. In metal–oxygen diagrams the partial pressure of oxygen determines what is the stable form of the oxide. 8.1 WHAT’S SPECIAL examples of where phase diagrams have very practical ABOUT CERAMICS? applications in the use of ceramics: Refractory silica brick: This was used for the roof of Since many ceramics are oxides, the oxygen partial pres- the open-hearth furnace, which was once an important sure, pO2, is an important variable. There is a lot of infor- method for steel production. Now silica refractories are mation about many metal–oxygen systems. In part, this is used in coke ovens and as roofs in glass tanks. Typical due to interest in how to obtain metals by direct reduction operating temperatures are 1625–1650°C. The phase from their oxides. A frequent way of representing free diagram tells us that the SiO2 needs to be quite pure (only energies of formation of oxides as a function of pO2 0.2–1.0 wt% Al2O3) or it will melt. and T is the Ellingham diagram (Ellingham, 1944) that Fire-clay brick: This is a classic clay product with was popularized by Richardson and Jeffes (1948) for iron composition close to kaolinite. Although it is used at and steel production. Much less is known about nitrides temperatures below 1587°C, the phase diagram tells us and oxynitrides or even that some liquid will carbides. often be present since Many ceramics are DALTON’S LAW OF PARTIAL PRESSURES these ceramics contain multicomponent materials PA = XA P 22–33 wt% Al2O3. This and, hence, many of the material is so important important phase diagrams PA is the partial pressure of A. because it performs the involve three or more com- XA is the mole fraction of A. task very well and is cheap ponents. Here are some P is the total pressure of the gas mixture. to produce. 120 ...................................................................................................................................... E q u i l i b r i u m P h a s e D i ag r a m s  Barium titanate: Pure cubic BaTiO3 single crystals Determining a phase diagram requires measuring which cannot be grown from a melt of that composition because phases are in equilibrium under well-defined conditions. the hexagonal phase is in equilibrium with the liquid at An especially critical factor for ceramics is being sure the solidification temperature (1618°C). Although the hex- that we have equilibrium. In ceramics we have two agonal phase is transformed to the cubic phase at 1460°C, challenges: the phase change is sluggish and thus the hexagonal phase can exist at room temperature. The hexagonal form of  We need to make measurements at high temperature BaTiO3 is not ferroelectric, which is the property in which where direct determination of phases is difficult. we are most often interested. In Chapter 29 we describe  The valence of the cations may change as the temper- how single crystals of cubic BaTiO3 can be grown. ature or pressure changes. If the cation is polyvalent, Adhesion of metals in integrated circuits: Aluminum then the valence depends on the oxygen activity, which, has been used for over 30 years as interconnect and top- as we will see later, depends on the partial pressure of level metallization in integrated circuits. One of the oxygen, pO2. reasons Al is so good is that it reduces SiO2 to form inter- facial metal–oxide bonds that promote adhesion and sta- To ensure we have equilibrium, the two bulk phases should bility. One of the problems with copper metallizations is really be in intimate contact separated by a flat (planar) that SiO2 is more stable than Cu2O. Despite this difficulty, interphase boundary. Cu has several significant advantages over Al and is now The number of techniques we can use for direct used in many commercial devices such as IBM’s processor determination of phase diagrams of ceramic systems is for the Apple G5, Intel’s Pentium IV, and AMD’s Athlon. quite limited because of the requirements for high The relative oxidizing powers of metals are represented temperatures. frequently on Ellingham diagrams. In Chapter 15 we will show how these diagrams can be useful in developing  High-temperature X-ray diffraction. The maximum brazes for ceramics. operating temperatures are up to 2500°C in high vacuum, 2400°C in inert atmospheres, and 1700°C in air. 8.2 DETERMINING PHASE DIAGRAMS  TEM with hot-stage. The maximum temperature is usually 1300°C, working in vacuum, typically ∼10−4 Pa, We refer you to basic thermodynamics texts for the details so there is no control of pO2. on the origin of phase diagrams and the phase equilibria book by Bergeron and Risbud. In this section we will just Most techniques that are used to determine phase dia- summarize some key points. First, some thermodynamic grams experimentally use an indirect approach. Note that background to phase diagrams is presented. often we are not trying to determine an entire diagram, but rather the specific parts that may be of interest, such as the  The phase with the lowest free energy, G, is thermo- solvus lines, the liquidus, or the eutectic temperature. dynamically stable. Figure 8.1 shows an example of using cooling curves to  The chemical potential, μi, of a component is the same determine the liquidus and eutectic temperature for a in all of the phases in which it is present. This require- binary system. Heating curves produce similar results and ment is used in the derivation of Gibbs Phase Rule. are often easier to achieve experimentally. Phase changes  At equilibrium the temperatures and pressures of all produce the deviations in the time–temperature curves. phases are equal. These measurements would be made using differential Phase Diagram Cooling Curves 5 T 1 2 3 4 5 1 2 3 4 A %B B t FIGURE 8.1 Illustration of the use of cooling curves to determine the liquidus and eutectic in a binary phase diagram. 8 . 2 D e t e r m i n i n g P h a s e D i ag r a m s ............................................................................................................................. 121  at a particular temperature, corresponds to the change in T slope. It is important that the conditions are sufficient for the system to reach equilibrium and that high-purity powders are used. We can calculate phase diagrams using the require- α β ment that the lowest free energy state is the equilibrium T1 one. If calculations are performed for a range of tempera- 1 2 3 4 5 6 7 8 tures then the phase boundaries can be determined. α+β Because we often do not know the absolute values for thermodynamic quantities, but changes in these, we use A x1 y1 B the following expression: Lattice n 3 4 5 6 ΔG = ΔH − TΔS (8.1) Parameter q 2 3 4 5 6 ΔH and ΔS can be determined at any temperature using α β the heat capacity, cp: 1 7 T2 m ΔHT2 − ΔHT1 = ∫ Δcp dT (8.2) 8 T1 p A x1 y1 B and Composition FIGURE 8.2 Parametric method for determination of the solvus T2 Δcp lines in a binary phase diagram. Δ ST2 − Δ ST1 = ∫ dT (8.3) T1 T The problem is that heat thermal analysis (DTA) or CLAUSIUS–CLAPEYRON EQUATION capacities are not known differential scanning calor- Change in vapor pressure (P) of a solid with a change for many compounds. As imetry (DSC). Maximum in T a result, we often make temperatures for these assumptions that allow us instruments are about dP Δ HS = to determine the part of 1700°C. At this tempera- dT T (V V − VS ) the phase diagram that is ture many of the important important to us. ceramics such as Al2O3 (melts at 2054°C), SiO2 ΔHs = enthalpy of sublimation of solid (melts at 1710°C), and VV = molar volume of vapor Estimation of ZrO2 (melts at 2677°C) are V S = molar volume of solid Liquidus and still solid. Another problem Eutectic Temperature with ceramic melts, especially those containing SiO2, is for a Binary System their high viscosity. Most oxide glasses are silicates. Crys- We can estimate the position of the liquidus assuming that tallization from these melts is often difficult and reaching our mixture forms an ideal solution, hence it obeys Raoult’s equilibrium can take a very long time (years!). law. From the Clausius–Clapeyron equation with some A frequently used method for studying phase equi- integration and algebraic manipulation we can obtain libria in ceramics is X-ray diffraction on samples that have been equilibrated at high temperature then quenched. This ΔHf ⎛ TM − T ⎞ technique is particularly useful for the solid-state portions ln X A = − (8.4) of the phase diagram, such as determining the position of R ⎝ TMT ⎠ the solvus lines. In each single solid-solution region of a binary phase diagram there is a change in lattice parame- where XA is the mole fraction of component A and ΔHf ter with composition. In is the enthalpy of fusion. the phase field where both Values of T are plotted solid solutions exist the SOME USEFUL DATA against composition. At the lattice parameter of each intersection of these lines solid solution remains con- NiO TM = 2257 K; ΔHf = 50.6 kJ/mol is the eutectic point. This stant with composition as MgO TM = 3073 K; ΔHf = 77.4 kJ/mol approach works well for shown in Figure 8.2. The BeO TM = 2830 K; ΔHf = 71.1 kJ/mol many alkali halide systems position of the solvus line, UO2 TM = 3150 K; ΔHf = 54.0 kJ/mol (such as the NaF–KF) but 122 ...................................................................................................................................... E q u i l i b r i u m P h a s e D i ag r a m s  T = 2427°C phase diagram. This system is one in which the compo- nents are mutually soluble in both the solid and liquid L states. Determination of the free energy curves uses -4 ΔG Eq. 8.5 and the free energy change associated with mixing (kJ/mol) Mixture of solid liquid NiO and liquid MgO, which can be calculated UO2 + BeO -8 using Mixture of -12 UO2 + L ΔG = RT[X ln X + (1 − X) ln (1 − X)] (8.6) -16 UO2 + L L BeO The use of computer methods for calculating phase dia- 2900 + grams is becoming increasingly important. The results of L many of these studies are available in CALPHAD: Com- T (°C) puter Coupling of Phase Diagrams and Thermochemistry 2700 (Saunders, 1998 and on-line). Figure 8.5 illustrates such computed phase diagrams. 2500 2427°C (2700 K) 2300 L UO2 + L BeO +L 2150°C 2100 2060°C 12 UO2 + BeO ΔG T = 2700 °C (kJ/mol) 1900 20 40 60 80 8 UO2 Mol % BeO BeO FIGURE 8.3 The UO2–BeO phase diagram determined using free 4 energy calculations. Mol% 0 Solid not so well for many oxides. For example, the PbO–B2O3 -4 system shows dissociation on melting. An alternative method to calculate the liquidus is to -8 calculate differences in free energy of the solid (Gs) and liquid (Gl) phases as a function of temperature: -12 Liquid TM Gs − G1 = −ΔHf ln (8.5) T 2800 2700° We need to know the enthalpy of fusion, ΔHf, and the 2600 melting temperature, TM. T (°C) Liquid Figure 8.3 shows how this method has been used to 2400 id qu construct the phase diagram for the UO2–BeO system. Li + The agreement with the published diagram is quite ss good. 2200 ss 2000 Estimation of Liquidus and Solidus for Systems with Complete Solid Solubility NiO 20 80 40 MgO 60 Mol% Figure 8.4 shows free energy versus composition plots at FIGURE 8.4 The NiO–MgO phase diagram and free energy 2700°C for the NiO–MgO system and the corresponding curves at T = 2700°C. 8 . 2 D e t e r m i n i n g P h a s e D i ag r a m s ............................................................................................................................. 123  800 updated diagrams, but the old diagrams found in the 771° T (°C) earlier volumes are still often quoted. Many of these dia- 700 grams resulted from research in the 1950s and 1960s, but there are many going back to 1915. The first diagram in the book (Fig. 1), produced in 1951, is for the system Al– 600 Al2O3 and shows the gaseous species over liquid Al2O3 as a function of T and P. One of the earliest is for the AgNO3 – 500 NaNO3 system that was devised in 1900 (Fig. 1040). 446° Unfortunately, this field is not currently well supported. 430° 0.295 In our brief discussion in this chapter, we take the approach 400 of “learn by example.” A warning on units is necessary. Since many of the 318° 300 0.463 274° 262° data were collected before the establishment of SI units, 250° the plots contain combinations of weight percent, mole 230 0.71 0.54 fraction, and mole percent, kbars and atm for pressure, but 200 KCl 0.2 0.4 0.6 0.8 ZnCl2 fortunately only °C (not °F for temperature). Mol % (A) 2400 8.4 GIBBS PHASE RULE T (K) We derive the Gibbs Phase Rule in three steps. 2200 2113° K Step 1. Consider the situation in which we have C com- 2000 ponents that exist in X phases. If Fe and O are the components, Fe and FeO would be examples of phases. 1825° K Mullite So there are XC composition variables. Adding the two 1800 Cristobalite important external variables in ceramics, P (pressure) 1755° K Tridymite and T, gives XC + 2 variables. 1600 SiO2 20 40 60 80 Al2O3 Start with XC + 2 Mol % Al2O3 (B) Step 2. If we described the composition of a phase in FIGURE 8.5 (a) CALPHAD phase diagram for KCl–ZnCl2. (b) terms of the mole fraction of its components, then CALPHAD phase diagram for SiO2–Al2O3. when we have described all but one of the mole frac- tions, the last one must be known because together the mole fractions all add up to unity. This happens for each of the X phases, so X of the variables are actually fixed. Deduct X 8.3 PHASE DIAGRAMS FOR CERAMISTS: Step 3. In equilibrium, the chemical potential of a com- THE BOOKS ponent must be the same in all the phases (otherwise it will not be equilibrium). If the concentration is Because the books are really important for ceramics we fixed in one phase then the chemical potential is will emphasize them here rather than just at the end of the fixed in that phase. The chemical potential must then chapter: all ceramicists must be familiar with “the books.” be fixed in all the phases since it is the same in all The first volume of the series, Phase Diagrams for phases. Thus, if the concentration is known in one Ceramists, was published in 1964 and is in daily use. The phase, then X − 1 variables (the concentrations in the series currently contains 12 volumes. The companion other phases) are automatically fixed (even though volume by Bergeron and Risbud is entitled Introduction they are not necessarily the same—their chemical to Phase Equilibria in potential is the same). Ceramics and should Since this is true for all always sit on the same GIBBS C, F, AND X C of the components, shelf. The books are unique C is for component (X − 1)C variables are in that the later volumes F is for freedom fixed (they are not inde- contain both new and X is for phase pendent variables). 124 ...................................................................................................................................... E q u i l i b r i u m P h a s e D i ag r a m s  Deduct (X − 1)C 100 Solid (metal) Liquid P Hence the number of independent variables is given by (GPa) F = (XC + 2) − X − (X − 1)C Rearranging gives us Gibbs Phase Rule 60 F+X=C+2 (8.7) Diamond Note that many texts use P for the number of phases and V for the degree of freedom. We use F for (degrees of) 20 freedom, P, an important variable, for pressure, V for volume, and X for the number of phases. Graphite Most of the time we just examine different systems 0 2000 T (°K) 4000 with up to three components (C = 1, 2, or 3). The difficulty FIGURE 8.7 The C phase diagram. sometimes is in counting the components. There are also four- and five-component diagrams in ceramics. We always have to be aware that the sample might contain nonequi- phases are in equilibrium (X = 2 and F = 1). If we vary librium phases. T, then P must vary so that we stay on the line. This diagram is a simplification of what we know now since there are many (11 or 12) other known crystalline 8.5 ONE COMPONENT (C = 1) forms of ice. The form that occurs in nature is called ice Ih (a hexagonal form) and has a density of In each of these examples, we have one component, 0.931 g/cm3 (water is 1.00 g/cm3: hence the iceberg meaning that the chemical composition of the material phenomenon). The other forms exist at either lower does not vary. From the phase rule we have P and T as values of T or higher values of P than shown in Figure two variables, which is what we plot in each case. Using 8.6. (We have kept this pressure in atm because the F + X = C + 2, for a one-phase region we can vary both most important equilibrium occurs at 1 atm.) P and T. For a two-phase region (the line), if we vary P Example 2: Carbon: One component (Figure 8.7). This is then T is determined. For a three-phase region in a one- a classic example of an element with three solid phases. component system there are no variables. We often remind owners that diamonds are only metastable, but fortunately the kinetics of the phase Example 1: Water: One component (Figure 8.6). X takes transformation are very slow. Notice where we live— its maximum value of 3 when F = 0. The three coexist- in a dot at the bottom left corner. ing phases are then solid, liquid, and gas at point A, Example 3: SiO2: One component (Figure 8.8). Silica is or the liquid and two solid phases at point B. Points A not only one of the most important ceramics, but its and B occur at unique combinations of temperature and pressure. Lines correspond to locations where two P 10000 Ice III Liquid P (atm) Liquid 1000 B β-Cristobalite g lass 100 Silica 10 to balite β2-Tridymite α-Cris 1.0 e ymit β-Trid 0.1 β-Quartz Ice I ymite 0.01 Vapor α-Trid A α-Quartz 0.001 -20 0 20 40 60 80 100 T (°C) T FIGURE 8.6 The H2O phase diagram. (1000 atm is ∼100 MPa.) FIGURE 8.8 The SiO2 phase diagram. 8 . 5 O n e C o m p o n e n t ( C = 1) ........................................................................................................................................ 125  phase diagram is also very interesting. Remember, the hence hydrogen) may be a component of the system. The composition is constant. This schematic diagram gas phase is not important if the valence of the cations emphasizes both the relationship between the glass is fixed and the total pressure, P, is fixed at 1 atm. and the liquid and the fact that the glass is the high- We will consider materials with variable valence in pressure phase; the glass is denser than any of the Section 8.8. crystalline forms (similar to ice). The phase rules always apply. Example 1: NiO/CoO: Two components and P fixed (Figure 8.10). The special feature about this diagram is that both oxides have a rocksalt structure. Pauling’s 8.6 TWO COMPONENTS (C = 2) rules tell us not to be surprised that they are fully interchangeable. However, it is reported that there is a Binary phase diagrams are very important for ceramics. two-phase region at low temperatures. Notice three The two most important cases for ceramics are the com- points: bination of a metal plus oxygen and the combination of two oxides. A model two-component system is shown in  At the high temperatures, the diagram contains only Figure 8.9 where we are now using the third dimension to dashed lines—intelligent guesses. display the data.  The two-phase region occurs where kinetics are quite slow. If there is one phase (X = 1) as at B, then the three varia-  The composition is given as a mole fraction. bles are pressure, temperature, and one other, for example, the composition (x/y ratio). This is a case in which you start with “the book” and If there are two phases present (X = 2) such as the liquid then go back to the original reference to learn how the and one solid phase at A, then F = 2. If, for example, pO2 was controlled, how the two phases were identi- we fix P, we are free to vary T and move along fied, etc. the liquid/solid phase Example 2: MgO/CaO: boundary (a surface). HUME–ROTHERY RULES FOR COMPLETE Two components and P SOLID SOLUBILITY fixed (Figure 8.11). This The special feature is diagram is a classic that we have introduced  Same crystal structure eutectic even though surfaces into the phase  Equal valence CaO and MgO both diagram. In ceramic mate-  Ionic radius within ±15% adopt the rocksalt struc- rials, the gas phase may  No chemical reactivity ture. Because the sizes be very important. This of the two cations differ is where ceramics are par- If we have two oxides we need consider only the sizes by more than 15%, solid ticularly different from and valences of the cations. solubility is limited. metals: oxygen (or nitro- gen or water vapor and 2000 Liquid T (°C) 1600 T (Ni Co)O(ss) A 1200 P C B 800 Two-phase region x y Composition 0.2 0.4 0.6 0.8 NiO Mole Fraction CoO FIGURE 8.9 A model binary phase diagram showing T, P, and composition as variables. FIGURE 8.10 The NiO–CoO phase diagram. 126 ...................................................................................................................................... E q u i l i b r i u m P h a s e D i ag r a m s  2800 2600 T (°C) T (°C) CaO(ss) + L 2400 MgO(ss) + L L MgO(ss) 2400 2370° 2200 CaO(ss) L+B A+L B3A+L 1980° BA3+L 2000 BA+L 1910° 1870° BA3 B+B3A 1890° +A 2000 MgO(ss) + CaO(ss) 1835° 1850° 1800 BA B3A+BA +BA3 20 40 60 80 BeO Wt % Al2O3 B3A BA BA3 Al2O3 FIGURE 8.13 The BeO–Al2O3 phase diagram. 1600 MgO 20 40 60 80 CaO Weight % CaO FIGURE 8.11 The MgO–CaO phase diagram. side. We can grow two eutectic structures; one essen- tially contains pure Al2O3. Example 4: BeO/Al2O3: Two components and P fixed Example 3: MgO/MgAl2O4 /Al2O3: Two components and (Figure 8.13). Notice that all the phases can be regarded P fixed (Figure 8.12). This is a particularly important, as combinations of BeO and Al2O3, so we can denote but relatively simple, system in ceramics. It involves them as B3A, BA, and BA3. From a chemical point of three widely used materials, which are also archetypi- view, the system looks quite similar to MgO/Al2O3, but cal structures. We can choose the two components to clearly it is very different; three separate eutectics are be MgO and Al2O3. Then in the one-phase region we shown; none of the compounds has the spinel struc- have one variable in addition to P and T. In the ture. BeAl2O4 is the mineral chrysoberyl and has a two-phase region we can vary T or the MgO : Al2O3 structure similar to olivine, which is not unrelated to ratio, but not independently. Notice that the composi- spinel. tion is given in weight percent, which is not too bad Example 5: MgO/TiO2: Two components and P fixed for this system but really distorts the related MgO/ (Figure 8.14). This system is interesting because of the Cr2O3 and NiO/Al2O3 systems. The spinel phase field is already quite wide at 1600°C and becomes wider at high temperatures, especially toward the Al2O3-rich 2800 M2T = Mg2TiO4 T (°C) MT = MgTiO3 MT2 = MgTi2O5 2800 T (°C) A = Al2O3 R = TiO2 S = MgAl2O4 2400 M = MgO 2600 M = MgO L 2400 L M+L S+L A+L 2000 M+L 2200 ~2135 R+L M(ss) ~2050 M2T+L 1842 ~2020 2000 MT2 + L 1732 S 1707 MT + L 1652 1630 M+S 1800 1600 1583 1592 1606 S+A M+M2T M M2T MT2+R +MT +MT2 1600 10 20 30 40 50 MA 90 M 10 20 30 M2T MT MT2 T MgO Wt % Al2O3 Wt % FIGURE 8.12 The MgO–Al2O3 phase diagram. FIGURE 8.14 The MgO–TiO2 phase diagram. 8 . 6 Two C o m p o n e n t s ( C = 2 ) ...................................................................................................................................... 127  occurrence of four different eutectics. Such eutectics in this and other systems have been used to prepare T some interesting two-phase materials. For example, when a liquid with composition in the MgO-rich region is cooled from the eutectic temperature at 1707°C it will produce a material that consists of alternating lamellae of nearly pure MgO and Mg2TiO4. Other systems show different structures, which are deter- mined in part by the interfacial energies. Of course, interfacial energies are usually not considered in the Z analysis of phase diagrams. X Composition on Co siti mp osi po tion m 8.7 THREE AND MORE COMPONENTS Co Y When three components (ternary systems; C = 3) are (A) present the phase diagrams become more difficult to draw K because we then have F + X = 5. If the pressure is fixed X T1 then we have four variables. We need one axis for each T2 component and one for the temperature, say, so we draw the compositions on a triangle and plot T as the vertical T3 3 coordinate as shown in Figure 8.15a. The base triangle is T4 called the Gibbs triangle. The example shown in Figure H 4 4´ T5 8.15a corresponds to the case in which three oxides form solid solutions (extending the NiO/CoO example). The 5´ 5 T6 6 example shown in Figure 8.15b is the case of three simple 6´ 7´´ T7 7 binaries each with a single eutectic (extending the MgO/ CaO example). Figure 8.15b is worth some effort to 7´ understand. The lines of constant temperature at the solid/liquid phase boundary are projected onto the base G of the Gibbs triangle. The location of each of the three eutectics is also projected and will correspond to an abrupt change in the curvature of the constant-tempera- ture contour. The three eutectics then meet at a “grand eutectic” at E. For sufficiently slow cooling, E will corre- E spond to the ultimate eutectic temperature—below TE the sample is solid. In the materials that are often most important, the diagrams are more complicated. The phase diagram H 7´´ B C books then often show them as projected triangles as in 6´ 5´ 4´ T1 X´ T2 Figures 8.16–8.18. 7´ T3 T6 T T4 5 S E G Example 1: MgO/Al2O3/SiO2: Three components and P fixed (Figure 8.16). Notice that there are perhaps three locations for E. This diagram contains several really A important ceramics. We have already examined one of (B) the binary diagrams included here (MgO/Al2O3) and FIGURE 8.15 (a) A model ternary phase diagram for a system will examine another below (MgO/SiO2). Diagrams showing three solid solutions. (b) A model ternary phase diagram like this have difficulty in showing what is happening for a system showing three eutectics. at temperatures other than the liquidus. Example 2: CaO/Al2O3/SiO2: Three components and P fixed (Figure 8.17). Figure 8.17 illustrates the exten- being crystalline. Notice that CS is close to the mid- sion of the use of abbreviations to three components. point, but that AS and CA are closer to Al2O3. It also illustrates how the eutectics can be combined Example 3: Na2O/CaO/SiO2: Three components and with a set of tie lines. The CAn ceramics are found in P fixed (Figure 8.18). This system is particularly inter- high-alumina cements. The phases are all shown as esting because of its relevance to soda-lime glass 128 ...................................................................................................................................... E q u i l i b r i u m P h a s e D i ag r a m s  1723° 1703° SiO2 ~1590° Crystalline Phases Notation Oxide Formula Cristobalite } v v Two Tridymite SiO2 Liquids Protoenstatite MgO•SiO2 Forsterite 2MgO•SiO2 v v Cristobalite Periclase MgO 0 1470° Spinel MgO•Al2O3 170 Corundum Al2O3 0 Mullite 3Al2O3•2SiO2 160 v v 1703° 0 1440° Cordierite 2MgO•2Al2O3•5SiO2 1 0 5 1600 1543° r id y m ite Sapphirine 4MgO•5Al2O3•2SiO2 T 1470° 1557° Protoenstatite 1355° 1400 v v MgO•SiO2 1367° Mullite Cordierite 1365° 16 1370° 2MgO•2Al2O3•5SiO2 00 1465° 18 v v 00 1453° 1460° 1482° 180 Sapphirine 2MgO•SiO2 1578° 0 Forsterite 1600 ~1900° v v ~1860° 1800 ~1720° v v 1800 ~1710° 3Al2O3•2SiO2 ~1850° 20 00 Spinel Corundum ~1840° v v 220 2000 0 240 Periclase 4MgO•5Al2O3•2SiO2 0 v v 260 0 0 200 v v v v v v v v v MgO ~1850° MgO•Al2O3 ~1925° Al 2O3 ~2800° ~2135° ~2020° FIGURE 8.16 The MgO–Al2O3 –SiO2 phase diagram. SiO2 CaO 1:1 1545° 10 40 v v Cristobalite 1:2:3 1280° Mullite 20 30 v v Pseudo- (1:3:6) Wollastonite (1707°) CS Anorthite αCaO • SiO2 1600 C3S2 1400 120 C3S2 CAS2 0 30 20 v v 1125° AS βCa 1125° O •2S 1300 Tw C2S Cri (2:1:3) iO oL Gehlenite 1500 2 sto 1030° iqu A3S2 bal Na2O • 2CaO • 3SiO2 1035° C3S αC2S (1:1:5) ids ite 40 1100 10 v v Corundum 1:3:6 C2AS 0 Tridymite 2:1:3 100 900 βC2S 827° 1:1:5 Quartz (1707°) Lime Na2O Na2O • SiO2 Na2O • 2SiO2 3:8 821° C3S CA C3A5 v v v v C3A 1:1 60 840° 1:2 70 3:8 80 90 SiO2 Wt % (1727°) CaO C3A C5A3 CA C3A5 Al2O3 FIGURE 8.18 The Na2O–CaO–SiO2 phase diagram. FIGURE 8.17 The CaO–SiO2–Al2O3 phase diagram.  increase the expense. The approach used is to fix the pO2 A using one of the following reactions: T 1 Txz CO + O2 = CO2 (8.8) T1 2 1 H2 + O2 = H 2 O (8.9) T2 2 T yz If there is no solid present then we just have one phase, T3 namely, the gas, and X + F = C + 2 gives F = 3. So we Txy can vary T, Ptotal, and the composition (CO2 /CO ratio or H2 /H2O ratio). TE If there is a solid present (e.g., graphite or Ni) then we have just two variables (since we have two phases, X = 2), Z which will fix the system. If Ni is present, for example, n then essentially the Ni/NiO equilibrium sets the pO2. The X Compositio same occurs if Fe is present. We will spend some time discussing the Fe–O diagram on i sit Co shown in Figure 8.20; here gas is important. In the Fe–O po mp m osi Co tio phase diagram, we have two components. We can call them n Fe and O or FeO and Fe2O3 as we wish. The special feature in Figure 8.20 is the fact that usually the lines of constant Y pO2 are horizontal whereas in two-phase fields they are FIGURE 8.19 Illustration of a cooling path in a ternary system. inclined to the horizontal. They are inclined when the phase field contains a single phase (wüstite or magnetite). In the two condensed phases region (region W + M: formation. Because of this interest, the diagram has wüstite plus magnetite) there are two condensed phases been limited to the silica-rich corner of the Gibbs plus the gas (O2), so X = 3. There are two components (C triangle. = 2; Fe and O), so we have only one degree of freedom: we can vary T or pO2. So the oxygen isobars (lines of Each of these diagrams shows the contours of the constant pO2) on the phase diagram must be horizontal. solid/liquid boundary. It is now a little more difficult to In the wüstite phase (region W) there is one condensed envision what occurs as we lower the temperature of the phase plus the gas (O2), so X = 2. There are two compo- liquid phase. The basic ideas are the same as for the two- nents (C = 2; Fe and O), so we have two degrees of component systems as shown in Figure 8.19. The cooling freedom (F = 2). The reason the isobars have the particu- path follows the steepest descent on the liquidus until, in lar slope is that they must connect the appropriate isobars this case, it reaches TE, at which point the whole sample at each side of their phase field. is solid and kinetics become the controlling factor. This is the special feature for ceramics, especially when processing ceramics 8.8 COMPOSITION PRESSURE CONVERSION with a variable-valence WITH VARIABLE cation in air: pO2 is OXYGEN PARTIAL −2 −1 1 Pa = 1 N m = 1 m ·kg s −2 important. PRESSURE 1 N = 1 m·kg s −2 The diagram in Figure 1 bar = 0.1 MPa 8.20b shows the Fe–O The gas phase, particularly 1 kbar = 100 MPa diagram as a function of the oxygen partial pres- 1 atm = 1.013 Pa oxygen activity, which is sure, pO2, is important 1 mm Hg = 1 torr = 0.1333 MPa essentially the pO 2. This when the valence of the diagram shows what con- cation can change. densed phase is stable at In ceramics, we usually run experiments at 1 atm, but each combination of temperature and pO2. Although this geologists are interested in much higher pressures, and hot diagram does not show as much information as Figure pressing is an established commercial method for processing 8.20a (because it does not show the composition of the ceramics. condensed phase), it does emphasize one special feature: There are two ways to control the pO2. Usually, we do if we increase the temperature while keeping the pO2 con- not try to change or control the total pressure—we avoid stant, the oxidation state of the Fe ion decreases. In Figure vacuum systems whenever possible because they greatly 8.20b, the areas show situations in which only one phase is 130 ...................................................................................................................................... E q u i l i b r i u m P h a s e D i ag r a m s  T (°C) Fe(L) H+L air 10 10 0 -2 +oxide(L) L 5.0 10 liquid -4 1600 10 -8 10 -6 104 δ-Fe M H Liquid Oxide +L W+L M+L 100 T (K) Liquid Fe 1600 10-6 1400 air γ-Fe 5.5 +L 10 -8 °C 10-2 1200 δ-Fe 10-12 γ-Fe 10-10 M+H -4 +W 10-14 W 10 6.0 1400 10-12 1000 10-16 10-14 10-6 γ-Fe W+ M -16 Wustite 10-18 10 10-8 800 -18 10 α-Fe 10-20 10-10 6.5 10-20 +W 10 -22 10-22 10 -12 10-24 10-24 600 10-26 10-26 10-14 1200 10-28 10-16 10-30 10-18 10-20 7.0 400 α-Fe+M Magnetite Hematite 200 FeO 10 20 30 40 50 60 FeO•Fe2O3 80 90 Fe2O3 7.5 Wt % -12 -8 -4 0 (A) log pO2 (atm) (B) 1700 T (°C) 1600 1600 10 10 1500 -4 -4 10 T (°C) -5 10 -5 10 -6 1400 10 1400 10 -7 -6 10 -8 10 10 1300 -7 -9 10 -1 10 0 10 -8 -1 1 1200 10 - 10 9 -1 1200 2 10 10 - -1 3 10 10 -1 1100 4 10 - 10 11 -1 5 10 10 -1 -1 10 - 6 2 1 1000 10 -1 3 10 - 7 18 10 -1 1000 10 - 4 19 10 -1 10 - 900 5 2 10 -16 10 - 0 2 10 -17 10 -2 1 10 -18 2 10 -2 800 10 -19 3 10 -20 10 -2 800 4 1 - 10 -2 10 -23 10 -22 0 21 5 10 -26 700 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 Log PH2O/PH2 -3.0 -2.0 -1.0 0 1.0 2.0 3.0 Log PCO /PCO (C) 2 (D) FIGURE 8.20 (a, b) The FeO–Fe2O3 phase diagram; (c) the H–O system; (d) the C–O system. 8 . 8 C o m p o s i t i o n w i t h Va r i a b l e O x yg e n Pa r t i a l P r e s s u r e .............................................................................. 131  Al Al(8/3-X/3)4O4-XNX SiO2 3Al2O3• 2SiO2 Al2O3 100 O (eq. %) Al2O3 X 80 8H AlN 60 O SiO2 O β 15R 40 Si Si3N4 N (eq. %) N (A) Si2ON2 12H 20 21R 27R 2H Si3N4 20 40 60 80 AlN Al (eq. %) (B) FIGURE 8.21 (a) The Si–Al–N–O phase diagram represented as a tetrahedron. (b) The Si3N4 –SiO2–Al2O3 – AlN phase diagram. present and all the lines represent two-phase regions. If we ceramics located in this system are then known collec- look back at Figure 8.20a, the areas there represented con- tively as the SiAlONs. We discussed the structures of ditions in which one or two phases are in equilibrium with these compounds in Chapter 7. a gas phase. Notice the use of the Ramsdell notation. This example Figure 8.20c and d shows the related diagrams for the is more complicated than in Section 6.13 because the H–O and C–O systems. These diagrams can be very chemistry is also changing. useful in the laboratory because this is how we try to reach the pressures indicated in Figure 8.20a: notice that neither system easily takes us below 10−23 atm. In each case the 8.10 CONGRUENT AND temperature is plotted against a gas partial-pressure ratio INCONGRUENT MELTING with the curves showing the contours for constant pO2. The curves are for the situation in which the total pressure Figure 8.22 shows an MnO–Al2O3 phase diagram. The is fixed at 1 atm, so we do not need a vacuum system. The equimolar composition melts congruently, i.e., there is a gray area in the C–O system is instructive—we cannot direct transformation between the solid and liquid states reach this in equilibrium because carbon would then form without a change in the number of phases (in this case and the solid curve would represent equilibrium. In the X = 1). BaO–TiO2 is another example of a two-component gas phase we have two components (C = 2) but only one phase (the gas), so F = 3. We can fix T and the total pres- 2050° sure and still vary pCO, pCO2, pO2, or a ratio of any two. 2000 If we precipitate out carbon, then we have two phases (gas T (°C) X plus carbon) and F = 2. If we fix T and the total pressure L 1850° (or any of the partial pressures), there is no remaining A+L variable. 1785° MA+L 1770° MA + L 23 8.9 QUATERNARY DIAGRAMS 1600 M+L AND TEMPERATURE 8 23 1520° 10 23 MA+A The diagrams are now becoming really difficult! Figure MA 8.21 illustrates an Si–Al–N–O tetrahedron that clearly has M+MA difficulty in showing temperature effects. The rectangle cut from this represents the SiO2–Al2O3 –AlN–Si3N4 M 20 40 60 80 A quaternary system. Now we can plot the different true MnO Wt % Al2O3 quaternary compounds as shown in Figure 8.21b. The FIGURE 8.22 The MnO–Al2O3 phase diagram. 132 ...................................................................................................................................... E q u i l i b r i u m P h a s e D i ag r a m s  1900 T (°C) 1830° 1800 1700 B 2T + L 1600° 1612° 1600 1563° Liquid T+L B2T + hBT 1500 1460° 1428° cBT + L BT4+L 1400 1357° B2T + cBT 1322° 1317° 1300 BT2 cBT + BT2 + BT4 + T BT3 1210° 1200 cBT + BT3 33.3 40 50 60 70 80 90 100 B 2T BT BT2 BT3 BT4 Mole % T T FIGURE 8.24 Image of small droplets of glass in a glass matrix. FIGURE 8.23 The BaTiO3 phase diagram. The composition of the glass is 16 wt% CaO, 10 wt% MgO, 14 wt% Al2O3, and 60 wt% SiO2. system (Figure 8.23). This diagram illustrates the concept  At the silica rich side of the miscibility gap there are of incongruent melting: there are actually three incongru- discrete spherical particles of a BaO-rich phase embed- ently melting compounds. The diagram also shows that we ded in a continuous matrix of an SiO2-rich phase. cannot produce pure cubic BaTiO3 by solidifying a liquid  Near the center of the miscibility gap there is a three- of that composition, which will be important when we dimensionally interconnected mixture of BaO and discuss crystal growth later. Notice that all the compounds SiO2 phases. on this phase diagram are BTn (BT, BT4, etc.) T (°C) 8.11 MISCIBILITY GAPS IN GLASS Liquidus Can glass be described by equilibrium phase diagrams? The question refers to the fact that glass is not itself in equilibrium. We can, however, describe some aspects 1500 of the glass microstructure in terms of phase diagrams, especially that of liquid immiscibility, which leads to the phenomenon of phase separation as illustrated in Liquid - liquid miscibility gap Figure 8.24. The random-network model considers glasses as homo- geneous. However, microscopic features on the scale of 3 nm to hundreds of nanometers can exist. These small features exist in a range of glasses and can result from a 1200 process of phase separation, in which a liquid that is homogeneous at high temperatures separates into two or more liquid phases on cooling. Figure 8.25 shows the phase diagram for the BaO– 1000 SiO2 system, which exhibits phase separation. The dome, shown by dashed lines because the system is metastable, is the key feature in a phase diagram in which phase sepa- ration occurs (a similar dome occurs for Al2O3/Cr2O3, so this dome is not peculiar to glass). The microstructure of glasses in the system BaO–SiO2 28 24 20 16 12 8 4 0 can be determined using transmission electron micros- Composition (mole % BaO) copy (TEM). We find the following: FIGURE 8.25 The silica-rich end of the BaO–SiO2 phase diagram. 8 .11 M i s c i b i l i t y G a p s i n G l a s s ................................................................................................................................. 133  ΔH Phase separation is important for some commercial glass formulations. 0 Vycor Process: Glass containing 75 wt% SiO2, 20 wt% B2O3, and 5 wt% Na2O melts at relatively low temperatures ΔG due to the high B2O3 content. It can then be formed into -TΔH desired shapes and heat treated in the range of 500–600°C so that the glass separates into two distinct phases, one A XB B consisting of almost pure SiO2 and another rich in Na2O FIGURE 8.26 Energy diagram for a hypothetical system in which and B2O3. If this product is exposed to a suitable solvent unmixing occurs. at modest temperature, the sodium borate phase is leached out, leaving an SiO2-rich framework with a network of pores that are ∼4–15 nm in  At the BaO-rich side of diameter. This porous GIBBS FREE ENERGY OF MIXING the miscibility gap For an ideal solution ΔG M is glass can be subsequently there are discrete spher- compacted at ∼1000°C to ical particles of an ΔG M = RT(XA ln XA + XB ln XB) yield a transparent glass SiO2-rich phase embed- containing about 96 wt% ded in a continuous and ΔHM = 0. SiO2. The advantage of matrix of a BaO-rich For nonideal solutions, ΔHM ≠ 0. this process is that we can phase. form this silica-rich glass at relatively low tempera- The B2O3 –PbO system is another glass-forming system ture. It would not be feasible to shape 96% silica glass by that shows a miscibility gap and phase separation. conventional methods because of the very high tempera- The reason for phase separation of a liquid into two tures required to decrease the viscosity of a high-silica phases may be found by consideration of the thermody- glass. namics of mixing. Figure 8.26 shows the three thermody- Pyrex: Pyrex glass also belongs to the Na2O–B2O3 – namic functions, ΔG, ΔH, and ΔS, plotted at temperature SiO2-system. It exhibits phase separation on a very fine T as a function of composition. scale, typically less than 5 nm. By controlling the cooling The common tangent to the minima in the free-energy process, we develop a glass with a special microstructure curve determines the composition of the two phases in the and very useful properties. It is the inclusion of a soluble glass and the proportions of each are determined by the phase within an insoluble one that explains the chemical lever rule. durability of Pyrex. CHAPTER SUMMARY Phase diagrams are the key to understanding many aspects of ceramic processing. Whether we are interested in forming a material by a solid-state reaction or growing a single crystal by solidification of a melt, the first approach is to look up the appropriate phase diagram. Knowing where to find these diagrams (in the “books”) is almost as important as being able to interpret them. The basic principles are the same for ceramics as they are for metals. So our approach was to highlight some important aspects of phase diagrams as they relate to ceramics. PEOPLE IN HISTORY Gibbs, Josiah Willard (1839–1903) was born in New Haven, Connecticut. He was educated at Yale University and was awarded his doctorate in 1863—the first doctorate of engineering to be conferred in the United States. He was appointed professor of mathematical physics in 1871 prior to having any publications. He published the first part of his very famous work On the Equilibrium of Heterogeneous Substances in 1876 and the second part in 1878. He published many other important papers in thermodynamics as well as other areas of physical science. Hume-Rothery, William (1899–1968) founded the Department of Metallurgy (now the Department of Materi- als) at Oxford University in the mid-1950s. HR, as he was known at Oxford, was the author of many books on metallurgy. One of his books, Electrons, Atoms, Metals, and Alloys, is a dialogue between an older metallurgist and a younger scientist. Le Chatelier, Henry (1850–1936) is known for his principle and for inventing the optical pyrometer in 1892. 134 ...................................................................................................................................... E q u i l i b r i u m P h a s e D i ag r a m s  GENERAL REFERENCES Bergeron, C.G. and Risbud, S.H. (1984) Introduction to Phase Equilibria in Ceramics, The American Ceramic Society, Westerville, OH. This should be available in every ceramics laboratory. DeHoff, R.T. (2006) Thermodynamics in Materials Science, 2nd edition, CRC, Boca Raton, FL. Gaskell, D.R. (2003) Introduction to the Thermodynamics of Materials, 4th edition, Taylor & Francis, New York. Hummel F.A. (1984) Phase Equilibria in Ceramic Systems, Marcel Dekker, New York. McHale, A.E. (1998) Phase Diagrams and Ceramic Processes, Chapman & Hall, New York. Muan, A. and Osborn, E.F. (1965) Phase Equilibria among Oxides in Steelmaking, Addison-Wesley Publish- ing. Co., Reading, MA. Reference for experimental determination of phase diagrams in ceramics. Inspi- rational with very helpful commentary; a “must see” text. Phase Diagrams for Ceramists, Vols. I–VIII, The American Ceramic Society, Columbus, OH: I (1964) edited by E.M. Levin, C.R. Robbins, and H.F. McMurdie II (1969) edited by E.M. Levin, C.R. Robbins, and H.F. McMurdie III (1973) edited by E.M. Levin and H.F. McMurdie IV (1981) edited by R.S. Roth, T. Negas, and L.P. Cook V (1983) edited by R.S. Roth, T. Negas, and L.P. Cook VI (1987) edited by R.S. Roth, J.R. Dennis, and H.F. McMurdie Volumes I–VI include mostly oxide and metal + oxide systems. VII (1989) edited by L.P. Cook and H.F. McMurdie (halide systems, many calculated diagrams with methods discussed) VIII (1990) edited by B.O. Mysen (geological, high pressure, and hydrothermal systems) Under a new series title, but continuous numbering, Phase Equilibria Diagrams, Vols. IX–XII: IX (1992) “Semiconductors and Chalcogenides,” edited by G.B. Stringfellow X (1994) “Borides, Carbides, and Nitrides,” edited by A.E. McHale XI (1995) “Oxides,” edited by R.S. Roth XII (1996) “Oxides,” edited by A.E. McHale and R.S. Roth The books are available on CD-ROM from www.esm-software.com/pd-ceramists but are too costly for most individuals. Also a part of this series are Phase Equilibrium Diagrams, Annuals ’91, ’92, and ’93, edited by A.E. McHale (these annuals contain a number of complex oxide systems), and Phase Diagrams for High Tc Supercon- ductors, edited by J.D. Whitler and R.S. Roth (1991). Ragone, D.V. (1995) Thermodynamics of Materials, Volume I, Wiley, New York. Swalin, R.A. (1972) Thermodynamics of Solids, 2nd edition, Wiley, New York. WWW http://thayer.dartmouth.edu/%7Eicelab/ The site of the ice laboratory at Dartmouth. http://www.ceramics.nist.gov/webbook/glossary/ped/glossary.htm NIST’s site for phase equilibria of ceramics. SPECIFIC REFERENCES CALPHAD [computer file], Elsevier, New York. Available in many university libraries on line. Ellingham, H.J.T. (1944) “Reducibility of oxides and sulfides in metallurgical processes,” J. Soc. Chem. Ind. (London) 63, 125. Hazen, R.M. (1999) The Diamond Makers, Cambridge University Press, Cambridge. Attaining the high pressures. Richardson, F.D. and Jeffes, J.H.E. (1948) “The thermodynamics of substances of interest in iron and steel making from 0°C to 2400°C,” J. Iron Steel Inst. (London) 160, 261. Saunders, N. and Miodownik, A.P. (1988) CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide, Pergamon, Oxford. Torres, F.C. and Alarcón, J. (2004) “Mechanism of crystallization of pyroxene-based glass-ceramic glazes,” J. Non-Cryst. Sol. 347, 45. EXERCISES 8.1. The iron–iron carbide phase diagram is probably the most important of all binary phase diagrams. Why is the diagram not a true equilibrium diagram? Does it matter? 8.2 Explain what we mean by the set of equations μ1a = μ1b = . . . = μ1c. What is the significance of this expression? C h a p t e r S u m m a ry .......................................................................................................................................................... 135  8.3 The maximum operating temperature of high-temperature X-ray diffraction is 2500°C in vacuum but only 1700°C in air. Why the big difference? What, if any, effect would the lower operating temperature in air have on the determination of phase diagrams? 8.4 The UO2–BeO system shown in Figure 8.3 does not show any solid solution formation. Would you expect it to? 8.5 With reference to the phase diagram for water (Figure 8.6), explain (a) how the boiling point of water would change if you were to climb to the top of a mountain and (b) why ice-skating is possible. 8.6 Using Figure 8.7 determine the necessary conditions for direct conversion of graphite to diamond. 8.7 Using Figure 8.8 indicate all the triple points in the SiO2 system. 8.9 Describe fully what happens when you cool down a melt of 40 mol% NiO–60 mol% MgO. Give the composi- tions of the phases and their relative amounts for at least three temperatures in the two-phase field. 8.10 Describe the phases that you expect to form as a liquid of composition BaTiO3 is cooled down to room tem- perature. Given the statement we make in Section 8.10 about the growth of single crystals of cubic BaTiO3, what factors besides thermodynamics determine our ability to grow single crystals? 136 ...................................................................................................................................... E q u i l i b r i u m P h a s e D i ag r a m s Part III Tools  9 Furnaces CHAPTER PREVIEW Furnaces are the essential equipment in any ceramics laboratory. They can range in size from small electrically heated box furnaces, often called muffle furnaces, which can fit on a bench, to the enormous gas-fired furnaces used to melt glass. In between these extremes there are furnaces of many shapes and sizes, designed to run at a range of temperatures and in a range of atmospheres. In addition to obtaining a high temperature, it is necessary to have furnace components that can withstand these temperatures without degradation. These materials are known as refractories. Much of our knowledge of refractory ceramics has come from early developments in the iron and steel industries. Whenever temperatures are high, vapor pressures may also be high, so be aware that the furnace material may contaminate the material you are processing. We will also describe methods for measuring high temperatures and some of the important safety considerations that you must know when using furnaces and working at high temperatures. 9.1 THE NEED FOR HIGH very corrosive, which provides additional considera- TEMPERATURES tions in the choice of refractories.  Crystal Growth: Most of the methods used to form There are many areas in ceramics where we need high single crystals, whether in the laboratory or in indus- temperatures: try, require the use of high temperatures. Many single crystals are produced from the melt or by using suita-  Sintering: Most bulk ceramic components are made by ble fluxes, and particular attention has to be paid to sintering a powder compact. We need to use high tem- avoiding contamination of the melt and controlling the peratures (>1200°C) because of the low self-diffusion temperature during growth. coefficients in the solid state. Even for liquid phase sintering, temperatures are still often >1200°C.  Reactions: Forming mixed metal oxides such as BaTiO3 9.2 TYPES OF FURNACE and NiAl2O4 by solid-state reaction of the component oxides requires the use of elevated temperatures. We can categorize the furnaces used to fire and sinter  Phase Transformations: An important phase transfor- ceramic components in several ways. One way is based on mation involves crystallization of a glass to form a the type of heat source used: glass-ceramic. Although the temperatures involved are not as high as those needed for glass melting, the phase  Combustion transformation is typically carried out at around 800°C.  Resistive Control of temperature is often necessary to ensure  Microwave, radiofrequency (RF), or infrared (IR)/ that the desired crystalline phase is formed and in the visible light optimum particle size.  Glass Melting: Glass products form the largest single Alternatively we could group them as segment of the ceramics industry. Glass production frequently requires melting of a batch consisting of a  Periodic or batch furnaces mixture of powdered metal oxides and metal carbon-  Continuous furnaces ates. The temperature necessary to form a homogene- ous liquid melt varies with batch composition, but is Electrical furnaces can produce direct (resistive) or typically in the range 1300–1600°C. The melt is also indirect (induction or microwave) heating. We will look at 9. 2 Ty p e s o f F u r n a c e ................................................................................................................................................... 139 the characteristics of each group of furnaces, keeping in TABLE 9.1 Standard Molar Enthalpies of Combustion, DH 0c mind that there is overlap. For example, we can have con- (kJ/mol) tinuous gas-fired furnaces or continuous electrically fired CH4 (g) 890 furnaces. Historically, continuous furnaces and gas-fired C2H2 (g) 1300 furnaces are usually found in industry. Batch and electri- C2H4 (g) 1411 cally fired furnaces are used widely in university labora- C2H6 (g) 1560 C4H10 (g) 2877 tories and in many small- to medium-sized industrial C6H12 (l) 3920 applications. The current trend toward more environmen- C6H14 (l) 4163 tal controls and demand for higher quality will continue C6H6 (l) 3268 to expand the applications for electrically powered fur- C10H8 (s) 5157 naces. Electric furnaces account for about 60% of the total CH3OH (l) 726 CH3CHO (g) 1193 industrial heating equipment market (about $3 billion in CH3CH2OH (l) 1368 total). There is still growth in the use of combustion CH3COOH (l) 874 furnaces, in particular, for applications in the metal and CH3COOC2H5 (l) 2231 cement industries. C6H5OH (s) 3054 This chapter is called furnaces, but it could have been called kilns or ovens, as all these terms are used to describe many of the same types of equipment. “Kiln” is widely Combustion is an oxidative process; for the case in used in the traditional ceramics industry and the pronun- which methane is the fuel: ciation is sometimes “kil.” In the Potteries in England, for example, you may encounter the alternative pronunciation. CH4 + 2O2 → CO2 + 2H2O (9.1) “Furnace” is used interchangeably with kiln. “Oven” is more often used for either equipment used for drying The standard molar enthalpy, or heat, of combustion (ΔH oc) ceramics (typically using lower temperatures) or for small may be calculated using Eq. 9.2: furnaces. ΔH oc = ∑ ΔH of (products) − ∑ ΔH of (reactants) (9.2) 9.3 COMBUSTION FURNACES For the reaction given in Eq. 9.1 we can write The most common combustion furnaces used in ceramic ΔH oc = ΔH fo (CO2) + ΔH fo (2H2O) − [ΔH fo (CH4) + processing are gas fired and use gaseous hydrocarbons ΔH fo (2O2)] as fuel. The large amount of energy produced heats the furnace and the parts inside. Gas-fired furnaces are used ΔH fo refers to the enthalpy of formation, and these values mainly in large industrial applications such as glass are tabulated for many substances. One source is the ther- melting, the production of ceramic colors, and firing of mochemical tables (e.g., Barin, 1989). Making the appro- traditional ceramic articles, for example, tiles and white- priate substitutions we get ware. Figure 9.1 shows an example of a commercial glass- melting furnace. ΔH oc = −393.51 + 2(−285.83) − (−74.81) = −890.36 kJ/mol (Note that ΔH fo for a material in its standard state is zero.) The simple idea is that the amount of energy released during combustion depends on the strength of the bond in the gas. Fuels with many weak (less stable) bonds such as C–C and C–H yield more energy than fuels with fewer such bonds or fuels that contain large numbers of strong bonds, e.g., C–O and O–H. Table 9.1 lists the standard molar enthalpies of combustion for a range of hydrocarbons. For many combustion reactions the standard enthalpy changes are listed as a function of temperature. If this information is not available then it is necessary to calcu- late the enthalpy change at the temperature of interest, ΔH oc(T) using Eq. 9.3. T FIGURE 9.1 Gas-fired batch furnace used in a commercial glass blowing operation. ΔH oc (T ) = ΔH oc (298) + ∫ Δc dTp (9.3) 298 140 ........................................................................................................................................................................... F u r n ac e s  TABLE 9.2 Temperature Dependence of Heat Capacities, relating the current, I, through a resistance, R, to the Cp,m applied potential, V. As current flows power (P) is Gases dissipated: (298–2000 K) a (J K −1 mol −1) b (10 −3 J K −2 mol −1) c (10 5 J K mol −1) P= VI = I2 R (9.7) H2 27.28 3.26 0.50 O2 29.96 4.18 −1.67 CO2 44.23 8.79 −8.62 What we are often most interested in is the amount of H 2O 30.54 10.29 0 energy converted into heat, Q, which is obtained simply CH4 23.64 47.86 −1.92 by multiplying P by time, t: l 2 Q = RI 2 t = ρ I t (9.8) where cp is the molar heat capacity at constant pressure, A which can be expressed in the form The units of Q are joules, but are often given as kWh (the kilowatt hour), the familiar unit used by power utility cp (T) = a + bT + cT −2 (9.4) companies to determine electricity usage. The heat source in the earliest electric furnaces was The temperature-independent coefficients a, b, and c are dc arcs formed between carbon electrodes, so the heating listed for several species in Table 9.2. It is important to element really was an element. Carbon (in the form of remember that a, b, and c are valid only over certain tem- graphite) is still used as a heating element, but most perature ranges. heating elements are now made from compounds. There Thermodynamics determines the maximum amount of are several different types of heating element and we will energy that can be produced by a combustion reaction. describe some of the important ones in Section 9.7. The This can be quantified by what is known as the adiabatic choice of heating element depends on the maximum tem- flame temperature, which is shown for several possible gas perature that is required and the environment to which the mixtures in Table 9.3. These values, and those for other element will be exposed. gas mixtures, can be calculated by solving the enthalpy There are several advantages to electric heating: balance (Kirchhoff’s law)  It is easy to measure power input T  It is easy to control heating rates and temperature ΔH oc (298 K ) + ∫ ∑ c dT = 0 p (9.5)  The furnace can operate in an atmosphere independent 298 K of the heating source The maximum temperature that can be achieved in a gas- fired furnace is well below the adiabatic flame tempera- The main disadvantage of electric heating is that it usually ture because of heat loss caused by incomplete combustion costs more per energy unit than gas heating. However, the and dissociation of the combustion gases (an endothermic total energy usage for electric furnaces may often be lower process) at high temperature. Heat is also lost by conduc- than for gas-fired furnaces. The cost issue is not normally tion through the refractories and imperfect insulation. a problem in a university laboratory, but it can be a major concern for industrial applications. Two other types of furnace that use electricity are induction furnaces and 9.4 ELECTRICALLY HEATED FURNACES microwave furnaces. Most electrically heated furnaces use the principle of Joule, or resistance, heating where current flowing through 9.5 BATCH OR CONTINUOUS a resistor produces heat. The starting point is Ohm’s OPERATION law: Figure 9.2 shows an example of a small electrically heated V = IR (9.6) batch furnace. These types of furnace are used for tem- peratures up to 1800°C and are designed to be used in air. Figure 9.3 shows another example of a batch furnace. This TABLE 9.3 Adiabatic Flame Temperatures of Various Gas particular furnace is known as a tube furnace. By flowing Mixtures gases along a tube placed inside the furnace the heating Fuels with air Fuels with O2 environment can be controlled. The usual operation of a Gas K °C K °C batch furnace involves inserting the ceramic parts into the furnace at room temperature, heating to the desired tem- H2 2450 2177 3395 3122 perature, then cooling back to room temperature. In some CH4 2276 2003 3849 3576 cases the parts may be inserted and removed while the C2H 2 2657 2384 3737 3464 furnace is at high temperature. For powders this approach 9. 5 Bat c h o r C o n t i n u o u s O p e r at i o n ....................................................................................................................... 141  FIGURE 9.4 A large batch furnace used in the production of traditional ceramic products. FIGURE 9.2 A small electrically heated box furnace. found in large industrial applications as shown in Figure 9.4. The advantages of batch furnaces are that they are simple to operate and flexible. does not usually produce any problems, but for large con- Figure 9.5 shows an example of a large industrial con- solidated parts the problem of cracking due to thermal tinuous furnace. The classic use is for firing bricks, pottery, shock is an important consideration. Batch furnaces are tiles, and whitewares. Similar furnaces are used in the mainly used for small-scale heating experiments and for production of advanced ceramics such as multilayer process development and evaluation. But they can also be ceramic chip capacitors. In a continuous furnace, the temperature at each loca- tion in the furnace is constant with time. The parts are moved through the furnace at a velocity giving the desired time–temperature profile. Continuous furnaces are best FIGURE 9.5 A large continuous furnace used in industry to produce traditional ceramic products and advanced ceramics such FIGURE 9.3 An electrically heated tube furnace. as multilayer chip capacitors. 142 ........................................................................................................................................................................... F u r n ac e s for mass production where large quantities of material are  It is clean and fast subjected to the same conditions. The disadvantages of  The process is easily reproducible continuous furnaces are that the furnace temperature must  It can be automated be maintained throughout the process and their lack of  Localized heating is possible (actually, it is flexibility. essential) Induction furnaces operate at frequencies from 60 to 9.6 INDIRECT HEATING 1000 Hz and are thus often referred to as RF furnaces. They can be used to obtain temperatures up to 3000°C. Induction furnaces. Induction heating provides a means Since the coil currents may be as high as 15 kA, the Cu for precise heating of electrically conducting objects. The coil conductors are usually hollow to permit water circula- object is immersed in an alternating magnetic field, which tion for cooling. is usually produced by an external coil energized by an ac Induction furnaces are generally used for melting and source. The magnetic field induces voltages in the conduc- surface hardening. They are sometimes used in sintering tive material, and these voltages produce circulating cur- in conjunction with hot pressing. These are the furnaces rents (called eddy currents). The magnitude of the induced used in the skull-melting process, which is used to produce voltage and the impedance of the material determine the cubic zirconia. size of the induced currents. It is the flow of induced cur- Microwave furnaces. Microwave heating is an applica- rents that produces Joule heating of the material. A piece tion of induction heating using higher frequencies. In of metal may be introduced to begin the heating process— many ways microwave furnaces are just expensive micro- we must be able to couple the applied field to the ceramic. wave ovens. If the material we want to heat is an insulator we can place Heat is generated in nonconducting materials when it inside a conductive crucible, such as graphite. A typical microwave radiation excites the molecules in the material. induction furnace is shown in Figure 9.6. The high-frequency radiation causes molecular polariza- Induction heating gives many advantages: tion and the ability of the molecules to follow the rapid reversal of the electric field results in the con- version of electromagnetic energy into heat within the irradiated material. The two predominant frequencies are 915 and 2450 MHz (the microwave region extends from about 1 GHz up to about 300 GHz). Household microwave ovens operate typically at 2450 MHz. The main difference between the microwave oven you use at home and those used in industrial applications is the power. The maximum power of a domestic appliance is about 700 W; industrial versions have powers up to 5 kW. Microwave furnaces currently are used for research and small-scale production because the available power sources are limited in size. Microwave processing is an area in which considerable research is being performed. The main direction for this research, and the possibility for future commercial applications, is in the reduction of production times and lowering the amount of energy con- sumption required for part processing. The term “microwave safe” is used for various ceramic, glass, and plastic food and beverage containers. All glass and glass-ceramic cookware is microwave safe because it can withstand the high temperatures that can occur when cooking foods that are high in fat or sugar. Many plastics do not satisfy this requirement. Arc-image furnaces. This is comparable to heating with electric light bulbs. The light is focused onto the sample using ellipsoidal mirrors. The heat is clean and the sample can be held in an inert or oxidizing atmosphere. An important application of arc-image furnaces is in the FIGURE 9.6 An induction furnace. The sample is mounted within growth of single crystals of ceramics with high melting the coils, which are usually water-cooled copper. temperatures (Chapter 29). 9. 6 I n d i r e c t H e at i n g ................................................................................................................................................... 143  Lasers and electron beams. These can be used to heating elements can be used up to 1500°C in air because provide local heating or to heat small quantities. The tem- of the formation of a protective oxide layer. At tempera- perature control is not great, but these techniques are very tures in the range 1500–1600°C SiC decomposes: versatile. Electron beams are used to vaporize silicon for thin-film deposition using molecular-beam epitaxy. A SiC(s) + O2 (g) → SiO(g) + CO(g) (9.9) focused laser beam is the basis of the pulsed-laser deposi- tion (PLD) thin-film growth technique (Chapter 28). There are three main methods used to produce SiC heating elements: 9.7 HEATING ELEMENTS  In situ reaction  Reaction bonding Never use a furnace like a black box. The heating elements  Sintering will go to certain temperatures, but even then you may not want that type of material close to your sample to mini- In the first method a carbon tube is heated to about mize contamination. Table 9.4 lists the materials used for 1900°C in a bed of sand (SiO2) and coke (C). The tube electrical resistance heating. may be directly resistance heated or heated indirectly by a sacrificial tube of smaller diameter. Silicon monoxide is  Furnaces operating in air at temperatures up to 1300°C generated from Reaction 9.9 and infiltrates the carbon usually use wire-wound Cr alloys. tube transforming it to SiC. The SiC tube is then removed  For higher temperatures in air either precious metals and the residual carbon is burnt out. The tube has a poros- or SiC rods are used. ity of about 30% and a large internal surface area. To  For very high temperatures requiring an oxidizing prevent internal oxidation during use, the outer surfaces environment ceramic elements, most commonly ZrO2, of the tube are coated with a thin layer of a calcium alu- are used. minosilicate glass and are then fired at about 1450°C. In  In cases in which reducing atmospheres can be toler- this form the tubes have a uniform resistance along their ated, graphite or refractory metals such as Mo and W length. A higher-resistance heating section is made by can be used. diamond sawing a spiral through the tube wall as shown in Figure 9.7. Adjusting the pitch of the cut varies the We will now look, in a little more detail, at some of resistance. the ceramic materials that are used as heating elements in In the second method a mix of SiC and carbon powders furnaces. We will also mention one other type of resist- and a polymer binder is extruded to a rod. The “green” ance element, SnO2, which is used in electrically heated form is then brought in contact with molten silicon. The glass-melting furnaces. liquid penetrates the pores reacting with the carbon to form silicon carbide and bonding the grains together. The resulting ceramic has low porosity and, consequently, a Silicon Carbide long service life. The resistance of the hot section of the Silicon carbide is the most widely used nonoxide ceramic rod is adjusted to the required value by spiraling, which for heating elements for high-temperature furnaces. SiC is easier to do when the ceramic is in the “green” state. TABLE 9.4 Electrical Resistance Heating Element Materials Material Maximum useful temperature (°C) Usable atmospherea Chromium alloys Chromel C, Nichrome, Kanthal DT 1100 ONR Kanthal A, Chromel A 1300 ONR Metals Pt 1400 ONR Pt–Rh alloys 1500–1700 ONR Mo 1800 NR W 2800 NR Ceramics SiC 1500 ON MoS2 1700 ON Lanthanum chromite 1800 O Thoria, stabilized 2000 ONR, shock Zirconia, stabilized 2800 ONR, shock Graphite 3000 NR a O, oxidizing; N, neutral; R, reducing. Shock, particularly poor resistance to thermal shock. 144 ........................................................................................................................................................................... F u r n ac e s  Joule heating is effective. At temperatures above 1000°C the ceramic becomes sufficiently conductive to be self- heating. Zirconia can also be used as a susceptor for induction heating. Tin Oxide SnO2 is frequently used as electrodes in glass melting furnaces, particularly those used for making glasses for optical components and lead “crystal” tableware. The requirements for the electrode material are very specific: FIGURE 9.7 Examples of SiC furnace elements.  Electrical conductivity must be high at glass-melting temperatures.  Resistance to corrosion by the molten glass must be high. In the third method, SiC powder is mixed with a  It should not discolor the glass. polymer binder and extruded. The rod is then sintered in a carbon furnace at approximately 2300°C. To give the The electrodes are formed by mixing SnO2 powder rod low-resistance terminations the ends are dipped into with small amounts of sintering aids such as ZnO and molten silicon, which is allowed to infiltrate along a pre- CuO and additives such as Sb and As, which make the determined length. In all cases the ends of the elements material semiconducting. Typical electrode compositions are coated with aluminum to make electrical contacts. contain more than 98 wt% SnO2. The oxide powders, The main disadvantage of silicon carbide heating ele- together with binders, are pressed or slip cast into cylin- ments is that they are extremely brittle and must be handled ders and fired in oxidizing conditions at temperatures of carefully, especially when being installed and wired. approximately 1400°C. The largest electrodes made in this way are in the form of cylinders 600 mm long and Molybdenum Disilicide 150 mm in diameter weighing about 60 kg. Cooling from the sintering temperature is carried out, in part, in a nitro- Many metals form conductive silicides that, like SiC, are gen atmosphere with the object of creating oxygen vacan- resistant to oxidation through the formation of stable cies and so increasing the room-temperature conductivity, layers of silicates or silica on their surfaces at high tem- which is typically about 0.1 S/m. A high conductivity peratures. Molybdenum disilicide (MoSi2) has been devel- minimizes Joule heating in the electrode region outside oped as a heating element for use in air at temperatures the molten glass. >1500°C. The resistivity of MoSi2 behaves in the same In electrically heated glass-melting furnaces the batch way as for a metal—it increases with increasing tempera- is preheated, using oil or gas, to about 1000°C, at which ture. The room-temperature resistivity of MoSi2 is 2.5 × time it has sufficient conductivity to be directly heated to 10−7 Ω-m; it increases to about 4 × 10−6 Ω-m at 1800°C. the “glass-fining” temperature (1300–1600°C) by power A commercial MoSi2 heating element, known as dissipated internally. By supplying the heat from within Kanthal Super, is composed of a mixture of MoSi2 parti- the body of the glass melt rather than from the outside, cles bonded together with an aluminosilicate glass phase, the free surface temperature is kept relatively low and which forms 20% of the total volume. The elements are loss of volatile elements, particularly lead, is avoided. fabricated by extruding a mixture of fine MoSi2 powder The process is economic since the heat is generated where with clay. The rods are dried, sintered, and cut to various it is required, i.e., in the glass. The elements are resistant lengths. The heating zones are bent to the required shape to attack by glass and last about 2 years before being at high temperature and are then welded to the larger- replaced. diameter terminal sections. The best grade of MoSi2 element is capable of operating at temperatures up to 1800°C. Graphite Graphite is a good choice as a heating element for resistive Zirconia heating because it has a high melting temperature and a very low vapor pressure even at temperatures above Cubic stabilized zirconia (ZrO2) is used as a furnace 3000°C. These characteristics led to the use of graphite element allowing temperatures >2000°C to be achieved. filaments in early incandescent lamps. (They were eventu- Because of the low conductivity of ZrO2 at room tempera- ally replaced by tungsten, which came into general use as ture, it requires preheating by gas or conventional resist- a filament for incandescent lamps in 1911.) The major ance elements to reduce the resistance to a level at which disadvantages of using graphite furnace elements are 9.7 H e at i n g E l e m e n t s .................................................................................................................................................. 145  TABLE 9.5 Refractories for Thermal Insulators Material Tmax (°C) k (W m −1 K −1) Glass, fiber 600 0.05 SiO2, fiber 1000 0.17 Firebrick, insulating 1200–1500 0.52 Fiberfrax 1650 0.12 Al2O3, bubble 1800 1.04 MgO, powder 2200 0.52 MgO, solid 2300 2.94 Carbon or graphite, powder 3000 0.09 Radiation shields, Mo 2100 0.69 ductivity, k. The lower the value of k, the better the thermal insulating effect for equal thickness. Figure 9.9 shows the arrangement of refractory bricks in a typical glass-melting furnace. Approximately 70% of all refractories used by industry are in the form of pre- formed bricks that come in a variety of shapes. There are several different types of refractory brick and the choice depends mainly on the maximum operating temperature FIGURE 9.8 A TEM image showing small particles of tungsten of the furnace and on the size of the furnace. contamination formed on SiC.  Silica brick is made from naturally occurring sources of silica and is bonded by adding 3–3.5% CaO to  Reactivity with oxide ceramics promote liquid phase sintering.  Susceptibility to oxidation  Semisilica brick is a silica brick containing between 18 and 25% Al2O3. All metal oxides are reduced when in direct contact with  Fireclay brick is made from kaolinite graphite at high temperatures. Even the most refractory (Al2O3 · SiO2 · 2H2O) with between 25 and 45% Al2O3. oxides will be reduced if the temperature is high enough.  High-alumina brick has an alumina content in the range 45–100 wt%. Molybdenum and Tungsten  Dolomite brick is made from dolomite (CaCO3 · MgCO3). Both of these refractory metals are used as heating ele-  Magnesia brick contains mainly MgO (typically >90% ments. Molybdenum reacts with oxygen above 700°C to MgO). form molybdenum trioxide (MoO3). For applications above  Chrome brick is made from naturally occurring chrome this temperature it is necessary to have a reducing environ- ore. It contains 34% Al2O3 and 30% Cr2O3. Often MgO ment or vacuum. The maximum usable temperature for is added to produce chrome-magnesia brick. molybdenum heating elements is about 1500°C. Above  Zircon is ZrO2 · SiO2. Zircon refractory bricks may this temperature creep is a problem. Tungsten can be used contain 4% CaO. for temperature up to 3000°C in inert atmospheres. Figure 9.8 illustrates a problem that can occur with any Doghouse furnace element—sample contamination. The sample is Melting end corner block Back α-SiC, which was heated in a tungsten furnace for 12 Working end side blocks wall hours at 1300°C. The dark features are tungsten particles side blocks Bridge evaporated onto the surface during heat treatment. Paving Bottom blocks 9.8 REFRACTORIES Bottom blocks Refractories are materials capable of withstanding high temperatures and not degrading in a furnace environment Cover blocks when in contact with corrosive liquids and gases. Refrac- Sleeper blocks tory insulators are used in high-temperature applications Throat Forehearth to reduce heat losses and to save fuel. Table 9.5 lists some entry blocks of the important furnace insulation materials together FIGURE 9.9 The layout of refractories in an industrial glass with their maximum usable temperature and thermal con- melting furnace. 146 ........................................................................................................................................................................... F u r n ac e s  ments of the insulating material and the porous micro- Castable structure ensures a very low k. We will discuss other factors that affect thermal conductivity in Chapter 34. In addition to their use in furnaces for ceramics 60% Alumina processing, refractories are also a very important sector faced with SiC of the ceramics industry because they are widely used in most high-temperature manufacturing processes: 45% Alumina  Iron and steel making (accounting for almost two- thirds of all refractories used) SiC  Copper and aluminum smelting faced with  Cement and ore processing castable  Petroleum refining SiC  Petrochemical manufacturing High-conductivity Flint-clay fine-pored C firebrick Standard High-conductivity 9.9 FURNITURE, TUBES, High alumina coarse-pored C AND CRUCIBLES Standard FIGURE 9.10 Diagram of a blast furnace indicating the type of Table 9.6 lists some of the important crucible materials. refractories used in each region. Crucibles and other furnace equipment such as boats and setter plates must meet the same requirements as refrac- tory materials used for furnace insulation, i.e., they must The schematic diagram of a blast furnace in Figure be able to withstand high temperatures and also contact 9.10 shows how different types of refractories are used with any corrosive liquids or gases used. Items such as within the furnace. The maximum temperature (>1700°C) crucibles and boats should also possess good thermal is reached toward the base of the furnace where the air “blast” comes in and where the slag is formed. Slag is a glassy waste product made up of limestone and silica TABLE 9.6 Crucible and Furnace Materials (impurities in the iron ore), ash, and oxides. It is lighter than the molten iron and so forms a layer above it. Usable Material Tmax (°C) (useful) atmosphere Refractories are one example where a high-density ceramic product is not desirable—the space-shuttle tiles Glasses being the extreme example. The thermal conductivity, kp, Pyrex 500 ONR of air is only 0.026 W m−1 K−1, significantly less than that Vycor 1100 ONR Silica glass (fused quartz) 1200 ON(R) of most crystalline ceramics. The thermal conductivity of Oxides a porous ceramic can be calculated using Eq. 9.10. Porcelain 1100–1300 ONR Steatite, talc 1250 ONR Firebrick, fireclay 1200–1500 ONR ⎛ 1 + {2Vp [1 − (kc / kp )] /[(2 kc /kp ) + 1]} ⎞ km = kc ⎜ ⎟ (9.10) Firebrick, high alumina 1600 ON(R) ⎝ 1 − {Vp [1 − (kc /kp )] /[(kc/kkp ) + 1]} ⎠ Mullite (3Al2O3 ·2SiO2) 1700 ON(R) Sillimanite (Al2O3 ·SiO2) 1700 ON(R) Zircon (ZrO2·SiO2) 1750 ON(R) kc is the thermal conductivity of the ceramic, kp is the Spinel (MgO·Al2O3) 1800–1900 ONR, shock thermal conductivity of air, and Vp is the volume fraction Alumina (Al2O3) 1850–1950 ONR of porosity. Magnesia (MgO) 2300 O, shock Zirconia, stabilized 2300 ON(R), shock When kc > kp, the resultant thermal conductivity is Thoria, stabilized 2700 ON, shock Metals km ∼ kc [(1 − Vp)/(1 + Vp)] (9.11) Iron, nickel 1100 (O)NR Platinum 1500 ONR As an illustration we can use Eq. 9.11 to estimate the Rhodium 1800 ONR Tantalum 2000 NR thermal conductivity of a silica firebrick containing 30 Iridium 2100 ONR vol% porosity, i.e., Vp = 0.3. The values of kc and kp are Molybdenum 2100 NR 1.4 and 0.026 W m−1 K−1, respectively. This gives a value of Tungsten 3000 NR km = 0.75 Wm−1 K−1. Other Consequently, ceramics containing a high volume Silicon carbide 1500 ON Silicon nitride 2900 ON fraction of porosity have low values of k. The ceramic Carbon, graphite 3000 NR provides the high strength and high melting point require- 9. 9 F u r n i t u r e , Tu b e s , a n d C ru c i b l e s ..................................................................................................................... 147  The degree of sintering is a function of time and tem- perature. Different processes use different soaking periods (the time at the desired firing temperature). For example, in the firing of thick-film inks the typical soaking period is relatively short, only 6–10 minutes. Figure 9.12 shows examples of much longer soaking periods used in the firing of clay-bearing ceramics. Crystallization and other phase transformations that may occur in a product as well as thermal contraction must be taken into account in the cooling stage. At the begin- ning of the cooling process the material is generally still rather plastic. It can be cooled fairly quickly at this stage, because the thermal contraction does not cause the stresses FIGURE 9.11 Kiln furniture used in the production of dinnerware. to increase very much. Below a certain temperature the plastic characteristics disappear. For many clay-based shock resistance as they may be heated and cooled rapidly. ceramics this is between 800°C and 600°C. In this range, Figure 9.11 shows an example of kiln furniture used for a higher cooling rate accompanied by a steep temperature the production of dinnerware. Any component in contact gradient can cause stresses to form in the product. In with a crucible or other piece of furnace equipment at high temperature ranges in which phase transformations accom- temperature can be contaminated. SiO2 is a major con- panied by volume changes take place, too high a cooling taminant unless you are very careful. rate can produce cracks. Especially when using raw mate- rials rich in quartz, the specification of the cooling rate requires special care. One of the goals in processing both 9.10 FIRING PROCESS traditional and advanced ceramics is to decrease the product throughput time. Fast firing seeks to reduce total A furnace is fired up in three stages. costs because of lower energy consumption and improved efficiency.  The heating-up stage  The soaking period  The cooling stage 9.11 HEAT TRANSFER The variations in the heating-up rate are chosen so that The liberation of heat energy is only the first stage of the the changes of state to which the product is subject and heating operation. This energy has to be transferred to the the stresses that arise from the thermal expansion of the material to be heated. There are three fundamental types product and the combustion of binders do not cause of heat transfer: conduction, convection, and radiation. All damage (e.g., cracks and pores). A common phase trans- modes of heat transfer formation that occurs during firing of silica-containing ceramics (such as whitewares) is that between α and β  Require the existence of a temperature difference quartz at 537°C.  Are from the high-temperature medium to a lower- Furnace design and the heating mechanism determine temperature one the maximum heating rate of a furnace. It is important to always check the operating manual that came with a A detailed study of heat transfer is best left to a specific furnace before setting the controller. course on this topic or you can consult one of the standard texts, for example, Chapman (1984). Below we give a very 1500 19 H 25 H 35 H brief description of each mode. T °C  Conduction is the transfer of heat from one part of a 1000 body to another part of the same body, or from one body to another that is in physical contact with it.  Convection is the transfer of heat from one point to 500 another within a fluid, gas, or liquid, by mixing of one portion of the fluid with another. In natural convection, #1 #2 #3 the motion of the fluid is entirely the result of differ- 0 ences in density resulting from temperature. 0 50 100 150 200 t (h)  Radiation is the transfer of heat from one body to FIGURE 9.12 Firing curves for clay-bearing ceramic compositions. another, not in contact with it, by means of wave The soaking periods are in hours. motion through space. 148 ........................................................................................................................................................................... F u r n ac e s  Any, or all, of these mechanisms may be important in ceramic applications are types K, R, and C. These are a particular heating application. Usually they operate used for temperatures up to 1250°C, 1450°C, and 2300°C, simultaneously, but often one predominates. At very high respectively. At lower temperatures it is preferable to use temperatures such as those encountered in ceramic sinter- a base metal combination such as chromel-alumel, which ing, radiation is often the most important. At lower tem- gives greater accuracy. peratures convection is most likely to predominate. In furnaces, the leads of the thermocouple are usually isolated from each other and other parts of the furnace by placing them either in thin alumina sheaths or by thread- 9.12 MEASURING TEMPERATURE ing alumina beads along their length. The thermocouple should ideally be placed directly into the furnace cavity In this section we will describe some of the approaches close to the object being heated. The external circuitry that used to determine the high temperatures employed in the measures temperature and, through an associated electri- processing of ceramics. More detailed information on tem- cal circuit, controls the power to the heating elements is perature measurement can be found in McGee (1988). kept outside the furnace. A thermocouple is a very accurate means of measuring temperature. But you should always bear in mind that the Thermocouples temperature being measured is that at the thermocouple The most common and convenient means of measuring tip. Unless the thermocouple is in intimate contact with temperature is to use a thermocouple. The principle behind the ceramic parts being heated, they may actually be at a the operation of a thermocouple is the Seebeck effect different temperature than that measured by the thermo- discovered in 1821 by Thomas Seebeck. If two wires of couple. A good illustration of this point is that thermocou- different metallic composition are connected at their ples are often used to give substrate temperatures during ends forming a closed circuit, an electric current flows if thin film growth. The thermocouple is frequently attached one of the connections is heated. Measuring the potential to be substrate support but is not in direct contact with the (emf) causing this current allows the determination of substrate itself. In controlled tests it has been found that temperature. In Seebeck’s original research the two metals the measured thermocouple temperature and the actual were bismuth and copper. surface temperature of the substrate can be off by as much There are many different types of thermocouples as 100°C or in some cases even more. available to cover temperatures ranging from −273°C to 2000°C; the most important ones are given in Table 9.7. Pyrometers The type of thermocouple you would use depends mainly on the temperature range over which you will be requiring At any temperature, above 0 K, all objects emit electro- information and the desired accuracy of the temperature magnetic radiation in accordance with the Stefan– reading. The most commonly used thermocouples for Boltzmann law: TABLE 9.7 Characteristics of Thermocouples Combination of metals Output a at Temperature Type or alloys 900°C (mV) limit °C Applications b T Copper-constantan 20.9 400 Mild oxidizing, reducing, vacuum, or inert. Good where moisture is present. Low temperature and cryogenic applications. J Iron-constantan 21.9 b 760 Reducing, vacuum, inert. Limited use in oxidizing at high temperatures. Not recommended for low temperatures. E Chromel-constantan 68.8 900 Oxidizing or inert. Limited use in vacuum or reducing. Highest EMF change per degree. K Chromel-alumel 37.3 1250 Clean, oxidizing, and inert. Limited use in vacuum or reducing. Wide temperature range. Most popular calibration. S Pt–Pt 10% Rh 8.4 1450 Alternative to Type K. More stable at high temperatures. Oxidizing or inert. Do not insert into metal tubes. Beware of contamination. High temperature. R Pt–Pt 13% Rh 9.2 1450 Same as Type S. B Pt 6% Rh–Pt 30% Rh 4.0 1700 Oxidizing or inert. Do not insert into metal tubes. Beware of contamination. High temperature. Common use in glass industry. G (W) W–W 26% Re 12.3 2300 Vacuum, inert, hydrogen. Beware of embrittlement. Not practical below 750°C. Not for oxidizing atmosphere. C (W5) W 5% Re–W 26% Re 16.4 2300 Same as Type G. Nonoxidizing atmosphere only D (W3) W 3% Re–W 25% Re 15.1 2300 Same as Type G. Nonoxidizing atmosphere only a The higher the output voltage, the simpler the associated circuitry and/or the more accurate the temperature reading. b Output at 400°C. 9.1 2 M e a s u r i n g Te m p e r at u r e .................................................................................................................................... 149  E = σT 4 (9.12) σ is the Stefan–Boltzmann constant, which has a value of 5.6718 × 10−8 JK−4 m−2 s−1. The total energy (E) emitted at all wavelengths is proportional to T 4. It is possible to estimate the temperature of a hot object by its color. In 1557 in his work on Renaissance pottery, Cipriano Piccolpasso described how the furnace operator was able to use color variations to judge furnace temperatures. As the temperature of an object increases the range of wave- lengths that it emits increases and shifts to shorter values. At temperatures above about 500°C there will be a red coloration that will become increasingly orange as the temperature increases beyond 1000°C. At 1400°C the object will appear bright white. Be careful when looking at hot objects and remember that an object can still be too FIGURE 9.13 Orton cones: the self-supporting type. The cones hot to handle even if it is not glowing red. shown are 6 cm tall in their initial state. Optical pyrometers allow direct measurement of the temperature of an object. The disappearing filament optical pyrometer works by matching the intensity of radiant energy coming from an incandescent source to the bend over in an arc so that the tip reaches the level of the intensity of a calibrated filament when both the source and base at a particular temperature if heated at a particular the filament are viewed through a red filter. When the fila- rate, as shown in Figure 9.13. The bending of the cones is ment and the source intensities are the same, the image of caused by the formation of a viscous liquid within the the filament disappears as it is superimposed on the image cone body, so that the cone bends as a result of viscous of the source. An obvious requirement of this technique flow. The endpoint temperature when the tip of the cone is that it can be used only to measure temperatures that touches the supporting plate is calibrated for each cone produce visible incandescence, above about 750°C. composition when heated at a standard rate. Values of The advantages of the disappearing filament pyrome- endpoint temperatures for Orton cones (the U.S. name) are ter are as follows: listed in Table 9.8 for the higher temperatures; the series actually runs from Cone 022 at 600°C, through Cone 06  The distance from the target to the source is not impor- at 999°C, to Cone 42 at the top of the scale. Since pyro- tant (it is only necessary to have a clear image to metric cones are sensitive to both time and temperature, compare with the filament image). the actual temperatures associated with each cone can  Various places on a target can be examined for tem- vary, but this is also one of the reasons why they are very perature distribution. useful for ceramic processing. Sintering, for example,  Very high temperatures can be measured. depends on both time and temperature.  The visible image ensures that the instrument is meas- uring the temperature of the desired portion of the target.  Reasonable accuracy (at best ±0.2°C at 775°C reduced TABLE 9.8 End Points of Orton Pyrometric Cones to ±1°C at 1225°C) can be obtained. Cone Cone number End point (°C) number End point (°C) The disadvantages are as follows: 12 1337 31 1679 13 1349 31−12 1699  The instrument either must be sighted under blackbody 14 1398 32 1717 conditions or the reading corrected for emittance. 15 1430 32−12 1730  Absorption by dust, windows, flame, and other optical 16 1491 33 1741 interference can produce errors. 17 1512 34 1759  The disappearing filament optical pyrometer is slow 18 1522 35 1784 19 1541 36 1796 and manual. However, other pyrometers such as the 20 1564 37 1830 photoelectric optical pyrometer can be automated. 23 1590 38 1850 26 1605 39 1865 27 1627 40 1885 Pyrometric Cones 28 1638 41 1970 29 1645 42 2015 Pyrometric cones are small triangular ceramic prisms that 30 1654 when set at a slight angle (known as self-supporting cones) 150 ........................................................................................................................................................................... F u r n ac e s 9.13 SAFETY Carbon monoxide (CO) is a deadly gas that can form from a reaction between trapped moisture (for example, The safety issues associated with the use of furnaces can in the furnace insulation) and carbon. The source of be divided into three categories. carbon may be the graphite used in some furnaces for heating elements or in graphite-felt insulation. Prob-  High-temperature hazards. Working with high tem- lems can be avoided by ensuring that the furnace is peratures is the obvious safety hazard when using fur- kept dry. Domestic CO alarms can be installed in the naces. Protective goggles or safety glasses should be laboratory area as an added precaution. used in all situations. As the temperature increases, the intensity of the emitted light rises and the maximum The importance of nitrogen ceramics, such as silicon shifts to shorter frequencies. This is apparent to an nitride, means that furnaces are often operated using observer. At 1000°C the color of a furnace enclosure nitrogen gas. At high temperatures it is possible to form is a pleasing red. At 1600°C it is a brilliant painful cyanide complexes such as cyanogen (CN) and hydrogen white and goggles or glasses with green lenses should cyanide (HCN). In graphite furnaces the following reac- be used. Handling objects that have come from a tion can occur: furnace should be done using specially designed tongs 1 and furnace tools and hands should be protected with C+ N 2 → CN insulating gloves. Even if an object is not glowing red 2 it can still be at a temperature of >500°C. Above temperatures of 2200°C the CN concentration  Electrical hazards. Electrical dangers should never be exceeds the lethal concentration guidelines. Fortunately underestimated. All electrical equipment operating at the gas is unstable and can be destroyed by passing it mains voltages can be lethal. A current >100 mA (ac through an oxidizing flame. Hydrogen cyanide can form or dc) would almost invariably be fatal if passed in graphite furnaces that contain mixtures of H2 /N2 (called through the body. Most electrical accidents are caused forming gas). by worn-out equipment or faulty wiring, both of which 1 1 can be avoided. All potentials in excess of a few tens H 2 + C + N 2 → HCN of volts must be properly insulated and physically iso- 2 2 lated before maintenance. A typical laboratory box Forming gas is used in metal sintering furnaces and in furnace uses 240 or 208 V single phase at 50 or 60 Hz some metallization processes to avoid oxidation of the to generate 10 kW of power. This requires a current of metal. HCN can also form when water vapor, graphite, about 40 A. All electrical equipment not fully insulated and nitrogen react: must be properly earthed in the interests of safety.  Chemical hazards. Some of the chemicals used in H2O + 3C + N2 → 2HCN + CO ceramic processing are toxic. One important example is lead and its oxides, which are widely used in the It is essential to maintain dry conditions in these furnaces, production of certain types of glasses and pigments. as the reaction is thermodynamically favored at all tem- Care should be taken to read safety data sheets that peratures. In cases that can involve the build-up of deadly accompany any chemicals and to take the necessary gases it is essential that the laboratory is well ventilated preventative action. Other safety issues can arise from and the discharge is vented away from the immediate unwanted reactions that occur within the furnace. work area. CHAPTER SUMMARY Furnaces are ubiquitous in all aspects of ceramics research, development, and production. High temperatures may be obtained through harnessing the heat generated by combustion reactions, but more usually resistance heating is used. Ceramic materials, most notably SiC, are widely used as resistive elements in electrically heated furnaces. They are also used to provide thermal insulation in all types of furnace. These materials are known by the collective term refractories because of their stability at high temperatures and their resistance to corrosive environments. Refractories are a major sector of the ceramics industry with the largest consumers being the iron and steel companies. PEOPLE IN HISTORY Joule, James Prescott (1818–1889), the English physicist born in Salford near Manchester, showed that heat is produced by motion and thus helped end the caloric theory. Kirchhoff, Gustav Robert (1824–1887) was born in Prussia (now part of Russia) and died in Berlin. He introduced the term black-body radiation, the laws of electrical networks, and much more. C h a p t e r S u m m a ry .......................................................................................................................................................... 151  Morse, Samuel patented the disappearing filament optical pyrometer in 1899. Norton, Frederick Harwood formed the Ceramics Division at MIT and wrote two classic texts on Ceramics. Orton, Edward J. Jr. established the first ceramic engineering program at The Ohio State University in 1894 and founded the American Ceramic Society in 1899. He created the Standard Pyrometric Cone Company, to make pyrometric cones, in a basement at Ohio State University; these cones became the standards for monitoring firings and are known as Orton cones. http://www.ortonceramic.com. Similar cones may have been used in China in the Northern Song Period—before 1127 ce, although Josiah Wedgwood used pyrometric beads instead. Outside the United States similar cones may be called Seger cones (after Hermann Seger) or Staffordshire Cones in the UK. Seebeck, Thomas Johann (1770–1831) was born in Estonia. He showed that a current flowed when you join two metals that are at different temperatures (the thermoelectric effect); this led to the invention of the thermocouple. GENERAL REFERENCES Barin, I. (1989) Thermochemical Data for Pure Substances, VCH Verlagsgesellschaft GmbH, Weinheim, Germany. Gives tables and compilations of thermodynamic data. Chapman, A.J. (1984) Heat Transfer, 4th edition, Macmillan, New York. A standard heat transfer text. Chesters, J.H. (1973) Refractories: Production and Properties, The Iron and Steel Institute, London. Gives comprehensive information about the composition and properties of the different types of refractory brick. Finn, C.W.P. (1991) “Furnaces and related equipment,” in Engineered Materials Handbook Volume 4 Ceram- ics and Glasses, ASM International, pp. 244–254. A review of furnaces and related equipment. Gilchrist, J.D. (1963) Furnaces, Pergamon Press, Oxford. Although more than 40 years old this is a useful (and concise) monograph with a great deal of useful information. It goes into much more detail concern- ing thermodynamics and the theory of heating and heat transfer than we do. McGee, T.D. (1988) Principles and Methods of Temperature Measurement, Wiley, New York. Nassau, Kurt (1984) Gemstone Enhancement: Heat, Irradiation, Impregnation, Dyeing and Other Treatments Which Alter the Appearance of Gemstones, and the Detection of Such Treatments, Butterworth Heine- mann, London. Appendix A is a brief and clearly written description of the different types of furnaces often encountered in ceramics laboratories. Norton, F.H. (1968) Refractories, 4th edition, McGraw-Hill, New York. This also covers furnace construction and the use of refractories in the metallurgical industries. Piccolpasso, C. (1557) The Three Books of the Potter’s Art; translated by R. Lightbown and A. Caiger-Smith, Scolar Press, London (1980). Remmey, G.B. (1994) Firing Ceramics, World Scientific, Singapore. WWW http://intarch.ac.uk/journal/issue1/peacey/toc.html is an excellent introduction to furnaces in archeology. It gives the definition of a muffle from Searle, A.B. (1930) The Encyclopedia of the Ceramic Industries, London as “A chamber, case or box of refractory material, which is built in a furnace, and used to heat articles out of direct contact with fl ames or other products of combustion. It serves a purpose similar to a saggar, but being larger, is more suitable for some purposes.” The muffle is actually the enclosed section that protects the material from the combustion products of the furnace. The heat is conducted to the sample through the walls of the muffle. www.claygirl.com/glossary.html gives other definitions for the potter. EXERCISES 9.1 Table 9.4 lists materials used as furnace elements for ceramic processing. Find the costs of each type of element. 9.2 Small electrically heated box furnaces are probably the most widely used furnaces in university ceramics laboratories. What are the characteristics of these furnaces that make them so useful? 9.3 Why is a muffle furnace so named? 9.4 (a) Explain briefly why the standard molar enthalpy of combustion for ethane (C2H6) is greater than that for methane. (b) Which is more useful as a fuel, methane or methanol? Briefly explain how you arrived at your answer. (c) Calculate the standard molar enthalpy of combustion of methane at 1000 K. 9.5 Explain why most refractory materials such as firebricks and fiber board insulation have high volume fractions of porosity. 9.6 Is a high thermal expansion coefficient an advantageous or deleterious property of a refractory brick? Explain briefly the reasoning behind your answer. 152 ........................................................................................................................................................................... F u r n ac e s  9.7 Briefly explain how a thermocouple works. 9.8 The most widely used thermocouples for ceramic processing are types K, R, and C. Explain what alloys are used for each type and under what conditions each would be most appropriate. 9.9 Pyrometric cones are widely used in industry for temperature measurement, yet they are rarely used in university ceramics laboratories. Why does this discrepancy exist? 9.10 Pyrex and Vycor are both glasses that are used as crucibles. Why is the maximum useful temperature of Pyrex less than half that of Vycor? C h a p t e r S u m m a ry .......................................................................................................................................................... 153  10 Characterizing Structure, Defects, and Chemistry CHAPTER PREVIEW In this chapter we will discuss techniques that can produce useful information about the struc- ture, chemistry, and bonding in ceramics. There are so many characterization methods avail- able that books are written on each one. Since we cannot cover all the details or even all the techniques, we will give examples and aim at making you aware of the key ones and their applications. We can group the techniques into six categories:  Imaging using visible (or nearly visible) light  Imaging using electrons [mainly scanning electron microscopy (SEM) and transmission electron microscopy (TEM)]  Imaging using sensing [atomic force microscopy (AFM) and other scanned probes that “sense” a force or field]  Scattering and diffraction (using X-rays, neutrons, α-particles, electrons)  Spectroscopy and spectrometry [using X-rays for energy dispersive spectrometry (EDS) and wavelength dispersive spectroscopy (WDS), Raman, infrared (IR), etc.]  Thermal analysis (measuring changes, e.g., enthalpy, as a function of temperature) Most of the techniques we describe can be used to study other classes of materials, but our examples will all be related to ceramics. The suitability of a characterization technique depends on the type of information we hope to obtain and may also be dictated by the size of our sample, what part of the sample is impor- tant, and whether we can destroy the sample. There are some limitations:  Reflection techniques examine only surfaces.  Techniques using electrons require the sample to be in a vacuum.  Techniques using transmitted electrons generally require the sample to be thin.  For nanomaterials we need high resolution. We always ask two questions:  How much material is required for the analysis?  Is it destructive or nondestructive? For example, TEM is invariably destructive, but you need a very small amount of material for the analysis. 10.1 CHARACTERIZING CERAMICS  Structure. Is the ceramic crystalline or glass or a mixture of the two? What polymorph is present? In characterizing a ceramic, whether it is a single crystal,  Microstructure. Is the structure the same throughout polycrystalline, or a glass, there are certain types of infor- the sample? Polycrystalline ceramics cannot be uniform. mation that we are interested in obtaining: Even glass can be structurally inhomogeneous.  Surface. Whether the sample is crystalline or not, the  Chemistry. What is the composition, how does it vary nature of the surface is often particularly important. If within the sample, etc.? the sample is crystalline then surface orientation may 154 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  TABLE 10.1 Summary of Tools for Ceramics Using be critical. Even the surface of a glass will be different Chemical and Physical Characteristics chemically and structurally from the bulk. In nanoma- Chemical characteristic Characterization tool terials the surface is the most important feature, since most of the atoms are there. Composition X-ray diffraction (XRD)  Defects. In crystals we often want to determine X-ray fluorescence (XRF) dislocation density. In both crystals and glass we may Neutron activation analysis (NAA) Mass spectrometry (Mass Spec) be interested in the nature, concentration, and distribu- Elemental distribution/local Scanning electron microscope tion of point defects. Techniques for characterizing chemistry (SEM) with X-ray energy- defects are dealt with mainly in their respective dispersive spectroscopy chapters. (XEDS) Electron probe microanalysis (EPMA) What we want to know determines which technique we Transmission electron should use. In the following sections our approach is to microscopy (TEM) with XEDS illustrate the type of information that can be obtained. TEM with electron energy-loss Most of these methods are applicable not only to ceramics spectroscopy (EELS) but to other classes of material. However, there are certain Surface/interface chemistry X-ray photoelectron spectros copy (XPS, ESCA) special features associated with ceramics: Auger electron spectroscopy (AES)  Techniques using electrons can be complicated because Secondary ion mass spectros many ceramics charge locally, thus deflecting an elec- copy (SIMS) tron beam. Rutherford backscattering spectrometry (RBS)  We are often interested in what happens while Ultraviolet photoelectron ceramics are being processed. Because of the en- spectroscopy (UPS) vironment or the high temperatures involved, such in Infrared (IR) spectroscopy situ studies may not be possible with the desired Raman spectroscopy resolution. Phase changes (e.g., Thermomechanical analysis decomposition and (TMA)  Ceramics are often multicomponent systems; knowing dehydration) Thermogravimetric analysis (TGA) the average composition may not be too useful. So we Differential thermal analysis (DTA) may need local compositional analysis on a scale that Differential scanning calorimetry may be in the nanometer range. (DSC)  Many ceramics contain light elements (e.g., B, C. N, Mass Spec (MS) In situ XRD O), which can be difficult to quantify. Surface area/porosity Small-angle neutron scattering  If we are interested in interfaces, for example, the (see Chapter 20) (SANS) interface may facet over short (<100 nm) distances and Small-angle X-ray scattering it may contain steps that are only nanometers high. In (SAXS) studying such interfaces, it is essential that both grains Mercury porosimetry Density homogeneity VLM be observed, so that techniques requiring the sample SEM to be broken along the interface would not be ideal X-ray radiography/CT scan (though they may be necessary). Ultrasound Die penetration Table 10.1 lists some of the techniques that you might Particle/grain size, VLM and quantitative stereology distribution, morphology, SEM and quantitative stereology consider to obtain specific information about your mate- and texture Electron backscattering rial. In most cases the use of a particular technique depends spectroscopy (EBSD) in part on its availability, and often a combination of TEM techniques is necessary to get the complete picture. XRD Phase identification/molecular XRD structure EBSD FTIR 10.2 IMAGING USING VISIBLE-LIGHT, Raman spectroscopy IR, AND UV EXAFS Neutron diffraction Light interacts with the specimen in many ways; we then Mössbauer spectroscopy Nuclear magnetic resonance study the resulting image contrast. Contrast is produced (NMR) by reflection, absorption, refraction, polarization, fluores- Phase transitions: e.g., DTA cence, or diffraction. This contrast can be modified by structural transformations DSC physically changing the optical components and illumina- TMA tion mode of the microscope. The final image can also be In situ XRD processed, now mainly using computer techniques. 10 . 2 I m ag i n g U s i n g Vi s i b l e - l i g h t, I R , a n d U V ..................................................................................................... 155  Visible-light microscopy (VLM) is used routinely for attractive images, because of the enhanced contrast. all ceramics. It is often referred to as optical microscopy, Nomarski microscopes are more expensive than con- but essentially all microscopy is optical. The magnifica- ventional VLMs because of the cost of the Wollaston tion of a VLM can range prisms. from 10× (a magnifying NSOM (near-field scanning NSOM PARAMETERS glass) to 50 k× using a optical microscopy, also Aperture size: 25–10 nm liquid between the known as SNOM). This is a Tip/sample gap 5–50 nm specimen and the lens. broad and growing topic. Modern VLMs are The idea is that the resolu- equipped with digital cameras (video or still) and feed tion in VLM is limited by λ. If the light source is straight into the computer. Ceramics are often transparent, a fiber with an aperture in the end and we detect especially (but not necessarily) if they are glass, so we can the reflected/scattered light with the same fiber, then use reflected or transmitted light. The sample can be then the spatial resolution is determined viewed supported on a table or inverted. The inverted by the diameter of the fiber. The limitation is that microscope has some advantages, in particular, you can since the aperture diameter is smaller than λ (Figure attach contacts to, indent into, or support liquids on the 10.2), the emerging wave is evanescent so the signal free surface. You also have more flexibility with the strength is small. The use of a laser provides the lighting. necessary intensity and defines λ. The usefulness of The lateral resolution using VLM is about 250 nm and the technique relies on the ceramics sample having the depth of field has a similar value. Because of the poor suitable features to scatter the light. The technique depth of field of the VLM we often examine polished can be used for other wavelengths and other signals surfaces (as in metallography). Vertical resolution can be (e.g., Raman). The latter technique is still being less than 1 nm using interference contrast, and this is bet- developed. tered only by the scanned probe techniques. IR and UV. Because semiconductors are transparent to IR Visible-light microscopy is usually available in every radiation, defects in these materials can be examined laboratory. While a conventional VLM may cost only with IR microscopy. A detector sensitive to IR is $2000, the best metallographic microscopes can cost required. With IR and ultraviolet (UV) light, a con- >$100 k. There are numerous imaging methods used in VLM so we list only a few here: Dark-field. The image is formed using only scattered light (if there is no specimen present then the image is dark). It is widely used in mineralogy where multi- phase materials are common. Polarized light. Polarized VLM distinguishes between isotropic and anisotropic materials and provides infor- mation on absorption color and boundaries between minerals of differing refractive indices. The technique provides local information on the structure and com- position of materials as shown in Figure 10.1, which is an image of a neodymium-doped yttrium ortho- vanadate laser crystal. Individual grains, separated by low-angle grain boundaries, are clearly revealed by polarized VLM. Nomarski (differential interference contrast). The idea here is that we use interference. Contrast is generated by phase differences between two rays (a sample ray and a reference ray). In the Nomarski microscope the two rays are created after the light has passed through the sample, where path differences occur because of regions having different refractive indices. The ray is split by a prism (called a Wollaston prism) and after passing through a polarizing filter it is recom- bined using a second prism at the image plane. By FIGURE 10.1 Slightly misoriented grains in a laser element using a rotating stage the image contrast can be imaged using polarized VLM. The crystal is yttrium orthovanadate varied. Using this technique it is possible to create very with 0.27% Nd. 156 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  Incident light Glass λ = 500 nm fiber Al coating FIGURE 10.3 X-ray topography image showing dislocations in KDP imaged using a 022 reflection. FIGURE 10.2 Schematic of the end of the fiber and the sample in NSOM. verter or detector is also required. An advantage of UV TEM), and can be used to observe very low dislocation microscopy is that because the wavelength of UV light densities (limit in TEM >104 mm−2). is smaller than visible light the resolution of these Computed tomography (CT) is used to determine microscopes is higher than VLMs. UV microscopy is inhomogeneities arising from local differences in density. widely used in the biological sciences to study sub- It is applicable to a range of ceramics and minerals and is cellular structures. Using intense vacuum UV sources particularly useful for identifying defects in single crys- (available at national laboratories) it is possible to tals. The sample is placed on an automated stage that obtain results on, for example, electronic states. rotates as a series of X-ray images (radiographs) is cap- tured (much like a medical CAT scan except that details as small as a few tens of micrometers can be resolved even 10.3 IMAGING USING X-RAYS AND in dense samples). A computer then processes the X-ray CT SCANS images and creates a three-dimensional (3D) reconstruc- tion of the sample. Areas of lower density such as cracks X-ray topography can be used to obtain images of indi- and voids appear as darker contrast against a lighter back- vidual lattice defects in single crystals. This technique has ground. Figure 10.4 shows density variations in the core been widely used to study crystal growth and, in particu- of an Nd-doped YVO4 sample. lar, silicon. It can be used in  Reflection (Berg–Barrett method)  Transmission (Lang method or Borrmann method) In either method it is the variation in intensity within the diffraction spot that is recorded. It is not usually the defects themselves that are imaged but rather the strain fields around them. These strains cause variations in plane spacing from their equilibrium value, thereby modifying the X-ray scattering process. Figure 10.3 shows a Lang topographic image of dislocations in potassium dihydro- gen phosphate (KDP; KH2PO4). KDP has a relatively large electrooptic effect and can be grown as large strain- free crystals. X-ray topography has several advantages for characterizing defects in single crystals. It is nondestruc- FIGURE 10.4 High-resolution X-ray CT images from the top and tive, does not require ultrathin samples (as is required in side of the same sample. 10 . 3 I m ag i n g U s i n g X- r ay s a n d C T S c a n s .............................................................................................................. 157 10.4 IMAGING IN THE SEM The basic layout of the SEM is shown in Figure 10.5. The SEM can have two imaging detectors, one for secondary electrons (SEs) and one for higher-energy backscattered electrons (BSEs). The SEM typically has a resolution in SE mode of 0.7 nm (at 25 kV) and 2.5 nm in BSE mode at 5 kV. In addition to the excellent spatial resolution, the other great advantage of the SEM is that it has a much greater depth of field than the VLM (the depth of field is several millimeters). So the images appear more three- dimensional. The physical reason for this is that the elec- tron beam is very narrow. SEs are low-energy electrons so they are very sensitive to surface topology. Figure 10.6 shows an example of an SE image illustrating the excellent depth of field. BSEs are higher-energy electrons and are sensitive to the atomic number of the scattering atom. Hence the intensity of the FIGURE 10.6 SE image showing steps on an alumina surface. BSE signal depends on a combination of the average atomic number and density of the ceramic. As the kilovolts Figure 10.7 the three regions correspond to three different are reduced, the scattering volume becomes more local- layers in a reaction couple. The MgO substrate is darkest, ized close to the surface of the sample. (The BSE electrons the In2O3 is lightest, and the spinel, MgIn2O4, is intermedi- penetrate further into the sample and have further to come ate. The very bright regions are Pt nanoparticles. out after being scattered.) Hence the BSE image can give Charging in the SEM is usually avoided by coating the excellent mass discrimination even at low voltages. In specimen (e.g., with a 1-nm layer of Pt). Working at lower accelerating voltages can also reduce charging effects, but then the resolution is compromised; electron lenses work better at higher resolutions. In low-voltage SEM imaging, you are trying to balance the electrons emitted as the specimen is irradiated with the charge building up on the Electron specimen. Another way to avoid applying a conductive gun -7 10 Torr coating is to use an environmental or low-vacuum SEM. Then, the charging of the specimen is essentially grounded Magnetic by the gas in the chamber. Variations in the SEM are sum- condenser lenses marized in Table 10.2. Projection aperture Magnetic Scan coils objective lens 10-4 Torr Detector 10-1 Torr Gas Inlet Speciman 1-20 Torr holder Stage Speciman chamber FIGURE 10.5 Schematic of an SEM showing examples of FIGURE 10.7 BSE image showing different contrast from different pressures used. materials in an MgO/In2O3 reaction couple. 158 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  TABLE 10.2 Comparison Summary of Signals Used in the SEM Signal Energy Source Use Secondary electrons ∼5 eV Loosely bound electrons Main signal for image scattered from surface formation Backscattered electrons Energies up to incident Beam electrons scattered Atomic number contrast, beam energy back after collision channeling patterns, magnetic contrast Characteristic X-rays Discrete values for Interband transitions Chemical analysis each element usually involving K and L Light UV, visible, IR Interband transitions Imaging dislocations in (cathodoluminescence) between higher energy semiconductors levels Environmental SEMs allow operation at pressures of is that we require the sample to be very thin (usually several torr (0.1–20 torr) in the sample chamber and at ≤200 nm). So the technique is destructive and specimen temperatures >1000°C. In addition to being able to preparation can be time consuming. The benefits, however, examine insulators it is also possible to follow dynamic are significant. Because of the large range of signals gen- processes such as drying of cement and crystallization. erated by the incident electron beam (Figure 10.9), a TEM allows full characterization of a sample at high resolution. 10.5 IMAGING IN THE TEM The conventional imaging modes in a TEM are bright- field (BF) imaging and dark-field (DF) imaging. In BF Figure 10.8 shows a state- imaging the image is of-the-art TEM with a field RESOLUTION formed using only the emission source. The key The higher the resolution the smaller the features we can direct beam. An aperture requirement for using TEM resolve. (the objective aperture) is used to exclude all the dif- fracted electrons from contributing to the image. In DF imaging the image is formed from one of the elastically scattered beams and the objective aperture blocks the direct beam and all the Electron gun other scattered electrons. The BF image in Figure 10.10a (source) shows a thick particle of NiO sitting on a thin film of Al2O3; the different gray levels in the films correspond to different thicknesses in the Al2O3 film. The DF image in Figure 10.10b shows the same region after reacting the two oxides at high temperature; by using a reflection that is excited only by the spinel product, we can see exactly where the spinel has formed. Sample High- holder voltage Incident supply high-kV beam Secondary electrons (SE) Backscattered electrons (BSE) Characteristic X-rays Auger Visible Z-contrast electrons Light detector “Absorbed” Electron-hole electrons pairs Bremsstrahlung Specimen X-rays Elastically Inelastically scattered Direct scattered electrons Beam electrons FIGURE 10.8 A TEM with key features labeled. FIGURE 10.9 Signals produced in a TEM. 10 . 5 I m ag i n g i n t h e Te m ............................................................................................................................................. 159  (A) (B) FIGURE 10.10 (a) BF and (b) DF image (using a spinel reflection) of a particle of NiO on a film of Al2O3 before and after reaction. The resolution of a TEM is determined by the energy of the electrons (controlled by the accelerating voltage), the thickness of the specimen (we want to avoid multiple scattering within the sample), the distance between the sample and the objective lens, and the inherent quality of the lens (defined by its spherical aberration coefficient). Figure 10.11 shows an image of SrTiO3 showing variations in the oxygen occupancy. At present, the best high- resolution TEM (HRTEM) has a resolution of ∼0.08 nm (sub-Å!), but 0.05 nm should be achievable. For nanotech- nology an HRTEM is an essential tool. An example is its use in studying crystals of KCl grown in a carbon nano- tube as shown in Figure 10.12. FIGURE 10.12 HRTEM image of a C nanotube partly loaded with FIGURE 10.11 HRTEM image of the structure of SrTiO3. a crystal of KCl. 160 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  To photodetector Tip bias Cantilever Tip Tip’s path Δz Tunnel current Tip Sample Sample FIGURE 10.13 Schematic of the tip/sample interaction in STM; the tip does not make physical contact with the sample. FIGURE 10.15 Schematic of the tip/sample interaction in AFM using a cantilever system. 10.6 SCANNING-PROBE MICROSCOPY probe microscopy. The most widely used is atomic-force microscopy (AFM), which is illustrated in Figure 10.15. The topic of scanned probe microscopy includes several Atomic-force microscopy is extensively used to study different techniques, which grew out of the development of the surfaces of nonconducting oxides. A pair of AFM scanning tunneling microscopy (STM) (for which images at low and high magnification is shown in Binnig and Rohrer shared the Nobel Prize in 1986). The Figure 10.16. The lines are straight single steps (0.4 nm basic principle is that the tip of the probe determines high) on the surface of (111) spinel; the high-magnification the resolution of the image as shown in Figure 10.13. image shows the origin of the steps as a pair of Scanning tunneling microscopy has been used to dislocations emerging at the surface. A nanoscale indenter study the atomic structure of ceramic surfaces. Figure can be attached to the AFM making it into an indenter 10.14 shows the reconstructed with integrated imaging. (110) surface of TiO2. In addi- AFM AND STM “IMAGE” ATOMS Table 10.3 summarizes tion to STM there are now Both AFM and STM provide atomic resolution, meaning the common operating several other types of scanned we can resolve individual atoms. modes of the AFM. (B) FIGURE 10.14 STM image of the (110) surface of TiO2. The features labeled ‘A’ have been assigned as oxygen vacancies; the features labeled ‘B’ have not been identified. The schematics show the TiO2 structure (compare to Fig. 6.11) and a model showing the proposed (A) surface reconstructon. 10 . 6 S c a n n i n g - p r o b e M i c r o s c o p y ............................................................................................................................. 161  10.7 SCATTERING AND DIFFRACTION TECHNIQUES The fundamental idea is that we scatter particles or waves from the constituent atoms in the sample. If the waves interfere constructively, we have diffraction, which implies that the sample is at least partly crystalline. If the sample is not crystalline, we may still learn about the distribution of the atoms from the radial distribution function (rdf). The process of scattering generally implies particles; dif- fraction generally suggests Bragg diffraction or construc- tive interference of waves. We can summarize some techniques in diffraction and scattering (of photons, electrons, neutrons, etc.). Photon scattering Raman and Fourier transform infrared (FTIR) are well- known techniques for the chemist and are increasingly (A) important in ceramics Electron diffraction Selected-area diffraction (SAD) in the TEM Convergent-beam electron diffraction (CBED) in the TEM Electron-beam backscattering diffraction (EBSD) in the SEM Reflection high-energy electron diffraction (RHEED) in UHV for surfaces Ion scattering Rutherford backscattering spectrometry (RBS) X-ray diffraction Powder diffraction for statistical determination of lattice spacings Laue back-reflection for orienting single crystals (B) Neutron scattering Small-angle scattering in a range of environments FIGURE 10.16 AFM image showing long (up to 10 μm) straight steps on the surface of an Mg–Al spinel. The steps are 0.4 nm high. The lower image shows the central region at higher Electrons interact most strongly with the sample, so magnification. for transmission the specimen must be thin and in a vacuum. Neutrons are at the other extreme, but can be TABLE 10.3 Modes of Operating the Atomic-Force used only in dedicated (usually national) facilities because Microscope they require radioactive sources. We will use diffraction in the TEM to study the crys- Mode of operation Force of interaction tallography of the interfaces and characterize other crystal Contact mode Strong (repulsive); constant force or defects. Bragg made the first direct determination of a constant distance crystal structure using X-ray diffraction (XRD), which is Noncontact mode Weak (attractive)-vibrating probe still generally the most accurate method for characterizing Intermittent contact mode Strong (repulsive)-vibrating probe Lateral force mode Frictional forces exert a torque on the crystal symmetry, providing the sample is large enough scanning cantilever and can be isolated. However, XRD does not provide a Magnetic force Magnetic field of the surface is high spatial resolution because the beam diameter is typi- imaged cally 1 mm, although with a rotating anode generator it Thermal scanning Variation in thermal conductivity is may be 0.1 mm and with a synchrotron 1 μm or less is imaged possible. 162 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  TABLE 10.4 Electromagnetic Spectroscopy E (eV) 10 −7 10 −5 10 −2 10 −1 101 103 >103 T (K) 1.16 × 10 −3 1.16 × 10 −1 1.16 × 102 1.16 × 103 1.16 × 105 1.16 × 107 >107 ν (Hz) 2.4 × 10 −7 2.4 × 109 2.4 × 1012 2.4 × 1013 2.4 × 1015 2.4 × 1017 >1017 λ (cm) 1.24 × 103 1.24 × 101 1.24 × 10 −2 1.24 × 10 −3 1.24 × 10 −5 1.24 × 10 −7 >10 −7 Radiation Radio Micro IR VIS UV X γ Atomic subsystem Nuclear spins Electron spins Rotation Outer shell electrons Inner shell Nuclei transitions vibration electrons Primary quantity Local interactions (magnetic, Atomic Energy levels Energy levels Energy levels measured electric field gradient) molecular potentials Kinetic parameter Diffusional atomic motions Vibrational Macroscopic, real time kinetic coefficients, point defect detected frequencies concentrations Effects on reactivity Transport Photochemistry Radiation chemistry activation by heat Characteristic sample 10 −1–10 0 10 −2–10 −1 ca. 10 0 10 −4 –10 0 10 −2 10 −3 [Fe(MS)] dimension (cm) (A1, 104 eV) 10 −1 [In(PAC)] Examples of methods NMR ESR Raman Absorption spectroscopy XAS Mössbauer, PAC 10.8 PHOTON SCATTERING Cryo-cooled HgCdTe detectors are used for weak signals or high resolution. The key component of an FTIR is the Electromagnetic spectroscopy involves the interaction of interferometer, which can be understood by considering electromagnetic waves and matter. We can use all regions the Michelson interferometer shown in Figure 10.17. A of the electromagnetic spectrum and each will give spe- parallel beam directed from the source is split at Bs so that cific information about a material. Table 10.4 provides a 50% of the light is transmitted and reflected back by summary and succeeding sections deal with each of the mirror MF, while the rest is reflected at Bs and then again methods in a little more detail with specific application to at MM. The beams recombine at Bs. The recombined beam ceramics. Once again, to really understand each of the will show constructive or destructive interference depend- methods you need to read a specialist text. ing on the difference in the path lengths Bs to MF and Bs to MM. As MM is moved smoothly toward or away from Bs the detector sees a signal that alters in intensity. If the recombined beam from Bs is passed through a sample 10.9 RAMAN AND IR SPECTROSCOPY before reaching the detector sample absorptions will show up as gaps in the frequency distribution. The complex Raman and IR spectroscopy both involve the scattering of intensity distribution received by the detector is Fourier light. In IR spectroscopy, the light is polychromatic and transformed by a computer to produce an absorption couples to vibrational modes in the solid through dipole spectrum. moments, which are associated with the vibration. These vibrational modes cause a dip in the transmission spectra or a peak in the absorption spectra. The IR range is from 0.78 to 1000 μm (12,820 to 10 cm−1). The region where M2 most fundamental vibrational modes occur, which is the source most useful for materials characterization, is between J 2.5 and 25 μm (4000–400 cm−1). This is sometimes called M1 M3 the mid-IR region. The light source is a heated ceramic BS (usually a conducting ceramic or a wire heater coated with move ceramic) that emits a range of frequencies. P1 P2  Spectroscopy: the art of using a spectroscope Mm  Spectrometry: the act of using a spectroscope Mf To sample J An important variant is the FTIR spectrometer. The & main advantages of FTIR are that it is much quicker detector because it measures all the frequencies simultaneously FIGURE 10.17 Schematic of the arrangement of mirrors and ray and it is more sensitive than dispersive IR spectrometers. paths in FTIR. 10 . 9 R a m a n a n d I R S p e c t r o s c o p y ............................................................................................................................. 163  Li0.1Mn2O4 Virtual Absorbance states 18h at 300°C h(ν0 – νn) h(ν0 + νn) hν0 hν0 hν0 hν0 8h at 250°C 800 600 400 Wavenumber (cm-1) FIGURE 10.18 FTIR absorption spectra from Lix Mn2O4 insertion νm electrodes after different heat treatments. νn Ground Rayleigh Stokes Anti-Stokes state IR spectra are output in the form of plots of intensity scattering scattering scattering (percent transmittance, %T, or absorbance, A) versus either FIGURE 10.19 Schematic of transitions occurring in Raman energy (in J), frequency (in Hz), wavelength (in μm), or spectroscopy. wavenumber (in cm−1). The use of wavenumber is pre- ferred, but some of the standard reference sources of IR shift (Raman shift in cm−1) in which the shift is calculated spectra use wavelength. FTIR can be used to determine relative to the laser line frequency that is assigned as zero. the oxygen content in silicon. The Si–O stretching band The material is TiO2 films prepared by the sol-gel tech- occurs at 1105 cm−1 and from the peak intensity the oxygen nique that have been annealed at temperatures between concentration can be determined using ASTM standard F 400°C and 800°C. The features in the spectra correspond 121. The FTIR absorption spectra in Figure 10.18 is from only to anatase until the film reaches 800°C. At this tem- Li0.1Mn2O4 after heating for 8 hours at 250°C and 18 hours perature, a mixed anatase–rutile phase is seen, while the at 300°C. These FTIR readily distinguishes them from the pure rutile phase is obtained only at 900°C. binary oxide MnO2. There are increasing applications for Raman spectro- In Raman spectroscopy, the light is nearly monochro- scopy. One application is its use in the identification of matic and is usually in the visible range. The light source different pigments in the characterization of historical is a laser, e.g., a 50-mW 785-nm diode laser. Raman spec- artifacts. Table 10.5 lists blue pigments used on or before troscopy has become a routine tool for exploring the struc- about 1850 that have been identified by Raman ture and chemical properties of materials. It can provide spectroscopy. more information than IR spectroscopy. There are three Variations in Raman spectroscopy include the types of signal in a typical Raman experiment as illus- following: trated in Figure 10.19. The scattering process can be anti-Stokes, Rayleigh, or Stokes. We are then interested in measuring the inten- sity and the Raman shift. A In Rayleigh scattering, a molecule is excited by the incident photon to a virtual energy level. This energy level is caused by a distortion of the electron distribution of a I covalent bond. The molecule returns to the vibrational ground state by emitting the same energy, E 0 (E 0 = hν0). Rayleigh scattering is an elastic process. R R Vibrational excitations can be created, which causes a 800 °C decrease in the frequency (i.e., in energy) of the scattered 700 °C light, or they can be annihilated, which causes an increase. 600 °C The decrease in frequency is called Stokes scattering and A A A 500 °C the increase is anti-Stokes scattering. Stokes scattering is 400 °C the normal Raman effect and Raman spectroscopy gener- 200 400 600 800 ally uses Stokes radiation. Raman shift (cm-1) Figure 10.20 shows a typical Raman spectrum. It is a FIGURE 10.20 Example of Raman spectra from TiO2 films heated plot of scattered light intensity as a function of frequency to different temperatures. R, rutile; A, anatase. 164 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  TABLE 10.5 Blue Pigments Identified by Raman Spectroscopy Band wavenumbers, cm −1 and Excitation Name Composition relative intensities l and power Notes and date Azurite Basic copper(II) 145w; 180w; 250m; 284w; 335w; 403vs; 514.5 nm Mineral Carbonate 545w; 746w(sh); 767m; 839m; 940w; 2 mW 2CuCO3 ·Cu(OH) 2 1098m; 1432m; 1459w; 1580m; 1623vw Cerulean blue Cobalt(II) stannate 495m(sh); 532s; 674vs 514.5 nm 1821 CoO·nSnO2 4 mW Cobalt blue Cobalt(II)-doped alumina 203vs; 512vs 514.5 nm 1775 Glass, CoO·Al2O3 4 mW Egyptian blue Calcium copper(II) 114m; 137m; 200w; 230w; 358m; 377m; 514.5 nm 3000 BC ; also known Silicate, CaCuSi4O10 430vs; 475m(sh); 571w; 597vw; 762w; 4 mW as cuprorivaite 789w; 992w; 1012w; 1040w; 1086s Lazurite S3- and S2- in a sodium 258w; 548vs; 822w; 1096m 514.5 nm Mineral (lapis lazuli) aluminosilicate matrix 4 mW Synthetic c.1828 = Na8 [Al6Si6O24]Sn ultramarine Posnjakite Basic copper(II) sulfate 135vw; 208vw; 278vw; 327vw; 467w; 632.8 nm Mineral CuSO4 ·3Cu(OH) 2·H2O 612w; 983vs; 1092vw; 1139vw 3 mW Prussian blue Iron(III) hexacyanoferrate(II) 282vw; 538vw; 2102m; 2154vs 514.5 nm 1704; earliest Fe4 [Fe(CN) 6 ] 3 ·14-16H2O 2 mW synthetic modern Smalt Cobalt(II) silicate 462vs; 917m 514.5 nm ∼1500 CoO·nSiO2 2 mW Laser Raman Microprobe: This allows information to be Fortunately, there are many isotopes, such as 29Si, 27Al, collected from small samples via the use of a VLM, and 11B, that are important for ceramics that are suitable. which allows the region to be selected from which the Notice that we have to use 29Si (I = 1/2) not the more Raman spectrum will be obtained. Surface-Enhanced abundant 28Si. Raman Scattering (SERS): This is used to examine When a nucleus that has a nonzero PI is subjected to surfaces, oxidation, catalysis, and thin films. a magnetic field of strength H, the energy levels are split Residual Stress Measurement: Scattering depends on local into 2I + 1 different values. The energy separation of the stress, which can be probed in regions as small as different levels is 0.7 μm in diameter by Raman spectroscopy. ΔE = γHh/2π (10.2) γ is called the gyromagnetic ratio of the nucleus. If we 10.10 NMR SPECTROSCOPY then subject this nucleus to electromagnetic radiation and AND SPECTROMETRY adjust the frequency, ν, to be ν0, so that it has the same energy ΔE (now hν0), the quanta of radiation can be Just as each electron has a spin of ±1/2, each neutron and absorbed as transitions between the different nuclear spin proton in the nucleus also has a spin, I, of 1/2. These spins energy levels occur. We then detect the NMR absorption combine so that each atom has a total nuclear spin of 0, in the spectrum as a single peak corresponding to ν0, 1/2, or 1, and an angular momentum PI, given by which is broadened because the atoms interact differently depending on their neighbors. There are two particularly important interactions to PI = (h /2π) [ I ( I + 1)] (10.1) consider: The principle of nuclear magnetic resonance (NMR)  The dipole interaction is the interaction between adja- is that the probing beam is tuned until it couples with the cent nuclei and the one you are probing (such as an natural angular momentum of the nucleus, which then interaction between magnetic dipoles). resonates and emits energy that is measured. The specific  The electrons surrounding the nucleus will also move quantities depend on the atom that is resonating. The because of the applied magnetic field; this is the chem- precise value of the energy involved changes slightly if ical shift—electrons determine chemistry. the electron distribution around the resonating nucleus changes, as is the case when the atom is bonded to other The technique can be carried out using either a continuous atoms; we use NMR to examine this chemical shift. wave (CW) or a pulsed spectrometer. The RF energy is Nuclear magnetic resonance thus probes the bonding of used to excite the nuclear magnetization. The mea- individual atoms. Clearly for the technique to be applica- surement is the response of the spin system to this excita- ble, the nucleus must have a nonzero total nuclear spin. tion. In CW the nuclear magnetization is irradiated at a 10 .10 N M R S p e c t r o s c o p y a n d S p e c t r o m e t ry ......................................................................................................... 165 constant level; the frequency of the irradiation or the mag- A B netic field is then swept across the resonance. Nuclear magnetic resonance systems are available in SiO2-90 SiO2-85 most research universities with a basic system costing Al2O3-10 Al2O3-15 from $200,000 up to more than $1,000,000, depending mostly on the desired field strength (1–14 T). The following examples are selected to illustrate why NMR is so valuable for the ceramist. The x-axis is in units 100 0 PPM 100 0 PPM of ppm, which is the chemical shift as a fraction of the applied field or frequency. In Figure 10.21, three NMR powder patterns are shown for silicon in three different chemical environments, but where the Si is tetrahedrally C D coordinated in each case. The differences between the SiO2-80 SiO2-70 spectra are due to the number of nonbridging oxygen Al2O3-20 Al2O3-30 ions that are attached to the Si nucleus being probed: a chemical-shift effect. The value of NMR for studies of silicate glass is obvious. Figure 10.22 shows a series of NMR spectra from Si– Al glasses. The field used was 11.7 T. The NMR spectra 100 0 PPM 100 0 PPM show that not only is the Al present in 4-fold, 5-fold, and 6-fold coordination, but there is also undissolved Al2O3 present in the glass (denoted “Cor” in the spectra). The Al(5) chemical shift has been determined using a standard of E F octahedral 27Al in AlCl3 solution. SiO2-60 SiO2-50 Cor Al2O3-40 Al2O3-50 Al(6) Al(4) 100 0 PPM 100 0 PPM FIGURE 10.22 NMR signals from an Al–Si glass. O O-1 O Si O O-1 Si O-1 10.11 MÖSSBAUER SPECTROSCOPY AND SPECTROMETRY O O-1 Q4 Q0 Mössbauer spectroscopy is specialized, but it can be inval- uable when it is available. The technique relies on the recoil-free emission and resonant absorption of γ-rays by nuclei that are bound in the solid state. (If it is not in a solid, the free nucleus recoils and no resonance is detected.) O-1 O-1 To see this resonance, we have to match the energy of the O Si O O Si O-1 γ-ray emitter to the energy of the absorber (the sample), which means that only a small number of elements can O O-1 be studied. Two that can be studied are tin and iron. The Q3 Q1 technique gives information on the bonding and coordina- tion, and on the valence (oxidation) state. Since the tech- nique relies on Z, it works for particular isotopes, 57Fe for iron with 57Co as the radioactive source of γ-rays. (Natural Fe contains ∼2.19 wt% 57Fe.) O-1 Figure 10.23 shows a schematic of a Mössbauer spec- O Si O-1 trometer. The radioactive 57Co source is embedded in a nonmagnetic matrix, which is chosen so as not to affect O the sample or to absorb the γ-rays too strongly. The system Q2 can be calibrated using Fe metal; the six peaks seen in Figure 10.24 correspond to the six transitions expected for 57 FIGURE 10.21 NMR signals from Si. Fe. The 57Co source has an emission peak at 14.4 keV; 166 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  Laser interferometer Source Sample Velocity Proportional Single channel transducer counter analyzer Velocity +v calibration/ Correction -v Real-time Velocity Waveform Waveform Computer/ multichannel amplitude generator Data storage analyzer FIGURE 10.23 Schematic of the set-up for Mössbauer spectroscopy. the source is moved through a range of velocities using a oxidation state and the coordination of the Fe ion. Nuclei velocity transducer. in different chemical surroundings from the source do not Mössbauer spectra from a series of glasses containing absorb at the same frequency; this is known as the chemi- Fe in different oxidation states are shown in Figure 10.25. cal (or isomer) shift and is the key feature of Mössbauer The differences in the curves are clear, but the analysis spectroscopy. needed to determine the percentage of Fe in the 2+ state Other isotopes that have been studied are 119Sn (source: requires extensive calibration of the system. (Notice that metastable 119Sn), 121Sb (source: metastable 121Sb), and 151 peak locations are shown in units of velocity.) The value Eu (source: 151Sm). Table 10.6 lists chemical shifts for of the technique is its sensitivity to determining both the tin. It is then quite straightforward to determine the valence state of an unknown tin-compound from its Mössbauer mI spectrum. This type of analysis has been used in studying 3 tin glazes and tin-containing ceramic pigments. It requires 2 quite small amounts of material, typically 50 mg of powder. I 1 Bulk materials can also be examined. 3 2 2 1 2 3 2 1 1 2 3 2 1 2 1 4 5 6 2 (A) FIGURE 10.25 Mössbauer spectra from glasses containing different concentrations of Fe2+ . 119 TABLE 10.6 Chemical Shift of Some Sn Compounds Valence state Electron configuration Chemical shift (mm/s) (B) Sn4+ 5s05p0 0 Sn (4-covalent) 5(sp3) 2.1 FIGURE 10.24 Transitions in Fe and the resulting Mössbauer Sn2+ 5s25p0 3.7 spectrum. 10 .11 M ö s s b au e r S p e c t r o s c o p y a n d S p e c t r o m e t ry .............................................................................................. 167 10.12 DIFFRACTION IN THE EM The techniques are  SAD in the TEM  CBED in the TEM  EBSD in the SEM Selected-area diffraction involves selecting an area on the sample (actually an image of the area) with an aperture and then looking at the diffracting pattern from that area. The diameter of the area can be as small as 100 nm with a modern machine. In CBED, the diffracting area is selected by focusing the electron beam onto a small area of the sample. The diameter of the area can actually be FIGURE 10.27 Schematic of the formation of an EBSD pattern. smaller than the unit cell. Figure 10.26 compares SAD and CBED patterns. From the positions of the spots (in SAD) and the discs (in CBED) we can obtain information about the structure and orientation of our sample. CBED pat- system is shown in Figure 10.27 together with an example terns often contain an additional fine structure, which of an EBSD pattern. allows determination of symmetry such as the point group. The value of CBED lies in its ability to provide informa- tion on lattice parameters, sample thickness, and local 10.13 ION SCATTERING (RBS) crystallography on a scale of 10 nm or better. We can use the technique to characterize polarity change across Rutherford backscattering spectrometry again uses ions (a antiphase boundaries (APBs) in GaN and AlN, to deter- high-energy He beam) to produce the signal, but is more mine the site occupancy in nickel-titanate spinel, and to akin to electron energy loss spectroscopy (EELS). We determine the thickness of a specimen. The latter param- analyze the energy of the backscattered ions and thus eter is used in analyzing the height of steps on surfaces determine what atoms they interacted with and where and in quantifying X-ray energy dispersive spectrometry those atoms were located in the sample relative to the (XEDS) data. surface. Rutherford backscattering spectrometry uses ions Diffraction in the SEM can take several forms, but (typically 2 MeV helium ions, 4He +) as the scattered par- EBSD is now becoming a routine addition to the SEM. ticle. We can picture the interaction mechanism as being The beam penetrates into the sample and is backscattered; a collision resembling that between two billiard balls; the we can use these electrons to form a BSE image or we can incoming ion transfers energy (and momentum) to the ion record the actual diffraction pattern. A schematic of the in the sample, it is detected as it recoils, and its energy is (A) (B) FIGURE 10.26 Diffraction patterns obtained using (a) SAD (TEM) and (b) CBED (TEM). 168 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  Sample Incident MeV ion beam Backscattered ions FIGURE 10.28 The backscattering process for RBS; the sample can be tilted to the beam to increase depth resolution. determined (Figure 10.28). The data are provided in the FIGURE 10.29 RBS data sets obtained using a 2.8-MeV beam form of a plot of backscattering yield versus energy and of He2+ ions with the samples tilted 45°. Each sample has been typical spectra are shown in Figure 10.29. Computer anal- annealed at 700°C for 2 hours followed by 1020°C for 5 hours; ysis of the spectrum gives us the types of atoms in a the Ni peak shows that the extent of the reaction varies with the sample, their concentration, and their depth. The depth surface orientation. resolution is about 20 nm and RBS has been widely used in studies of ceramic thin films deposited onto ceramic 10.14 X-RAY DIFFRACTION substrates such as BaTiO3 on MgO. AND DATABASES Rutherford backscattering spectrometry has a poor sensitivity to light elements such as oxygen and nitrogen, X-ray diffraction is used in several forms depending on which are both important in many ceramics. However, an the equipment, the sample, and what you want to know. enhanced oxygen signal can be obtained at an incident The great advantage of the technique is that a vacuum is energy of 3.045 MeV. It is also used to determine the not required and that the X-rays can travel through a con- composition of bulk ceramics and impurity profiles in tainer before and after interacting with the specimen. For semiconductors, e.g., As distribution in Si. example, the specimen can be heated inside a quartz tube When the ion beam interacts with the sample, it pro- to 1600°C and examined at that temperature. Using a duces particle-induced X-ray emission (PIXE), which is synchrotron, the beam size and, hence, the spatial resolu- directly analogous to the production of X-rays in the SEM. tion can be reduced to ∼1 μm. A monochromatic beam can Particle-induced X-ray emission has some special advan- be produced such that changes in energy due to absorption tages over EDS in the SEM in that the background emis- can be accurately measured. Table 10.7 lists types of anal- sion is lower, the depth penetration is large, and the ysis that can be undertaken using X-rays and the specific sensitivity is high. technique. TABLE 10.7 X-Ray Diffraction Analysis Type of analysis Method Sample Crystal geometry Moving crystal-spot pattern Single crystal Computer positioned diffractometer Single crystal Solution of d-spacing equations Powder Arrangement of atoms Analysis of diffracted intensities Single crystal Refinement of whole pattern Powder Symmetry Moving crystal-spot pattern Single crystal Stationary crystal-spot pattern Single crystal Identification of compound Identification of cell parameters Single crystal Matching of d-I set Powder Crystal orientation Single-crystal back reflection Large single crystal Texture analysis Powder compact Size of crystal Line broadening Powder Magnitude of strain Line shifts Powder compact Amount of phase Quantitative analysis Powder Change of state Special atmosphere chambers Single crystal or powder Crystal perfection Direct imaging Single crystal Line shape analysis Powder 10 .14 X- r ay D i f f r ac t i o n a n d Data b a s e s ................................................................................................................ 169  One of the most useful the diffractometer PDF CARD NUMBERS sources of information for corresponds to an 21–1272 Anatase crystal structure data is the integral width of 29–1360 Brookite Powder Diffraction File (PDF). 0.32 nm. The PDF is a collection of Figure 10.31 shows single-phase X-ray powder diffraction patterns in the form the main components of an X-ray diffractometer. The impor- of tables of interplanar spacings (d) and corresponding tant features include the following: relative peak intensities. There are more than 80,000 pat- terns in the PDF. In the early days the patterns were  X-ray source. Often Cu Kα λ = 0.154184 nm because printed as 3″ × 5″ index cards and even though everything is now on computer the files are still referred to as of its high intensity.  Sample. Usually a powder, but it can be pressed or “cards.” Powder XRD is one of the most widely used tech- sintered. Only a few milligrams is needed.  Detector. There are two main types: proportional niques to characterize ceramics. The material is in the form of a powder so that the grains will be present in all detectors use photoelectrons generated in Xe; semi- possible orientations so that all d spacings, or θ values, conductor detectors use electron-hole pairs created in will appear in one pattern. The classical powder pattern p-i-n junctions formed in silicon. was recorded on photographic film. Now the data are in the form of a plot (known as a diffractogram) of counts In the θ/2θ X-ray diffractometer, the sample and detec- or intensity versus scattering angle (2θ) as shown in Figure tor rotate relative to the X-ray source; when one moves 10.30. A computer that contains the entire PDF is usually through θ, the other moves through 2θ. Alternatively, the used for peak identification. In many examples you will sample can be held fixed and the detector and source see in the literature phase identification is the extent to rotated in opposite directions. The conventional XRD which powder XRD is used. This ability alone makes it a geometry is often referred to as the Bragg–Brentano powerful and indispensable tool for the ceramist. In a geometry. Several different geometries and modifications multiphase material the relative amounts of each phase are used for studying ceramics. can be determined from the peak areas. Powder XRD can be used to estimate the sizes of particles. The Scherrer formula states that Thin-film diffractometer. A glancing angle geometry is used with the sample surface at an angle of 5–10° to Δθ · Δx = 2π (10.3) the X-ray beam. The basic idea is that the penetration depth of the X-rays is reduced so they are analyzing where Δθ is the peak width (scattering angle half-width) the surface. Longer wavelength X-rays can be used, and Δx is the average particle diameter. The resolution of which also reduces penetration (switch to a Cr Kα Detector X-ray source Counts 311 131 400 511 331 512 313 423 1050°C 950°C 850°C 20 30 40 50 60 70 Sample 2θ (deg) support FIGURE 10.30 XRD patterns from a mixture of Ca oxide and alumina recorded while heating the sample at different FIGURE 10.31 XRD apparatus showing the location of the source, temperatures. sample, and detector (Siemens D5005). 170 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  source λ = 0.229100 nm). Polycrystalline thin films TABLE 10.8 Properties of X-rays and Neutrons down to a few tens of nanometers thick can be Property X-ray Neutron examined. Microdiffractometer. Collimators as small as 10 μm are Wavelength 0.05–0.25 nm 0.01–2 nm used to produce a small X-ray spot size. The geometry Energy 12.4 keV 80 MeV Velocity 3 × 108 m/s 4 × 103 m/s of the detection system is also different from a con- Production X-ray tube Nuclear reactor ventional diffractometer in that it uses an annular Synchrotron Electron linear accelerator detector that allows sampling of the entire cone of dif- pulsed source fracted radiation. Proton spallation pulsed Hot-stage XRD. The sample is placed inside a quartz source 10 Detection Photographic film BF3 or 3He proportional furnace tube that can be heated to temperatures up to counter 1600°C often in a range of different atmospheres. The Proportional counter 6 Li scintillation counter main uses are to study phase changes and structural Scintillation counter transformations as a function of temperature. Pole figure. This uses a Eulerian goniometer cradle attached to the diffractometer to determine preferred crystal orientations. Single-crystal XRD. A single-crystal diffractometer allows the orientation of the crystal to be controlled in such a way that every set of planes can be moved into a diffraction condition. The X-rays are usually detected by scintillation. The technique is not as The obvious question is: Why use them when other routine as powder XRD and determination of a crystal particles do interact strongly? Neutrons offer distinct structure can take many days or even turn into a advantages over X-rays and other probes. They have a thesis. magnetic moment so they can detect magnetic ordering. Laue technique. The diffracted beams produce a pattern Because they do not interact strongly they can be used consisting of an array of spots. It is used to orient to obtain bulk information. A major application is single crystals (with an accuracy in a range of 0.3° to residual stress measurement in materials as a function of 1°) prior to cutting and polishing. depth. Neutrons have been used to study glasses and show a first sharp diffraction peak at low angles. This implies that 10.15 NEUTRON SCATTERING there is some ordering in the glass. Intentional patterns of voids in glasses give rise to such peaks. Table 10.9 pro- The initial obvious statement is that, overall, neutrons vides a comparison of the parameters for XRD and neutron interact with matter even less strongly than do X-rays. diffraction. Table 10.8 summarizes the differences between the two Neutrons are produced in several ways, but each way probes. For both neutrons and X-rays, it is not as easy to requires a reactor. Thus neutron diffraction facilities are direct the beam as it is with electrons or ions. In both generally national facilities. In the United States there are cases, the experimental method involves measuring the seven centers for neutron scattering and there are about intensity of the scattered beam as a function of scattering 30 in the world. A schematic of a neutron diffractometer angle. is shown in Figure 10.32. TABLE 10.9 Scattering of X-rays and Neutrons Dependence X-ray Neutron Nonmagnetic atom Electrons scatter Nucleus scatters θ dependence Depends on θ through f(θ) Depends on isotropic scattering length b̄ Variation with Z F(0) = Z b̄ varies with Z Phase change on scattering π Not always π Isotope dependence None b̄ depends on isotope Anomalous dispersion Near an absorption edge Near an absorption resonance Magnetic atom Nothing extra Additional scattering (depends on θ) Absorption coefficient Absorption large Absorption usually small 10 .1 5 N e u t r o n S c at t e r i n g ......................................................................................................................................... 171  1st Beam shutter Beam tube Silicon Diaphragms H8 filter Monochromator Shielding 2nd Beam shutter 4-Slits diaphragm 64 Cell multidetector 2θ2 arm Casemate doors Monitor 2θ1 arm Diffusion Sample vacuum pump chamber λ/2 Filter FIGURE 10.32 Schematic of a neutron scattering workstation. The width of the view is 10 s of meters. 10.16 MASS SPECTROMETRY 10.17 SPECTROMETRY IN THE EM Mass spectrometry is used to provide qualitative and The chemistry of interfaces can be probed using both quantitative chemical analysis. For ceramics we are mainly XEDS and parallel recording of electron energy-loss interested in analyzing solids, so a method for ionizing the spectra (PEELS). material is necessary. In spark source mass spectrometry In the earliest studies of solid-state reactions between (SSMS) we use a high-voltage spark in a vacuum. The ceramic oxides, the width of the reaction product pro- positive ions that are produced are analyzed by the spec- duced by bulk diffusion couples was determined by VLM. trometer based on their mass. For insulating ceramics the Using an SEM with a field-emission gun a much more material must be mixed with a conducting powder such as precise EDS profile analysis can be performed providing graphite or silver. Other methods can be used to ionize the chemical analysis at a spatial resolution of ∼2 nm. Figure sample: 10.33 shows a typical XEDS spectrum: a plot of counts versus X-ray energy. The X-rays are produced as a result 1. Laser ionization MS uses an Nd : YAG laser and is of electron transitions within the atoms in the sample. The ideal for insulators, but is qualitative more than quantita- transitions and, hence, the peaks are characteristic of spe- tive because of the absence of standards. cific atoms. A doped silicon crystal is used to detect the 2. Glow discharge ion source uses a gas discharge X-rays, where they cause the formation of electron-hole between two electrodes, so the sample must be conductive pairs. New methods for detecting the X-rays are being and formed into the cathode. developed that use the change in temperature caused by 3. In secondary ion mass spectroscopy (SIMS) an inci- the X-ray and are known as colorimeters. dent ion beam with energy in the range of 4–15 keV is used The electron microprobe or WDS can provide accurate to create secondary ions from the sample. This provides chemical analysis or a chemical profile across the inter- high-resolution depth profiles with a detection limit down face. The wavelength of the X-rays emitted when the to 1 ppb. electron beam interacts with the sample is measured. Wavelength dispersive spectroscopy is more accurate than Secondary ion mass spectroscopy is like SEM, but it uses XEDS, but is a serial acquisition, so it is slower. Table (usually Ga +) ions instead of electrons. Since the ions have 10.10 compares WDS and XEDS. more energy, they eject near-surface atoms out of the Electron energy-loss spectroscopy (EELS) counts the sample; these are collected and the chemistry of the number of electrons that have lost particular quantities of near-surface area is thus determined. By scanning the ion energy when the incident electron beam passed through beam we can generate a chemical image of the surface the TEM specimen. The energy loss can occur by interac- and by repeating this process (each time ejecting the tions with different components of the structure (phonons surface atoms) we can generate a 3D profile of the and plasmons) or by the beam exciting core electrons to a sample. different energy state. The EELS spectrum thus contains 172 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  FIGURE 10.33 Example of an XEDS from a sample containing CeO2 and YSZ in the range up to 20 keV. information on the bonding and chemistry of the speci- men. Since the beam in the TEM can now be as narrow as 0.1 nm, EELS can give highly localized information; it is particularly important in ceramics where low-Z elements tend to be particularly important. Figure 10.34 shows part of an EELS spectrum from two commercial ceria abrasives. The fine structure of the EELS can be compared to the fine structure in X-ray scattering. It can be used in purpose- built chambers or, more recently, in the TEM. In the TEM you have the great advantage of knowing where you are getting the spectrum from—it is site specific. The diffi- culty with TEM, as usual, is that there are usually two surfaces to consider (you can try REELS—see REM). This technique will be used more in the future with the FIGURE 10.34 Example of EELS from two commercial ceria wider availability of TEM guns with a smaller spread in powders. TABLE 10.10 Comparison of WDS and XEDS Factor WDS XEDS Reason for difference Time for complete spectrum (minutes) 25–100 0.5–5 Collection efficiency XEDS measures whole spectrum simultaneously Count rate on one peak (cps/nA) 1,000 10,000 Collection efficiency Peak/background ratio 1,000 50 XEDS collects spurious X-rays and has high inherent noise Maximum count rate (cps) 100,000 30,000 XEDS counts all channels simultaneously, and saturates Resolution, 0.1–10 keV (eV) 5–10 150–200 Currently possible 80–100 Theoretical limit; WDS inferior to XEDS above 25 keV (suitable crystals not available) Detector limits (weight ppm) 50–1,000 2,000–5,000 WDS used at higher beam current, fewer overlapping peaks XEDS better if current is restricted, e.g., to avoid beam damage Accuracy of analysis (%) ±1–2 ±6 Experimentally determined Light element analysis (min. atomic 4 4 Both have ability for light element detection providing number) windowless or polymer window used Rough surface work Bad Good XEDS insensitive to source position 10 .17 S p e c t r o m e t ry i n t h e E M .................................................................................................................................. 173 energy. A major applica- AUGER NOTATION Figure 10.35 shows tion for EELS, which we KVV refers to the series of electron transitions respon- examples of carbon KVV have only recently begun sible for the Auger electron. V refers to electrons coming Auger electron spectra to use, is the direct meas- from the valence band of a solid. generated from the surface urement of bonding. of two different carbides, diamond and graphite. The spectra are in the form of derivative electron yield versus electron energy and show the chemical shift effect and 10.18 ELECTRON SPECTROSCOPY how this could be used for “fingerprinting” an unknown sample. Auger electron spectroscopy is the spectroscopist’s In the group of techniques known as photoelectron variation of low-energy electron diffraction (LEED). Its spectroscopy (PES) electrons are emitted from their main use is to provide information on the chemistry, rather filled electronic states in the solid by the absorption of than bonding, and more specifically to determine if the single photons. Traditionally the energy of the photons sample is clean enough for LEED. The beam can be corresponds to the UV or X-ray wavelengths and the scanned across the sample to produce an image, hence techniques are known as ultraviolet photoelectron spec- scanning Auger microscopy (SAM). troscopy (UPS) or X-ray photoelectron spectroscopy In XPS electrons with binding energy (Eb) are ejected (XPS). X-ray photoelectron spectroscopy used to be called from core levels by an incident X-ray photon with energy electron spectroscopy for chemical analysis or ESCA E 0. The ejected photoelectron has energy (E 0 − Eb). Output and is still the most used surface-sensitive technique. electron energies are typically >10 eV. X-ray photon spec- The difficulty for ceramics is the usual one—as we troscopy, like AES, has excellent depth resolution and is remove electrons from the sample, the sample becomes sensitive to the near surface region of a material. The charged and attracts the same electrons, which can distort spectrum has the form of intensity versus binding the results. In principle you could use a flood gun to resup- energy. ply the electrons, but the challenge is getting the balance By sputtering the surface in between acquisition of right. The techniques do explore the surface region, not either an AES or XPS spectrum it is possible to obtain just the surface, so the surface effect must be separated depth profiles. Sputtering must be conducted in the same from the larger bulk effect. Variations of the technique system as the spectrometer to avoid contamination of the include angle-resolved photoemission spectroscopy (ARPES). These techniques are mainly used for quantitative chemical analysis of surfaces by detecting electrons emitted from the surface. They can be differentiated by how the electrons are produced. In Auger electron Mo2C spectroscopy (AES) the incident species are electrons. dN(E) In XPS and UPS the incident species are photons. In dE XPS we illuminate the sample with X-rays and measure the energy of electrons that are then emitted. If the elec- SiC trons come from regions close to the surface, we can obtain data on the chemistry and bonding close to the surface. The X-rays can be generated in a synchrotron and this will have both high spatial resolution and high intensity. Auger electrons are created when an incident electron Graphite beam ionizes an atom by removing an inner-shell electron. An electron from a higher energy level will fill the hole and the resulting kinetic energy will be transferred to a loosely bound electron, which is detected. These Auger electrons have relatively low kinetic energy and, conse- quently, a short mean free path. They come from the top Diamond 0.5–3 nm of the surface. Their energy is characteristic of the atomic energy levels of the atom from which they came. Therefore, they are sensitive surface probes of chemical composition. Auger electron spectroscopy has 200 250 300 been used extensively to study oxide surfaces. The problem E (eV) is that the surface must be very clean and examined in FIGURE 10.35 Derivative C KVV Auger electron spectra from two UHV. carbides, graphite, and diamond. 174 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry surface. Ultraviolet photoelectron spectroscopy uses UV TABLE 10.11 The Sensitivity for Detecting Elements by light to produce electrons. Using these lower photon ener- NAA gies (typically ∼21 eV) only the valence levels are acces- (Sensitivity ng) Elements sible. A major application of UPS is in determining the band structure of solid surfaces. 0.1 Dy, Eu 0.1–1 In, Lu, Mn 1–10 Au, Ho, Ir, Re, Sm, W 10–100 Ag, Ar, As, Br, Cl, Co, Cs, Cu, Er, Ga, Hf, I, La, 10.19 NEUTRON ACTIVATION Sb, Sc, Se, Ta, Tb, Th, Tm, U, V, Yb ANALYSIS (NAA) 100–1,000 Al, Ba, Cd, Ce, Cr, Hg, Kr, Gd, Ge, Mo, Na, Nd, Ni, Os, Pd, Rb, Rh, Ru, Sr, Te, Zn, Zr 1,000–10,000 Bi, Ca, K, Mg, P, Pt, Si, Sn, Ti, Tl, Xe, Y The basis of neutron activation analysis is that if a material 10,000–100,000 F, Fe, Nb, Ne containing certain rare earth elements is exposed to a 1000,000 Pb, S beam of neutrons it can become highly radioactive. If the induced radioactivity is then measured, it is possible to identify the elements that are present in the samples and 5-second irradiation with a flux of 8 × 1013 neutrons quantify the amount present. The neutron interacts with cm−2 s−1. The γ-rays are then counted for 720 seconds, the target nucleus and forms an excited nucleus, i.e., the which gives a γ-spectrum (PGNAA) for short-lived ele- neutron loses energy. The excited nucleus then quickly ments (Al, Ba, Ca, Dy, K, Mn, Na, Ti, V). The samples relaxes back to a more stable state by emitting a charac- in quartz are irradiated for 24 hours with a flux of 5 × 1013 teristic γ-ray (this is an n,γ nuclear reaction). The new neutrons cm−2 s−1. After leaving the sample for 7 days, the nucleus may be radioactive, in which case it will then γ-rays are counted for 2000 seconds. This middle count begin to decay by emitting additional characteristic γ-rays, gives medium half-life elements As, La, Lu, Ne, Sm, U, but the rate of emission will be slower due to the longer and Y. After a further 4 weeks, the final count (9000 half-life of the decaying nucleus. Figure 10.36 gives a seconds) give a measure of the long half-life elements Ce, schematic of the NAA process. Co, Cr, Cs, Eu, Fe, Hf, Ni, Rub, Sb, Sc, Sr, Ta, Tb, Th, The quick emission of the γ-ray produces the PGNAA Zn, and Zr. The results are then compared to those from (prompt γ-ray NAA) technique and the slower emission the known material. The accuracy can be better than parts produces the more usual DGNAA (delayed GNAA but per billion. often just called NAA) technique. Of the three principal Applications have included identifying the origin of different types of neutron sources (reactors, accelerators, archeological ceramics: obsidian can be fingerprinted and and radioisotope neutron emitters), nuclear reactors gen- the trade patterns of the Olmec civilization can be fol- erating neutrons by U fission give particularly high fluxes lowed by identifying the area from which the clay they of neutrons. Thermal neutrons have energies <0.5 eV; if used in their pots originated and the source of contamina- the neutrons are in thermal equilibrium with the modera- tion in semiconductors can be traced at the 1 ppb level. tor of the reactor, they have a mean energy of 25 meV, which means they have a velocity of 2.2 km s−1. A 1-MW reactor will have a peak flux of thermal neutrons of 10.20 THERMAL ANALYSIS ∼1013 cm−2 s−1. Table 10.11 shows how sensitive NAA is for detecting elements in a sample. The term “thermal analysis” actually covers many differ- As an example of an analysis, crush a sample to a fine ent techniques that measure a change in a material as a powder and put 150 mg in a plastic vial and 200 mg in a function of temperature. Thermal analysis is particularly high-purity quartz capsule. Reference samples of known useful in characterizing decomposition and crystallization composition are also prepared. The plastic vial is given a during ceramic powder processing. It is then possible to Prompt Beta particle gamma ray Target nucleus Incident neutron Radioactive nucleus Product nucleus Compound Delayed nucleus gamma ray FIGURE 10.36 Schematic of the NAA process. 10 . 2 0 Th e r m a l A n a ly s i s .............................................................................................................................................. 175  TABLE 10.12 Common Thermoanalytical Techniques Common Method abbreviation Property measured Thermogravimetry TG (TGA) Mass Differential thermal DTA ΔT between sample analysis and reference Differential scanning DSC Heat absorbed or calorimetry evolved by sample Evolved gas analysis EGA Nature and amount of evolved gas species Thermodilatometry TD Dimension Thermomechanical TMA Deformation/ analysis nonoscillatory load Dynamic DMA Deformation/oscillatory FIGURE 10.37 DTA and TGA measurements showing the reaction thermomechanometry load as CA 2 crystallizes. Thermomagnetometry TM Relative magnetic susceptibility increased the sample loses weight and by about 600°C weight loss is complete. The DTA plot shows that the CA 2 determine optimum calcination temperatures. A list of the crystallization is exothermic. main thermal analysis techniques is given in Table 10.12. Thermal analysis techniques are widely used to study The two most common are ceramic processing. In addition to determining decompo- sition and crystallization processes it is also possible to  Thermogravimetric analysis (TGA), which measures monitor the burnout of organic binders, which are com- weight loss during heating monly added to powders prior to shaping, and shrinkage  Differential thermal analysis (DTA), which mea- during drying. One of the earliest uses for DTA was in sures relative changes in sample temperature during studying clay minerals. In montmorillonite the position heating of certain cations can have an influence on the dehydra- DTA and TGA can be performed separately or simultane- tion behavior. Analysis of DTA curves from samples of ously. Figure 10.37 shows examples of DTA and TGA montmorillonite containing Li, Na, or K shows that the analysis on an initially amorphous CA2 powder as it crys- presence of Li stabilizes the water of hydration and higher tallizes. The TGA plot shows that as temperature is temperatures are required for dehydration. CHAPTER SUMMARY There are many different techniques for studying ceramics. The choice of which one to use depends on the type of information that we want to obtain and how valuable our material is. Transmission electron microscopy is destructive, but so are many other methods if we have to produce a fine powder. Whereas some of the techniques we described, such as VLM and SEM, are universal, there are many techniques that are available in only a few sites. Those requiring nuclear reactors or very high flux photon beams are usually found at National User Facilities. A full understanding of a material or a process may require the use of several complemen- tary techniques. For example, electron diffraction in the TEM combined with FTIR and Raman spectroscopies can unequivocally determine what polymorph of SiO2 is present in a sample. For example, AES can give us the composition of the surface of a sample, AFM can give us the surface morphology, and RHEED can give us the surface crystallography. The technological importance of nanomaterials means that we need high-resolution tech- niques. It is the need to understand the structure of nanomaterials and processes that happen on atomic and molecular levels that leads to the development of new instrumentation for char- acterizing materials. PEOPLE IN HISTORY Binnig, Gerd (1947–) and Heinrich Rohrer (1933–) of the IBM Research Laboratory in Switzerland won the Nobel Prize in Physics in 1986 for their invention of the STM. Mössbauer, Rudolf (1929–) received the Nobel Prize in Physics in 1961 for the discovery of the Mössbauer effect. Raman, Sir Chandrasekhara Venkata (1888–1970), the Indian scientist, discovered the phenomenon in 1928 while studying CCl4; he was awarded the Nobel Prize in Physics in 1930. 176 ......................................................................................... C h a r ac t e r i z i n g S t ru c t u r e , D e f e c t s , a n d C h e m i s t ry  Rutherford, Ernest (1871–1937) demonstrated ion scattering and its utility for chemical analysis. He won the 1908 Nobel Prize in Chemistry. Stokes, George Gabriel, born 13 August 1819, died 1 February 1903, was Professor of Mathematics in Cam- bridge when Rayleigh was an undergraduate. Strutt, John William (Lord Rayleigh) was born 12 November 1842 and died 30 June 1919. He won the Nobel Prize in Physics in 1904 for discovering Ar and succeeded James Clerk Maxwell as the Cavendish Profes- sor in Cambridge. GENERAL REFERENCES Cahn, R.W. (2005) Concise Encyclopedia of Materials Characterization, 2nd edition, Elsevier, Amsterdam, The Netherlands. A good place to check out any technique. Chu, W.K., Mayer, J.W. and Nicolet, M-A. (1978) Backscattering Spectrometry, Academic Press, New York. Detailed information about RBS. Hartshorne, N.H. and Stuart, A. (1970) Crystals and the Polarizing Microscope, 4th edition, Arnold, London. Hollas, J.M. (2004) Modern Spectroscopy, 4th edition, Wiley, Chichester, England. Covers a wide range of topics at the level you will need if you use the techniques. Loehman, R.E. (Ed.) (1993) Characterization of Ceramics, Butterworth-Heinemann, Boston. Provides “case studies” in which various techniques are used. Wachtman, J.B. (1993) Characterization of Materials, Butterworth-Heinemann, Boston. Overview and com- parison of the different characterization techniques. SPECIFIC REFERENCES Binnig, G., Rohrer, H., Gerber, Ch., and Weibel, E. (1982) “Tunneling through a controllable vacuum gap,” Appl. Phys. Lett. 40, 178. Paper describing the STM. Blanpain, B., Revesz, P., Doolittle, L.R., Purser, K.H., and Mayer, J.W. (1988) “The use of the 3.05 MeV oxygen resonance for He-4 backscattering near-surface analysis of oxygen-containing high Z com- pounds,” Nucl. Instrum. Methods B34, 459. Describes the RBS method used to obtain the enhanced oxygen signal. Philp, E., Sloan, J., Kirkland, A.I., Meyer, R.R., Friedrichs, S., Hutchison, J.L., and Green, M.L.H. (2003) “An encapsulated helical one-dimensional cobalt iodide nanostructure,” Nature Materials 2, 788. Raman, C.V. and Krishnan, K.S. (1928) “A new type of secondary radiation,” Nature 121, 501. The original description of the “Raman effect.” “Standard Test Method for Interstitial Atomic Oxygen Content of Silicon by Infrared Absorption,” F 121 Annual Book of ASTM Standards, Vol. 10.05, ASTM, Philadelphia, pp. 240–242. EXERCISES 10.1 Construct a chart summarizing the principal scattering techniques used to characterize the structure, chem- istry, and bonding in ceramics emphasizing which of the three features is most directly addressed by each technique. 10.2 In Figure 10.1 the grains boundaries are described as low-angle grain boundaries. Could this information be obtained directly from VLM? If not, what other methods might have been used to make this determination? 10.3 In Figure 10.6, why does the image have a 3D appearance? 10.4 In Figure 10.7 the image distinguishes the regions with different chemistry directly and with high spatial resolution. Explain the physical process underlying this observation? 10.5 During the processing of ceramics containing crystalline quartz a phase transformation occurs on cooling/ heating between the α form and the β form. The phase transformation produces an appreciable change in volume that can lead to cracking. How would you determine from a fragment of a ceramic plate whether you had the α or β phase present in the sample? 10.6 How would you determine whether water vapor has chemisorbed onto the surface of particles of silica gel? 10.7 If we are examining steps of atomic dimensions in figure 10.14, redraw the schematic to scale and thus explain the factors that determine vertical and lateral resolution in AFM. 10.8 Compare the value of NMR and Mössbauer analysis for ceramic materials. 10.9 Referring to Figure 10.33, explain why we see multiple peaks for Y and Zn occur at different energies, and why we see Cu. 10.10 Examine the DTA/TGA plots in Figure 10.37. What can you say about the curves as the temperature is increased from 25°C to 1200°C? C h a p t e r S u m m a ry .......................................................................................................................................................... 177 Part IV Defects  11 Point Defects, Charge, and Diffusion CHAPTER PREVIEW Point defects are particularly important in ceramics because of the role they can play in deter- mining the properties of a material. The entire semiconductor industry is possible because of minute concentrations of point defects that are added to Si: the dopants determine if the Si is n-type, p-type, or semi-insulating: they determine the electrical properties. Solid-oxide fuel cells work because of the large concentrations of oxygen vacancies present: the vacancies provide fast ion conduction pathways. CZ is cubic because of the presence of point defects that stabilize the cubic structure. We will address three principal questions in this chapter and leave the properties associated with point defects to later chapters where we will discuss conduction, light, and color, for example.  What point defects are possible?  How many point defects are present?  How easily can they move? To determine what defects are possible in a crystal we need to know its structure. Point defects also exist in glass, but there is the extra problem of how to define what is being “defec- tive.” (What is the perfect structure of the glass?) To estimate the concentration of point defects, we should know (1) what types of defects are present and (2) how they form, which, in turn, determines (3) how many of each kind there will be. Answering the third question will give us many of the properties of the materials containing these defects. In some cases we want them to move quickly and in other cases we actually would rather they were immobile. To really understand this subject thoroughly you will need a good knowledge of thermodynamics and kinetics. These topics are so large that there are many texts devoted entirely to them. 11.1 ARE DEFECTS IN CERAMICS The really special feature of ceramics is that they can DIFFERENT? contain charged defects; metals cannot. There are some definite differences when we compare defects in ceramics Until now we have considered the ideal structures of crys- to similar ones in face-centered cubic (fcc) metal crystals tals only when each atom or ion is on a regular site in the such as Cu. crystal. Real crystals contain a variety of imperfections or defects. In crystalline ceramics and glasses, the structure  The concentration of impurities in ceramics is usually and chemistry of the material will be determined by the much greater than that of intrinsic defects. kinetics of defect movement. For example, the kinetics of  Dislocations are usually much less important for defor- the glass-to-crystal transformation are slow if the tem- mation mechanisms than they are in metals. perature is low (typically less that 1000°C) because the  Surfaces and interfaces are even more important for transformation occurs by atoms moving—in ceramics, ceramics. this usually occurs by point defects moving. If point  Pores and voids are often very much more important defects move too slowly, for ceramics. the structure with the lowest energy (the equilib- THE OTHER DEFECT CHAPTERS The importance of rium structure) may never Dislocations—Chapter 12 pores and voids is a actually be achieved. How Surfaces—Chapter 13 good illustration of how fast they move is deter- Grain boundaries—Chapter 14 time changes our view of mined by their structure. Phase boundaries, particles, and voids—Chapter 15 materials. In the past, 11.1 A r e D e f e c t s i n C e r a m i c s D i f f e r e n t ? ............................................................................................................. 181  TABLE 11.1 Defect Hierarchy Dimension Name Example Zero Point defect Vacancy One Line defect Dislocation Two Planar defect Grain boundary Three Volume defect Pore processing ceramics often meant trying to remove pores and voids during sintering because they weakened the final material. While they still generally do so, we are now also very interested in highly porous ceramics because such materials can have a very large surface area, which may be critical in their application as catalysts, catalyst supports, or filters. In this chapter we concentrate on point defects, but remember that they do relate to all other defects in ceramics and their importance is that they determine many important properties. FIGURE 11.1 Schematic of a Schottky defect drawn in 2D. Associated centers: When two point defects interact so 11.2 TYPES OF POINT DEFECTS that they can be considered as a single defect they are called an associated center or, if more atoms are Defects are often classified in terms of a dimensionality. involved, a defect cluster or a defect complex. Expos- This is known as the defect hierarchy. The classifications ing a material to ionizing radiation such as X-rays and are given in Table 11.1. In spite of this table, remember γ-rays can create large numbers of defect clusters. that all these defects are three-dimensional. We will first Solute (substitutional) atoms: In Cu alloys, we can add summarize the different types of point defect that can up to 30 at% Zn before the structure is changed. All occur in crystalline materials. To provide some idea of the the Zn atoms sit on Cu sites so they substitute for the importance of point defects, we will consider some spe- Cu and the crystal is said to be a solid solution of Zn cific examples. in Cu. The effect is to add electrons to the d band of the alloy and it is this change in the electronic struc- Vacancies: If an atom is not present on the site that it ture that determines the solubility limit. We can simi- should occupy in a perfect crystal then a vacancy is larly substitute Ge in Si, but the solubility is limited located at that site. A Schottky defect is a set of vacan- due to the difference in atomic size. In GaAs we can cies created by removing one atom for each atom in replace the Ga atom by Al on the group III sublattice the chemical formula. Thus, in a stoichiometric crystal such as MgO, we get a pair of vacancies, one on the Mg sublattice and one on the O sublattice, as shown in Figure 11.1. In spinel, a Schottky defect consists of seven vacancies. Interstitials: If an atom is present on any site that would be unoccupied in a perfect crystal then that atom is an interstitial. A Frenkel defect is a vacancy + interstitial pair formed by removing an atom from its site in the crystal structure and putting it into an interstice as illustrated in Figure 11.2. Frenkel defects formed in iodine-containing AgBr are essential to the photo- graphic process. Misplaced atoms: If an atom is present on a crystal site that should be occupied by a different atom, that atom is a misplaced atom and may be called an antisite defect. Antisite defects usually form in covalent ceram- ics such as AlN and SiC, but can also occur in complex oxides that have several different types of cation, for example, spinels and garnets. (We do not expect to see cations on anion sites and vice versa.) FIGURE 11.2 Schematic of a Frenkel defect drawn in 2D. 182 ................................................................................................................... Point Defects, Charge, and Diffusion  TABLE 11.2 The Kröger–Vink Notation for the Binary MX we form a vacancy on both anion and cation sublattices, so Defect Notation Comments we have to have a method for distinguishing these defects. The Kröger–Vink notation for the reaction we have just Vacancy Vx V is also the chemical symbol for described is the element vanadium; if there is a possibility for confusion, VNaCl → V′Na + VCl • such as expressing a vacancy on a vanadium site, then use We need such a notation because of one of the most special “Va” for the vacancy features about ceramics—the charge. Other notations are Interstitial Mi and Xi No “site” Antisite atom MX and XM Usually in covalent solids sometimes used, but the Kröger–Vink notation is the most Associated defect (MiXM ) Larger associations called widely accepted. (You may see variations in this notation “clusters” so be careful in translating from one text to another.) The Solute SX Impurity substitution topic of point defects should not be completely new to you. Electron and hole e′ and h Some of the fields in which you may have encountered Schottky (VMV X) Special associated defects Frenkel (VMMi) point defects before are listed in Table 11.3. giving a complete solid solution, Ga xAl1−xAs, with x 11.3 WHAT IS SPECIAL FOR CERAMICS? running from 0 to 1. GaAs and AlAs have the same structure and similar lattice parameters. We can replace Point defects are special in ceramics when they involve As by P on the group V sublattice to give another either charge (ionic materials) or dangling bonds (covalent continuous solid solution. This type of substitution materials). occurs in both covalent and ionic ceramics as well as in metals. Vacancies, interstitials, and substitutional defects can  Electronic defects: Electrons and holes can both exist in all be charged. The special point defect in ceramics is ceramics. They may be associated with particular ions, the charged vacancy. Frenkel and Schottky defects are in which case they are simply charged point defects. overall neutral.  Association of defects is particularly important for This leads to the topic of color centers, which color alkali halide crystals, amethyst, diamond, etc. ceramics because Coulombic interactions are both strong and long-range. We use the Kröger–Vink notation to identify these dif-  Electronic structure is increasingly important. In ferent point defects, which is summarized in Table 11.2. the past, the electronic structure was important This notation is completely general in that it can apply to only because the materials have a large band gap. any crystalline compound or even to pure crystals. In this Ionic materials are insulators. This is no longer notation, structural elements are denoted as SPc. the case—many old “insulators” (like SiC) are We will make use of now also wide-band-gap Kröger–Vink notation in semiconductors! many sections in this NOTATION SUMMARY FOR ScP  Nonstoichiometry is so chapter. We can write S: Species important because the simple equations to P: Position in the crystal concentration of point describe the formation of c: Charge relative to the perfect crystal defects can be very point defects or their inter- Charge notation: large. In ionic materials, actions. For example, if we Negative: dash, ′ point defects are usually remove a molecule, NaCl, Positive: point, • charged and they are from a crystal of rocksalt, Neutral: x often numerous. TABLE 11.3 Examples of Commonly Encountered Point Defects in Materials Type of point defect Application Comments Solute atoms Doping silicon for ICs Concentration of dopant atoms very small, ∼0.0001% can cause a 100 times increase in conductivity Solute atoms Solid solution strengthening A 50 Cu–50 Ni alloy has twice the tensile of metals strength of pure copper Interstitial Carburizing of iron and steel Surface hardening by heating metal in a hydrocarbon gas Vacancies Kirkendall effect Failure mechanism in Au–Al bonds, e.g., Au wire bonds on Al metallizations in ICs Vacancies and interstitials Cold working of metals At T < 0.4 Tm solid-state diffusion is slow 11. 3 Wh at i s S p e c i a l f o r C e r a m i c s ? ........................................................................................................................ 183 Some special rules for ceramics: 11.5 EQUILIBRIUM DEFECT CONCENTRATIONS  The number of sites is constant. This is the same as in metals, but we often have very different sites available We need to know how many point defects are present in in ceramics. thermal equilibrium. One of the simplest point defects that  The total charge is still zero. can occur in a crystal is a vacancy. In a binary compound,  Intrinsic defect concentrations are often very much e.g., MgO, where only vacancies exist, we must have an lower than impurity concentrations. equal number of each type of vacancy to maintain the stoichiometric formula. At a given temperature there is an equilibrium concen- tration of point defects in a crystal. The implication of this statement is that a crystal containing point defects must 11.4 WHAT TYPE OF DEFECTS FORM? have a lower free energy, G, than a corresponding crystal without any defects. From Chapter 3 we know that the Crystals with open lattice structures will tend to favor change in free energy accompanying a process, such as Frenkel defects. These crystals have structures with the creation of vacancies, is given by low coordination numbers and large interstitial sites, for example, the würtzite structure has CN = 4. If ΔG = ΔE − TΔS (11.1) there is a large difference in size between the cations and anions, We can use ΔH or ΔE in Frenkel defects are usually Eq. 11.1. ΔH would refer SCHOTTKY DEFECTS: THE CALCULATION specifically to the enthalpy formed by displacing the Show that the number of Schottky defects is to form a point defect. ΔE smaller ion. In Al2O3, for example, the cation is is the change in the inter- ns ≈ N exp(−ΔEs /2kT) Box 11.1 nal energy on forming the smaller and we would expect to form cation defect. The internal energy The units of ΔEs are J/defect. Then determine entropy of the disordered crystal is Frenkel defects. However, using probability theory. the energy of the perfect anion Frenkel defects will form in UO2, CeO2, crystal plus nE. S = k ln W Box 11.2 E is strongly affected and ThO2, which all have large cations. In contrast, W = N!/[(N − n)!n!] Box 11.3 by the nearest neighbors we would expect to find and the interatomic WA = N!/[(N − ns)!ns!] Box 11.4 bonding. It costs energy to Schottky defects in crystals with high coordi- WB = N!/[(N − ns)!ns!] Box 11.5 produce point defects; we nation numbers such as have to break bonds. The WA = WB Box 11.6 internal energy increases MgO. Vacancies may be WT = WAWB Box 11.7 when the number of point present on different sites defects increases. At the ΔS = k ln WT = k ln{N!/[(N − ns)!ns!]}2 Box 11.8 same time the entropy for the same type of ion. For example, NiFe2O4 is an ΔS = 2k ln{N!/[(N − ns)!ns!]} Box 11.9 (randomness of the struc- inverse spinel ture) increases, and the [Fe(NiFe)O4]; Fe3+ ions sit Next use math: product TΔS also increases. in both tetrahedral and The change in entropy is octahedral sites. Thus, we ln N! ≈ N ln N − N Box 11.10 complex and consists of can have Fe3+ vacancies on terms due to the vibration ΔS = 2k{N ln N − (N − ns) ln(N − ns) − ns ln ns} Box 11.11 of the atoms around the the tetrahedral or octahe- dral sites, but these two defects and terms due to Finally do the substitutions: the arrangement of defects types of vacancy are not the same. You can imagine in the crystal. This config- ΔG = nsΔEs − 2kT{N ln N − (N − ns) ln(N − ns) urational entropy relies on how complex the situation − ns ln ns} Box 11.12 statistics (how many) and becomes for more complex crystals. We usually ignore (∂ΔG/∂ns)T,P = 0 Box 11.13 mechanics (how it is such complications because moving); the subject is sta- ΔEs = 2kT ln[(N − ns)/ns] Box 11.14 tistical mechanics. So even they are too difficult to handle, but be aware that ns = (N − ns) exp(−ΔEs /2kT) Box 11.15 though it requires energy we are making this to create vacancies, overall ns ≈ N exp(−ΔEs /2kT) Box 11.16 G may decrease because of simplification. 184 ................................................................................................................... Point Defects, Charge, and Diffusion  E nΔE (Note that we are neglecting thermal entropy effects.) W is the number of ways of distributing n defects over N sites at random. ΔG 0 The number of ways we can distribute the nS cation vacancies over the available sites in the crystal will be given by Eq. Box 11.4; we can write a similar expression - TΔS for the anion vacancies as shown in Eq. Box 11.5. Because AB is a stoichiometric compound we can n=0 n* n write Eq. Box 11.6. The total number of ways, WT, of dis- FIGURE 11.3 Schematic showing how the free energy decreases tributing these defects is given by the product of WA and, to a minimum as the number of vacancies increases. WB, so we have Eq. Box 11.7, and therefore the change in entropy caused by introducing Schottky defects is given by Eq. Box 11.8, which we can rewrite as Eq. Box 11.9. the entropy contribution. The challenge is that to know Now we use a standard trick for large N: Stirling’s ΔG, we have to know S, the entropy. approximation (Eq. Box 11.10) eliminates the factorials, Figure 11.3 is a plot of nΔE, ΔS, and ΔG. From this which leaves us with an expression for the entropy change plot you can see that introducing vacancies lowers the free associated with the formation of Schottky defects (Eq. energy of the crystal until an equilibrium concentration is Box 11.11). reached; adding too many vacancies increases G again. At Substituting Eq. Box 11.11 into Eq. 11.1 gives the higher temperatures the equilibrium number of vacancies overall change in Gibbs free energy for forming ns pairs increases. The implications are important. In pure crystals (Eq. Box 11.12). At equilibrium, the free energy change we expect to find point defects at all temperatures above is a minimum with respect to the number of defects and 0 K. Since these defects are in thermodynamic equilib- is given by Eq. Box 11.13. We can thus differentiate Eq. rium, annealing or other thermal treatments cannot remove Box 11.12 and set the result equal to zero so that after a them. little rearrangement we arrive at Eq. Box 11.14; in terms of the number of defects we write Eq. Box 11.15. The final Usually the concentration of point defects is controlled by step is another approximation: N is usually very much impurities. greater than nS. So we arrive at Eq. Box 11.16 (i.e., Eq. Box 11.1). Dopant-induced defects will also be in thermodynamic We give some experimental values for the enthalpy of equilibrium so that the overall equilibrium is controlled formation of Schottky defects in Table 11.4. We can use by the dopants. these numbers to calculate equilibrium defect concentra- Schottky defects do not change the composition of the tions as we have for NaCl in Table 11.5. The population material. The concentration of Schottky defects in a crystal of point defects is very low, but it is clear from Eq. is deduced using standard statistical mechanics that Box 11.1 that vacancies are stable in the crystal at any appears in most thermodynamics textbooks (because it is temperature above absolute zero. Because energies for such a clear application of basic thermodynamics). For point defect formation in stoichiometric oxides such as most ceramics, we just need the result from the calcula- tion. Notice that charge is not mentioned and the deriva- tion assumes a pure simple binary compound, like MgO or NiAl. TABLE 11.4 The Formation Enthalpy of Schottky Defects in ΔEs is the energy to form a Schottky defect, and k, the Some Compounds of Formula MX Boltzmann constant, is in J/°C. If ΔEs is given in J/mol, Compound DEs (10−19 J) DEs (eV) then the number of Schottky defects in a unit volume is the same with R replacing k. MgO 10.574 6.60 CaO 9.773 6.10 We will review how nS is derived for a stoichiometric SrO 11.346 7.08 crystal AB. The derivation shows the importance of dis- BaO 9.613 6.00 order. In this discussion, we have separated the equations LiF 3.749 2.34 from the text and mainly comment on the logic of the LiCl 3.397 2.12 derivation. LiBr 2.884 1.80 LiI 2.083 1.30 If nS is the number of Schottky defects per cubic cen- NaCl 3.685 2.30 timeter in the crystal at T K, then we have nS vacant cation NaBr 2.692 1.68 sites and nS vacant anion sites. In addition, in a crystal of KCl 3.621 2.26 this type there are N possible cation sites and N possible KBr 3.797 2.37 anion sites per cubic centimeter. We can determine the KI 2.563 1.60 CsBr 3.204 2.00 entropy change, ΔS, in a system of occupied and unoccu- CsI 3.044 1.90 pied sites by using the Boltzmann equation (Eq. Box 11.2). 11. 5 E q u i l i b r i u m D e f e c t C o n c e n t r at i o n s ............................................................................................................. 185  TABLE 11.5 Schottky Defect Concentrations in NaCl TABLE 11.6 Formation Enthalpy of Frenkel Defects in −3 Some Compounds of Formula MX and MX 2 Temperature (°C) Temperature (K) n s /N n s (cm ) Material DEf (10−19 J) DEf (eV) −20 27 300 4.79 × 10 2.14 × 103 127 500 2.56 × 10 −12 1.14 × 1011 UO2 5.448 3.40 427 700 5.25 × 10 −9 2.34 × 1014 ZrO2 6.569 4.10 627 900 3.63 × 10 −7 1.62 × 1016 CaF2 4.486 2.80 SrF2 1.122 0.70 AgCl 2.564 1.60 MgO and CaO are so high, the concentration of intrinsic AgBr 1.923 1.20 defects is going to be very much less than impurity con- β-AgI 1.122 0.70 centrations (usually ∼100 ppm or greater). Even close to the melting temperature we find that only one or two sites in one billion are vacant due to intrinsic effects. The actual type of defect found in the crystal will To give you an idea of what these numbers mean cal- depend on the energy of formation. There may be either culate the equilibrium number of vacancies that would be more Frenkel defects or more Schottky defects depending in a single crystal of MgO the size of the earth (rearth on which has the smaller energy of formation. As we have ∼6400 km) at room temperature; it is still a pretty small already mentioned, Frenkel defects are more likely to be number. important in crystals with open structures that can accom- Intrinsic vacancies are much more numerous in metals. modate the interstitials without much lattice distortion. For example, in a 1-cm3 crystal of aluminum at room Frenkel defects are the key to the photographic process. temperature there are about 9 billion vacancies. In a Photographic film contains crystals (called grains) of crystal of silicon in equilibrium at room temperature there AgBr or I-doped AgBr. These are dispersed in gelatin, are only about 1 × 10−18 intrinsic vacancies per cubic cen- often along with various other chemicals known as sensi- timeter. This is considerably less than typical concentra- tizers, on a thin plastic film (it used to be on glass). AgBr tions of extrinsic point defects (dopants) in silicon—about has a rocksalt structure, but rather than containing mainly 0.0001%: another fortunate fact. Schottky defects (as we find in NaCl) it contains mostly Vacancies are important for dislocation motion at high cation Frenkel defects. temperatures: the dislocations then move by During irradiation with climb—they absorb vacan- light, electrons are excited cies, which are more SILVER POINT DEFECTS from the valence band to numerous at higher tem- the conduction band. The peratures (the vacancies Ag•i + e′ → Agx band-gap energy is 2.7 eV, also move more easily at Agx + e′ → Ag′ which corresponds to a elevated temperatures). wavelength of 460 nm Frenkel defects, like Ag′ + Ag•i → Ag2x (blue light). An electron Schottky defects, also Ag2x + e′ → Ag′2 will neutralize one of the involve vacancies in the silver interstitial ions. To crystal structure. In this Ag′2 + Ag•i → Ag3x produce what is known as case, though, the vacancies a latent image it is neces- exist on only one sublattice sary for silver atoms to form clusters of at least four atoms and the atom that should occupy the vacant positions is on the surface of the grains. The silver interstitials are placed in an interstitial site in the crystal. The interstitial mobile and can diffuse to the surface. The exact mecha- is a very special defect: it can exist on one or more non- nism for cluster formation is not well understood, but this equivalent sites, which are not normally crystal sites, so set of equations shows a possible sequence of reactions. the Frenkel defect is not unique either. The clusters act as catalysts that lead to the reduction of The calculation of the number of Frenkel defects (nf ) the AgBr grains in the presence of a suitable developer. in a crystal proceeds along lines that are similar to those for Schottky defects where we consider the number of ways of distributing N vacancies over N* available inter- 11.6 WRITING EQUATIONS FOR stitial positions. POINT DEFECTS The values for ΔEf are usually quoted in J/mol and we therefore use the following equation: In many instances we have to consider reactions that nf ≈ (NN*) exp(−ΔHf/2RT) 1/2 (11.2) cannot be expressed within the normal chemical nomen- clature. For example, if a dopant is incorporated into a Experimental values of the energy of formation of Frenkel crystal it can have profound effects upon the physical defects in some oxide compounds are given in Table and chemical properties of the substance because of the 11.6. defects that are necessarily introduced. However, defects 186 ................................................................................................................... Point Defects, Charge, and Diffusion do not occur in the balance of reactants expressed in the Rule Example Comments traditional equations, and so these important effects are lost to the chemical accounting system that the equations Size factor CdS–CdSe If the size represent. Using the Kröger–Vink notation we can build (the “<15% rS = 0.106 nm difference is rule”) rSe = 0.116 nm outside this range up a defect chemistry, provided the normal rules for then substitution balancing chemical equations are preserved. In writing will be limited or equations for point defect reactions we must obey the fol- may not occur lowing rules: Valence factor Ni2+ in MgO This is not the same in metals where we do not  Maintain the ratio of the number of sites, e.g., in MaXb have to consider the ratio a/b is constant. charge  VM and M x require sites; Mi does not require a new Chemical affinity Al3+ in MgO The possibility of a site. MgAl2O4 new phase can  Maintain electrical neutrality overall. limit solid solubility  Surface sites are treated as if they are bulk sites (but Structure type MgO and NiO (same) The more similar could be treated separately). SiO2 and TiO2 (similar) the structures, the greater the solubility Example: Point Defects in the Model Oxide M2O3 We will illustrate how to formulate the Schottky and We can summarize the comparison to metals: cation Frenkel defect reactions using Kröger–Vink nota- tion for the model oxide M2O3. For the Schottky defect  In metals, we have the same rule for the formation of reaction alloys regarding size; the new factor in ceramics is the charge. 2M Mx + 3OOx ⎯M⎯⎯ 2 O3 → 2VM′′′ + 3VOii + M2 O3 (11.3)  In elemental semiconductors, the rules are approxi- mately the same; these are ceramics with a large We imagine that the molecule of M2O3 condenses at the covalent component to the bonding. The valence dif- surface of the material or at another interface. In writing ference is important in forming p-type and n-type Eq. 11.3, we maintain the ratio of M-to-O sites and balance semiconductors. the charge.  We will see that the silica-based glasses are some- For the cation Frenkel defect reaction where between elemental semiconductors and ionic materials, but introduce other challenges. M Mx + V ix ⎯M⎯⎯ 2 O3 → Miiii + V M′′′ (11.4) Solid-Solution Example 1: FeO1-x The vacancy on an interstitial site is simply that there is no interstitial initially. Notice that Eq. 11.4 can be written for a We saw in our discussion of phase diagrams that FeO single cation. We do not need to consider the number of sites, never exists. Consider wüstite with composition Fe0.95O. etc. The anion Frenkel defect reaction would be similar, but To compensate the charge of V″Fe (i.e., for electrical neu- is unlikely to occur in a material such as Al2O3. trality), we need to replace 3Fe2+ ions by 2Fe3+ ions. This is the important point: the Fe ions change their valence from 2 to 3. This point defect reaction happens automati- 11.7 SOLID SOLUTIONS cally. You can imagine it occurring by dissolving Fe2O3 (s) in FeO(s). We consider solid solutions here because we can think of them as being formed by distributing a large number of Fe 2 O3 (s) ⎯FeO ⎯⎯ → 2 Fe •Fe + 3OO + VFe′′ (11.5) point defects in a host crystal. As always, we must balance charge and be sure that the size of the “impurity” (guest) To exhibit nonstoichiometry, the cation must be able to ion is appropriate to fit into the available site. If the impu- exist in two different valence states (so this is not the same rity ions are incorporated in regular crystal sites the result- as nonequimolarity that we saw for spinel). The ions Fe, ing phase is a substitutional solid solution. In an interstitial Co, and, to a lesser extent, Ni can do this; Mg cannot. An solid solution the impurity atoms occupy interstices in the alternative way of writing this point defect reaction is to crystal structure. The rules for substitutional solid solu- bring oxygen from the gas state into FeO. tions (the Hume–Rothery rules) can be summarized as follows. Note that the last two requirements are really very 1 closely tied to the first two. 2Fe Fe + 2OO + O2 (g) ⎯FeO ⎯⎯ → 2Fe •Fe + 3OO + VFe′′ (11.6) 2 11.7 S o l i d S o l u t i o n s .................................................................................................................................................... 187  TABLE 11.7 Composition and Structure of Wüstite vacancies as a function of pO2. Brouwer diagrams (also Edge of unit cell Density known as Kröger–Vink diagrams) are used to represent Composition Atom % Fe (nm) (g/cm3) defect concentrations as a function of pO2. The complete diagram for an oxide of the type MO is shown in Figure Fe0.91O 47.68 0.4290 5.613 Fe0.92O 47.85 0.4293 5.624 11.4. There are three distinct ranges (I to III) that corre- Fe0.93O 48.23 0.4301 5.658 spond to different values of the oxygen partial pressure. Fe0.945O 48.65 0.4310 5.728 It is important to keep in mind that these Brouwer diagrams, while useful, can provide an indication only of what might happen; the equilibrium constants needed for accurate calculations are not widely available. Similar dia- What we are doing is oxidizing an oxide. Oxides in which grams can be drawn for nonoxide systems. the cation can change its valence state, in general, show a variation of composition with oxygen partial pressure. This dependence can even cause a change in the dimen- Solid-Solution Example 3: Zn1+x O sions of the crystal lattice as shown in Table 11.7. The point defect chemistry of ZnO is different partly because there are two charge states of Zn, namely 2+ (as in ZnO) and 1+. When we heat ZnO in Zn vapor, we form Solid-Solution Example 2: Co1-x O a Zn-rich oxide, Zn1+xO. Experimentally it is found that The nonstoichiometry of CoO is similar to that of wüstite the excess Zn sits on interstitial sites (as you would expect but not so pronounced. from the crystal structure). We can write the basic defect equation for the singly charged interstitial as 1 2CoCo + O2 (g) ⎯CoO ⎯⎯ → 2CoiCo + OO + VCo ′′ (11.7) Zn(g) → Zn•i + e′ (11.13) 2 We can write this in an alternate form. We then write the equilibrium constant for the reaction in the usual way 1 O2 (g) ⎯CoO ⎯⎯ ′′ + 2 h • → OO + VCo (11.8) [ Zn ii ][e′] 2 K= (11.14) ( PZn ) We can apply equilibrium thermodynamics to Eq. 11.8 and write the equilibrium constant, K, for the reaction From the reaction equation we know that there is one electron for every Zn interstitial. ′′ ][ h i ]2 [OO ][ VCo K= (11.9) [Zn•i] = [e′] (11.15) ( pO2 ) 1/ 2 (PZn) 1/2 ∝ [Zn ] • i (11.16) The concentration of anions on anion sites, [OO], is essen- tially unity. For each vacancy on the Co sublattice, there The excess zinc could be incorporated as a divalent inter- are two electron holes; i.e., the concentration of vacancies stitial, which means that there is a second reaction on cation sites is twice the concentration of holes. possibility: 2[V″Co] = [h•] (11.10) Zn(g) → Zn••i + 2e′ (11.17) POINT DEFECTS AND VARIATION IN pO2 ′′ ]4[ VCo [ VCo ′′ ]2 Range I—Low pO2 (PZn)1/3 ∝ [Zn••i ] (11.18) K= (11.11) ( pO2 ) 1/ 2  The number of O vacancies increases. Experimentally, we can  The oxide is reduced. measure the electrical con- Thus, there is a direct rela-  n = 2V O•• ductivity as a function of tionship between the the partial pressure of Zn, oxygen partial pressure, Range II—Intermediate pO2 plot the results, and then pO2, and the extent of the look at the exponent. We nonstoichiometry.  Schottky defects dominate. find that (PZn)1/2 ∝ [Zni], which indicates that the Zn (pO2) 1/6 ∝ [V″Co] (11.12) Range III—High pO2 interstitial has a charge of +1. When you heat ZnO We can confirm this rela-  Increase in cation vacancies. to high temperatures and tionship by measuring the  The oxide is oxidized. control the oxygen partial concentration of cation 188 ................................................................................................................... Point Defects, Charge, and Diffusion  log c range I range II range III log c range I range II range III stoichiometry -1 hÕ 6 1 hÕ eÕ eÕ 6 -1 1 VO•• VMÕÕ VO•• 6 6 ÕÕ VM Ki ÕÕ KS 1 -1 VM hÕ 6 Ki -1 6 eÕ 1 6 KS 6 1/4 VO•• 1 -1 hÕ -1/4 2 2 -1 1 1 -1 6 eÕ ÕÕ VM 6 6 stoichiometry 6 VO•• eÕ = 2VO•• VO•• = VM ÕÕ ÕÕ = hÕ 2VM eÕ = 2VO•• eÕ = hÕ ÕÕ hÕ = 2VM log PO log PO 2 2 FIGURE 11.4 Examples of Brouwer diagrams in an oxide MO. pressure the composition of the oxide will change. The CaO(s) ⎯ZrO ⎯⎯ 2 → Ca ′′Zr + OO + VOii (11.19) equilibrium condition depends on pZn or pO2. ZnO is a particularly important ceramic semiconduc- The cubic structure can also be stabilized using MgO tor: its conductivity decreases with increasing pO2. A (with essentially the same equation) or with Y2O3 (to form major application for ZnO that makes use of its electrical YSZ) when the equation is a little different. Later we will properties is the varistor (variable resistor). see other rare earths partly substituting for Y to give CZ a wide range of colors. The large number of oxygen vacan- Solid-Solution Example 4: cies makes CZ a material of choice for solid-oxide fuel ZrO2 Doped with CaO cells. The material is an electrical insulator but an ionic conductor: oxygen moves quite rapidly through CZ. Doping ZrO2 with Ca is a special example of a ZrO2 solid solution. We can incorporate ∼15% CaO in the structure to form Ca-stabilized cubic zirconia (CSZ). (CZ is the 11.8 ASSOCIATION OF POINT DEFECTS general abbreviation for cubic zirconia.) The special feature here is that the cubic (fluorite structure) phase is This phenomenon often occurs when defect concentra- not stable at room temperature unless the ZrO2 is heavily tions reach more than about 1 mol%. Then the defects are doped. However, we write the point defect equations as if very close together and defect interactions may result in it were always stable. The Ca2+ cation substitutes for the lowering the overall energy for defect formation and Zr4+ cation as shown in Figure 11.5. Since the charges are in defect clustering. Clustering is especially important in different, we must compensate with other point defects. nonstoichiometric oxides such as Fe1−xO and UO2+x. This idea is special for ceramics because the effect is greatly enhanced due to the fact that the point defects are charged. In particular, since vacancies behave as if they are charged point defects, cation and anion vacancies can be strongly attracted to one another to form a defect complex denoted in the following equation by the parentheses. M2+ V′Na + VCl • = (V′Na, VCl • ) (11.20) We can write a law of mass action equation relating the fractional molar concentration of the vacancy pairs. At V equilibrium M4+ ′ , VCli )] [(VNa =K (11.21) ′ ][ VCli ] [ VNa O 2– We can then relate the equilibrium concentration of the FIGURE 11.5 Accommodation of Ca 2+ in ZrO2. Note: this is just vacancy pair to their free energy of formation, ΔGvp, half of the unit cell. using 11. 8 A s s o c i at i o n o f P o i n t D e f e c t s .......................................................................................................................... 189  Al 2 O3 ←⎯⎯ MgO → 2AliMg + VMg ′′ + 3OO (11.26) -4 MgO Õ ] [ VNa = • ] [ VCl log [V] • [ FMg ] = 2[ VÕÕMg ] Õ ] = [F• ] [ VNa Cl The Al3+ sits on Mg sites requiring that vacancies be -6 created on the Mg sublattice. Notice that the reaction can lead to precipitation of spinel, but then we are creating a -8 [ VCl• ] new structure and, thus, new sites. Õ V • )] [(VNa Cl -10 Mg Mg + 2AliMg + VMg ′′ + 4OO ←⎯⎯ MgO → MgAl2 O 4 (ppt) ÕÕ V •• )] [(VMg O (11.27) -12 This equation emphasizes that four sites are required on -14 [ VOÕÕ ] each sublattice. We can write the law of mass action equa- tion for the precipitation reaction -16 ΔH ppt ⎞ NaCl [ Mg Mg ][ AliMg ]2 α exp ⎛⎜ + ⎟ (11.28) -18 ⎝ kT ⎠ 0.2 0.6 1.0 1.4 1.8 mp MgO 1000/T (K) mp NaCl ΔHppt is the enthalpy of formation. (A) (B) FIGURE 11.6 Plots of the vacancy concentrations varying with T −1: [Al•Mg] ∝ 2[V″Mg] (11.29) (a) MgO; (b) NaCl. 1/3 ΔH ppt ⎞ ′′ ]α ⎛⎜ ⎞⎟ exp ⎛⎜ + 1 [ VMg ⎟ (11.30) ⎝4⎠ ⎝ 3kT ⎠ ΔG = −RT ln K (11.22) In summary, we ask again what is special for ceramics— Hence why don’t we do this for metals? The special feature is the formation of defect associates as a result of the strong ′ , VCli )] −ΔGvp ⎞ = Z exp ⎛⎜ [(VNa ⎟ (11.23) attraction between oppositely charged point defects. Of i ′ ][ VCl ] [ VNa ⎝ kT ⎠ course, defect associates and precipitates are related, and both are clearly volume defects. In Eq. 11.23, Z is the number of distinct orientations of the defect complex; it accounts for the configurational entropy. For example, if the vacancies sit on adjacent sites in NaCl, Z would be 12. Figure 11.6 shows calculated 11.9 COLOR CENTERS concentrations of Schottky defects and vacancy pairs in NaCl and MgO. The term color center is now applied to any defect, includ- ing an impurity, that produces color in an insulator. The original observation was made in Germany using X-rays Association of Point Defects due to Doping to color alkali halides by producing F centers (“F” is for Dissolving CaCl2 in NaCl increases the number of vacan- Farben: German for color). The color is the complement cies on the Na sublattice. of what is absorbed by the color center. Colors are pro- duced in most of the alkali halides following irradiation CaCl 2 ⎯NaCl ⎯⎯ → Ca iNa + VNa ′ + 2Cl Cl (11.24) with ionizing radiation and are characteristic of the crystal not the radiation source used. These F centers are due to If the Ca2+ cations form a defect complex with such a an electron or hole trapped at an anion vacancy site. Other vacancy (not now on adjacent sites), we can express this types of color center can give other colors. combination as Several different types of color center have been identified and some of the common ones are illustrated Ca•Na + V′Na → (Ca•Na, V′Na) (11.25) in Figure 11.7 for the alkali halides. V centers are is cation vacancies with trapped holes. Color centers can A Second Example COLOR OF F CENTERS also form in oxides such as of Doping The crystal and color: MgO. When a single elec- Consider what happens NaCl—orange-brown/blue tron is trapped at an anion when we dissolve a small KCl—violet/green vacancy in MgO, the defect amount of Al2O3 in MgO. KBr—blue green/orange is positively charged and is 190 ................................................................................................................... Point Defects, Charge, and Diffusion  M+ impurity by heating in either high or low pO2. In Nd-doped yttrium aluminum garnet (YAG)—the most widely used FA-center F-center F ’-center solid-state laser crystal—the Nd is incorporated into the + – + – + – + – + – + YAG structure (it substitutes for Y3+ in small amounts) e when Nd2O3 is added to the YAG melt. A single crystal, – + – + – + + – + – which contains the Nd ions in solid solution, is pulled e e + + – + – + – + + from the melt using the Czochralski method (see e Chapter 29). – + – + – + – + – + – If a crystal is annealed at a sufficiently high tempera- + – + + – + + – + ture and for long enough, then the equilibrium concentra- tion of vacancies will increase. Abrupt quenching of the – + + – + – + + – material can “freeze in” unusually high concentrations of + – + – + + – + + point defects. Vacancies, usually Schottky defects or Frenkel pairs, – + – + – + + – + – can be produced as a result of ion bombardment in a – – – – – process known as ion implantation. For example, many + + + + + + defects are formed in single crystal MgO when it is bom- F2-center X--center barded with high-energy Xe + ions. Figure 11.8 is a TEM H-center 2 image of MgO following implantation with 1014 Xe + cm−2 FIGURE 11.7 Schematics of color centers in alkali halides. ions at 200 keV in a particle accelerator. The dark regions are typical of numerous point defect clusters. A large amount of work on ion implantation was performed to referred to as the F + center. An F center in MgO is a simulate what happens to materials inside a nuclear reactor vacancy with two when they are bombarded electrons. with fast neutrons (ener- IONIZING RADIATION CAUSING Smoky quartz and gies > 0.1 MeV). Now the amethyst are two natural POINT DEFECTS topic is again important examples of color centers. Ultraviolet light E ∼10 eV as ceramics are used to In smoky quartz a small X-rays E = 10–100 keV contain radioactive waste amount of Al impurity γ-rays E = 1.25 MeV and we start to plan for atoms can substitute for Si. High-E electrons E = 100 keV–0 MeV fusion (rather than fission) Because of the different High-E protons E = 2.20 MeV reactors. Ion implantation valence of the two cations, Fast neutrons E > 0.2 keV is also the technique that is electron neutrality is main- tained by hydrogen ions. Ionizing radiation releases an electron from the [AlO4]5− group, which is then trapped by the hydrogen ion: [AlO4]5− + H + → [AlO4] 4− + H (11.31) The color center is the [AlO4] 4− group, which is electron deficient, and we can think of it as having a trapped hole. In amethyst the color center is [FeO4] 4−, which is due to Fe3+ impurities substituting for Si. We will discuss more examples of how impurities give rise to color in Chapter 32, but it is interesting to note that NaCl crystals, doped to modify the color and increase the density of point defects, can be used for the NaCl color- center laser. 11.10 CREATION OF POINT DEFECTS IN CERAMICS There are several ways that we can create point defects in ceramics. We have seen already that point defects can FIGURE 11.8 TEM image of defect clusters formed by ion be produced in nonstoichiometric oxides, such as ZnO, implantation into MgO. 11.10 C r e at i o n o f P o i n t D e f e c t s i n C e r a m i c s ..................................................................................................... 191 used to introduce dopant atoms to defined depths during  An interstitial atom increases density. the formation of semiconductor devices or to harden the  If a substitutional atom replaces a heavier atom the surface of metals and ceramics. density may be reduced. Any form of ionizing radiation can be used to produce point defects in materials. The term ionizing radiation is used to describe radiation sources that generate electron 11.12 DIFFUSION or holes when interacting with matter. Diffusion occurs by atomic THE DRIVING FORCE defects moving through If there is no bias (gradient in the chemical potential), the crystal; it is not a con- then there is no driving force. tinuum process. We thus analyze diffusion as a sta- 11.11 EXPERIMENTAL STUDIES OF tistical process. This is the kinetics part of the story. Dif- POINT DEFECTS fusion of point defects is the key to understanding their properties. There are four basic mechanisms that can, in It is very difficult to see individual point defects in a mate- principle, occur; these are illustrated in Figure 11.10. rial. It is not that they are too small [transmission electron microscopy (TEM) has the resolution], but they have to  Direct exchange (difficult and not energetically be surrounded by atoms so we tend to see the surrounding probable) atoms instead! Because point defects (especially substitu-  Ring mechanism (cooperative motion: possible but not tional atoms) are so important in determining the electri- demonstrated) cal properties of semiconductors, a great deal of work has  Vacancy mechanism (most common, dominant in been done to understand these defects. Figure 11.9 is a metals) high-resolution scanning transmission electron micros-  Movement of interstitials (occurs when you can put copy (STEM) image showing columns of silicon atoms in interstitials in); an example is Zn in ZnO. a sample of Sb-doped Si. The brightest columns contain one Sb atom. Diffusion is a thermally activated process so we plot In Table 11.7 we showed how the lattice parameter the free energy versus distance. The region of high energy of iron oxide changes as a function of the oxygen-to- in this plot corresponds to an “activated complex.” It iron ratio. The lattice parameter can be determined to a occurs because there is an activation energy barrier to high precision using X-ray diffraction and the precise diffusion. We can use reaction rate theory to understand lattice-parameter method. It can then be correlated diffusion behavior. First we consider two features of the with the oxygen/iron ratio process. determined by chemical analysis. NOTATION FOR DIFFUSION ACTIVATION  Each step in a difficult We can also correlate AB* The activated complex process is relatively point defect concentrations K* K for the activated complex simple; if it appears with a property measure- ν The Debye atomic jump frequency, 1013 Hz more difficult, we break ment such as electrical χ The potential gradient per atom it into smaller steps. conductivity, σ, or density, N Avogadro’s number ρ. The density will show whether the dopant enters interstitially or is a replacement for the host ion. d e c a b FIGURE 11.9 Atoms of Sb in Si; the Z-contrast image does not FIGURE 11.10 Possible mechanisms occurring during diffusion. show where the atom sits in the column. (a) Exchange, (b) ring, (c) vacancy, (d) interstitial, (e) knock-on. 192 ................................................................................................................... Point Defects, Charge, and Diffusion   The reaction path of each step, such as an individual log DK 104 atom jump, involves an activated complex, which gives (cm2/sec) log [VÕK] an energy maximum. 10 2 10-2 ΔHs 1.3eV = 2k k For the chemical reaction (the route of transition of the [V ÕK] = [F°K] 0 activated complex, AB*, into the product) 10-4 A + B → AB* (11.32) 10-2 10-6 ΔHp 0.4eV = 2k k The concentrations are related by the equilibrium constant 10-4 1.0 1000/T 2.0 K*. [AB*] 10-6 = K* and ΔG* = − RT ln K* (11.33) [F•K] ≈ 10-4 ΔH † ΔHS [A][B] k + 2k 10-8 The reaction rate, k, is ν[AB*], which can be written as [F•K] ≈ 10-5 † ΔH νK*[A][B]. So the reaction rate for unit concentration is k just νK*. If there is no net flow to the right or left, because 10-10 each time a point defect jumps to the right one also jumps ΔH † ΔHP + to the left, we need to add a driving force, i.e., a potential 10-12 k 2k gradient, to produce a flux. Now the flux of atoms is the rate in the forward direction minus the rate in 10-14 the backward direction. ΔG forward is ΔG* − 2–1χλ for unit concentration forward. The analysis makes two assumptions: 10-16 0.0 1.0 2.0 3.0 1. The activity coefficient is unity. 1000/T (K) 2. D does not vary with the composition. FIGURE 11.11 Diffusion coefficients in the intrinsic and extrinsic ranges. KCl with 10−4 and 10−5 atomic fraction divalent cation The diffusion coefficient does have a strong depend- impurities. ence on temperature. −Q ⎞ D = D0 exp ⎛⎜ ⎟ (11.34) the intrinsic concentration of vacancies, [V], is ∼10−4 at ⎝ RT ⎠ 2000°C. As we lower the temperature, T, the equilibrium The diffusion equations are summarized by Fick’s laws. concentration of vacancies, [V], decreases too. One assumption that is Figure 11.11 shows a explicit in the derivation plot of intrinsic and extrin- of these equations is that FICK’S LAWS sic diffusion coefficients. there is a well-defined The first part of this plot is ∂c value of D. We will see Fick’s first law J = − D ⎛⎜ ⎞⎟ almost never observed: later that because of the ⎝ ∂x ⎠ most ceramics are never high concentrations of ∂c ∂c 2 this pure (the exceptions defects in ceramic materi- Fick’s second law =D 2 are the semiconductors, Si ∂t ∂x als, there will be many and Ge, and a few others). important situations in This means that an impu- which this assumption is not valid; i.e., D often does rity concentration of between 1 part in 105 (10 ppm) and 1 depend on the composition. part in 106 (1 ppm) is sufficient to dominate the vacancy concentration. There is always an attraction between oppositely charged point defects so that they will associate 11.13 DIFFUSION IN IMPURE, with one another, which will in turn affect their effective OR DOPED, CERAMICS concentrations. (Consider how far apart point defects can be if the concentration is 1 in 106 —∼20 nm, maximum.) Now you can compare diffusion in stoichiometric oxides We will now consider examples that illustrate special with diffusion in nonstoichiometric oxides. The first ques- features of diffusion in ceramics. tion concerns the diffusing species when two species are present. For many ceramics ΔEs is large. For MgO, Al2O3, CaCl2 in KCl shows the effect of changing the charge on and B2O3, ΔHs is ∼600 kJ/mol (∼6 eV/formula unit). Thus the cation. 11.13 D i f f u s i o n i n I m p u r e , o r D o p e d , C e r a m i c s ................................................................................................... 193 ZrO2 doped with CaO is special because the structure of ⎯→ Ca iK + VK′ + 2Cl Cl CaCl 2 (s) ⎯KCl (11.39) CSZ requires the Ca to be present and CZ is a fast conductor of oxygen. Once CaCl2 is dissolved and you change T, nothing much Zn1+xO is special because interstitials dominate and can will change because you have fixed the concentration of have different charges. vacancies. FeO1−x and CoO1−x are special because neither oxide is ever stoichiometric because the cation is always present in [V′k] = [Ca•K] = fixed (11.40) two charge states. CuO1−x is special because it is oxygen deficient but behaves At high T we have a high intrinsic vacancy concentration; differently from Zn1+xO; it shows the importance of at low T we have a low intrinsic vacancy concentration. crystal structure. At low T the diffusion coefficient is controlled by the starred (dopant) quantities. In each case, we clearly have to understand the defects before we can understand their behavior. ΔS * DKi = γλ 2 ν[Ca iK ] exp ⎛⎜ ⎞ exp ⎛ −ΔH * ⎞ ⎟ ⎜ ⎟ (11.41) ⎝ k ⎠ ⎝ kT ⎠ Diffusion Example 1: CaCl2 in KCl The slope is determined only by ΔH/kT. If we increase [Ca] to 10−4, the curve will move up. When we dope KCl with CaCl2 diffusion of K+ cations In general, even at high T, [V′k] due to thermal equilib- occurs by an interchange between K+ cations and cation rium is less than [V′k] due to [Ca•K]. This is the case for vacancies. The concentration of cation vacancies is given most ceramics. by  Intrinsic diffusion is controlled by defects that are ΔGS ⎞ [ VK′ ] = exp ⎛⎜ ⎟ (11.35) present at thermal equilibrium. ⎝ 2kT ⎠  Extrinsic diffusion is controlled by dopants (impuri- ties) that are present. ΔG S is the Schottky formation energy. The diffusion coef- ficient can then be written as The intrinsic part is not usually observed because an impurity concentration of between 1 in 105 and 1 in 106 is ΔG ⎞ DKi = [ VK′ ]γλ 2 ν exp ⎛⎜ − ⎟ (11.36) sufficient to control the vacancy concentration. There is ⎝ kT ⎠ another complication we should consider: as we saw in Section 11.8, there is attraction between [Ca•K] and [V′k] Here, γ is an orientation factor. The Gibbs free energy can that results in defect complexes. The concentration of then be rewritten as usual: these complexes depends on the strength of this attraction; formation of these complexes will probably reduce the ΔG = ΔH − TΔS mobility of the point defects and thus decrease diffusion rates. So the diffusion coefficient is DKi = γλ 2 ν exp ⎛⎜ (ΔSs / 2) + ΔS* ⎞ ⎛ (−ΔHs / 2) + −ΔH* ⎞ Diffusion Example 2: ZrO2 Doped with CaO ⎟ exp ⎜ ⎟ ⎝ k ⎠ ⎝ kT ⎠ We noted above that if ZrO2 is doped with 15 at% CaO we (11.37) can stabilize the cubic phase. The resulting material can be described as Zr 0.85Ca0.15O1.85. Experimentally we find In this equation, −ΔH* is the enthalpy of motion of an that D O decreases as the concentration of oxygen vacan- atom while ΔHS is the enthalpy of formation of a Schottky cies increases. Hence we know that oxygen diffuses by a defect. The constants are all well known: λ is ∼0.2 nm, γ vacancy mechanism. is ∼0.1, and the Debye frequency, ν, is 1013 s−1. ΔSs /2k and In UO2, which has the same fluorite structure, oxygen ΔS*/2k are small positive numbers. Hence we can estimate diffuses by an interstitial mechanism. (Look back to the that discussion of the structure of fluorite to see why this might be so.) D O increases as the concentration of oxygen vacan- (ΔSs / 2) + ΔS* γλ 2 ν exp ⎛⎜ ⎞ ≅ 102 ⎟ or 103 (11.38) cies increases. In such an interstitial mechanism, the ⎝ k ⎠ interstitial moves onto a regular site and bumps the ion occupying that site onto an interstitial site. If you study Why is diffusion controlled by a small amount of impurity diffusion using tracer atoms, the tracer atom has now in KCl? We can write an equation describing what happens temporarily stopped moving, but the interstitial ion may when we dissolve CaCl2 in KCl. repeat the process and move on through the crystal. The 194 ................................................................................................................... Point Defects, Charge, and Diffusion process is thus rather complicated. A typical activation energy for this process might be ∼120 kJ/mol. Notice that the crystals in these two examples both 10-11 D have the fluorite structure, but the diffusion mechanism (cm2/sec) that operates is very different because the point defects involved are different. Experimental data for diffusion in several oxides are plotted in Figure 11.12. 10-12 Diffusion Example 3: Zn1+x O In our discussion of point defects in nonstoichiometric ZnO, we noted that excess zinc is present as interstitials; 10-13 0.1 1 10 the oxide is metal rich. p Zn (atm) FIGURE 11.13 Plot for DZn as it varies with T −1. Zn(g) → Zn•i + e′ (11.13) Figure 11.13 shows a plot for D Zn: the steeper the slope, the larger the activation energy. Varying the partial pres- care about the partial pressure of the Zn; the Zn atoms sure of Zn, PZn, has a large effect on D Zn in ZnO because, diffuse by a vacancy mechanism, but the concentration of as we saw above, PZn is proportional to the interstitial vacancies does not depend on PZn. concentration. Thus, as PZn increases, the density of inter- stitials increases and the diffusion of Zn through the struc- ture increases. This result again emphasizes the difference Diffusion Example 4: FeO1-x and CoO1-x between a metal and its oxide: in metallic Zn, we do not As we noted above, the group of binary oxides, FeO, NiO, CoO, and MnO (all have rocksalt structure), is metal defi- cient. The most important of these is Fe1−xO. FeO does not T (°C) exist (i.e., it is not stable) and can contain as many as 1716 1393 1145 977 828 727 15 at% vacancies due to the equilibrium concentration of 10-5 D Fe3+ cations; we saw earlier that this equilibrium occurs (cm2/sec) Co in CoO Na in β-Al2O3 by the cation changing its valence: Fe2+ changes to Fe3+ . 10-6 We can write an equation to dissolve excess oxygen in Fe1−xO. We can generalize the equation we wrote for FeO 10-7 and CoO as O in CaxZrO2 - x 1 10-8 O in Y2O3 2Mm + O2 (g) → O 0 + VM′′ + 2M Mi (11.42) 2 • 10-9 Here M is the metal and MM represents an Fe3+ cation Cr in Cr2O3 2+ sitting on an Fe site. The rest of the analysis follows from our discussion of CoO. The important point is that diffu- 10-10 sion depends on pO2 as illustrated for several oxides in Al in Figure 11.14. There is an energy associated with the reac- Al2O3 10-11 tion and an energy associated with the motion of defects, O in UO but point defects are always present in FeO. -12 Ni in NiO Good experimental observations are available for CoO. 10 air We can show that the diffusion coefficient for Co can be expressed as Ca in CaO 10-13 O in TiO2 ΔS ΔS* 1/3 DCo = γνλ 2 ⎛⎜ ⎞⎟ pO21/6 exp 0 exp 1 10-14 ⎝4⎠ 3k k i ⎛ ΔH 0 ΔH* ⎞ exp ⎜ − − O in MgO ⎟ 10-15 ⎝ 3kT kT ⎠ (11.43) 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1/T x 103 (K-1) FIGURE 11.12 Arrhenius plots for different oxides: diffusion Experimentally, we find that D Co is proportional to coefficients varying with T −1. pO1/n 2 with the value of n depending on T. 11.13 D i f f u s i o n i n I m p u r e , o r D o p e d , C e r a m i c s ................................................................................................... 195  10-6 Now, D Co ∝ pO1/22 and n is 2. Experimentally we find n is D ∼3 so we can thus conclude that the vacancy must be (cm2/sec) CoO (1350°C) associated with between one and two electron holes. It is 1 DCo α PO24 not obvious that we actually make another assumption in this treatment. We perform a diffusion experiment, 10-7 measure D Co, and then assume that a vacancy in a complex moves at the same velocity as the free vacancy. So we should say that if the association of a vacancy and holes does not affect the movement of vacancies, then each vacancy must have between one and two electron holes associated with it. 10-8 NiO (1245°C) Finally, we comment on the mobility (BV) of the 1 DNi α PO2 6 vacancy; BV is proportional to ΓV, the jump frequency. Similarly, for holes Bh is proportional to Γh. In CoO all the Fe3O4 (1115°C) electrical current is carried by the electron holes (i.e., it is 1 DFe α PO2 2.5 a p-type semiconductor) so that the mobility of holes is 10-9 much greater than the mobility of the vacancies. In CoO we can say that MnO (1000°C) Bh >> BV 1 DMn α PO2 3.1 Γh >> ΓV 10-10 Nb2O5 (1100°C) 1 DO α PO2 4 So when a vacancy jumps, holes follow. Thus a hole/ vacancy pair will move at a rate determined by the jump frequency of the vacancy, the slower moving defect. 10-11 1 10 102 103 104 PO2 (relative units) Diffusion Example 5: CuO1-x FIGURE 11.14 Diffusion coefficients varying with pO2. CuO is an example of a group of oxygen-deficient oxides, MO1−x, where the nonstoichiometry is accommodated by oxygen vacancies. We write the equilibrium equation in  n = 3.1 at 1000°C the usual way.  n = 3.3 at 1200°C  n = 3.6 at 1350°C 1 O0 → O2 (g) + VOii + 2e′ (11.48) 2 We expected D Co to be proportional to pO1/62 . This means that as we increase pO2, the value of D Co increases faster We can determine the equilibrium constant and relate this with vacancy concentration than we had predicted. The to the Gibbs free energy ΔG. reason is that the defects are charged and that there is an association of defects (see the discussion of KCl above). 1/3 ΔGO ⎞ [VOii ] ≅ ⎛⎜ ⎞⎟ ( pO2 )−1/6 exp ⎛⎜ − 1 We must consider two possibilities. A single cation vacancy ⎟ (11.49) ⎝4⎠ ⎝ 3kT ⎠ might form a complex with one hole or with two holes. In the first case we write ΔG* ⎞ DO = γλ 2 ν[VOii ]exp ⎛⎜ − ⎟ (11.50) ⎝ kT ⎠ 1 O*2 = [ h i ] + [(VCo ′′ h i )] + O0 (11.44) ΔGO ⎞ exp ⎛ − ΔG* ⎞ 1/3 DO = γλ 2 ν ⎛⎜ ⎞⎟ ( pO2 )−1/6 exp ⎛⎜ − 2 1 ⎟ ⎜ ⎟ ⎝4⎠ ⎝ 3kT ⎠ ⎝ kT ⎠ [ h i ][ VCo ′′ h i ] 1/2 = K1 (11.45) (11.51) pO 2 [h•] = [(V″Coh•)] (11.46) If you increase the pO2, then the diffusion coefficient will decrease. This is found for a very wide temperature so that [(V″Coh•)] is proportional to pO1/4 2 and n is 4. range and implies that diffusion is a complex process. It If two holes are involved in the complex, then is interesting to compare this case to that of ZnO. Both cations exist in the 2+ or 1+ charge state, but the crystal [(h•V″Coh•)] ∝ pO1/2 2 (11.47) structures and point defect chemistry are very different. 196 ................................................................................................................... Point Defects, Charge, and Diffusion 11.14 MOVEMENT OF DEFECTS these interfaces is much faster than in the bulk. There may also be an excess charge of one sign at the grain boundary We often think that only cations move in ionic materials plane, which must be compensated in the bulk (the space- because so much work has been carried out on oxides or charge region) and will again affect the diffusion of halides where the anion is much larger than the cation, for charged point defects. example, MgO, Al2O3, and NaCl. Ceramics that are being used for electronic applications often contain heavier (hence larger) cations so that the assumption is not neces- 11.15 DIFFUSION AND IONIC sarily valid. In solid-oxide fuel cells, it is the oxygen ion CONDUCTIVITY that diffuses. Most perfect ceramic crystals have more unoccupied Some ceramics are important because they are ionic con- volume than there is in metals, so they tend to be less ductors. The band gap energy, Eg, of these materials is dense. There is thus more open volume through which large (typically > 5 eV) and the only mechanism for con- point defects can move. duction of charge is by the movement of ions. In some Covalent bonds are directional in character and must cases the rate of movement of the ions is very rapid and be “broken” as defects move. We will see that dislocations large conductivities are possible. In this section we will in Si do not move easily at room temperature so the mate- mention one application of ionic conductivity; we will rial does not easily deform plastically and is brittle at this consider more examples and details in Chapter 30. The temperature. This simple fact has many consequences for ionic conductivity, σ, is the electronics industry. Where would silicon technology be if dislocations moved readily under an applied stress? σ = ∑ qi N μi (11.52) i The same consideration applies to point defects except that interstitials in Si do not need to break bonds! Here, qi is the effective ionic charge, μi is the mobility, The charge can affect the concentration of point and N is the number of mobile defects. defects. FeO contains at Mobile defects contrib- least 5% vacancies on the uting to ionic conductivity cation sublattice so the CORROSION include Schottky defects. formula should be written Diffusion of oxygen in oxidation scales occurs along Figure 11.15 shows the as Fe1−δ O [or better grain boundaries. Corrosion of metals is controlled by example of Na + motion in Fe(II)1−2δFe(III) δO]. The formation and diffusion of point defects in the ceramic. NaCl. Two different routes superconductor YBCO Corrosion of polycrystalline ceramics also occurs most are shown for how the Na + must be off stoichiometric quickly along grain boundaries. ion might reach the vacant to optimize its supercon- site. The direct route, ducting properties (YBa2Cu3O7−δ or YBa2Cu3O6+x). although shorter, is unlikely because the two Cl− ions will The movement of grain boundaries is very important be very close together (“touching”) creating a large energy in ceramics because of the method of processing and their barrier for the migrating Na + ion to overcome. Route 2 is high-temperature applications. However, the properties of more likely. The Na + ion first passes through the face of grain boundaries are very different from the bulk material the octahedron, then into the vacant tetrahedral site and they may contain a second phase. Grain boundaries between the octahedra, then through the face of the oppo- in ceramics are not as dense as in metals because the site octahedron and into the vacant site. We cannot prove bonding is different (remember the open space in Si and that this is what happens, but we expect the ion to follow Al2O3) so diffusion of point defects along, and across, the lowest energy pathway, which looks like route 2. 12 3 4 FIGURE 11.15 A probable diffusion X- M+ V mechanism in NaCl. M+ 11.1 5 D i f f u s i o n a n d I o n i c C o n d u c t i v i t y ............................................................................................................... 197   Diffusion may occur along grain boundaries and dis- locations (these are more rapid paths than bulk diffusion). 101  Electronic contributions to σ are low (this is the case σ T (S m-1) in wide band gap materials at low T). For a simple vacancy transport mechanism both σT and D would obey Arrhenius relationships 100 σT = A exp(−Q/kT) (11.54) D = D 0 exp(−Q/kT) (11.55) A and D 0 are temperature-independent constants and Q is the activation energy. 10-1 Figure 11.16 shows the variation in σT with T for a relatively pure sample of NaCl. As you can see, the rela- tionship is complicated. The activation energy Q consists of two components, one due to the creation of the defect and one due to its motion, and these may have different 10-2 temperature behaviors. For NaCl at temperatures above 550°C there is good correlation between D and σ. Below 550°C the trend is similar, i.e., there is the same change in slope, but the D values are greater than σ because of the presence of impurities. We can summarize some important characteristics of the plot. 10-3 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7  Stage I′—Anion disorder 103/T (K-1)  Stage I—Intrinsic conductivity; cation migration FIGURE 11.16 Ionic conductivity of NaCl varying with T −1. dominates  Knee region—where the slope changes: separates the If ionic conductivity and diffusion occur by the same intrinsic dominated region from the impurity region mechanism then μ and σ are related to D by the  Stage II—Extrinsic conductivity dominated by cation Nernst–Einstein equations vacancies  Stage III—Vacancy-impurity association σ = ⎛⎜ Nq ⎞ 2 μ = ⎛⎜ ⎞D q ⎟ ⎟D (11.53) An application that makes use of ionic conductivity is ⎝ kT ⎠ ⎝ kT ⎠ the ZrO2 oxygen sensor illustrated in Figure 11.17. These sensors are used, for example, to measure the pO2 in In using Eq. 11.53 we have to be aware of the following automobile exhaust gases or in the gases present in the points: carburizing process used to harden steel components. Polycrystalline CZ (stabilized with either Ca2+ or Y3+ sub-  Some defects may contribute to D but not to σ (paired stituting for Zr4+) is the electrolyte. At the operating tem- cation and anion vacancies in the alkali halides, for perature of the sensor (∼900°C), CZ is a good oxygen example). ion conductor. The substitution for Zr4+ results in the Exhaust Gas Outer electrode Zirconia thimble Reference air Ceramic heater Inner electrode - Spinel + (B) Metal shield Exhaust Gas FIGURE 11.17 Schematic of a ZrO2-based oxygen sensor (A) and an actual sensor unit. 198 ................................................................................................................... Point Defects, Charge, and Diffusion formation of oxygen vacancies and these lead to high ion TABLE 11.8 Comparison of Calculated and Observed mobilities on the oxygen sublattice. Solid-oxide fuel cells Defect Formation Energies in Ionic Crystals use the same electrolyte or another with the same struc- Calculated Experimental ture and work on a similar principle. Compound Defect energy (eV) energy (eV) NaCl Schottky pair 2.32 2.30 CaF2 Frenkel pair 2.75 2.7 11.16 COMPUTING MgO Schottky pair 7.5 5.7 ZnO Cation Frenkel pair 2.51 — Computer modeling is becoming a more widespread AgCl Cation Frenkel pair 1.4 1.45 method of studying point defects because computers are now capable of addressing large numbers of atoms. In ceramics, although the structural aspects of point defects may be short-range, interactions tend to be long-range This modeling approach is discussed in more detail later. because of Coulombic forces. Atomistic simulation calcu- The size of the modeled crystal must be considered and lations usually require several steps, and the actual energy its other physical properties modeled. Modeling the poten- may depend on how the structure is able to relax around tial is already much more difficult when the material is a the defect. compound rather than an elemental solid and we add charge. The choice of the starting model is important since  Choice of a modeling approach calculations may suggest structures that are metastable but  Choice of an interatomic potential describing the atoms are not the lowest-energy configuration. Table 11.8 com- or ions pares calculated values and experimental values of defect  A starting model for the point defect or defect cluster formation energies for which the agreement is good. CHAPTER SUMMARY This chapter is one of the most basic in ceramics and for the student, the easiest to learn. You need to know the different types of point defects and their names, the thermodynamic princi- ples leading to the calculation of point defect concentrations, and how point defects make dif- fusion possible. The next level of complexity concerns how point defects interact with one another. We touch on much of this in the examples of real materials where we bring in the fact that the point defects are often (usually) charged. The importance of the topic is that point defects not only affect the properties of materials but, in many cases, determine and control the properties that interest us. An interesting question is how does this discussion change for nanoceramics—are point defects in nanoceramics important? The initial answer is that the surface (a two-dimensional defect) dominates everything when the particle is small, but one point defect in a nanoparticle can be a very high concentration! PEOPLE IN HISTORY Boltzmann, Ludwig (1844–1906) lived in Vienna and eventually committed suicide supposedly because his theory was ridiculed by some colleagues. He died before his theories were experimentally proven correct. Fick, Adolf Eugen (1829–1901) is best known for his laws, which he first applied in 1855. He was actually also a physiologist and developed a technique for measuring cardiac output, but also was one of the first to experiment with contact lenses in 1887. Frenkel, Jacov Il’ich was born 10 February 1894 in Rostov-on-Don, Russia and died 23 January 1952 in Leningrad, Russia. He worked on dislocations, twinning, and much more. Kröger, Ferdinand Anna born Amsterdam (1915–2006) was the lead author on the paper that gave the Kröger–Vink notation. He retired as Professor from USC in ∼1990. Schottky, Walter was born July 23, 1886 in Zürich and died March 4, 1976 in Pretzfeld, Germany. He worked under Max Planck in Berlin. He discovered both the electron hole and the Schottky defect. Wedgwood, Thomas (son of the famous potter) and Davy, Sir Humphrey, in 1802, reported in a communica- tion to the Royal Institution in London a photographic process using AgCl to record an image. GENERAL REFERENCES Hayes, W. and Stoneham, A.M. (1985) Defects and Defect Processes in Nonmetallic Solids, John Wiley & Sons, New York. Chapter 3 (pp.106–168). Very nice but more advanced than our treatment. C h a p t e r S u m m a ry .......................................................................................................................................................... 199  Kröger, F.A. (1964) The Chemistry of Imperfect Crystals, North-Holland, Amsterdam. Kröger, F.A. and Vink, H.J. (1956) “Relations between the concentrations of imperfections in crystalline solids,” Solid State Phys. 3, 307. The original proposal of the notation that is now universally used to describe charged point defects. This is an invaluable paper when you have time to study it. The official notation is given in the IUPAC Red Book on the Nomenclature of Inorganic Chemistry, Chapter I-6. Smyth, D.M. The Defect Chemistry of Metal Oxides, Oxford University Press, Oxford 2000. Clear and at the right level. Swalin, R.A. (1972) Thermodynamics of Solids, 2nd edition, John Wiley & Sons, New York. Chapter 11. Tilley, R.J.D. (1987) Defect Crystal Chemistry and Its Applications, Blackie, Glasgow. Chapter 1. A very readable text. Wagner, C. and Schottky, W. (1929) Thermodynamik, Springer, Berlin. The book by the masters—not often read. Wagner, C. and Schottky, W. (1930) “Theory of regular mixed phases,” Z. Phys. Chem. B11, 163. An original paper. WWW MARVIN was originally authored by David H. Gay and Andrew L. Rohl. The program is “an advanced computer code for performing static and dynamic modeling of surfaces and interfaces.” http://www.ri.ac. uk/DFRL/research_pages/resources/MARVIN_data/main.html EXERCISES 11.1 What, if any, is the difference between a Schottky defect in Mg and a Schottky defect in MgO? 11.2 Would you expect Frenkel defects to be more likely in Al or Al 2O3? What factors do we need to consider in answering this question? 11.3 How might you expect Si to diffuse in an alumina furnace tube at high temperatures? Would the mechanism be different if the alumina were in the form of a single crystal? 11.4 We form a Schottky defect in KCl. What is the difference in energy of the system if the two vacancies are 5.5a apart or 3.5a apart (a being the lattice parameter). Why do we choose 3.5 rather than 3, etc.? Discuss. 11.5 We dissolve (add) 100 ppm of Al2O3 to a cube of MgO (1 mm on the side). How many vacancies are formed and how much bigger is the cube? 11.6 Construct a table of defects and discuss the different types of point defects in Fe2O3. Compare this table with the table you produce for Fe3O4. 11.7 Write down a point defect reaction for ZnO in which you produce twice as many singly charged defects as doubly charged ones. 11.8 Write a balanced defect reaction equation using Kröger–Vink notation for substitution of Ca2+ in CaF2 by Y3+ . 11.9 During the movement of the Na + ion in Figure 11.15, how does the CN of the Na + ion change as it moves through route 2. 11.10 Express using Kröger–Vink notation the formation of Frenkel defects in AgBr and explain why you think these are more numerous than Schottky defects. How might you increase the concentration of Schottky defects in AgBr? 200 ................................................................................................................... Point Defects, Charge, and Diffusion  12 Are Dislocations Unimportant? CHAPTER PREVIEW We will begin our discussion with a reminder of the basic properties of single dislocations and conclude by considering combinations of dislocations, which will lead nicely into the next three chapters, which consider different types of interfaces. Most students understand dislocations best by thinking about schematic diagrams and high- resolution transmission electron microscopy (TEM) images. Dislocations are line defects, but like all crystal defects, they are actually volume defects; i.e., we should think of them as tubes, or pipes, whose properties change across the tube radius and that generally do not have cylin- drical symmetry. We are not trying to cover everything about dislocations here; rather we will review the basic features of dislocations and then introduce the complexities of ceramics. Remember the important experimental observation that led to the “invention” of dislocations: the stress required to deform a metal single crystal is at least 103 times smaller than the theoretical value. Two vectors define the fundamental properties of any dislocation:  The line direction  The Burgers vector The glide plane of the dislocation is the plane that contains both vectors. To summarize: Geometry Burgers vector and line direction define the glide plane. Displacement When a dislocation is present, atoms are displaced from their positions in the perfect crystal; the material is strained so there must be a stress. Movement Dislocations move and interact (they even intersect). Reacting We generate dislocations, they multiply and combine (by intersecting). Why consider dislocations in ceramics? Conventional wisdom says that dislocations are not nearly as important in the mechanical deformation of ceramics as they are for metals. The reason is that dislocations in ceramics do not move as easily as those in metals and they are usually not as numerous. So we should be asking why the last sentence is true. Dislocations in ceramics are extremely important because of what they do not do: they do not glide easily. Si devices would not work for long and ceramics, in general, would not be brittle if dislocations could glide easily. Understanding dislocations also helps us understand other more complex defects, how they interact with point defects, and how they can cause planar defects. Disloca- tions become very important when we use thin crystalline ceramic films, particularly when grown on crystalline substrates. What is special about dislocations in ceramics?  Complex and large unit cells are the norm rather than the exception.  Charge—if you insert an extra half plane to make an edge dislocation, you must consider the charge.  Directional bonds—if you break a bond, does it reform? For the student, dislocations are a great test of whether the structure of a crystal is understood. They give a fine probe of what is happening in the material. Be aware though that much of C h a p t e r P r e v i e w ........................................................................................................................................................... 201  our understanding of dislocations comes from metallurgy, particularly from studies on Cu alloys. We often compare our dislocations to these, since those in metals are quite well under- stood, but ceramics do introduce new complications. A detailed understanding of dislocations and planar defects in ceramics is not as advanced as that of point defects. 12.1 A QUICK REVIEW OF 12.1a. The Burgers vector is perpendicular to the dis- DISLOCATIONS location line, u. The Burgers vector will be opposite if the extra half plane is below the glide plane. Line defects in a crystalline material are known as dislo-  Screw dislocation: Successive atomic planes are con- cations (unless they are disclinations, which will be nected to form the surface of a helix (or screw) around ignored because they are much more difficult and not the dislocation line as shown in Figure 12.2 where the nearly as important in ceramics). In contrast to point dislocation is perpendicular to the planes: like the core defects, dislocations never exist in thermodynamic equi- of a spiral, parking ramp. The Burgers vector is paral- librium because they have formation energies of ∼1 eV (or lel to the dislocation line and can point up or down for more) per atom along the line and there is no significant a left- or right-handed screw. balancing entropy contribution as there is for point defects.  Glide plane: This is the plane containing both the dis- They are almost always present in crystals because of how location line and the Burgers vector. the crystal grew or because it was deformed. Therefore dislocations usually form due to nonequilibrium condi- tions, such as thermal and mechanical processing, or for thin films and single crystals, during growth. There are two special types of dislocation. 1 2  Edge dislocations  Screw dislocations All other dislocations are referred to as “mixed.” Defining the Burgers Vector and the Glide Plane The Burgers vector is defined by constructing a closed S circuit around the dislocation line. We first draw a circuit around the dislocation in a clockwise (right-handed screw) F 3 direction from the start (S) to the finish (F) as shown in Figure 12.1a. We then transfer this circuit to a perfect crystal as shown in Figure 12.1b. If there is a dislocation, this second loop will not close on itself. We then define 1 2 the vector FS, which is required to close the loop in the perfect crystal, as the Burgers vector. This method of defining the Burgers vector, b, is known as the FS/RH perfect-crystal convention. (The vector is named after J.M. Burgers so there is no apostrophe.) The Burgers vector is then defined with respect to the perfect crystal; you would not want to define it in the imperfect crystal! It is important that you are consistent in using this convention. Some other texts, and even some of the classic papers, use a convention that produces the opposite S sign for the Burgers vector. For example, they might use an anticlockwise circuit, set b = SF, or draw the circuit in F t2 b the perfect crystal first. You must use a convention consistently. t1  Edge dislocation: An extra half-plane of atoms is FIGURE 12.1 The Burgers circuit in the imperfect and perfect inserted above the glide plane as illustrated in Figure lattices for an edge dislocation in a simple-cubic crystal. 202 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ?  Circuit B u2 b2 u3 b3 0 Circuit A u1 b1 FIGURE 12.3 Diagram used for proving Frank’s rule for conserva- FIGURE 12.2 Schematic of a screw dislocation. tion of b. The glide plane is not SIGN OF b same, i.e., b1. It is more usually an actual plane of The sign of the dislocation is important: it determines usual to define the Burgers atoms, rather it is a plane the direction of motion when you apply a stress. circuits by making a clock- between two planes of wise circuit around each atoms. (Where actually is  Edge: b points to the left or right: this determines dislocation line looking out- the dislocation line?) Dis- whether the extra half-plane is above or below the ward from the nodal point. locations are often more glide plane. This reverses the line sense complicated than sug-  Screw: b is parallel or antiparallel to u: this deter- (and hence the Burgers gested by the two simple mines whether the spiral goes up or down (clockwise vector of dislocation 1 examples above, but they or anticlockwise). becomes −b1) on the left- can always be resolved hand side, and then Eq. into a combination of edge 12.1 becomes and screw components. Dislocation lines can end at the surface of a crystal Σbi = −b1 + b2 + b3 = 0 (12.2) and at grain boundaries, but never inside a crystal lattice. Thus, dislocations must either form closed loops or branch Elasticity into other dislocations. The meeting of three or more dis- locations at a point, or node, is a necessary condition We usually assume that elasticity (how stress is related to indicating that the Burgers vector is conserved. Consider strain) is linear. The assumption is that strains are small the dislocation b1 in Figure 12.3, which branches into two so that stresses are linearly related to strains (Hooke’s dislocations with Burgers law). We then think of the crystal as a continuum (a struc- vectors b2 and b3. A Burgers tureless “sponge”) with circuit has been drawn R FOR A SCREW DISLOCATION two independent elastic around each dislocation The displacement of any point on this surface from its constants (for example, μ, according to the line sense, “perfect-crystal position” is given by the shear modulus, and ν u, indicated, and it follows Poisson’s ratio At the core from the diagram that b is bφ of the dislocation, the R= strains are too large for conserved. 2π this assumption to be valid b1 = b2 + b3 (12.1) (φ is a fraction of 2π). The strain in the complete so we exclude this region from our calculation and unwrapped surface is then The large circuit on the replace it by a fudge factor right-hand side of Figure involving ro, the core b 12.3 encloses two disloca- γ= radius (not ideal because it tions, but since it passes 2πr assumes nothing varies through the same good across the core and we do material as the b1 circuit The shear stress due to the screw dislocation is then not know what ro is). One on the left-hand side the consequence of linear Burgers vector must be the τ = μγ elasticity is that when 1 2 .1 A Q u i c k R e v i e w o f D i s l o c at i o n s .................................................................................................................... 203 Burgers vectors are sepa- STRESSES FOR AN EDGE DISLOCATION will exert a force on any rated into screw and edge The stresses are referred to xyz corrdinates for a disloca- other neighboring disloca- components, the stresses tion parallel to z. This dislocation does not have cylin- tion. The force is given by due to these separate drial symmetry. components can be treated F = σb (12.3) individually and then μb x2 (3 x + x ) 2 2 added to give the total σ11 = − 1 2 Box 12.1 If we were being rigorous stress. 2 π(1 − ν) ( x12 + x ) 2 2 2 we would express the force We do not usually think as bσ since b is a vector of ceramics as being elastic μb x2 ( x12 − x22 ) and σ is a tensor. but do not confuse local σ 22 = Box 12.2 stresses with macroscopic 2 π(1 − ν) ( x12 + x22 )2 F = (b · σ) × u (12.4) behavior. Macroscopically the ceramic may be brittle, σ33 = ν(σ11 + σ22) Box 12.3  The term b · σ repre- but if the atoms move sents a force per unit slightly off their perfect- μb x1 ( x12 − x22 ) length, F, which acts in crystal sites because of an σ12 = Box 12.4 a direction that is nor- applied force, that is an 2π(1 − ν) ( x12 + x22 )2 mal to b. elastic deformation. We can also have anisotropic THE STRAIN ENERGY An important result of elasticity (which becomes For a screw dislocation applying Eq. 12.4 is that important for noncubic the force acting on disloca- ceramics) and nonlinear 2 tion 1 due to the stress field 1 ⎛ b ⎞ elasticity, but usually ap- dE = μ l 2πrdr of dislocation 2 depends on proximate to the simple 2 ⎝ 2πr ⎠ b1 · b2: if b1 · b2 is positive, case. then the dislocations repel μ b2 dr one another; if it is nega- dE = l Displacement Fields 4π r tive, then the interaction is attractive (but be careful We usually derive the dis- about the line direction). R μ b2 R placement field of a screw E = ∫ dE = ln dislocation because it is r 4π r0 0 Dislocation Strain much easier than deriving For an edge dislocation this equation becomes Energy the edge dislocation. The screw dislocation Since a dislocation creates is formed from a cylinder R μ b2 R a strain field, which in turn E = ∫ dE = ln of crystal by making a cut r 4 π (1 − ν) r0 0 creates a stress field, each along the cylinder and dis- placing one side relative to the other by a vector b where b is the same value every- b where on the cut and is parallel to the axis of the cylinder; we first have to cut out a cylinder at the core so as to make this process physically possible. We take the screw dislo- cation in Figure 12.4 and “unwrap” the surface at a dis- tance r away from the dislocation core; remember that b is parallel to the dislocation line so it does not matter where we start the unwrapping process. We then calculate b θ 2πr the strain, γ, in the unwrapped surface and then calculate γ the shear stress due to the screw dislocation. As you move r z away from the center of the cylinder, the strain decreases −1 as r and, as noted earlier, when r becomes very small (∼r 0), the assumptions of elasticity break down, so this relationship does not hold in the core region. Remember μ depends on the interatomic bonding and b depends on the crystal lattice. For the edge dislocation, we will just quote the result FIGURE 12.4 Deducing strain by “unwrapping” a screw for the stress field (Eqs. Box 12.1–12.4). This stress field dislocation. 204 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ? dislocation will have an FREE ENERGY OF A DISLOCATION We normally just take the associated strain energy. In Chapter 11 we showed how ΔG could be determined constant α to be between This strain energy is termed for the formation of point defects in a crystal using 0.5 and 1.0. This result the self-energy of the dis- provides a criterion for location. We can then deter- ΔG = ΔE − TΔS what dislocations can be mine the strain energy per formed in a given crystal. unit volume by integrating ΔS was obtained using statistical mechanics methods. Those with the smallest over the volume affected What are the contributions to the entropy of a disloca- allowed Burgers vector by the strain field (i.e., by tion? There are three. have the lowest strain determining the area under energy and, consequently, the triangle in the stress  Positional entropy—similar to the configurational are the most likely to form. versus strain plot shown in entropy we described for point defects. (This will be very impor- Figure 12.5). For the screw  Entropy due to vibration of the dislocation line about tant for a ceramic with a dislocation, l2πrdr is an its equilibrium position. large unit cell; e.g., YAG.) element of volume at radius  Changes in the vibrational entropy of the surround- The crystal determines r around a length l of the ing lattice because of the large strains near the dis- the actual value of b. If b dislocation. location core. is a perfect lattice vector, At the center of a dislo- then the structure of the cation the crystal is highly The total entropy contribution is only ∼0.5 eV/atom. crystal will not be changed strained with atoms dis- Less than E, but not negligible. by the passage of a disloca- placed from their normal tion. If b is not a lattice sites and we cannot use vector, then a planar defect linear elasticity so we (a stacking fault) will be again exclude this region DISSOCIATION present on one side of the from the calculation by dislocation and a second making the inner limit r 0. b → b1 + b2 + b3 + · · · · b10 so-called partial (or imper- There must be a contribu- b → b1 + b 2 + b 3 + · · · · + b 10 2 2 2 2 2 fect) dislocation will be tion to the self-energy of required to remove the the dislocation from this For dissociation into two Shockley partial dislocations stacking fault. core, but we need atomis- The important point is tic modeling to estimate a a a that the elastic energy the value; it is usually b = [110] → [121] + [21 1 ] = bP + bP depends on three factors: 1 2 2 6 6 assumed to be about 10% of the total strain energy of  An elastic constant, μ, the dislocation. As before, we just quote the result for the because the energy of the dislocation depends on the edge dislocation. The only difference compared to the stress and strain that it causes in the lattice, and ν if screw dislocation is the 1 − ν factor. We can express there is an edge component. the energy of a mixed dislocation as  The radii, R and r (and r ), because the total energy of 0 the dislocation depends on the volume of crystal it μ b2 ⎛ sin 2θ ⎞ R effects. E= ⎜⎝ + cos2θ⎟ ln (12.5) 4π 1 − ν ⎠ r0  The Burgers vector, b, because this determines the magnitude of the strain. The important result is that the strain energy of a disloca- tion is proportional to the square of the Burgers vector b We will assume linear isotropic elasticity throughout this and the shear modulus of the material. discussion. E = αμb2 (12.6) Compact Core versus Spread Core If a dislocation dissociates into partial dislocations, the self-energy will be reduced providing the angle between σ the Burgers vectors is acute (they are parallel not antipar- allel). As a simple demonstration, consider the possibility 1 that 10 partial dislocations each with Burgers vector b/10 2 σε are formed. The strain energy is reduced by a factor of ε 10! Once formed, these dislocations will repel one another FIGURE 12.5 Elastic energy of a screw dislocation from a plot of since they have parallel Burgers vectors. However, since stress versus strain. the Burgers vectors of these partial dislocations are not 1 2 .1 A Q u i c k R e v i e w o f D i s l o c at i o n s .................................................................................................................... 205 lattice vectors, a planar defect is created between each pair sider the force balance. The two partial dislocations will of partial dislocations. If the energy required to form these try to repel each other (bP · bP > 0), but they cannot sepa- 1 2 planar defects is greater than the reduction in the strain rate too much because of the SF. Although we have energy, then the dissociation will not occur. The best- deduced this dissociation for fcc metals using an energy known example of dislocation dissociation is found in argument, it is also important for the behavior of the dis- face-centered cubic (fcc) metals. The dissociation pro- locations. In fcc metals, these partial dislocations allow duces two so-called Shockley partial dislocations, which the atoms to move over “valleys” instead of over “hills” do not have parallel Burgers vectors. as the dislocation glides, and they restrict glide to the In an fcc crystal, the special feature of this dislocation plane of the stacking fault. In Cu and Si, dislocations are dissociation is that the planar defect formed between the widely (Δ ∼ 4 nm) dissociated, but the same dislocation in two partial dislocations can be regarded as a mistake in Al has a rather narrow core. the stacking of the close-packed layers as shown in Figure If the dislocation changes its line direction for a short 12.6. The term stacking fault is then applied to all such segment, this segment is called a kink if it lies in the glide planar defects and the energy per unit area is the stack- plane or a jog if it causes the dislocation to step out of its ing-fault energy (SFE or γ, but do not confuse this γ with glide plane. strain). Of course, for the general concept, the planes do In general, a dislocation will itself contain many such not need to be close-packed planes; you can stack any defects along its length. planes incorrectly! When calculating the SFE, we do not equate the SFE to the energy required to create the fault; instead we con- 12.2 SUMMARY OF DISLOCATION PROPERTIES We have not reviewed all the properties of dislocations, but have concentrated on those you should know when considering dislocations in ceramics.  Dislocations cannot end inside the crystal lattice.  We almost always assume that strains are so small that linear elasticity is a good approximation; so, Hooke’s law holds.  The displacement field for any dislocation falls off as r −1 as we move away from the dislocation.  The strain energy (or self energy) of a dislocation actu- ally depends on the character of the dislocation, but setting E = αGb2 is a good estimate, where α is ∼0.5.  Parallel dislocations repel one another if the angle between their Burgers vector is less than 90°. (Be (A) careful with u.)  A dislocation can always lower its strain energy by spreading its core or dissociating. Whether this will lower the total energy depends on the energy required to form the distorted region between the “partial dis- locations.” If dissociation occurs (forming identifiable partial dislocations) then this region is called a stack- ing fault.  Dislocations glide by the movement of kinks and climb by the movement of jogs. Since climb requires chang- ing the number of point defects (reacting or absorbing them), we call it nonconservative motion. 12.3 OBSERVATION OF DISLOCATIONS (B) We can divide the techniques used to “see” dislocations FIGURE 12.6 The intrinsic stacking fault in an fcc crystal. into two categories: 206 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ? 1. Direct 2. Indirect Direct techniques allow us to see the arrangement of atoms around the dislocation. The most useful direct technique is high-resolution transmission electron micro- scopy (HRTEM). The resolution of commercial instru- ments allows direct observation of columns of atoms and edge dislocations can be identified as terminating planes of atoms as shown in Figure 12.7. These images look very much like the schematics we draw to illustrate FIGURE 12.8 Diffraction contrast from dislocations in Al2O3. edge dislocations, and the Burgers vectors can be deter- mined directly from the image using the Burgers circuit construction (unless there is a screw component present). Indirect techniques rely on the fact that dislocations the questions that arise about the nature of dislocations in create a strain field and are regions of high energy. The a material. most widely used of the indirect methods is again TEM. We will show you several examples of TEM images of  Is the dislocation interacting with other dislocations, dislocations in ceramics in later parts of this chapter. or with other lattice defects? Figure 12.8 shows how planes near a dislocation may be  Is the dislocation jogged, kinked, or straight? bent into an orientation where they are strongly diffracting  What is the density of dislocations in the sample? even when the rest of the crystal is not. The intensity of  Has the dislocation adopted some special configura- the direct beam will be reduced (and that of the diffracted tion, such as a helix? beam increased) and the dislocation will appear as a dark line in the bright-field image. Images of dislocations are By tilting our specimen in the TEM to a condition in often quite difficult to interpret and the position of the which the dislocations are invisible (or at least appear faint dislocation in the TEM image will generally not corre- in the image), if we know the diffracting conditions (spe- spond exactly to its actual position in the crystal. However, cifically the diffraction vector g), then we can obtain b this approach is extremely useful in answering many of using the invisibility criterion (generally needing three independent g vectors). g·b = 0 (12.7) Another indirect (but lower resolution) approach is the etch-pit method. In this technique the surface of the sample is polished and immersed in a suitable chemical etchant. The rate of removal of material around the dislocation (where the crystal is strained) is usually more rapid than in the surrounding crystal and pits are formed where the dislocation line intersects the surface. The clearest dem- onstration that etch pits are associated with dislocations is shown for Si in Figure 12.9a where the dislocations can be seen in cross section due to absorption of IR illumina- tion by the Cu decorating the dislocation; today, this task might be more easily accomplished using a focused ion- beam (FIB) instrument. Figure 12.9b shows a plan-view image of etch pits in a single crystal of Nd-doped YAG. The etch pits were revealed by immersing the polished crystal in concentrated phosphoric acid at 250°C for 8 minutes. The etch pit method is usually best when disloca- tion densities are low (<104 mm−2). If the dislocation densities are too high the etch pits overlap each other and it is very difficult to resolve their shape and count FIGURE 12.7 HRTEM of the core of a dislocation in Al2O3. densities. 1 2 . 3 O b s e rvat i o n o f D i s l o c at i o n s ........................................................................................................................... 207  Perhaps the more important question is: why learn about dislocations in ceramics when ceramics do not deform plastically as easily as metals? This question then leads us to question why this statement is true. Is it always true? Can we change anything? Modern materials often involve interfaces. Interfaces are directly related to dislocations. The growth of thin films often involves dislocations. Dis- locations also play an important role in radiation damage of ceramics. So there are many reasons for understanding dislocations in ceramics. (A) 12.5 STRUCTURE OF THE CORE Not much is really known about the core of dislocations in ceramics. For the examples we will show, you should remember that we have usually chosen one Burgers vector (usually the most important one), one line direction, and thus one glide plane. Furthermore, we usually draw the edge dislocation because it is easiest to draw, not because it is the most important. In this section, we will assume that the dislocation core is compact. The examples are chosen to illustrate particular features.  NaCl: it is relatively simple and illustrates the effect of charge.  Si: it illustrates the effect of directional (covalent) bonding.  Al2O3 and olivine: they are noncubic materials. Although NaCl and MgO structures are both based on the cubic-F Bravais lattice, like Cu, there is no evidence for any dislocation dissociation. There are detailed atom- (B) istic calculations that confirm that the compact core is FIGURE 12.9 Etch pits at dislocations emerging at a surface in Si. preferred. A schematic diagram of such a dislocation (a) The cross-sectional view in Si; (b) the plan view in YAG. viewed along the [001] direction is shown in Figure 12.10. All the ions seen here lie in the same (001) plane. If we remove this plane of atoms the structure looks the same, 12.4 DISLOCATIONS IN CERAMICS but all the ions are reversed in sign. So charge is balanced as long as there are no jogs or kinks on the dislocation. In discussing dislocations in ceramic materials, the prin- The glide plane for dislocations in NaCl and MgO is ciple is always the same. We deduce the possible Burgers {110} rather than the {111} you might expect for fcc. You vectors first, then the glide planes. We will begin by asking may read that the glide plane is {110} because this plane if there is anything special about dislocations in ceramics; is electrically neutral and motion on this plane avoids we can preempt the answer by saying yes, as usual, the charged layers gliding over one another. However, ErAs, bonding and charge can add their own effects. The second an exotic semimetal (no ionic charge), with the NaCl best-known special feature of dislocations in ceramics is structure, has the same glide system. PbS, a semiconduc- actually that the unit cell of such materials is usually tor with this structure, shows glide occurring on {001} larger than for the simple metals, so we will see similari- planes and in TiC dislocations glide occurs on {111} ties to other materials such as the intermetallics that also planes. The real reason for the {110} glide plane is still have large unit cells. being studied. The suspicion is that the core actually does The structure of the dislocation core in ceramics spread on different planes, but that still does not tell us depends on three factors why the spreading depends on the material. The simplest covalently bonded ceramics are Si and 1. Charge of the ions Ge. The covalent bond formed by two atoms sharing elec- 2. Size of ions trons is a localized and directional bond. Cubic ZnS has 3. Presence of directional bonds the same structure, but the Si–Si basis is replaced by Zn– 208 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ?  – + A [110] – AÕ – – – – (001) + + + + + + + + + – – – – – – – – – + + + + [110] + + + + + – – – – – B – – – – – – D BÕ + + + + + + DÕ + + + + – – – – – – – + + + + + + + – – – – – C – – + CÕ + + + + + + – – – – – – – + + + qA = + 18 e qAÕ = – 18 e qB = – 18 e qBÕ = + 18 e qC = – 18 e qCÕ = + 18 e qD = – 18 e qDÕ = + 18 e FIGURE 12.10 The core of a dislocation in NaCl. S, although the bond still has a large covalent component. steps from a type I plane to a type II plane: it dissociates This feature is important in determining the characteris- on one but not on the other because the SFE is different tics of dislocations in covalent materials. Dislocations in on the two planes. The step from the shuffle plane to the these materials tend to be immobile at low temperatures. glide plane is a special jog. The dangling bonds can then Extensive slip occurs only at elevated temperatures. reconstruct; now the bonds are distorted but not dangling! Of the many covalent crystals, the diamond-cubic and However, this dislocation cannot move without rebreaking c-ZnS structures are among the simplest and most widely the reconstructed bonds so the dislocation is sessile. studied. Since the crystal lattice is fcc, perfect dislocations If we left the half-plane 1234 where it is but removed have the fcc Burgers vector –21 <110> (b2 always wins). Like the other half, we would create a dislocation with the dislocations in fcc metals, dislocations in Si, Ge, and c- opposite b, but instead of the last atom being R(S) it would ZnS glide on {111} planes. Figure 12.11a shows a (11̄0) be T(U): Zn instead of S! The core of the dislocation is projection of c-ZnS; you can recognize the {111} planes fundamentally different: it is still a shuffle dislocation. (also shown by the projected tetrahedron). We make a These two dislocations are fundamentally different dislocation by cutting out half a plane, as shown by the because the zinc blende structure does not have a center box labeled 1564. Then we merge the atom at P and Q; of symmetry. Similar considerations will hold for materi- since these are on different levels (one is a large circle and als such as AIN and GaN, which also lack a center of the other is small), the dislocation will have a component symmetry but have the wurtzite structure crystal struc- of b into the page: it is a 60° perfect dislocation. However, ture. The stacking fault in the diamond-cubic structure is we could have removed the slice of material 1234 and described as AbBbCcBbCcAaBb: the pair of planes Aa joined atoms R and S to make exactly the same b. There- behaves just as if it were one fcc plane in this case. Two fore, there are two possible {111} slip planes, type I and possible SFs are shown in Figure 12.11d. type II, and two possible dislocation cores. [These slip The thoroughly studied metals are either cubic or they planes are usually called the glide (I) and shuffle (II) have the closely related hcp structure. Many ceramic planes, which can be confusing since the dislocation can materials are neither cubic nor hcp. Olivine and sapphire glide on both!] The 60° dislocation is shown with its extra both have oxygen sublattices that can be thought of as plane ending at a type II plane. Imagine removing material distorted hexagonal close packed (hcp), but the distribu- 1234: there is then one unpaired bond per atom along the tion of cations makes them very different. dislocation core as shown in Figure 12.11b. This defect is Olivine. In the olivine group of minerals (important called a dangling bond. This type of dislocation does exist orthorhombic silicates), the energies of the [100], [010], as illustrated in Figure 12.11c. Here, the dislocation alter- and [001] dislocations are all different. In fact, the energy nates between the compact core and a dissociated struc- of the [010] dislocation will be much greater since it has ture. The explanation for this change is that the dislocation a much larger Burgers vector. 1 2 . 5 S t ru c t u r e o f t h e C o r e ...................................................................................................................................... 209  1 4 + + + B + + + a + + + A + + + c ) (111 (111) U + T + U + C + + + b 2 3 + 5 6 + + B S [112] + R S + + a R P Q Q [111] + + + A + + c (A) (B) (C) A B C A B C I A A I I B B A A (D) (E) FIGURE 12.11 Models for forming dislocations and stacking faults in sphalerite. (a) Two cuts in which to make an edge dislocation; (b) dislocation made by removing 1234; (c) two structures for a dislocation with Burgers vector b in Si; (d and e) intrinsic and extnnsic in Si. For forsterite (Mg2SiO4): a = 0.475 nm, b = 1.020 nm, and Sapphire. Al2O3 is also very anisotropic although c = 0.598 nm. we can use pseudoisotropic values of μ and ν when For fayalite (Fe2SiO4): a = 0.482 nm, b = 1.048 nm, and dislocations are confined to lie on the basal plane. The c = 0.609 nm. most common perfect dislocations do have the shortest For monticellite (CaMgSiO4): a = 0.4815 nm, b = 1.108 nm, Burgers vector –31 <112̄0> as seen in Figure 12.12, but and c = 0.637 nm. other perfect dislocations have been reported including [0001]. Even when they have the shortest b, they may The added complication is that olivine is not an iso- glide (if they do at all) on other planes such as {11̄00}. tropic material so using μ and ν (which automatically Examples of dislocations in Al2O3 are shown in Figure implies elastic isotropy) would be a simplification. 12.13. 210 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ?  is illustrated schematically and experimentally for spinel in Figure 12.15 (more on this below). The result of this 1 transfer is that one dislocation undergoes positive climb 3 [1120] while the other undergoes negative climb. 1 3 [1100] Details on Glide Dissociation Glide dissociation occurs when one of the partial disloca- tions moves on its glide plane. The classic example is Si, which, as we saw in Figure 12.11, can dissociate on a {111} just like the fcc metals. Compounds such as ZnS, SiC, and GaAs, which have a zinc blende or sphalerite structure, behave in the same way. The illustration in Figure 12.14a–c is instructive. This 60° dislocation in graphite lies on the (0001) plane and we are looking onto this plane. The FIGURE 12.12 Schematic used to show b of perfect dislocations partial dislocation on the left is pure edge while that on the in Al2O3. right is 30°. Notice that there are no broken bonds within the layers in this structure. The only broken bonds occur between the layers and these are the very weak van der 12.6 DETAILED GEOMETRY Waals bonds. For the same reason the SFE is very small, so such partial dislocations may be widely separated as As we saw in Section 12.1, dislocations would always like shown; graphite is sometimes seen to stack in the ABCABC to dissociate since this reduces the strain energy. Whether sequence instead of ABAB. The SFE is small in talc and a particular dislocation will dissociate or not thus depends MoS2 for similar reasons. Talc provides an interesting on the magnitude of the energy associated with the stack- example in which more than one type of partial dislocation ing fault. If the dislocation core spreads on the glide plane, is formed, as we can see in Figure 12.14d and e. it is glide dissociation; otherwise it is at least partly climb dissociation. Details on Climb Dissociation The glide dissociation seen in fcc metals does occur in ceramics. It is seen in III–V compounds, MoS2, graph- Climb dissociation occurs when the stacking fault does ite, and talc. (The last two are shown in Figure 12.14; more not lie parallel to the glide plane of the partial disloca- on this below.) In ceramics, since b is generally large, the tions. The phenomenon has not been seen in pure fcc energy (∝b2) can be very large. Crystals with the garnet metals, but it can occur in intermetallics. It is found in structure are body-centered cubic (bcc) and the lattice both covalent and ionic ceramics. We can make two com- parameter is ∼1 nm. We can expect core spreading to ments here: occur, but there are very few observations available. Climb dissociation need not require adding or removing point  Climb dissociation is always possible, but it may be defects to the dislocation as a whole because we can move more common in ceramics. point defects from one partial dislocation to the other, as  Climb dissociation does not necessarily refer to how the configuration was achieved. Climb dissociation may be more important in a ceramic than in an fcc metal because in fcc metals the glide plane is also the plane with by far the lowest SFE. A point to remember is that the word “dissociation” refers to the final configuration; it does not tell you that the perfect disloca- tion ever had a compact (undissociated) core. An example involves a complex oxide, spinel. The smallest Burgers vector for a perfect dislocation in spinel is –12 <110>, which is ∼0.7 nm long. Such a dislocation can dissociate according to the reaction 1 1 1 [110] → [110] + [110] (12.8) 2 4 4 This reaction reduces the total self-energy by 50%. Since FIGURE 12.13 Images of dislocations in Al2O3 from two directions. –14 [110] is a perfect lattice vector of the oxygen sublattice, 1 2 . 6 D e ta i l e d G e o m e t ry ............................................................................................................................................. 211 a c a b a b a c a b b b a a a (A) b1 σ b2 A b2 b1 b (B) C (C) FIGURE 12.14 Dislocations in ceramics with low SFE. (a–c) Dissociation in graphite; (d and e) dissociation in talc. this dissociation creates a stacking fault that exists only “stacking” situation is actually quite complex since we in the cation sublattice, so it has a low SFE. We know are stacking different layers and even when the layers are that in spinel stacking faults can form on {001}, {110}, the same they may be rotated 90°, which is important if and {111} planes. In the example shown in Figure 12.15, the layer (as is the case here) does not have 4-fold the dislocation is dissociated on a {110} plane. The symmetry. 212 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ?  A B C dA dB dC (D) (E) FIGURE 12.14 Continued b 2 b b 2 (A) (B) FIGURE 12.15 Climb dissociation of a dislocation in spinel: (a) schematic; (b) HRTEM image. 1 2 . 6 D e ta i l e d G e o m e t ry ............................................................................................................................................. 213  + – + – + – + – + – + Edge e + 4 + – + – + – + – Even – + + – + .eps + – – Surface + – (B) – + + – + + + – – – + – + – + – + – + + e – + 4 Face – + – + – Corner (A) Odd (C) FIGURE 12.16 Schematic showing local charge on defects in rocksalt. (a) A corner is always charged; (b and c) possibilities for jog on an edge dislocation. 12.7 DEFECTS ON DISLOCATIONS Even less is known experimentally about this subject for — + — + — + — ceramic materials than for metals. However, the theory + — has been developed quite extensively and shows that this + — + — + — + is one area in which ceramics are fundamentally very dif- — + — + — + — ferent from metals. + — + — + — + — + Consider a cube of NaC1 cut so that every corner is Neutral occupied by a Na + ion (Figure 12.16a). The overall extra — + — + — + — kink + charge of the cube is +e. So, each corner has an effective [101] + — + — — + — + charge of +e/8. We can extend this argument to show that there can be a charge at a jog. Consider a jog on a perfect — + — + — + — + — edge dislocation in NaC1 as shown in Figure 12.16b and + — + — + — + c. Assume that there is a charge +q on the jog. Now we — + — + — + — can add a negative ion to the jog to produce the same + — configuration, but with the charge on the terminating ion + — + — + — + reversed. The charge is now −q. Thus, we can identify q. (101) ξ b +q + (−e) = −q (12.9) — + — + — + + — + The charge associated with the original jog was q = +e/2. + — + — + — — + — Notice that you could not add a charge +e because the jog — + — + — + + — + is already positively charged. If a jogged dislocation in + — + — + — — + — NaCl glides it can transfer a charge (carry a current). The Kink with transfer of current by deformation of NaCl has been meas- — + — + — — + — + –—charge ured experimentally. You can convince yourself of some — — — — + + + + + properties of dislocations in NaCl. [101] — + — + — — + — +  Straight dislocations are not charged. + — + — + + — + —  Dislocation kinks may be neutral or charged.  The point at which an edge dislocation meets a surface — + — + — — + — + carries a charge equal to ±e/4. + — + — + + — + — (101) Figure 12.17 shows two examples of a kink on a screw ξ b dislocation. In one case, the kink is charged while in the FIGURE 12.17 Schematic of kinks on a screw dislocation showing other it is neutral. they may or may not be charged. 214 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ? 12.8 DISLOCATIONS AND DIFFUSION Since point defects exert a strain on the surrounding lattice, they will interact with dislocations. It is simplest to consider Figure 12.2a. Large impurity atoms or inter- stitials will preferentially move toward the dilated part of the core at the edge dislocation while smaller impurity atoms or vacancies will move to the compressive side of the core. Screw dislocations will show no size preference since the strain field is produced by pure shear. However, point defects also produce a local change in the elastic constants (since they change the local bonding), which does cause an interaction with screw dislocations. We might say that some point defects are “hard” while others are “soft.” The dislocation core is always a more open region of the crystal. The number of bonds will be lower or there will be preexisting broken bonds. Thus, vacancies, inter- stitials, and other point defects can move more easily in the dislocation core. This leads to the concept of disloca- tion pipe diffusion. Taking the NaCl structure again, if we condense a cation vacancy V′Na on a screw dislocation we can form a pair of kinks and a pair of jogs. Notice that all of (A) these “steps” can glide along the screw dislocation. These steps can then move apart as shown in Figure 12.18a. On this screw dislocation, kinks are neutral but the jogs each carry a charge of −e/2 (giving a total charge of −e), so this separation is encouraged by the repulsion of like charges. This process is the nucleation of the transforma- tion of a screw dislocation into a dislocation helix; exam- ples of such helices are shown in Figure 12.18b. Such a dislocation will be difficult to move. (What is the glide plane?) Dislocation pipe diffusion may be quite important in ceramics because there are generally many more point 1 2 e J Cation vacancy K 1 J e K 2 G G G i ii iii iv (A) (B) FIGURE 12.19 Dislocation loops in sapphire. defects present than found in metals. Although we have very little information on this phenomenon, loop shrink- (B) ing has been studied in Al2O3. Rows of dislocations loops FIGURE 12.18 Forming a pair of kinks and a pair of jogs and how formed by the break-up of a long loop (dipole) are shown this leads to helical dislocations in MgO. in Figure 12.19. 1 2 . 8 D i s l o c at i o n s a n d D i f f u s i o n ............................................................................................................................. 215  Movement of neutral atoms can also be enhanced Climb is nonconservative motion because vacancies along dislocation cores. For example, if there is a gra- and/or interstitials must be absorbed or emitted (their dient in the oxygen potential, oxygen might move much number is not conserved). When a jog moves, it can more rapidly along the dislocation core than through either glide or climb. The special point to remember is the lattice. Such a process would not require charge that the glide plane of a jog is not the same as the glide balance since the diffusing species is neutral; the point plane of the dislocation on which is sits. If we force a defect is simply using the enhanced distortion at the dislocation jog to move on a plane, which is not its glide dislocation core to move more easily: bonds are already plane, it must adsorb or emit point defects, but it can broken so they are easier to distort a little more, if glide. Since it is charged, it carries a current when it necessary. glides. We know that as a general rule, it is more difficult to move dislocations in ceramics than in most metals. In fact, at low temperatures it is often easier to fracture the sample 12.9 MOVEMENT OF DISLOCATIONS than it is to propagate dislocations. We must then ask the following questions : A dislocation can move in its glide plane or on another plane. In the first case the motion is glide; in the second  Why do dislocations not move more readily? case climb must be involved. We nucleate kinks and jogs  When they move, what is the chosen glide plane? in pairs, except at a surface, where we can create them  Why do they move more readily as T increases? one by one. Pairs of kinks and jogs are shown in Figure 12.20. The dislocations move as the kinks or jogs move apart. The dislocation is usually drawn as a straight line We know that dislocations in Ge move on {111} planes, because dislocations in fcc metals should lie along close- but they too can also move on {001} and {011} planes. Is packed directions (the Peierls valleys). The kinks step the the choice of glide plane due to the Peierls barrier or is it dislocation line from one valley to the next. determined by the need to break bonds? Glide of an edge dislocation occurs when a half-plane of atoms is moved over the atoms below the glide plane. The movement occurs by the nucleation and movement of 12.10 MULTIPLICATION kinks. Remember that the reason that dislocations are so OF DISLOCATIONS important in plasticity is because it is easier to move one block of material over another (shear the crystal) one half- The concentration of dislocations is conventionally defined plane of atoms at a time. Similarly, it is easier to move a as the number of dislocation lines that intersects a unit dislocation by moving a kink along it one atom at a time. area. Carefully prepared crystals may contain 102 disloca- In fcc metals, the Peierls valleys are not deep, so the tion lines per square centimeter, and some bulk crystals energy required to form a kink is small and dislocations and crystal whiskers have been prepared free, or nearly bend (create kinks) quite easily. free, of all dislocations; after plastic deformation the con- centration of dislocations increases tremendously, being as high as 1010 to 1011 dislocations per square centimeter for some heavily deformed metals. (We should not use cm−2 units so beware.) Dislocation multiplication occurs when the disloca- tions are made to move during deformation. One possible multiplication mechanism is the Frank–Read source. Suppose that a dislocation is pinned at two points, which b are a distance l apart, as shown in Figure 12.21a. Under the action of an applied stress the dislocation will bow out. (A) The radius of curvature R is related to the applied shear stress, τ0. μb τ0 = (12.10) R b Increasing the stress further causes the bowing to increase, (B) i.e., R decreases. A minimum value of R is reached that is FIGURE 12.20 Schematics of (a) a pair of kinks and (b) a pair equal to l/2 (a segment of a circle in the isotropic case). of jogs. As the stress is inversely proportional to R, this minimum 216 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ? R configuration must correspond to the maximum stress. Consequently, once the dislocation has passed the critical configuration, the half-loop will continue to expand until the two segments, X and Y, meet and annihilate each other forming a complete loop and reforming the pinned dislo- cation. The complete loop continues to expand and moves away from the source. The pinned dislocation then repeats (A) the process. Figure 12.21b is an experimental observation of such a source in Si; Figure 12.9a showed a related situ- ation in Si in which half-loops had been punched into the sample. Notice that as a screw dislocation bows, it adds small increments of edge character. The converse is true for bowing edge dislocations. The ease with which either type of dislocation moves depends on the relative ener- gies of the screw and edge components. As you can see from the equations for these energies, the screw disloca- tion always has the lower energy in an isotropic mate- rial, so bowing a screw dislocation is harder than bowing (B) FIGURE 12.22 Schematic and IR image of a single-ended Frank– Read source in Si. an edge dislocation. Dash illustrated the Frank–Read source in Si. Low-temperature deformation of Si causes straight dislocations because they lie along the Peierls valley. Another glide source that has been observed is the single-ended dislocation source. You can visualize this “mill” by removing half the Frank–Read source as shown schematically in Figure 12.22. In crystal growth, dislocations are often generated at the neck of the growing crystal; this is a highly stressed region and dis- locations glide more easily at high temperatures used for growth. So the dislocation source will be close to the surface. The Nabarro–Herring source is very similar to the Frank–Read source, but the dislocations move by climb instead of glide. 12.11 DISLOCATION INTERACTIONS Interactions and Motion When dislocations moving on inclined glide planes intersect one another they form nodes and locks. After the intersection is complete they will have created jogs or kinks in the other dislocation. The intersection FIGURE 12.21 Schematic and IR image of a Frank–Read process can instead result in the two dislocations knit- dislocation source in Si. ting together to form part of a dislocation tangle; the 1 2 .11 D i s l o c at i o n I n t e r ac t i o n s ............................................................................................................................... 217  (A) (B) FIGURE 12.23 Dislocation nodes in (a) AlN; (b) spinel. product dislocation may have a glide plane that is not a Nodes favored glide plane for that structure. The Lomer– Dislocation nodes occur when any three dislocations meet, Cottrell dislocation in fcc metals is an example of such when one dislocation divides into two, or when two dislo- a less mobile dislocation. It is referred to as a lock or cations join to form one. Nodes are quite common. The barrier because it stops the interacting dislocations from example in Figure 12.23 shows a node in AlN; Figure 12.14 moving and impedes the movement of other gliding showed nodes in graphite. Observations of such defects dislocations. can give a measure of the stacking-fault energy so that we can, in principle, learn something about bonding in such materials. The catch is that the stacking-fault energy may Dipoles be significantly lowered by segregation of impurities Dipoles are commonly seen in MgO and Al2O3. They may because the structure of the material is different at the SF. form by dislocations trapping one another or they may be More interesting in ceramics are nodes where climb- pulled out by a moving dislocation that is pinned some- dissociated dislocations meet. Consider the node in spinel where along its length. If the temperature is high enough, shown in Figure 12.23b: this is a special defect because it they anneal out as they form. We can learn a little about is also the junction of three noncoplanar SFs. local diffusion by carefully annealing samples containing dipoles (Figure 12.19). Consider how a dipole is annihi- Walls and Networks lated and how this process is different in metals. To anni- hilate a dipole in MgO, we must add or remove ions on both We will discuss walls and networks in more detail when sublattices. In metal alloys these different atoms can sit on we talk about interfaces. We can arrange an array of the other lattice giving an antisite defect. This exchange is dislocations to form a wall or grain boundary. Arrays of unlikely in ceramics because of the charge. It can, however, dislocations are essentially two-dimensional defects, i.e., occur in compound semiconductors, which we sometimes the dislocations knit together to form a network. The dis- think of as ordered covalently bonded alloys. location array in Figure 12.14 is actually a network. 218 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ?  FIGURE 12.24 Dislocation in TiN intersecting the surface causing a spiraling step. 12.12 AT THE SURFACE tion line is relative to its Burgers vector to be able to say that it has screw character; it could be a pure edge Dislocations cannot end inside the crystal, but they can dislocation! end at a surface as we saw in Figure 12.9 where they were reveled by chemical etching. They can also be revealed by thermal etching, which is particularly important since it 12.13 INDENTATION, SCRATCHING, can provide insight into how the reverse process, namely AND CRACKS crystal growth, occurs. Figure 12.24 shows a dislocation emerging at the surface of a TiN crystal. Notice two Crack tips are line defects, but may resemble disclinations points: (1) if this interpretation is correct, then if you more than dislocations if the sides of the crack are inclined bonded an atomically flat surface to the surface imaged to one another rather than parallel. The differences are here, you would form a single-ended Frank–Read source; significant: deformation at the crack tip may be very large (2) we cannot be sure about the Burgers vector because leading to the generation of dislocations in the plastically such atomic force microscopy (AFM) images do not tell deformed region even in brittle ceramics. If this plastic us about the component of b parallel to the surface. Note deformation is large, it actually blunts the crack tip and that dislocations producing spirals such as shown here are toughens the ceramic. not necessarily screw in character even though you will Dislocations also form when we indent ceramics and often see them referred to as such (even in some of the are particularly important for nanoindentation studies classic papers). All that is needed is that a component of (Figure 12.25). The reason cracking during indentation is the dislocation’s Burgers vector is inclined to the surface different is that the sample is much more constrained. you are examining; you have to know where the disloca- Cracks also form under the indenter tip itself and may dominate as the process continues, but to see the crack you usually remove the load, which allows it to heal. We can actually use indentation techniques to study the nucle- ation of dislocations. Again, in the nanoregime we have the additional advantage that computer modeling can be used for samples of similar dimensions. Scratching is essentially a moving indentation test, but is not as well controlled; in ceramics, it is the basis of the Mohs test. As shown in Figure 12.26, dislocations are emitted from the FIGURE 12.25 Dislocations being emitted at a crack tip in Si. FIGURE 12.26 Dislocations produced by scratching Al2O3. 1 2 .13 I n d e n tat i o n , S c r at c h i n g , a n d C r a c k s ........................................................................................................ 219 region under the indenter and for low temperature tests reported in SiC and GaN; an example is shown in Figure will tend to move out on glide planes (since there are no 12.27. In each case, the dislocation is a growth defect, not mobile point defects). This deformation thus provides a a deformation defect. Coreless dislocations can, in princi- method for studying the movement of dislocations in ple, also occur in materials that are not ceramics, but ceramics at room temperature. observations of dislocations in metals tend to concentrate on deformation where such cores are unlikely to occur. Dislocations can also act as sites for local amorphiza- 12.14 DISLOCATIONS WITH tion of a ceramic because the bonds are already distorted DIFFERENT CORES at the core. This is a case of a phase transformation being initiated at a dislocation. An example of this occurring in Frank predicted the existence of coreless dislocations long quartz during electron irradiation is shown in Figure before they were unambiguously observed. The idea is that 12.28. The dislocation appears to become much broader, the surface energy associated with a hollow tube may be but it actually becomes a tube of amorphous material (not less than the strain energy associated with a large Burgers unrelated to the coreless dislocation). It would be very vector. Of course, you have to form this large-b disloca- difficult for such a dislocation to move since the core tion first. Observations of coreless dislocations have been would need to recrystallize. (B) (A) FIGURE 12.27 Coreless dislocations in (a) SiC (side view) and (b) GaN (end-on view). 220 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ?  (A) (B) FIGURE 12.28 Amorphization of a dislocation core in quartz during observation in the TEM. CHAPTER SUMMARY Dislocations are often most important in ceramic materials for what they do not do: they do not usually move very easily unless the temperature is very high. Dislocations can be used as local probes, for example, when we look at loop annealing to learn about pipe diffusion versus bulk diffusion. It is important to understand dislocations if we want to understand structured interfaces, whether grain boundaries or phase boundaries, since these often consist of arrays of dislocations (or even dislocated arrays of dislocations). When materials are used for elec- tronic applications, dislocations become quite common because these materials are often pro- duced by epilayer growth. The discovery of the light-emitting properties of GaN suddenly made all the work on dislocations and interfaces in AlN relevant again. The most important points to remember is that there are two key parameters: the Burgers vector and the line direction. After this you need the crystal elasticity parameters and the lattice parameters. The rest follows, with the only complications being charge and directional bonding. PEOPLE IN HISTORY Burgers, Johannes (Jan) Martinus (1895–1981), the brother of crystallographer W.G. Burgers, introduced the Burgers vector in 1939; his work was mainly on fluid dynamics. Frank, Sir Charles (1911–1998) was born in Durban, South Africa (knighted 1977). He obtained his degrees from the University of Oxford. During World War II he worked for the Chemical Warfare Establishment at Porton Down and then for the scientific intelligence group at the Air Ministry. He moved to work on physics at the University of Bristol in 1946; he retired from Bristol in 1976, but remained active and shared a partitioned office with CBC in 1985/1986. In addition to dislocations, his interests included crystal growth, liquid crystals, nuclear physics, and even polymers. Hooke, Robert (b. 1635 Isle of Wight; d.1703 London) proposed the elasticity theory. He also coined the term cell in his book Micrographia (1665) and much more; he feuded with Newton. C h a p t e r S u m m a ry .......................................................................................................................................................... 221  Peierls, Sir Rudolf Ernst (1907–1995) helped a colleague (Orowan) solve some “simple” math. The result is the Peierls valley and the Peierls–Nabarro force. Peierls was also part of the British contingent of the Manhattan Project. Volterra, Vito (1860–1940) was born in Ancona, Papal States (now Italy). His began working in mathematics at age 11, obtained a Doctor of Physics degree in 1882, and was then Professor of Mechanics and then Chair of Mathematical Physics. During World War I Volterra was in the Air Force and returned to Rome after the war. He denounced fascism and left Italy to live mainly in Paris. Some say his most famous work was on integral equations. GENERAL REFERENCES Amelinckx, S. (1964) “The direct observation of dislocations,” Solid State Phys. Suppl. 6. One of the best “papers” ever written on the subject. Hirth, J.P. and Lothe, J. (1982) Theory of Dislocations, 2nd edition, Wiley, New York. One of the two standard works on the subject. Inspirational. Professor Hirth retired from Washington State University in 2003. Hull, D. and Bacon, D.J. (1984) Introduction to Dislocations, 3rd edition, Pergamon Press, Oxford. Bedtime reading for the materials scientist. Nabarro, F.R.N. (1987) Theory of Crystal Dislocations, Dover Publications, New York. This was first pub- lished by the Clarendon Press (Oxford University Press) in 1967. The other standard work by one of the founders of dislocation theory. Professor Nabarro also edited the series Dislocations. Weertman, J. and Weertman, J.R. (1992) Elementary Dislocation Theory, Oxford University Press, New York. Similar to H&B but with more equations and no micrographs. SPECIFIC REFERENCES Amelinckx, S., Bontinck, W., and Dekeyser, W. (1957) “Helical dislocations and spiral etch-pits,” Philos. Mag. 2, 1264. Carter, C.B. and Kohlstedt, D.L. (1981) “Electron irradiation damage in natural quartz grains,” Phys. Chem. Minerals 7, 110. Hornstra, J. (1960) “Dislocations, stacking faults and twins in the spinel structure,” J. Phys. Chem. Sol. 15, 311. Kodambaka, S., Khare, S.V., Swiech, W., Ohmori, K., Petrov. I., and Greene, J.E. (2004) “Dislocation-driven surface dynamics on solids,” Nature 429, 49. Kronberg M.L. (1957) “Plastic deformation of single crystals of sapphire—basal slip and twinning,” Acta Metal. 5, 507. Lee, W.E. and Lagerlof, K.P.D. (1985) “Structural and electron-diffraction data for sapphire (alpha-Al 2O3),” J. Electron. Microsc. Techn. 2, 247. Narayan, J. (1972) “Self-climb of dislocation loops in magnesium-oxide,” Philos. Mag. 26, 1179. Rabier, J. and Puls, M.P. (1989) “On the core structures of edge dislocations in NaCl and MgO. Consequences for the core configurations of dislocation dipoles,” Philos. Mag. A 59(4), 821. Ray, I.L.F. and Cockayne, D.J.H. (1971) “The dissociation of dislocations in silicon,” Proc. R. Soc. Lond. A 325, 543. Washburn, J., Kelly, A., and Williamson, G.K. (1960) “Direct observations of dislocations in magnesium oxide,” Philos. Mag. 5, 192. Weertman, J. (1957) “Helical dislocations,” Phys. Rev. 107(5), 1259. EXERCISES 12.1 What is the shortest perfect-dislocation Burgers vectors in the following materials: (i) CsCl, (ii) NiO, (iii) fluorite, (iv) BaTiO3, (v) CZ, (vi) YAG, (vii) β-cristobalite, and (Viii) GaAs. 12.2 What are the two shortest (crystallographically different) perfect-dislocation Burgers vectors in the following materials:(i) alumina, (ii) graphite, and (iii) MoS2. 12.3 What are the three shortest (crystallographically different) perfect-dislocation Burgers vectors in the following materials: (i) olivine, (ii) wurzite, and (iii) YBCO. 12.4 Draw an end-on diagram for a perfect edge dislocation in PbS having a (001) glide plane. Label b and show its direction with an arrow. 12.5 Draw an end-on diagram for a perfect edge dislocation in NaCl having a (110) glide plane. Label b and show its direction with an arrow. 12.6 Consider a climb-dissociated –21 [110] edge dislocation in spinel. Draw a model for the atomistic structure. 12.7 How can 1 cm 2 of MgO have a dislocation density of 106 yet only contain one dislocation. 222 ................................................................................................................................ A r e D i s l o c at i o n s U n i m p o r ta n t ?  12.8 If 1 cm 2 of NiO contains one screw dislocation that is 2 cm long, how many distinct planes does the crystal contain? 12.9 A jogged edge dislocation in LiF lies parallel to the (110) surface, which is perpendicular to its Burgers vector. The dislocation contains a series of unit jogs, each with the same sign, spaced every 50 nm along its length. A stress is applied that makes the dislocation glide from the center side of a 1-mm cube until it exits the crystal. Assuming that the dislocation initially always lies parallel to the initial surface, estimate the current that flows across the sample. 12.10 Examine Figure 12.21. Estimate the stress required to make this mill operate. Explain all the assumptions and deductions you make—there will be many. C h a p t e r S u m m a ry .......................................................................................................................................................... 223  13 Surfaces, Nanoparticles, and Foams CHAPTER PREVIEW This chapter is the first of a three-part series on interfaces. We are dividing the discussion only to make it manageable. An interface is a planar region separating two domains or materials. Hence we have the definition of a surface as the region that separates a solid or liquid from a gas or vacuum. The word “region” is used to make it clear from the beginning that the surface has a thickness; it is not the mathematical definition. Powder processing is the traditional route for forming ceramics; in powders the ratio of surface area to volume is large. With nanoparticle powders, the ratio can be huge. We will first discuss two important questions concerning surfaces.  What do we mean by the word surface?  Why are surfaces so important for ceramics? We will then consider, from several viewpoints, the two most important properties of surfaces.  The energy associated with a curved surface is greater than for a flat surface.  We add material to the bulk solid by attaching it to the surface. As always, we keep in mind the following question: what is special about ceramics? 13.1 BACKGROUND TO SURFACES all ceramic processing we can assume that the surface is not perfectly clean. A surface is just the interface between a solid (or liquid) Throughout our discussion of ceramic surfaces, we are and a gas or vacuum. In general, the surface of a mate- concerned with four interrelated concepts; these are rial, or any interface between materials, is a region of energy, formation, movement, and charge. As usual, only excess energy relative to the bulk or matrix. To maintain the final one, charge, is particular to ceramics. the lowest total energy for the system, the configuration of the surface adapts itself to minimize this excess  The energy of any surface depends on many factors, energy. Impurities or dopants that lower the surface including the material and structure (crystalline or energy tend to concentrate in the surface. Similarly, such not), and if crystalline, the crystallography and plane. defects will move to the interface if by segregating there We will discuss how to measure this parameter. they lower the overall energy of the system even if it  Formation will occur only if energetically favorable. raises the interfacial energy. The surface will tend to We need to discuss the relevance of Wulff plots to orient parallel to certain crystallographic planes that have understand surfaces. a lower energy.  Movement can occur if this does not increase the total The surface energy can be intentionally lowered using energy or if it minimizes this increase. a wetting agent or a (liquid or solid) surfactant. For  Charge distribution, and thus the bonding, will be example, the interfacial energy of liquid Ni in contact with different at a surface. Charge must influence the value Al2O3 can be changed by the presence of Ti at the surface. of the surface energy, but it is almost an unknown The Ti is strongly attracted to the oxide interface because factor. of its high chemical reactivity with oxygen. This type of interaction is so common that a major problem in studying Many features of surfaces, and interfaces in general, ceramic surfaces is to know if the surface is clean. During are similar in all materials. 224 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s   A pressure difference SURFACES OF MINERALS So to answer what is is always present across Interactions of minerals with the environment are impor- special we need to summa- a curved surface tant in decreasing contamination and waste manage- rize the features that are (thermodynamics). ment. This is sometimes referred to as the field of common to all materials  The structure of sur- first. Then we can ask: environmental mineralogy. Topics include microbial faces can relax from the interactions with minerals, anthropogenic influences, what is different in com- bulk-terminated con- contaminated land, and waste management. parison to metals? Ionic figuration (physics). materials and covalent  Surfaces can be wetted materials (e.g., Si, Ge, by a thin layer of impurity or a second phase GaAs) both have local charge variations. The directional (energetics). bonding of the covalent materials means that they can  The ionicity or covalency and crystallography can have “unsatisfied” bonds; these are known as dangling affect surfaces (chemistry). bonds. We have encountered these before in discussing dislocations. Surfaces and their interaction with impurities and parti- cles are being extensively modeled using the computer. Some researchers might say that computer modeling might 13.3 SURFACE ENERGY be the only method for studying clean surfaces. Surface energy is clearly a very important quantity. It is almost never well known if it is known at all. There are 13.2 CERAMIC SURFACES two important questions that we need to answer about surface energy: The surface is particularly important for ceramics because we are often using powders at some stage of processing:  How do we define the energy of a surface? the surface area-to-volume ratio is larger for powders than  What factors determine the surface energy? bulk materials. Many uses of ceramics rely on their inert- ness or reactivity, but nanoparticles of “inert” ceramics The easiest way to define surface energy is to start with can be very reactive, partly because of this enhanced ratio. a liquid (it could, for example, be a molten ceramic) and Failure of a ceramic usually occurs first at the surface. imagine that it is suspended in a wire frame. One bar of Catalysis is enabled at the surface. Sintering, perhaps the the frame is movable and allows us to increase the surface most important processing route for ceramic materials, is area by an amount dA. The force that we have to apply the process of joining two surfaces together. Remember must be sufficient to overcome the opposing surface during this discussion that in the thermodynamic analysis tension, γ. The work done, dw, in increasing the surface of surfaces, surface energy and surface tension are proper- area is ties of the continuum. Surface tension is usually assumed to be synonymous with surface energy, but this is not dw = − γdA (13.1) necessarily so. We must consider how to relate these con- tinuum parameters to the atomic structure. The term “tension” is a little confusing when we consider  Surface steps: when we need to consider the atomi- solids because it implies that there is an associated stress. stics. Special surface sites influence the energy of With our example of a liquid in a metal frame we are surfaces. actually stretching the surface and the atoms in the liquid  Composition: is the surface clean? If it is clean, does it are moving from the bulk to the surface to increase the have the bulk-terminated structure or has it relaxed? surface area. We could not imagine doing the same thing with a solid except perhaps close to the melting tempera- So what is special about surfaces of ceramics? We have ture. In solids we regard γ as the energy required to form to think about surface structure otherwise we will not the surface. It is important to note that the surface energy appreciate what is special. is not usually equal to the surface stress, the work required to deform the surface, though we often assume it is. For a  The charge and covalent bonds: charge cannot neces- liquid they are equal. sarily be redistributed. From the combined statement of the first and second  Surface energy tends to be much more dependent on laws of thermodynamics we can write that the change in the plane in ceramics. internal energy, dE, is  These two points are probably not independent. dE = TdS − PdV + γ dA + ∑ μ i dni (13.2) Because the properties of interfaces vary so much, the morphology of interfaces in real ceramics may be unusual. We can then define the surface energy as 13 . 3 S u r fa c e E n e r g y .................................................................................................................................................... 225  TABLE 13.1 Surface Energies of Various Materials in ΔHS Vacuum or Inert Atmospheres ε= (13.5) 0.5ZNA Material Temperature (°C) Energy (mJ/m2) ΔHs is the molar enthalpy of sublimation (the energy to Water Liquid 26 72 Cu Liquid 1120 1270 break all the bonds), Z is the coordination number, and NA Ag Liquid 1000 920 is the Avogadro number. Alumina Liquid 2080 700 The work, w, required to form a surface, for example, Cu Solid 1080 1430 if we cleave a crystal, is going to depend on the number Ag Solid 750 1140 of bonds, x, per atom that we break (so x depends on the Alumina Solid 1850 905 (100) NaCl Solid 25 300 cleavage plane). MgO Solid 25 1000 x xΔHS w= ε= (13.6) 2 ZNA ∂E The surface energy, γ, is then γ =⎛ ⎞ (13.3) ⎝ ∂A ⎠S ,V, n i xΔHS ⎛ N ⎞ γ = (13.7) A similar expression involving the Gibbs free energy can ZNA ⎝ A ⎠ be written: The term (N/A) is the number of atoms per unit surface dG = − SdT + VdP + γ dA + ∑ μ i dni (13.4a) area. You can see from Table 13.1 that this approach gives only a very approximate (but not unreasonable) result, And the surface energy is written as although it looks very precise. The reason is that second- nearest neighbors are not considered in the calculation ∂G ⎞ (these are, of course, extremely important in ionic crys- γ =⎛ (13.4b) tals) and it is also assumed that the strengths of the remain- ⎝ ∂A ⎠ P ,T, n i ing surface bonds are the same as the bulk values. The calculation also does not consider charge—an important Some examples of surface energies are given in Table 13.1. consideration for ionic ceramics! Estimated values for The range of values is quite large. Even if we compare metals compare much more closely to the experimental only the values for solids you can see that for NaCl values. (The calculation for Cu is given, for example, by γ = 300 mJ/m2; it is three times greater for MgO (think Ragone, 1995.) What calculations using Eq. 13.7 do show about the charge). As a general rule, the surface energy us is that γ varies with the crystal structure and surface decreases as the temperature increases (Eötvos rule). The orientation. The practical application of these differences surface energy of a liquid is lower than that of the corre- is evident when we try to etch materials using acids. sponding solid. For example, we can compare values for Different planes etch at different rates. The chemical etch Al2O3: rates for Ge on the (100), (110), and (111) planes are 1.00, 0.89, and 0.62, respectively.  Al2O3 (solid)γ = 905 mJ/m2 The implication is that the (100) plane of Ge has a  Al2O3 (liquid)γ = 700 mJ/m2 higher energy than either the (110) or (111) planes. The importance is that often when we try to etch a semicon- In general, you should be very wary when given precise ductor we want to produce a smooth surface rather than a values for surface energies. facetted one—unless we want to make V-MOS devices. Approximation of CALCULATING A SURFACE ENERGY Surface Energies We can estimate the value of γ for the (100) face Effect of Structure of NaCl. Take x = 1. ΔHs = 235,000 J/mol (value for and Orientation The surface energy of a solid depends on its crystal NaCl from Kubaschewski and Alcock, 1979). For NaCl, The surface energy, γ, structure and orientation Z = 6. depends on the structure, and can be estimated by which depends on the a simple calculation. First NA = 6.022 × 1023 mol−1 orientation. We have devel- we assume that the binding (N/A) = 1.26 × 1019 m−2 oped two approaches for energy of an atom is the considering this orienta- result of bonds to its nearest (aNaCl = 0.5640 nm) tion dependence: the Wulff neighbors. The energy, ε, plot and the inverse Wulff of one bond is then This gives γ = 0.82 J/m2 plot. 226 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s  Wulff plane A (001) γ plot Figure 13.2 shows an example of a bulk UO2 sample that has been heat treated so that the pores achieved a near equilibrium shape. The length of the facets in the small A B void can be used to determine the relative energies of (100) and (110) planes. γ001 (111) γA 13.4 SURFACE STRUCTURE C γ111 We will illustrate some special surfaces using a series of (110) figures. In continuum models of surfaces the surface is a 0 smooth curve; at the atomic level, it is always faceted. A terminology for the different surfaces is summarized in Figure 13.3. The surface can form large flat facets (F) that are really facets on two planes separated by a ridge (S) and surfaces that are not atomically smooth at all (K). Beware of the bias that carries over from metals, such as Equilibrium surface the picture that crystals are built by stacking cubes or that all ions are hard sphere. Ions can relax into the surface FIGURE 13.1 Wulff plot looking along the [11̄0] direction for an fcc (relative to their bulk positions) and this relaxation depends crystal. on the crystallography of the surface. The relaxations will also be different at steps on the surface.  The Wulff plot draws a graph of γ versus θ. This con- Flat surfaces. The surface of a spinel crystal with an struction was developed to allow the equilibrium shape emerging dislocation is shown in Figure 13.4. The reason of crystals to be determined when the surface energy for choosing Figure 13.4 is that it shows a ceramic surface depends on crystallography. that is atomically flat parallel to the step in this figure for  The inverse Wulff plot shows 1/γ as a function of θ. a distance over 10 μm. Step heights can be multiples of a The Wulff plot is the conventional plot for surfaces; an unit value. When the unit cell is large, the definition of an example of such a plot is shown in Figure 13.1. The most atomically flat surface is less clear. For example, the important point is that you have cusps in γ versus θ. In surface of a zeolite is important in processing, but the ceramics, this certainly occurs; if the energy were iso- surface and near-surface pores are connected: the surface tropic, the Wulff plot would be a circle. What is not certain area is much greater than the geometric area of the surface. is how many cusps you have. It is instructive to compare (Remember the idea of the Möbius strip!) surfaces with grain boundaries (section 14.3). In the latter Rumpled surfaces. The term rumpled refers to the case it is necessary to define the orientation of the grain- local undulations on the surface. The rumpled surface is boundary plane, i.e., having fixed θ, you must still fix n, the crystallographically flat, but local displacement of the normal to both grains. ions means that it is not geometrically flat. The difference Experimentally we can determine the equilibrium between relaxation and rumpling is that the term relax- shapes of crystals by annealing small single crystal parti- cles at high temperature in an inert atmosphere or by A annealing small voids (inverse particles) in a crystal. B K C C F S B A FIGURE 13.3 Terminology for facets, steps, and kinks on FIGURE 13.2 Faceting of small voids in UO2. surfaces. 13 . 4 S u r fa c e S t ru c t u r e .............................................................................................................................................. 227  2 [110] [110] 4 4 4 2 4 4 (B) FIGURE 13.4 A faceted shallow thermal etch pit on the (001) surface of spinel. 2 and 4 refer to the height of the steps (0.2 nm and (A) 0.4 nm). ation refers to the average change in the spacing of the form if a ridge forms. Facet growth thus involves surface plane nearest to the surface and the second plane when diffusion normal to the geometric surface. compared to the bulk value; rumpling, on the other hand, We might say that the surfaces of nanoparticles are refers to the displacement of the cation layer relative to the their most important feature since this determines all their anion layer in a direction normal to the surface. properties. As is clear from Figure 13.6, the facet junctions If an initially flat surface is not in its lowest-energy on nanoparticles are also much more prominent. configuration, then it will facet when heated to a high The chemistry of surfaces can be very different from enough temperature. You can envision how this process the bulk material. Clearly the bonding is different on the can occur by considering Figure 13.5. The surface is ini- surface. On oxides, in particular, OH groups may be tially flat; if no extra material is added then a trench must present even if you think the environment is dry. Detect- 5.0 nm 0 A B C x 5.0 0 1.0 2.0 μm (B) (A) FIGURE 13.5 The initiation of faceting on the m plane of sapphire. 228 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s  (A) (B) (C) (C) (D) FIGURE 13.6 Illustrating the fraction of atoms sitting at the surface of a nanoparticle. (a) Ten atoms, all on the surface; (b) 92 atoms with 74 on surfaces (80%); (c) 792 atoms with 394 on surfaces (50%). (d) An HRTEM image of a faceted nanoparticle of CdSe. (D) FIGURE 13.5 Continued ing hydrogen in or on a material is tricky. Such hydrated surfaces behave differently and the surface energy can differ from that of the dry surface. One special feature of ceramic surfaces is the result of covalent and ionic bonding. Ceramics have charges and charge dipoles; these charges are often uncompensated at the surface, at least on the short range as illustrated in FIGURE 13.7 Relating dangling bonds to the 7 × 7 reconstruction Figure 13.7. of the {111} Si surface. 13 . 4 S u r fa c e S t ru c t u r e .............................................................................................................................................. 229 13.5 CURVED A VERY IMPORTANT BUT provides a large driving SURFACES SIMPLE CALCULATION force. If r is ∞, then r −1 and AND PRESSURE The pressure in the void must do work to change the ΔP are zero. The result is surface area. The equilibrium condition is then given by that we can think of the The idea is the same as the energy balance. pressure above a curved discussed for the bowed surface as being different dislocation, but we have from that above a flat ΔPdv + γdA = 0 added a dimension. If we surface. reduce the area of the surface, we lower the For simplicity, assume that the void is a sphere (in using energy. Hence, if a surface one value for γ, we have already assumed that the energy 13.6 CAPILLARITY is curved, we can imagine is isotropic). We know dv and dA terms of r. that there is a force that We will discuss wetting wants to reduce the area of dv = 4πr 2 dr shortly, but you are already the surface: the force acts dA = 8πrdr familiar with the capillar- on an area of the surface ity effect from the tradi- and force divided by area tional mercury-based or Combining these three equations gives is pressure. Picture how spirit-based thermometer. you can take a small ring, From Figure 13.8 we can 8πr ⎛ dr ⎞ 2 2γ fill it with a soap film, and ΔP = γ 2 ⎝ = γ = obtain the following 4 πr dr ⎠ r r expression: blow a bubble. The pres- sure is provided by the air: if you stop blowing, the A surface will have two principal curvatures, r1 and r 2 2γ 2 cosθ surface becomes flat again. (which can either be positive or negative); we write ΔP = =γ = ρgh r r The analogy is quite close, (13.8) ΔP = γ ⎛ + ⎞ except that the surface 1 1 energy of the soap film is ⎝ r1 r2 ⎠ rρgh γ= (13.9) isotropic (and there are 2cosθ actually two surfaces). There will actually also be a torque term in the surface The equation ΔP = 2γ/r is very important because it says tension, just as there is for curved dislocations, but this if r ≠ ∞, then ΔP ≠ 0. The vapor pressure above a curved term is usually ignored. To make this force more physical surface is not the same as the pressure above a flat surface to us, we will regard this surface energy as a surface due to ΔP. tension. The pressure difference across a curved interface is real and occurs in all materials. In small gas-filled voids V ΔP = RT ln = V γ ⎛ + ⎞ P 1 1 created by implanting Xe into MgO (or Si or Al), the Xe (13.10) P0 ⎝ r1 r2 ⎠ will be crystalline if the void is small enough because the internal pressure is so high; the Xe can interact with other Here V = molar volume, P = vapor pressure, P0 = vapor defects just like any small crystal inside a crystalline pressure over a flat surface, and R = the gas constant. matrix, unless the defect is a crack! A simple example is calculated in Table 13.2. Vγ ⎛ 1 Mγ ⎛ 1 + ⎞ = + ⎞ (13.11) P 1 1 The concept of pressure due to surface curvature is ln = P 0 RT ⎝ r1 r2 ⎠ ρ RT ⎝ r1 r2 ⎠ very important in ceramics because we often encounter very curved surfaces, e.g., at small grains, voids, or parti- cles, which are present because we start processing with r cosθ θ powders. Thus we can have a large pressure difference that r h TABLE 13.2 Pressure due to Surface Curvature for Silica Glass (1700°C; g = 300 mJ/m2 ) r P Sphere diameter (mm) DP (MPa) P0 0.1 12 1.02 1.0 1.20 1.002 10.0 0.12 1.0002 FIGURE 13.8 The geometry used to calculate the capillarity equation. 230 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s  clean glass slide, it remains as a drop on the surface even though it develops a glass/liquid interface. If you add soap to the water, it spreads over the surface; the liquid wets the glass and the interfacial (contact) area increases. The soap is a surfactant and lowers the energy of the glass/ liquid interface. We will see later that we can use sur- factants to treat ceramics and liquids other than water. An example of this being used commercially for glass sur- faces is the development of new coatings for automobile windshields. As usual ceramics tend to be more complicated; at the (A) higher temperatures encountered when processing ceram- 400 ics, vaporization can also occur. At these higher tempera- δL tures, the solid might not be inert, so it may react with the (nm) liquid; this is known as reactive wetting. When we talk 200 about wetting or dewetting, one of the materials need not be liquid (both, or neither, could be), but we do need mobility (surface diffusion) for the wetting/dewetting 0 layer to be able to move across the surface. 0 100 200 300 400 500 The relationship between surface and interfacial T (°C) energies determines, to a large extent, the wetting beha- (B) vior of a liquid on a solid surface. Later we will see that FIGURE 13.9 Capillarity effect in a silica nanothermometer. it also determines the phase morphology of mixtures of two or more phases. There are several interfacial tensions, γ, to contend with, and these are identified by the sub- scripts f, s, and v, which represent film, substrate, and Now, M = molecular weight and ρ = density. When vapor, respectively. r1 = r 2, Eq. 13.11 becomes If we consider the stable configuration of a liquid P Vγ 2 placed on a solid surface, the equilibrium shape conforms ln = (13.12) to the minimum total interfacial energy for all the phase P0 RT r boundaries present. If the solid–liquid interfacial energy From Eq. 13.12 we can see that: (γsl) is high, the liquid tends to form a ball having a minimum interfacial area as shown in Figure 13.10 (Hg  The vapor pressure of a spherical particle is a function on a glass slide will do this). If the liquid–vapor interfacial of its radius. energy (γsv) is very small, the spreading of the liquid will  The vapor pressure at the surface of a particle is higher depend entirely on the interfacial energy (γsl), but note the if r is small. converse. Young’s equation relates the angle between the solid We can also show that surface and the tangent to the liquid surface at the contact point. (It is a force balance in the horizontal direction  Small particles or small voids have large surface because we assume the surface is not free to move in the energies. vertical direction.) This contact angle, θ, may vary between  At high temperatures small particles will tend to 0 and 180°. This angle specifies the conditions for mini- dissolve while large particles will grow (Ostwald mum energy according to the relation ripening).  Small particles have lower melting temperatures than γlv cos θ = γsv − γsl (13.13) large particles. The thermometer shown in Figure 13.9 was made by V filling a silica nanotube with Ga instead of Hg. L θ θ 13.7 WETTING AND DEWETTING L The concepts of wetting and capillarity were first explained S in ∼1800; again, history is important in understanding the FIGURE 13.10 Drops on a solid surface showing wetting, terminology. If you place a drop of water onto a really nonwetting, and a real equilibrium (inset) 13 .7 We t t i n g a n d D e w e t t i n g .................................................................................................................................... 231 Therefore, the contact angle θ depends only on the surface properties of the materials involved. The importance of this equation is that it provides a method for comparing interfacial energies. Thomas Young first derived Eq. 13.13 in 1805 (Young, 1805), but often it is also referred to as the Young–Dupré equation (Dupré, 1869). Contact angles can be measured experimentally by the sessile drop tech- nique. To study the wetting of glass on a ceramic or metal (A) surface a small particle of the glass would be placed on the solid surface inside a tube furnace, one end of which is clear, allowing observation of the droplet, using a telemicroscope, and the contact angle, as a function of temperature. Experimentally it can be difficult to obtain reproducible values for θ. One of the problems is that of macroscopic surface roughness, which can be expressed as (B) FIGURE 13.11 Experimental observations of glass droplets on the cos φ = r cos θ (13.14) surface of Al2O3: (a) c plane, (b) m plane. where r is the roughness, φ is the observed contact since the glass can be very angle, and θ is the true CONVENTION reactive at the high tem- contact angle. The other The contact angle, θ, is measured “through” the liquid. peratures where the wetting problem is that of hystere- actually takes place. For sis—the measured angle example, at 1600°C a sili- θ depends on whether the LOTUS LEAF cate glass can dissolve liquid is advancing or Water “rolls off” the leaf because the surface is rough. alumina. The situation is receding. shown experimentally in Table 13.3 shows meas- Figure 13.11 for the (0001) ured contact angles for several metals and for a basic slag and {101̄0} surfaces: the glass/Al2O3 surface energy is (think of the slag as liquid silicate glass) on MgO single- different for different surfaces. How the glass actually crystal surfaces (MgO is used as a furnace lining). As dewets the surface depends on the crystal orientation of noted earlier, the surface energy of solids is dependent on that surface. the crystallographic orientation, which is demonstrated by Wetting/dewetting is also a concern for nonoxides the variation in wetting angle with crystallographic planes (especially when you want to join them to other materials) for MgO. and for metal/ceramic interfaces such as the metal/Si, Layers of glass can be deposited on polycrystalline metal/SiO2, and metal/Si3N4 interfaces in the electronics substrates and heat treated. The resulting faceting of the industry and systems such as Al/Al2O3, which is important surface can be monitored while varying the annealing in protecting metals against corrosion. temperature, quench rate, etc. The glass/Al2O3 interfacial energy is not isotropic. An important feature of this dem- onstration is that the glass does affect the faceting behavior 13.8 FOAMS of the surface. This wetting of single surfaces by a glass is more complex than the wetting of most solids by a liquid Foams, which have been known forever, have been studied for over a century. They are hot topics in coffee shops and cosmology, but are not as well known in ceramics. When they are discussed in ceramics, they are not necessarily TABLE 13.3 Measured Contact Angles of Liquids on recognized as such, as is the case with pumice. (More Single-Crystal MgO about this is given in Chapter 21.) These cellular ceramics Test temperature are also referred to as microporous or macroporous ceram- Liquid (°C) (100) (110) (111) ics depending on the size of the cells. The common feature Cu 1300 106 159 149 of these materials is that they consist of thin membranes Ag 1300 136 141 147 of ceramic that enclose pores of various sizes. Thus they Co 1600 114 153 144 have a large surface and they are lightweight, but they still Fe 1600 59 110 90 retain many of the properties of the ceramic. They are Basic slaga 1400 9 17 32 rigid, can be used to relatively high temperatures, and can a Composition: 40% SiO , 20% Al O , 40% CaO. 2 2 3 be quite inert to chemical reactions. 232 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s  the strength is to use tape casting (more about this is given in Chapter 27) to provide layers of material of different pore size, thus producing a graded porous structure. We will see these foam geometries again when we discuss glass films in grain boundaries. 13.9 EPITAXY AND FILM GROWTH We have two immediate questions:  What is epitaxy?  Why discuss it here? The reason for discussing it here is that it essentially involves depositing one material onto the surface of (A) another. If the thin layer coating the substrate is stable, then it is wetting the substrate. If the thin layer is aligned crystallographically with respect to the substrate such that directions in the films are aligned with those in the sub- strate, we say the film is epitactic. In this case it is likely to wet the substrate—the interfacial energy is relatively low. Most thin films are not epitactic. Two ancient Greek words επι (epi—placed or resting upon) and ταξισ (taxis—arrangement) give the root of the modern word epitaxy, which describes an important phe- nomenon exhibited by thin films. Epitaxy refers to the formation of an oriented (single crystal) film on top of a crystalline substrate. Most people say epitaxial, which is grammatically incorrect, but is now in dictionaries. Epitaxic or epitactic would be the correct adjectives. We will discuss details (matching, chemistry, bonding, lattice matching, and misfit dislocations) of such inter- (B) faces in Chapter 15 as well as what it means for them to FIGURE 13.12 The surface of foam. be incommensurate. We will also discuss the different techniques for analyzing them there. For now, we want to consider how the atomistic topography of the substrate surface influences the behavior of the film. So we are Many cellular ceramics, as shown in Figure 13.12, are concerned with surface steps and how they influence made by using natural materials such as wood, itself a graphoepitaxy (an alignment of the film induced by surface cellular material, as a template: they are biomimetic topography). To complicate matters further, in ceramics, ceramics—they mimic the biological materials. (More the film and the substrate may be amorphous, polycrystal- about this is given in Chapter 35.) Rattan cylinders have line, or monocrystalline. been infiltrated with Si liquid and zeolites to make a mixed microporous/macroporous ceramic. The rattan stems were first pyrolyzed, then infiltrated with liquid Si 13.10 FILM GROWTH IN 2D: NUCLEATION to give the Si/SiC matrix, and finally the internal surfaces were functionalized with a zeolite. The resulting materials During film growth, atoms or molecules in the vapor was tested as a catalyst for n-hexane cracking. phase arrive at the substrate, creating aggregates that will The honeycomb of the catalytic converter provides a either grow in size or disintegrate into smaller entities large surface area to support the catalyst particles and through dissociation processes. ensures that the gases pass close to these particles. When used as filters the pore (channel) diameter is engineered Nucleate the New Phase on the Substrate to suit the purpose. The synthetic bone needs the pores to encourage the intergrowth of regrowing natural bone, but When an atom from the vapor strikes a solid surface the if the pores are too large then the ceramic is weakened. collision decreases the energy of the atom so that it One technique used to provide the porous structure and becomes partially bound to the crystal surface. Thus any 13 .10 F i l m G r o w t h i n 2 D : N u c l e at i o n ................................................................................................................... 233  Terrace C Kink Step adatom model) we consider the heterogeneous nucleation of a Step or admolecule solid film on a planar substrate. B Terrace 13.11 FILM GROWTH IN 2D: vacancy MECHANISMS A Terrace adatom or admolecule The many observations of film formation have pointed to FIGURE 13.13 Surface attachment sites and the nucleation of thin three basic growth modes that can be distinguished on the films in 2D. basis of Eq. 13.13; these are illustrated schematically in Figure 13.14. Each mode is named after two scientists who did not necessarily work together. further motion of the atom is restricted to the surface of the substrate. Isolated nuclei are then formed from groups  Island growth (Volmer–Weber) occurs when the small- of such atoms coming together by chance through their est stable clusters nucleate on the substrate surface and thermal motion. A mobile “new” atom is most easily built then grow in three dimensions to form islands. This into the crystal structure at a ledge corner, since this atom happens when atoms or molecules in the deposit will interact strongly with three neighboring atoms and are more strongly bound to each other than to the the local surface energy of the surface due to unsaturated substrate. surface bonds will not increase. Another convenient posi-  Layer-by-layer growth (Frank–van der Merwe) involves tion will be sites such as steps, shown in Figure 13.13; in the extension of the smallest stable nucleus, which this way a continual supply occurs overwhelmingly in of atoms will lead to the CONTACT ANGLE AND THE MODELS two dimensions, resulting completion of the entire Island growth: θ > 0 in the formation of planar crystal plane. sheets. In this growth mode γsv < γfs + γvf the atoms are more strongly bound to the substrate than Stabilize the Nucleus Layer-by-layer growth: θ = 0. The deposit “wets” the to each other. The first substrate. complete monolayer is then Continuation of the growth covered with a somewhat process will rely on the formation of a new stable γsv = γfs + γvf less tightly bound second layer. Providing the de- nucleus, shown schemati- Layer-by-layer growth: crease in bonding energy cally as a thin cylinder. is continuous toward the This new nucleus involves an increase in free energy γsv > γfs + γvf bulk crystal value, the layer growth mode is sustained. due to the atoms at the edge and a decrease of free energy as the atoms are incor- porated in the interior. Thus the stability of the nucleus Frank-van der Merwe Volmer-Weber Stranski-Krastanow will depend upon the ratio of volume energy to surface energy, and there will be a critical radius of the nucleus, rc, such that if r > rc the nucleus is stable and can grow. Grow the Nuclei If the lateral growth mechanism is relatively rapid, the rate of formation of the new nuclei on the completed planes will be the decisive factor in controlling the overall growth rate. The free energy change accompanying the formation of an aggregate of mean dimension r is given by ΔG = a3r 3ΔGv + a1r 2γvf + a2r 2 γfs − a2r 2 γsv (13.15) In Chapter 15 we will consider homogeneous nucleation of a solid in a liquid. Here (using a simple qualitative FIGURE 13.14 The three modes of thin-film growth. 234 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s   Layer-plus-island (Stranski–Krastanow) growth is a area of interface (U), taking v to be the usual frequency mechanism involving an intermediate combination of factor and a 0 the distance that the interface moves when these two modes. In this case, after forming one or an atom is added, can then be determined. more monolayers, subsequent layer growth becomes unfavorable and islands form. The transition from two- to three-dimensional growth is not completely 13.12 CHARACTERIZING SURFACES understood, but any factor that disturbs the monotonic decrease in binding energy characteristic of layer The techniques for characterizing surfaces are applica- growth may be the cause. tions or extensions of those discussed in Chapter 10. They basically fall into two groups: the direct and indirect Growth ledges: Experi- (D and I) techniques, mentally we know that which are summarized for the growth of crystals ENERGY OF SITES IN FIGURE 13.13 surfaces in Table 13.4. from the vapor phase often Site Energy Gain Here we emphasize the occurs at measurable rates, A E1 + 4E2 application of techniques even at low values of super- B 2E1 + 6E2 that are particularly im- saturation. This has been C 3E1 + 6E2 portant for ceramic sur- associated with growth faces. Each approach taking place at steps pro- provides different informa- vided by dislocations intersecting the interface. Such dis- tion and none answers all the questions we have. A major locations can provide a self-perpetuating source of steps difficulty in studying ceramic surfaces is that many do not as molecules are added to the crystal. The emergence conduct electricity well. Thus techniques using electron point of the dislocation acquires a higher curvature until beams can have limited application. To study surfaces in a steady state is reached in which the form of the spiral the transmission electron micrograph (TEM) or scanning remains constant and the whole spiral rotates uniformly electron micrograph (SEM) we may need to coat the sample around the dislocation. This process was illustrated in with C or even Pt to prevent charge building up on the Figure 12.24. surface and thus deflecting the electron beam. In doing so, Experiment: Start with well-defined facets so you have we hope we have not changed the surface, but of course we regions of planar surfaces. Then consider two cases. have. Rather than just describing each technique, we will go  Large entropy change produces smooth surfaces and through a set of examples to show just what is possible faceted interfaces. Examples are growth of silicates for the different techniques. In each e-beam technique, from the melt and the growth from vapor or dilute coating may be necessary—the rule is try it first then solutions. gradually increase the thickness of the coating. In SEM,  Small entropy charge is isotropic with many growth for example, lowering the kV may allow you to avoid sites. An example is the growth of a metal from the coating altogether. Sometimes, single-crystal sapphire melt. can be studied in the TEM without coating. This possibil- ity may depend on how clean your TEM is. You can also We can consider sites on the growing phase and in a flash the sample with an electron beam to induce conduc- simple model (shown in Figure 13.13) of counting the tion for the short time that you make the observation/ nearest neighbors, assign a binding energy to each of these measurement. sites. Let E1 be the energy of attachment at the first nearest Scanned probe microscopy is the method of choice for neighbor and E2 at the second nearest neighbor. We can studying surfaces because it gives a direct picture of the then draw up a table for each site. The growth rate per unit surface, can give superb resolution, and can even give TABLE 13.4 Surface Characterization Techniques Technique Example Special information Limitations AFM D Al2O3 How smooth? V: ∼0.1 nm, L: ∼0.2 nm SEM D Fracture Self selective Structure 0.7 nm chemistry 1.5 nm TEM D MgO, Al2O3 Faceting; plan view See two surfaces at the same time TEM D CeO2 Faceting; profile Must be flat parallel to the beam TEM D REM Plan view Tricky, foreshortens the image LEED I Al2O3 Average; vacuum UHV technique RHEED I Al2O3 Average; vacuum UHV technique STM D Fe3O4 Steps Must conduct electrons and UHV STM D Si 7 × 7 Reconstruction UHV technique Auger D La 2O3, Y2O3 Chemistry UHV technique 13 .1 2 C h a r a c t e r i z i n g S u r fac e s ................................................................................................................................ 235  1 the energy of the electrons is low, the beam probes only the region closest to the surface. This is the Step strength of the technique, but it also means that edge the surface must be absolutely clean. Thus LEED experiments are carried out in UHV chambers under conditions that are never encountered in ceramics processing. Figure 13.19. Reflection high-energy electron diffraction (RHEED) is the high-energy version of LEED. Because 2 3 Step edge 4 5 FIGURE 13.15 STM of a surface of Fe2O3. 1–5 indicate different rows of atoms. spectroscopic information. It is also much quicker, easier, and cheaper than TEM. Figure 13.15. Not only the well-known semiconducting ceramics (Si, Ge, GaAs, etc.), but also the less well known, but adequately conducting oxides, Fe2O3 and NiO, have been successfully imaged by scanning tun- neling microscopy (STM). The main advantage of STM is that it gives better resolution normal to the (A) plane than any other technique. Thus we can examine the out-of-plane relaxations and rumpling that are so important in determining surface energies. Figure 13.16. When the ceramic is not conducting we can use atomic force microscopy (AFM) to examine the surface. The vertical resolution is not quite as good as STM, but the main loss is in the lateral resolution. This is because the geometry of the probe tip will influence the image as seen from the width of the lines in this figure. There are variations of AFM, as summarized in section 10.6, which can provide information on magnetic fields or even on the mechanical properties. We can characterize the shape of the AFM tip using SEM and can even functionalize the tip by coating it as shown in Figure 13.17. In principle, using such a coating allows us to very the chemistry of the tip/ sample contact point. Diffraction techniques are the classic approach and were widely used by surface scientists before the advent of 0.2nm scanned probes. steps Figure 13.18. Low-energy electron diffraction (LEED), as (B) its name implies, produces data in the form of a dif- FIGURE 13.16 Sub-unit-cell surface steps on (a) sapphire and fraction pattern, which must then be interpreted. Since (b) spinel. The steps are 0.2 nm high in each case. 236 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s  0.2nm The TEM is used to study surfaces in many ways; here steps we will emphasize three imaging techniques, but note that combining diffraction with imaging at near atomic resolu- tion in the TEM is its unique ability. We should dispel one bias immediately: TEMs can be UHV instruments. Usually they are not operated as such since they are required to be multiuser facilities, which is usually incompatible with UHV. So even though you may see surface steps, the TEM sample will usually have a layer (intentional or otherwise) of amorphous material on both surfaces. Another myth is that TEM samples are so thin that they do not represent the bulk. If you need a thick sample, you use a high- voltage machine where an Si TEM sample can be 5 μm thick (but you will not see atoms). Another myth is that the area viewed in the TEM is tiny. This is wrong: if the sample is prepared using a focused ion beam (FIB), the thin area can be greater than 25 μm square, have a uniform thickness, and be taken from a precisely located region of a bulk sample. 1 μm (C) Figure 13.20. Plan-view (conventional) TEM (CTEM). FIGURE 13.16 Continued The electron beam is approximately normal to the plane of the thin TEM spinel and Al2O3 samples the electron energy is higher, the beam now probes (although a sample may subsequently be tilted by as deeper into the sample, but this is partly compensated much as 70°). by the beam being incident on the surface at a glancing Figure 13.21. Cross section TEM (XTEM). The sample is angle. RHEED is particularly valuable during thin- usually prepared as a sandwich, and a thin section is film growth in which the fact that it requires only a cut to be normal to the median plane. This geometry reasonably good vacuum may not be a disadvantage. allows us to see how features change as we move from (B) (A) FIGURE 13.17 SEM image of AFM probe tips (a) end-on (SEM) and (b) side view (TEM); the latter has been coated to test the interaction with the sample. 13 .1 2 C h a r a c t e r i z i n g S u r fac e s ................................................................................................................................ 237  FIGURE 13.18 LEED patterns from GaN on Al2O3 as the accelerating voltage is changed. FIGURE 13.19 RHEED pattern from anatase film grown on FIGURE 13.21 Cross section HRTEM image of a surface of Fe2O3. LaAlO3. (A) (B) FIGURE 13.20 Plan view TEM images of steps on MgAl2O4 and Al2O3 ; the steps occur when the thickness of the TEM sample changes abruptly. 238 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s  TEM is a superb tool for examining surfaces of ceramics; one problem is that you always probe two surfaces at once (except in REM). The SEM is used to study surfaces in many ways; as noted above, diffraction is also possible, and again SEMs can be UHV instruments. In fact, this is necessarily the case in the electronics industry. 13.13 STEPS We saw in chapter 12 that dislocations move by the move- ment of jogs or kinks that are, themselves, defects on the dislocation. When we consider the movement of surfaces at an atomic scale, the surfaces (like dislocations) actually move by the translation of defects along them. The prin- cipal surface defects are line defects known as steps, or ledges if they are higher than a few lattice planes, and FIGURE 13.22 REM image from a GaAs substrate with a these, in turn, translate by kinks moving along them. Alx Ga1−x As/GaAs superlattice; the substrate has cleaved perfectly. We usually assume that steps on ceramic surfaces will be quite straight, as shown for spinel in Figure 13.16b, but they can appear to be smoothly curved as seen in images of steps on the {001} surface of MgO. The lowest-energy the bulk toward the surface; it is particularly useful in plane for MgO is the {100} plane, which is also the cleav- thin-film growth where we need to see the surface and age plane. Some observations suggest that the {111} plane how the layers developed. also has a low energy, but this surface may be stabilized Figure 13.22. Reflection electron microscopy (REM) is an by water. Steps are also usually multiples of unit cells in old technique that was revived in the 1980s but is still height, but those shown in Figure 13.16a are pairs of steps not widely used. The sample is essentially bulk mate- on the basal plane of Al2O3 that are only 0.2 nm high. rial with just one surface viewed. The electrons are Steps on MgO, wurtzite, and rutile surfaces are shown diffracted off the surface as in RHEED (the diffrac- in Figures 13.23. The steps on the MgO show theoretically tion pattern looks just like any other RHEED pattern), predicted displacements at the step. [Since there is a peri- and are then imaged by the TEM in the usual way. The odic set of steps, this surface could be called the (501) resolution is about 0.7 nm and chemical analysis can surface.] The special feature of the steps on the wurzite be considered as shown by the Al xGa1−xAs/GaAs surface is the presence of the dangling bonds, which are superlattice in this image; square millimeters of surface localized at the step. The rutile surface shows that even can be viewed just by scanning the sample. Notice the when the surface is modeled using hard spheres, the struc- foreshortening. ture of the steps depends on their orientation. [These two vicinal surfaces could be called (223) and (443).] + – + – + – + – + – + – + – + [1010] [0001] d = 0.26 nm + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + (A) FIGURE 13.23 Different representations of surface steps: (a) (100) cross section of MgO; b) wurtzite; (c) (110) TiO2. (B) 13 .13 S t e p s ...................................................................................................................................................................... 239  [001] [110] [001] [110]  FIGURE 13.24 Studies of changes occurring at the surface of TiO2 FIGURE 13.23 Continued using LEEM. A total of 20 seconds separates the four images. The different contrast occurs because of the surface reconstruction. 13.14 IN SITU technique we want to use to make the observation/meas- Many techniques can be adapted to study surfaces in situ urement. EMs operate best in the highest vacuum, and a at temperature, which is not the case for most other defects glass lens placed to close too an object at 1400°C will because they are not so accessible; the question is: can we quickly degrade. learn anything new? The techniques we would most like Although low-energy electron microscopy (LEEM) to use are AFM and STM, neither of which is suitable currently operates only to ∼900°C, it could in principle go because the high temperatures will quickly change the higher. LEEM is particularly attractive since it is a direct probe tip. The idea of in situ observation is simply that we imaging technique and gives excellent resolution on the do not need to cool the sample to room temperature before height of steps. Use of LEEM to study the surface of TiO2 examining it, which is a terrific advantage when materials is illustrated in Figure 13.24. REM should be able to change as we cool them. The problem is that we often provide similar data. The TEM can provide information cannot control the conditions (such as the environment) as on samples at temperatures up to 2000°C, but the detail well as we would like when making such studies because tends to become less controllable as the temperature controlling the environment is often incompatible with the increases. In the image shown in Figure 13.25 a film of FIGURE 13.25 Changes occurring at a surface studied by in situ TEM. An NiO film has been reduced to Ni, which then dewets the sample and grows on the sapphire substrate. 240 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s  (A) Radius (Å) 25 16.7 12.5 5.82 1800 Lattice Melting Parameter T in K bulk (Å) 1600 5.8 1400 5.78 1200 5.76 1000 5.74 800 5.72 600 5.7 400 2 3 4 5 6 7 8 9 10 20 30 40 50 100/R (Å ) -1 Radius (Å) (B) FIGURE 13.26 Nanoparticle melting: (a) computer modeling for Au; (b) showing the lattice parameter and melting temperature changes as the size of CdS nanoparticles decreases. NiO has been reduced to Ni metal while heating in the becomes more rounded starting at the edges. The shapes TEM at 1000°C. New microscope holders and stages are shown were calculated using a potential for Au; the graphs becoming available so we will see much more use of in are experimental measurements for CdS. situ TEM in the future. Most of the work has been carried There are examples in which the structure of a parti- out using the SEM; environmental SEMs can heat the cular phase appears to be stabilized when in nanoparticle sample to ∼1500°C, but again the challenge is in control- form just as some thin films can have their structure stabi- ling the local pO2, etc. lized by being in contact with a substrate. Perhaps the best- known example is that γ-Al2O3 appears to be the stable structure at high T when in the form of nanoparticles. 13.15 SURFACES AND NANOPARTICLES Surfaces are generally thought to melt before the bulk. 13.16 COMPUTER MODELING Hence the melting temperature of small particles is lower than that of the bulk. Such measurements can be made The use of computers to model surfaces and many other only while the particles are at temperature, so we know aspects of ceramics is a rapidly broadening field in which this is very difficult experimentally. In comparison, for the great caution is always needed. Commercial software computer it is quite straightforward as long as we can packages are now available for PCs and supercomputers. simulate physically meaningful situations. Computer However, if a computer analysis is relevant to your modeling can be used to provide clues, as shown in Figure research, how can you know if the code was right, if the 13.26, which is a case where we are not taking account of program has been applied correctly, if the input data were the environment. Notice that the surface gradually correctly typed, what potentials were used to describe the 13 .16 C o m p u t e r M o d e l i n g .......................................................................................................................................... 241 ions, etc? Details like how the cell was constructed for the Wulffman (NIST) is a software package that allows calculation are usually given, but it is very easy for these you to model the Wulff shapes of crystals interactively. powerful black boxes to produce nonsensical results. You can specify the crystal symmetry. The source for The Madelung problem for surfaces is, in one impor- NIST’s Wulffman program is available for you to use tant way, more complicated than for bulk crystalline mate- (www.ctcms.nist.gov/wulffman). There are commercial rials: a bulk sample must be neutral overall and the programs that address the same problem. positions of the ions are well defined for each unit cell, At the surface, this is not necessarily the case. MARVIN (the acronym for Minimization And Relaxation of Vacancies 13.17 INTRODUCTION TO PROPERTIES and Interstitials for Neutral surfaces program) is one of the best-tested software packages. The essential part of The properties of ceramic surfaces are so broad and far using any software package is that for the material in reaching (as we said in the beginning) that we will just question, it must be able to reproduce some experimen- provide a few examples, beginning with the general and tally determinable facts that were not used as input to the becoming more specific, to emphasize this range of topics. program! The value of computer modeling is illustrated The emphasis of this section is to introduce the fundamen- by a nanoparticle of SrO growing on an MgO substrate tal ideas so that you can be aware of the possibilities and in Figure 13.27; although the two oxides have the same the pitfalls. structure, the SrO is slightly misoriented as it grows. There are three distinctly different ways to terminate Growth. Thin films are invariably grown on surfaces. a (0001) surface in alumina: a single layer of Al3+ ions, a Catalysis. A catalyst is either the surface itself or it is double layer of Al3+ ions, or only O2− ions. This basal- supported on a surface, with usually one or both of plane surface of alumina has a lower energy than the these components being a ceramic. Reactions occur at rhombohedral-plane surface because the single outer layer reactive sites, but the principle of catalysis is that the of Al3+ ions can relax by moving in toward the bulk. We material facilitates, but is not chemically changed by, “know” this from computer modeling. It is very difficult the process. to “observe” structure experimentally. Joining. Materials are joined together by contacting two Surface Evolver is one of the most fascinating freeware surfaces. In ceramics, the ionic and/or covalent nature packages available to materials scientists. The program of the bond tends to make this process more difficult (by Ken Brakker) uses finite-element analysis to compute than it is for metals or plastics. the morphology of surfaces that are subjected to various Nanoparticles. The shape of a nanoparticle is determined forces, such as surface tension and interface stress. It runs in part by the surface energies, but the junctions on most computers, not just the Mac. If you are interested between surfaces (double and triple junctions, i.e., in modeling droplet geometries, for example, this is the edges and points) become more important as the size program. of the particle decreases; we know very little about these surface features. Voids. We rarely encounter real voids in ceramics except in the computer (they all contain something). They have all the challenges of particles, including the junctions, and can have nanoparticle dimensions. Gen- erally, they have not been extensively studied experi- mentally because they are difficult to see! Superconductors. The high-Tc superconductors are being used by industry, but not to support high-speed trains as some had proposed in the early days. The applica- tions often use thin films, for example, in SQUID devices produced by engineering the surfaces to produce particular grain boundaries. Surface charge. The fact that ceramic surfaces can become charged means that it is possible to align nanoparticles, for example, using this charge. That this can be achieved is illustrated in Figure 13.28 for Pt particles on Al2O3. The concluding message is that we can clearly make enor- mous use of ceramics without understanding surfaces, but FIGURE 13.27 Computer modeling of oxide clusters on an oxide if we do understand them then we can start using ceramics surface. to their full potential. 242 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s  FIGURE 13.28 Self-assembly of Pt nanoparticles due to charging along a surface ridge in Al2O3: the particles sit on the ridge not the valley! CHAPTER SUMMARY The two key properties of any surface are that it has an associated energy and it is directly connected to the two media that it separates (e.g., a gas and a crystal). It is difficult to over emphasize the importance of surfaces especially in ceramics. We can summarize some of the most important results of this chapter quite briefly.  The energy of crystal surfaces depends on the orientation of the surface.  There is always a tendency for a curved surface to lower its energy by becoming flat.  The surface is critical in the growth of thin films.  Wetting and dewetting describe the addition or removal of material from a surface. The important consideration is why does one, or the other, occur and how can we make use of it.  We can explore the surface structure and chemistry of surfaces at the atomic level because they are so accessible but the problem is keeping them clean. In ceramic processing, sur- faces are rarely clean. In nanotechnology surfaces become increasingly more important because a greater fraction of the atoms are at the surfaces. In the smallest nanoparticles, all the atoms may be at the surface of the particle. This property is quite closely related to a completely different group of materials, the foams. One difference between these two situations is the local curvature of the surface. We will see in the following chapters that the surface is also critical when crystal grains join together (forming grain boundaries by sintering, etc.) or are separated (fracturing ceram- ics). We will also mention the role of surfaces in the polishing process. PEOPLE IN HISTORY Binnig, Gerd was born in Frankfurt, Germany in 1947. He joined the IBM research laboratory in Zürich in 1978. With Rohrer he developed the scanning tunneling microscope for which they shared the 1986 Nobel Prize in Physics. Rohrer, Heinrich was born in St. Gallen, Switzerland in 1933. He did his PhD work at ETH (Swiss Federal Institute of Technology) on superconductivity and spent a 2-year postdoctoral at Rutgers University in New Jersey. In 1963 he joined the IBM research laboratory. Young, Thomas was born in Milverton, Somerset (UK) in 1773. He was a physicist and physician who made contributions in many areas of science. He introduced the modulus of elasticity (known also as Young’s C h a p t e r S u m m a ry .......................................................................................................................................................... 243  modulus) and the equation used to analyze the wetting of surfaces. His work in optics gave us Young’s fringes and Young’s slit. He was also an Egyptologist who helped decipher the Rosetta Stone. He died in London in 1829 and is buried in Westminster Abbey where his epitaph states that he was “a man alike eminent in almost every department of human learning.” Synge, E.H. (Phil. Mag. papers 1928–1932) proposed NSOM 50 years before it was discovered. GENERAL REFERENCES Bailey, S.W., Frank-Kamenetskii, V.A., Goldsztaub, S., Kato, A., Pabst, A., Schulz, H., Taylor, H.F.W., Fleischer, M. and Wilson, A.J.C. (1977) Acta. Cryst. A33, 681. International Union of Crystallographers/ Mineralogists report on Nomenclature (epitaxy). This report from a committee of eminent scientists defined the correct formation of adjectives for epitaxy and topotaxy. It was a lot of work and is generally ignored. Boys, C.V. (1959) Soap Bubbles: Their Colors and the Forces which Mold Them, Dover, New York. A series of lectures for “juvenile and popular audiences.” Henrich, V.E. and Cox, P.A. (1996) The Surface Science of Metal Oxides, Cambridge University Press, Cambridge. Very useful. Herring, Conyers (1951) Some Theorems on the Free Energies of Crystal Surfaces, Phys. Rev. 82(1), 87. This is a paper you can read. Israelachvili, Jacob (1991) Intermolecular & Surface Forces, Academic Press, London. The classic book on this topic. Kolasinski, Kurt W. (2002) Surface Science, Wiley, Chichester. An excellent introduction to the complexities of the surfaces of materials in general. Lagally, Max G., Ed. (1991) Kinetics of Ordering and Growth at Surfaces, Plenum, New York. Noguera, C. (1996) Physics and Chemistry at Oxide Surfaces, Cambridge University Press, Cambridge. Very useful. Perkowitz, S. (2000) Universal Foam, Walker & Co, New York. Puts foam into perspective. Should be required reading for materials science. Porter, D.A. and Easterling, K.E. (1981) Phase Transformations in Metals and Alloys, Van Nostrand Reinhold, New York. Chapter 3 gives a basic introduction to surface energy. Schwartz, A.J., Kumar, M., and Adams, B.L., Eds. (2000) Electron Backscatter Diffraction in Materials Science, Kluwer, New York. Young, Thomas (1805) An Essay on the Cohesion of Fluids. Phil. Trans. R. Soc. Lond. The paper was read on 20 December 1804. Worth reading yourself. Vaughan D.J. and Pattrick, R.A.D., Eds. (1995) Mineral Surfaces, Mineralogical Society Series, Chapman & Hall, London. The source for information on this topic. SPECIFIC REFERENCES Binnig, G., Rohrer, H., Gerber, C., and Weibel, E. (1982) “Surface studies by scanning tunneling microscopy,” Phys. Rev. Lett. 49, 57. Burton, W.K., Cabrera, N., and Frank, F.C. (1951) “The growth of crystals and the equilibrium structure of their surfaces,” Philos. Trans. R. Soc. London Ser. A 243, 299. Classic. Dupré, A. (1869) Théorie Mécanique de la Chaleur, Paris, p. 207. Frank, F.C. (1949) “The influence of dislocations on crystal growth,” Disc. Farad. Soc. 5, 48. (1952) “Crystal growth and dislocations,” Adv. Phys. 1, 91. Classics and easy to read. Goniakowski, J., Noguera, C., and Claudine, C. (1995) “Relaxation and rumpling mechanisms on oxide sur- faces,” Surf. Sci. 323(1–2), 129. Kubaschewski, O. and Alcock, C.B. (1979) Metallurgical Thermochemistry, 5th edition, Pergamon, Oxford, Table D, p. 367. Values are given for many materials in kcal/mol; the conversion factor is 1 cal = 4.184 J. Lord, E.A. and Mackay, A.L. (2003) “Periodic minimal surfaces of cubic symmetry,” Current Sci. 85(3), 346. This paper on surfaces is an example of what you can do with Surface Evolver; not easy but fascinating. Ragone, D.V. (1995) Thermodynamics of Materials, Volume II, Wiley, New York, p. 100. Werner, J., Linner-Krcmar, B., Friessc, W., and Greil, P. (2002) “Mechanical properties and in vitro cell compatibility of hydroxyapatite ceramics with graded pore structure,” Biomaterials 23, 4285. Wulff, G. (1901) “Zur Frage der Geschwindigkeit des Wachstums und der Aufläβ der Krystallflachen,” Z. Kristallogr. 34, 449. The original paper on the Wulff construction. Young, T. (1805) “An essay on the cohesion of fluids,” Phil. Trans. R. Soc. London 95, 65. Zampieri, A., Kullmann, S., Selvam, T., Bauer, J., Schwieger, W., Sieber, H., Fey, T., and Greil, P. (2006) “Bioinspired rattan-derived SiSiC/zeolite monoliths: Preparation and Characterisation,” Microporous Mesoporous Mater. 90, 162. 244 ....................................................................................................................... S u r fac e s , N a n o pa r t i c l e s , a n d F oa m s  WWW www.intelligensys.co.uk/sim/metamorph.htm (050728) is the site for MetaMorph. EXERCISES 13.1 A droplet of liquid silver is placed on an MgO substrate. The MgO(s)-Ag(l) interfacial energy is 850 mJ/m 2. (a) Calculate the contact angle of the Ag droplet. (b) Does the Ag wet the MgO? (c) If not, how might you lower the contact angle? 13.2 Repeat question 13.1 for the Al2O3 (s)/Ag(l) system. The Al2O3 (s)/Ag(l) system interfacial energy is 1770 mJ/m2. 13.3 Determine the number of free bonds/m 2 on the (100), (110), and (111) planes of germanium. The lattice parameter of Ge is a = 0.5658 nm. 13.4 Using Eq. 13.7, compare the energy of the (110) and (001) surfaces in MgO. 13.5 Can you deduce any properties about the materials from the observations and graph in Figure 13.9? 13.6 Figure 13.6b indicates that there are 74 surface atoms. How is a surface atom defined in this context? 13.7 Estimate the number of atoms in the particle imaged in Figure 13.6. 13.8 Rank the following systems in terms of increasing interface energy: Al 2O3 (s)-silicate glaze(l), Al2O3 (s)-Pb(l), SiO2 (glass)-sodium silicate(l), and SiO2 (glass)-Cu(l). Discuss how you arrived at your ranking system and state any assumptions that you make. 13.9 You are attempting to grow a copper thin film on MgO. What characterization technique (or techniques) might you use to determine which of the three growth modes shown in Figure 13.14 occur? What growth mechanism would you think would be most likely? 13.10 The most useful way to express surface area is in terms of m 2 /g. Using these units what is the surface area of Pt catalyst particles in Figure 13.28? C h a p t e r S u m m a ry .......................................................................................................................................................... 245  14 Interfaces in Polycrystals CHAPTER PREVIEW This chapter is part 2 of the three-part series on interfaces. Crystalline solids usually consist of a large number of randomly oriented grains separated by grain boundaries (GBs). Each grain is a single crystal and contains many of the defects already described. A GB is defined as the surface between any two grains that have the same crystal structure and composition. Many GBs, but not all, can be modeled as arrays of dislocations. The dislocation model can be misleading; the GBs that may be most important in a ceramic may be the ones that do not appear to contain dislocations. So the warning is, we may some- times concentrate on a particular type of GB just because we can understand that type of GB. Unless we fully understand GBs in ceramics, we will never have a full understanding of what happens during ceramic processing or why ceramics have certain mechanical properties, con- ductivity (thermal or electrical), etc. GBs become even more important as fine-grained nanos- tructured ceramics become more available. We also need to understand the junctions formed when three or four grains join: these are known as triple junctions (TJs) and quadruple junc- tions (QJs), which we might regard as new line and point defects, respectively. We conclude with a discussion of properties, not because they are unimportant (nor because of the bias of the authors). We want to understand GBs so as to explain some properties and to predict others. 14.1 WHAT ARE GRAIN BOUNDARIES? rotation axis and meet on a plane, which may be curved. The rotation axis is fixed only for a given boundary and Grain boundaries are internal interfaces and behave much is not unique, even for that boundary; there are different like external surfaces, but now we have to be concerned ways to form the same GB. We start by considering two with two crystal orientations, not one. Just as for surfaces, identical grains. Fix one grain and rotate the other about we have a pressure difference associated with the GB any axis. Cut each crystal parallel to a particular flat plane curvature and a driving force that tends to lead to an (to keep it simple) in space and join the grains at this overall increase in grain size whenever possible. Grain plane. This plane is the GB. Then allow the atoms to relax morphology and GB topology are two aspects of the same to a low-energy configuration (which may not be the topic. It is instructive to think of the model of soap minimum energy). foams: a soap film is flat when in equilibrium and it The conventional approach is to consider four types of has a finite thickness. Three soap films meet along a GB based on the symmetry operation used to create them: line—a TJ. If you blow on twist, tilt, mixed, and a soap film (apply a pres- twin. sure) it bows out until the TWIST, TILT, TWIN, LOW, HIGH, The first two (and hence “surface tension” balances AND “GENERAL” the third) designations are the applied pressure. Twist n normal to plane really helpful only when Whenever we join two Tilt n parallel to plane the misorientation angle is grains of the same compo- Twin boundary Mirror across GB plane small (low-angle GBs). sition and structure, we Low-angle GB θ < 10° (low is small!) This description is based form a GB. The grains are High-angle GB Structured, θ > 10° on the location of the rota- related to one another by a General GB Not a special GB! tion axis. 246 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s   Tilt boundary. Rotation axis (n) is in the boundary plane.  Twist boundary. Rotation axis is normal to the bound- ary plane. 2 3 A symmetric twin boundary can also be described as a twist boundary or a tilt boundary—the difference 1 depends on which aspect of the symmetry we think is most important. Not all twin boundaries are parallel to a mirror plane. There are two well-known models of GBs that were developed primarily from studies of metals by considering Lattice Point the relative misorientation of the adjoining grains. These are the coincidence-site lattice (CSL) theory and the dis- placement-shift-complete lattice (DSCL). We first define two special quantities Σ and Γ. Imagine two infinite arrays of lattice points (one array for each crystal): they both run throughout space and have a common origin. For certain orientations, a fraction of the points in each lattice will be common to both lattices. CSL We call this fraction Σ−1. (Then Σ is always an integer.) The lattice made up by these points is called the coincident-site lattice or CSL. The CSL is a lattice of common lattice sites, not common atoms. DSCL If you translate one grain relative to the other, Σ is not (A) changed. The Idea of S It is easiest to understand these concepts by looking at simple illustrations as shown in Figure 14.1 for both Σ = 3 (for Al2O3) and Σ = 5 (for MgO). (Look back to Chapter 6 for the crystal structures.) The Σ = 3 diagram shows two twin-related unit cells with the lattice sites identified. Overlapping these two cells produces the pattern in the shaded box and you can see that one in three lattice sites are common to the two grains (the ones at the corners of the box). The CSL for Σ = 5 (just the lattice sites are shown) is also identified in the shaded box. Note that we must take account of both ions in considering the actual (B) structure (see later). Sometimes it appears that the most FIGURE 14.1 Schematics of two low-Σ GBs. (a) Σ = 3; (b) Σ = 5. valuable feature of the CSL model is that it gives a short- hand notation for talking about GBs. Low-angle bounda- very different. Γ can equal 1 for the Σ = 3 GB, but could ries are all Σ = 1 GBs. Especially in ceramics, not all twin be 3, 9, or greater. boundaries have Σ = 3. (Σ = 3 occurs in face-centered Throughout our discussion of GBs, you should keep in cubic (fcc) crystals because the stacking of close-packed mind that there are many similarities to surfaces. planes is ABCABC, so one in three planes is coincident across the twin boundary.) For a particular GB, if we  There is a pressure difference across a curved GB just choose any plane, then a certain fraction of points will lie as there is across a surface. on this plane in both lattices. We call this fraction Γ −1.  Charge affects the structure and chemistry of GBs. Again, it is easiest to appreciate the meaning of these  The structure of a GB determines its properties and definitions by studying the examples in the following sec- behavior. tions. Γ is not widely used but might be the most important  GBs can be wet and dewet by GB films just as surfaces factor and it reminds you that the different planes may be are by surface films. 14 .1 Wh at a r e G r a i n B o u n da r i e s ? .......................................................................................................................... 247  Computer modeling of GBs can give considerable  Since the unit cells of all but the simplest binary com- insights, but be careful when using older results in the pounds are large, it is likely that a GB with a fixed literature. The complexity of ceramic structures and the misorientation angle and interface plane will probably Madelung problem cause difficulties and some older simu- (rather than possibly) exist in more than one (meta)stable lations may not be reliable, in part, because they used too configuration. There will still only be one minimum little material in the calculation because of the capabilities energy. of the computers.  Energy is dependent on the GB plane, just as it is for We will discuss the properties of GBs later, but should surfaces. Accordingly, steps and facets (large steps) on keep in mind some features as we work through the these GBs will also be important. They are actually chapter. necessary for the GB to move.  Many ceramics are processed in the presence of a  The density of atoms in GBs is less than in the bulk second or third phase far away from conditions of crystal. thermodynamic equilibrium, and a remnant of this  The chemistry of a GB is not the same as the bulk phase may remain at the GB even if it is not the lowest- (because the bonding must be different). energy configuration. Impurities segregate to GBs  Properties of GBs must differ from those of the bulk. as illustrated by the XEDS and EELS plots in All GBs have a thickness (just like the soap films) and Figure 14.2. the GB is not uniform across that thickness; so GBs are  There is the problem of specimen preparation for analy- actually volume defects again. sis of interfaces in ceramics. In general, we cannot prepare a sample without altering the GB in some way. 14.2 FOR CERAMICS The extra difficulty is that we may never see a clean GB and, unlike surfaces, we have no way to clean one: Ceramics are usually used in a polycrystalline form. GBs ultrahigh vacuum (UHV) does not help us once the GB is in ionic and covalent materials must be better understood there. What is different in comparison to metals? Metals to improve the science of processing of many modern try to make the density of atoms uniform due to the nature ceramic materials; the properties of polycrystalline ceram- of the electron gas. GBs in ceramics may be much more ics depend directly on the geometry and composition of open. The density of atoms in the GB can be very different GBs. The types of GBs commonly found in ceramic mate- from that in the bulk grains. rials range from situations in which the distance between Is CSL theory important for ceramics? The CSL theory the grains is ≥0.1 μm and such grains are separated by a is relevant only when the adjoining grains are in direct second phase (glass), to the basal twin boundary in Al2O3, contact. In ionic materials, we know that surfaces are which is atomically abrupt and potentially very clean. almost never clean. Adsorption phenomena occur at We need to understand how the presence of glass internal interfaces as they do at surfaces. The driving affects GBs in crystalline materials. This glass can be force for segregation to GBs can be large. In fact, most present on the surface of grains or within GBs as an inter- GBs that have been studied have been “dirty.” Pure poly- granular film (IGF) in either single-phase materials or in crystalline ceramic materials do not exist. The layer of materials with an intentionally high (or unavoidable) glass glass that may be present at the GB is invariably content. associated with impurities. Such films are unusual in sem- The type of GB present in a sintered (or hot-pressed) iconductors (although they can exist) and would be excep- compact may be significantly influenced by the surface tional in metals. characteristics of individual particles before and during As with other materials, it is difficult to discuss so- sintering. Obviously if there is glass on the particle, there called general GBs rather than special ones. Even special is likely to be glass in the GB. We need to understand the GBs in ceramics are not well understood. Both general behavior of the surface at high temperatures under condi- and special boundaries are likely to be far less clean than tions appropriate to sintering (Chapter 24). Since GBs can models of such interfaces might assume. Methods for ana- be structured or can contain a thin noncrystalline layer, lyzing interfaces containing IGFs have been compared. It the chemistry of the region close to the GB is important. was concluded that the results can be ambiguous even We start by asking what is special about GBs in ceram- when a combination of techniques is used. Unambiguous ics? This is the question we asked about surfaces and dis- characterization will be achieved only when the structure, locations and the answer is basically the same. chemistry, and bonding are assessed simultaneously. What facts are actually known about GBs in ceramics?  Ceramics have localized charge or covalent bonds. We can make the following statements. Dangling bonds exist at GBs.  Since the bonding is ionic, covalent, or mixed ionic/  Structured GBs do exist in ceramic materials. This covalent, there may be large local changes in density conclusion applies to both high- and low-angle at the interface. Ceramic GBs have a space charge. GBs. 248 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s  0.08 Solute/Zn Peak E (+) (—) Ratios 0.06 Bi Co Fe 0.04 Approximate detection 0.02 limit 0 -80 -40 0 40 80 d (nm) (A) (B) FIGURE 14.2 Solute distribution at GBs. (a) Profiles using XEDS; (b) EELS spectra used to analyze a GB in sapphire. In (a) the integrated X-ray solute/Zn peak ratios are plotted against d, the distance from the GB.  GBs in ceramic materials do exist that are not “struc- 14.3 GB ENERGY tured” but are, instead, wet over their entire area by an amorphous phase (an IGF). The energy of a GB is a very important quantity, but it is  The structure of GBs in ceramic materials tends to be even less well known than for surfaces, and is usually relatively more open (less dense) than is found for determined in relation to surface energies. There are two interfaces in metals that are otherwise crystallographi- key questions: cally similar.  The effects of several ions being present in the unit  How do we define the energy of a grain boundary? cell can be recognized. They can produce special  What factor causes a GB to have a low interfacial interfaces in which only one sublattice is affected or energy? can cause a modification of the interface structure itself. The GB energy, γ, depends on the misorientation of  A particular interface may not have a unique structure the two grains and on the orientation of the plane. We can because of the presence of two ions or because two again use the Wulff plot (γ versus θ where θ now means or more structures are possible that do not have the misorientation) and the inverse Wulff plot (γ −1 versus significantly different energies. It is also likely that θ). The challenge of γ versus θ plots is to define the the presence of impurities at the interface will modify orientation of the GB plane, i.e., having fixed θ, you must the structure by favoring different polyhedral sites. still fix n, the GB normal for both grains. Keep in mind 14 . 3 G B E n e r g y .............................................................................................................................................................. 249  10 particles can be determined using TEM; the angles Σ=25 Σ=15 Σ=17 Σ=5 between different {001} planes are measured much as f(θ) x 100 Haüy originally did for single crystals. We now do this 8 more accurately using diffraction patterns or high-resolu- tion transmission electron microscopy (HRTEM) images. This experiment is special for ceramics because we are joining nanoparticles at high temperatures although we do 6 not actually know when they joined so we do not know the sintering temperature. Figure 14.3 shows an example of such particles together with the frequency of occur- 4 rence, f(θ), of the misorientation angle. The oxide bicrystal particles form with a strong preference for certain orientations in which the two crystals have a frac- 2 tion of their lattice sites in common: the coincidence boundaries. This experiment has long been one of the bases for believing that Σ is an important parameter in determining the energy of GBs. It does not measure γ but 0 0 5 10 15 20 25 30 35 40 45 does suggest that γ is related to Σ. Unfortunately, results θ (Deg) from computer modeling suggest that this is not necessar- (A) ily the case, but it is such an attractive intuitive concept that it persists. Energy of Low-Angle GBs When θ is small, the energy of a low-angle GB is approxi- mated as the total self-energy of the dislocations within a unit area of the boundary. However, as θ increases the stress fields of the dislocations progressively cancel out so that the energy increases at a decreasing rate and may peak before decreasing to a low value at a special orienta- tion as shown in Figure 14.4. When the dislocation spacing is small, the dislocation cores overlap, so that when θ exceeds 10° (somewhere in the range of, say, 10–16°) it is not possible to identify the individual dislocations. The Read–Shockley formula for the energy, E, of a low-angle GB considers the stress field and the core energy of the dislocations. E = E 0θ(A − lnθ) (14.1) (B) E 0 is a constant that is a function of the elastic properties FIGURE 14.3 Rotated MgO nanoparticles and their relation to Σ. The frequency of measuring a rotation θ is f(θ). of the material (and hence of the stress field) and A is a 1 that we expect γ to decrease as the temperature increases as is found for surfaces (Eötvos rule); this dependence on E arb temperature will be important in sintering. One approach units to the problem is to plot the individual Wulff plots for the two separate grains and then to consider what happens 0.5 when the two grains are joined along a particular plane. MgO Smoke One method used to examine the possibility of low-energy 20 40 60 80 100 120 GBs is the classic MgO smoke experiment. Mg metal is θ (°) burned in air and the resulting MgO smoke particles are FIGURE 14.4 Cusp in a plot of GB energy versus misorientation caught on a grid. The relative orientations between cube angle, θ. 250 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s constant that depends on the core energy (remember our discussion of r 0, the dislocation core radius). We can also define the Gibbs adsorption isotherm for grain boundaries. We extend the analysis from surfaces to the internal interface. ∂γ = −Γ i (14.2) ∂μi where Γi is the excess moles of i per unit area of the GB. All the other variables (e.g., P and T) are held constant. 14.4 LOW-ANGLE GBs Low-angle GBs contain arrays of dislocations. In its sim- plest form, the structure of the twist boundary consists of two sets of orthogonal screw dislocations as shown in Figure 14.5a and b; the schematics show the structure before and after relaxation to form the screw dislocations. Figure 14.5c shows how dislocations in a twist boundary (A) might be seen emerging at the surface; you can see that part of the grain is physically twisted relative to the other because of the screw dislocations. The simplest tilt GBs consist of one set of edge dislocations as shown in Figure 14.6. Note that the statements both include the word “sim- plest.” Most tilt boundaries will have two different sets of edge dislocations, and twist boundaries in noncubic mate- rials may be accommodated by only one set of disloca- tions! Figure 14.6b shows that we must use two sets of edge dislocations if the GB is not symmetric. (We some- times have to, even if it is symmetric.) Figure 14.7 is a TEM image of a twist boundary in Si; a tilt boundary in NiO is shown in Figure 14.8. The image of this tilt boundary is particularly interesting because it shows that the density is different at the GB. The spacing of the dislocations, D, is related to the boundary misorientation angle, θ, and the Burgers vector of the dislocations, b. b/2 b D= ≈ (14.3) sin θ / 2 θ The latter relation holds only if θ is very small. In this (B) case, we can either reveal the individual dislocations by decorating them or by etching the surface as shown in Figure 14.9. Equation 14.3 has been well tested for fcc metals and some simple ceramics. Sh1 Sh2 Sh3 FIGURE 14.5 Schematics of a low-angle twist GB. (a) Before and (b) Sv1 S Sh4 v2 Sv3 S after local atomic relaxations. (c) The twist when the GB emerges at the v4 surface. (C) 14 . 4 L o w -a n g l e G B s ..................................................................................................................................................... 251  θ b D FIGURE 14.7 Two sets of orthogonal screw dislocations in a low- angle (001) twist GB in Si. (A) E C tion of the presence of two types of ions is well known in [100] ceramics since it results in the phenomenon of dissociation by climb of dislocations in the lattice or in the GB. The phenomenon has been recorded for materials such as φ – 12θ spinel, Al2O3, and garnet. Actually, this phenomenon can also occur in more complex metallic, ordered alloys for precisely the same reason. In Al2O3 and MgAl2O4 the partial dislocations created by the dissociation process are “perfect” dislocations of the oxygen sublattice; the stack- ing fault thus formed is therefore only a fault on the cation sublattice. A [100] φ+ 12 θ B (B) FIGURE 14.6 Schematics of low-angle tilt GBs. (a) Symmetric; (b) asymmetric. The structure of dislocations and interfaces in ionic and covalent materials has been the subject of much theo- retical and experimental research, motivated in part by the realization that the extensive body of information and the concepts that have been accumulated for metallic systems cannot necessarily be directly transferred to these nonme- tallic systems. The structures of all defects in ceramic materials can be more complex than those of similar defects in the more FIGURE 14.8 Dislocations in a low-angle tilt GB in NiO. The thoroughly studied pure metals because of the presence of defocus (Δf ) images show a change in density at the dislocation two or more ionic species on two sublattices. The implica- cores. 252 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s (A) FIGURE 14.11 Low-angle {111} and {001} twist GBs in spinel showing two structures in each case. structure shown in Figure 14.10. In the spinel (111) twist boundary, an a2– [11̄0] screw dislocation can dissociate on the (111) plane into two parallel –a4 [11̄0] screw partial dis- locations. (Because a is large and this dissociation pro- duces dislocations that would have been perfect if we considered only the O ions.) Since the self-energy of a dislocation is proportional to b2, this dissociation halves (B) the total dislocation self-energy. The partial dislocations FIGURE 14.9 Seeing low-angle GBs by (a) decoration (silver are separated by a stacking fault (SF), but the energy of particles on a GB in KCl) and (b) etch pits (LiF). this fault depends on whether the glide plane of the plane of the stacking fault is A or B. Thus, there are two differ- The effect of the large ent SFs on a {111} plane unit cell is well illustrated and two different stacking by the low-angle 111 twist MULTIPLICITY Low-angle and high-angle GBs and twin boundaries that fault energies (SFEs). The boundary in MgAl2O4. consequence of this multi- The (111) interface plane appear to be macroscopically the same can exist with more than one different structure. plicity in the value of the can be chosen as A or B in SFE is illustrated in the schematic of the crystal Figure 14.11 where the width of the SF takes on two distinct values for both GBs. (110) (001) Figure 14.12 shows the climb dissociation of edge dis- locations in a spinel tilt boundary. (This is just an exten- sion of Figure 12.15.) In Figure 14.13 we can see a so-called extrinsic dislocation (along [100]) interacting with the (A) (111) (111) A B (B) FIGURE 14.10 Spinel structure projected along <11̄0> summariz- FIGURE 14.12 A low-angle tilt GB in spinel showing an array of ing the important crystallographic planes. A and B are parallel but climb-dissociated edge dislocations. (a) The GB viewed at an structurally different (111) planes. angle; (b) at higher magnification, the dislocations viewed end-on. 14 . 4 L o w -a n g l e G B s ................................................................................................................................................... 253  B 100 nm FIGURE 14.13 An extrinsic dislocation interacting with a low-angle {001} twist GB in spinel. Note how all the dislocations are changed by the interaction as seen in the enlarged inset. screw dislocations that are already present in the interface (to accommodate the twist) in the (001) twist GB. 14.5 HIGH-ANGLE GBs FIGURE 14.15 Schematic of the (001) Σ = 5 twist GB in NiO When θ is >10°, the interface is referred to as a high-angle showing anions and cations. This structure cannot occur unless GB. Figures 14.14 and 14.15 show schematics of the Σ = some ions are removed. 5 GB in NiO in the tilt and twist configuration, respec- tively, taking account of the presence of two ions. The situ- ation is clearly complex: only the lower structure in Figure 14.14 could exist (the others have similarly charged ions too close together). The same considerations hold for the twist GB shown in Figure 14.15: when two ions of like charge are adjacent, one must be removed. As in the low- angle case, high-angle GBs can exist with more than one structure. Figure 14.16 shows images of two special GBs in ZnO; the difference between a symmetric high-angle GB FIGURE 14.14 Schematics of the [001] Σ = 5 tilt GB in NiO; only FIGURE 14.16 HRTEM images of two high-angle GBs in ZnO: the lower one is actually possible. (a) near-symmetric; (b) asymmetric. 254 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s  tors and support the earlier interpretation of experiments on MgO “smoke.” However, such interfaces have been the subject of extensive computer-modeling studies that often give a contradictory view. As these observations show, the plane adopted by a high-angle GB is a very important factor. Such GBs in ceramic materials show a particularly strong tendency to facet, so the plane must be important. These facet planes are almost invariably parallel to low-index planes in one or both grains. The basic argument is that low-index planes are the most widely separated planes and thus involve less energy when a “stacking error” is present in the crystal. A particularly striking illustration that makes us ques- FIGURE 14.17 Schematic of a GB in Al2O3 showing the creation of tion the importance of Σ as a measure of the energy of a new polyhedra in the GB. The inset shows a tilted view of the GB is provided by observations of the Σ = 99 and Σ = 41 repeating group of polyhedra. boundaries in spinel, where, by chance, the interface can and the lower-angle asymmetric counterpart is striking; facet parallel to several pairs of (different) low-index this type of asymmetric faceting often involves low-index planes in both grains simultaneously. A similar situation planes as shown here. You can imagine why asymmetric exists for phase boundaries. It could be that the faceting units might be favored by examining Figure 14.17, which onto low-index planes would lower the energy to below shows a schematic of a GB in Al2O3. Polyhedra that that of similar GBs having a lower Σ. There are no atom- were not present in the perfect crystal in Chapters 6 and 7 istic calculations for such GBs. can be present at a high-angle GB, and these can accom- modate larger impurity ions than can the bulk. 14.6 TWIN BOUNDARIES More complex high-angle GBs have been the subject of far fewer studies, in part because of the experimental As in metals, twin boundaries are common in many difficulties in characterizing them. This lack of informa- ceramic materials including MgO, spinel, Al2O3, Fe2O3, tion is unfortunate since these interfaces are ubiquitous the rare earth oxides, quartz, Si, and, of course, the new in sintered materials. High-angle GBs formed by hot- high-Tc superconductors. Indeed, it seems certain that pressing together two single crystals of MgO appear to such interfaces will occur in all crystalline ceramic behave as would have been anticipated from studies on the materials. Some special twin relationships observed in corresponding interfaces in fcc metals and semiconduc- minerals are illustrated schematically in Figure 14.18. The Fluorite (cubic). Spinel (cubic). Cassiterite (tetragonal). Interpenetrant cubes Contact type: twin across {111} ‘Knee-twin’. Contact type Rotate 60° about <111> Can start with the octahedron shown Twin plane is (011) FIGURE 14.18 Examples Aragonite (orthorhombic) Staurolite (orthorhombic) Orthoclase (monoclinic) Gypsum (monoclinic) of twinned grains found in Contact twin Interpenetrant Twin axis is z. The Carlsbad twin Swallow-tail twin different minerals. (110) twin plane Twin-plane (032) Interpenetrant across 010. Composition plane (100) 14 . 6 Tw i n B o u n da r i e s .................................................................................................................................................. 255 observation of so many twin boundaries is interesting because they are found to facet parallel to low-index D E D E planes in at least one grain. We noted that such interfaces can accommodate impurity ions, and this can E lead to the phenomenon of chemical twinning, wherein apparently different crystal structures can be related to one another by the periodic repetition of a pair of twin interfaces. This concept can be used to understand the actual mechanism of a phase transformation in a ceramic system. Several different types of twin boundaries have been seen in Al2O3; the basal twin boundary is the Σ = 3 GB, (1104) which was discussed in Figure 14.1a. We can form a variety of twin boundaries in Al2O3 by mirroring the structure across low-index planes that are not mirror planes in the perfect crystal; hence the (1̄102) plane, the (11̄04) plane (illustrated in Figure 14.19), and the (112̄3) plane all give twin boundaries [as does the (0001) plane, of course]. A rhombohedral twin boundary [the (101̄2) twin boundary] is shown in Figure 14.20; notice that it is A faceted. B A All interfaces in spinel, even the Σ = 3, (111) twin B A boundary, can exist with at least two different structures. In a formal treatment of such interfaces the different struc- FIGURE 14.19 Schematic of a (11̄04) twin boundary in Al2O3. The tures considered here can, in principle, be described by arrows show the <0001> directions; the letters show the hcp choosing different rigid-body translation vectors. However, stacking of the anions. The cations are omitted but sit in the such translations are not the small relaxations familiar in, octahedral—shown by the shaded rhombi. for example, the {112} lateral twin boundary in Al, but are more closely related to stacking faults in fcc metals. This translation, which is parallel to the {111} plane, is The image illustrated in Figure 14.21 shows two parallel seen because of the location of the cations. As far as the {111} twin boundaries (separated by a microtwin). The oxygen sublattice is concerned, the twin interface is actu- translations at the two twin ally a mirror plane: it is boundaries are different as THE TWINS just like the {111} twin you can see in the insets. A twin is a grain; a twin boundary is a GB. boundary in fcc Cu. 1102 0006 1104 (B) (C) FIGURE 14.20 Rhombohedral twin boundary in Al2O3 and its diffraction pattern. (A) 256 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s  A A B FIGURE 14.22 Curved twin boundaries in a thin film of NiO on an 5 nm Al2O3 substrate. (The hexagonal pattern is a moiré interference B effect.) FIGURE 14.21 Two parallel {111} Σ = 3 twin boundaries in spinel having different structures (identified by the arrows). The insets The circles are tetrahedral cations. Essentially, the shear- show regions A and B at higher magnifications. ing acts to change the chemistry along that plane. Crystal- lographic shear planes are thus like regular stacking faults, but the chemistry also changes—they are chemical stack- The lateral Σ = 3 twin boundary in spinel is also ing faults. An example of WO3−x encapsulated in WS2 is special. The structure of this interface can be entirely shown in Figure 14.25. described in terms of {111} segments (which may have Twin boundaries, like other GBs, can accommodate different structures, as noted above) and triangular-prism new ions so that the chemistry changes along the twin channels, which lie along <110> directions and are observed as white spots in HRTEM images. The faceting consists entirely of ordered (aligned) arrays of these prism b = 0.794 nm columns; the interface shown here is actually dislocation free, although the prisms can be modeled as an array of 50 100 83 83 dislocation dipoles. There was no local strain contrast in Ca2+ the TEM image. The image shown in Figure 14.22 is from a thin film a= 67 of NiO and reminds us that GBs that correspond to a 0.494 nm 100 50 83 special twin orientation are not necessarily flat. In that case, they are probably more similar to other high-angle 83 83 boundaries. The twin boundaries in the NiO film occur 50 100 CO32- because NiO can grow on a basal-alumina substrate in two twin-related orientations. We see the twin boundaries 50 100 83 100 67 because the density is lower at the GB. An example of how twins can form in a more complex 67 50 100 50 system is shown schematically in Figure 14.23 for arago- 83 83 nite. This figure shows the CO2− 3 anions as triangles (as we saw in calcite) while the closed circles represent Ca2+ ions. 50 100 83 (The numbers give heights of ions in the cells and serve to emphasize the twin symmetry.) A special group of closely related oxides is illustrated 83 in Figure 14.24. These oxides consist of blocks of MO6 octahedra (seen as squares along the cube direction), which can be shifted parallel to certain crystallographic FIGURE 14.23 Mimetic twinning in aragonite. This gives rise to planes (known as shear planes) to produce new structures. trilling twins when the operation is repeated. 14 . 6 Tw i n B o u n da r i e s .................................................................................................................................................. 257  S F FIGURE 14.24 Shear planes in WO3. Dark and light lines are at heights 0 and 0.5. plan. A periodic repetition of alternating twin planes, each 2 nm of which accommodates ordered impurities, can then give FIGURE 14.26 The structure of β-alumina as a repetition of rise to a new structure. This process is known as chemical chemical twin boundaries. S and F are a block of spinel and an twinning. The result for β″′-alumina is illustrated in Figure SF, respectively. 14.26. Planar defects can readily be incorporated into this structure. This particle of β′″-alumina contains a sheet of spinel; the spinel is like a sheet of a second phase. As we have seen in Section 7.12, we can also think of the struc- ture of the β′″-Al2O3 as being blocks of spinel that twin on every six {111} oxygen planes. The attractive part of this description is that we can then understand the fault in the structure where the twin occurs after only four {111} oxygen planes. Remember that the twin planes are not actually spinel twin planes because the chemistry is dif- ferent on the twin plane. 14.7 GENERAL BOUNDARIES General boundaries may be curved with no specific value of Σ. Can we determine if the GB is clean or what its structure is? We can know if it is not clean and put an upper limit on the impurity content, but we still will not know its structure. The relationship between the physical parameters of any individual interface and the mechanical strength or properties of that interface has not been directly FIGURE 14.25 A defect W oxide encapsulated in a fullerene. determined for any ceramic material. As with many 258 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s properties of ceramic materials, measurements on GBs are likely to be controlled by dopants or impurity phases; the latter may be present at the 10% level. Computer modeling is usually carried out for pure materials. Finite element modeling (used for fracture studies, crack initiation and propagation, etc.) generally makes assumptions regarding the elastic parameters, which may be very different at an impure interface in comparison to bulk material; the bonding at the interface is different, so the elastic proper- ties must be different too. 14.8 GB FILMS In Chapter 13 we discussed how a liquid behaves on a solid surface if the solid is not inert. We noted that the (A) situation could change due to evaporation at high tempera- tures and that the wetting phase need not be a liquid to wet or dewet.  GB films are directly analogous to films on surfaces or substrates.  How thick must a film be before it is a new phase?  Is a GB containing a film one interface or two? The simple view of whether a glass film will be ener- getically favorable is that if 2γsl < γGB, then the film is preferred. This statement is too simplistic, in part because GB films are unlikely to be uniform across their thickness. If γsl is ∼γGB then we would expect the GB to be stable, but even in this case, the glass must go somewhere. Any of the four types of GB could contain a GB film. (B) How stable the film would be will clearly depend on the FIGURE 14.27 Examples of HRTEM image of IGFs in Si3N4. (a) energy of the GB with the film versus without it and the Phase-contrast image; (b) Z-contrast image showing ordering of rare-earth dopant at the glass/crystal interface. availability of a mechanism for removing the film if this would lower the energy. We know that liquid phases can be very important in polycrystalline ceramic materials. We also know that most interfaces in some ceramics (e.g., Si3N4) contain a very added to lower the processing temperature via the thin (∼1–5 nm) IGF as illustrated in Figure 14.27. Thin process of liquid-phase sintering. amorphous layers have been reported to be present in a  The width of glassy GB films can vary from ∼1 nm to wide range of ceramic materials (see Table 14.1). It is >1 μm. sometimes incorrectly assumed that all GBs (other than  The TEM techniques used to identify these films do special twin boundaries) in Al2O3 contain such a thin not always give unambiguous results. amorphous film. In some materials the same interface may  At high temperatures the mechanical properties of a or may not contain an amorphous film, depending on how ceramic may be drastically lowered if a glass is present. it was processed. For example, the viscosity of the glass decreases sig- nificantly at a relatively low temperature leading to  Glass is very often present in ceramic materials whether enhanced creep and related phenomena; remember intentionally included that the viscosity of soda- or not. In many oxides lime-silica glass varies it is present because of IGFs from 1015 dPa·s at 400°C impurities in the initial A note on very thin films: if a film is ∼1 nm thick and to 102 dPa·s at 1300°C. materials used to the system is in equilibrium, then the film may be better At the higher temperature process the compact. In described as an absorbate layer. Experimentally, the glass cannot support a others it is intentionally challenge is knowing that the system is in equilibrium. shear stress and allows 14 . 8 G B F i l m s ................................................................................................................................................................. 259  TABLE 14.1 Examples of Intergranular Phases matter along and across the intergranular regions is then even faster than when no glass is present. It is important Property System affected Notes to realize that the glass does not simply act as a catalyst, but also changes the character of the interfacial regions. Glass in Si3N4 Mechanical Glass forms from components The glass can dissolve the crystalline grain and reprecipi- added as sintering aid and tate it elsewhere. In particular, it tends to encourage facet- oxide on particle surface Glass films in Mechanical Impurities in the glass can ing of the grains; the scale of this faceting may vary from Al2O3 affect its properties nanometers to micrometers. After processing, the glass Bismuth oxide Electrical The IGF is the key to the may remain as a thin layer in the interface during prepara- in ZnO operation of varistors tion of the polycrystalline compact as was initially dem- YAG in AlN Thermal Y2O3 added as sintering aid to onstrated for Si3N4. The glass may also crystallize to form allow lower cost production of substrates an intergranular crystalline layer or it may withdraw from Surface Chemical Oxidation of SiC can passivate the planar interfaces into three-grain and four-grain junc- contamination the surface tions (the dewetting process). Even though great care may Clean GB in YBCO Electrical GB may not be be taken to ensure that no glass is present during process- superconducting; if very thin ing, the glass may subsequently enter the interfacial region it can act as weak links during processing or service of the component. In either case, the properties of the ceramic may be greatly influ- enced by the presence of any glass in the grain boundary; rapid deformation of the material. In other circum- a dramatic example is the effect on mechanical properties stances, the presence of the glass may be beneficial (e.g., for Si3N4 or Al2O3), which also aids sintering, since it may assist in the branching and blunting of although other properties (e.g., the thermal conductivity cracks by generally weakening grain boundaries. for AlN) may be just as strongly affected.  It is much easier to process ceramics in the presence Figure 14.28 illustrates another feature associated with of a liquid phase, in part for the same reason—the glass in crystalline ceramics. The pairs of grains joining glass allows deformation at lower temperatures; diffu- at these two boundaries are similarly oriented. Both of the sion is also faster through a glass. The glass thus allows interfaces contain dislocations, i.e., they were glass free the sample to be shaped and/or densified at lower after processing. The topology of the two interfaces is, temperatures. however, clearly different. In Figure 14.28a the interface  The composition of the IGF may vary across its width. is wavy, while in Figure 14.28b it is flat. The difference In Figure 14.27, the rare-earth dopant has formed an can be explained by the processing history; the bicrystal La-rich monolayer at the glass/crystal interface. in Figure 14.28b initially contained a layer of glass, while that in Figure 14.28a was kept as clean as possible It is well known that the presence of glass in GBs during processing. So the difference in the topography is greatly enhances sintering, in part because transport of ascribed to the effect of the glass while it was present in (A) (B) FIGURE 14.28 The same GB in Al2O3 processed with and without glass. 260 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s  characteristics of TJs (they are not TEM friendly) or their role in determining mechanical properties. Figure 14.30 shows a Σ = 13 GB in alumina that was processed with an initial layer of anorthite glass that had a uniform thickness of ∼100 nm. The glass is still present in the interface after processing, but it varies in thickness along its length. Here the explanation for the thickness variations is clear: the two glass/crystal interfaces facet independently except in the regions where they appear to touch. The controlled preparation of such interfaces is not, in principle, limited to special boundaries, since any two such surfaces can be so joined and both the composition and the initial amount of glass can be predetermined and controlled. Dewetting of GBs has been observed in Si where the glass was the native oxide, SiOx (x∼2). Figure 14.31 shows TEM images of a Σ = 1 (low angle) <110> tilt boundary and a Σ = 5 (001) twist boundary. In both cases abrupt changes in contrast can be seen where the glass has dewet the interface to accumulate in pockets. The pockets actu- ally facet parallel to {001} and {111} places due to the crystallography of the Si. Thus, even the Σ = 5 GB can achieve its low-energy structure, including the secondary dislocations, in the presence of a dewetting glass film. Crystallizing intergranular glass layers after process- FIGURE 14.29 SEM image of glass-infiltrated MgO showing glass ing has been used to modify the mechanical properties of located at the GB and at TJs, but even in a GB it need not be a uniform layer. the resulting compact. The yttria-rich glass in polycrystal- line Si3N4 and monticellite glass in MgO can be crystal- lized after liquid-phase sintering to change the properties of the polycrystal. An important remaining question concerns how the presence of the second glass/crystal interface (in a GB) the interface. Clearly this effect can potentially be very might affect the crystallization process. If topotactic crys- important in understanding such GBs, but it presents a tallization nucleates at one glass/crystal interface, it is major difficulty; the key component required to explain unlikely that the crystallizing glass will form a complex the structure of the GB had already disappeared before (high-energy) interface when it reaches the adjacent grain. the processed compact could be examined. Similarly, if crystallization nucleates at both glass/crystal Water in silicate GBs can significantly change the interfaces, a complex grain boundary, possibly with resid- mechanical properties of the GB. The GBs really are wet ual glass, will form when the crystallized glass layers in the everyday sense! The crystal structure of the grains grow together. causes ordering in the water and thus changes the viscos- ity of the water. The behavior and effects of water in GBs are important topics in geology. There has been much discussion on the thickness of intergranular glass films. There may be an equilibrium thickness for such films, as has been reported for Si3N4, but a more common situation is shown in Figure 14.29. This sample was a dense, small-grain, glass- free polycrystal that was intentionally infiltrated with monticellite glass. Here the width of the glass layer clearly varies from boundary to boundary and even along a par- ticular boundary. Nearby boundaries can show a layer that is nearly uniformly 2 μm wide or that is apparently glass free at this magnification. This image illustrates an impor- tant factor that is often overlooked: most of the glass is contained in TJs and QJs. These junctions serve as “pipes” FIGURE 14.30 An IGF in Al2O3 that was initially uniformly thick for transporting the glass. Very little is known of the varying in thickness after heat treatment. 14 . 8 G B F i l m s ................................................................................................................................................................. 261  A schematic diagram showing how GBs, TJs, and QJs change with changes in wetting behavior is shown in Figure 14.33. Wetting is clearly important when we process ceramics using a liquid phase. For the liquid phase to be effective in densification we want it to wet the grains, hence φ = 0. But for optimum properties of the final ceramic we may not want the grains covered with a second phase. A good example is in AlN ceramics for electronic packaging. The second phase, which will almost always have a much lower thermal conductivity, should form iso- lated pockets at the TJs leaving a “clean” GB enabling maximum phonon transport. A TJ can act like a capillary. The TJ in Figure 14.34 was covered with liquid glass at the processing tempera- ture. When the sample was cooled, the liquid withdrew (A) into the TJ like water escaping a bath (but the physics is different). (1010) (B) FIGURE 14.31 Dewetting of IGFs in Si GBs: (a) Σ = 1 {111}; (b) Σ = 5 {001}. (A) (1010) 14.9 TRIPLE JUNCTIONS AND GB GROOVES We will not spend much time on TJs because not much is known about them. We can identify three different types of TJ. 1. One composition: Three-grain junctions 2. Two compositions: Two phase boundaries plus a GB 3. Three compositions: Three phase boundaries Thus, for example, the groove formed when a GB emerges at a free surface is an example of a two-composition triple junction. Three TJs meet at a QJ. The pockets of second phase at TJs in Figure 14.32 could each be considered as 500 nm (B) sets of three two-composition TJs. Incidentally, looking at the surface will not give us an unambiguous picture of the FIGURE 14.32 Examples of TJs: (a) Si3N4 using TEM; (b) MgO dimensions. using SEM. 262 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s  φ = 45° φ = 135° φ = 90° Polished sections φ=0 φ = 135° FIGURE 14.33 Schematics showing the relationship between IGFs, TJs, and QJs in 3D as the wetting angle is changed. Lower: a reminder that we usually see sections of these structures. 14.10 CHARACTERIZING GBs Internal interfaces are fundamentally different from surfaces because of their inaccessibility. The key tool for When studying a GB, we want to know the structure, studying GBs is the TEM. This should be obvious chemistry, and bonding. How do we characterize a GB? from the number of TEM images in this chapter! Although What are the parameters we need? Just to understand the the material must usually be thinned prior to examination structure, we have to know all the crystallographic in the TEM, the area of the GB we do examine is parameters, then the chemistry, and then the bonding. No unchanged. single technique gives us all this information. No ceramic GB has been fully characterized, although we are getting TEM can be used to observe a periodic array of edge dis- close with a few. locations; we use Burgers circuit to characterize the dislocations Plane of boundary—Is the GB flat? We can probe a GB by STM only where it intersects the Axis of misorientation—The GB is an internal interface, surface. Atomic force microscopy, however, (AFM) is so we need the orientations of both grains. a key tool for characterizing GB grooves Atomic structure of boundary—The GB must be flat for HRTEM. The specimen preparation problem for TEM: GBs in ceramics must be considered in terms of both their struc- ture and chemistry (even in so-called pure materials). Just as the wetting behavior of a surface may be altered by the doping of the surface layer, so it is important to identify and characterize the segregation of impurities and addi- tives to GBs in these materials. The problem here is 2-fold: the features of the GB (its misorientation and plane) must be identified and the distribution of “foreign” elements must then be accurately measured. The last part of this process is actually even more difficult than you might expect. The added complexity arises from the methods that are, at present, routinely used to prepare samples of ceramic materials for examination in the TEM. The TEM specimen is usually thinned by ion-milling; crushing will fracture the sample along GBs. This thin- ning process has been shown to result in cross-contamina- tion of the specimen and in the formation of a groove at FIGURE 14.34 Direct evidence for the capillary effect at a TJ; the the interface. The degree of contamination depends on a glass recedes into the TJ on cooling. large number of factors: 14 .10 C h a r ac t e r i z i n g G B s .......................................................................................................................................... 263  Pore due to factors other than the presence of a thin amorphous film. It is important to use a combination of techniques to characterize, as fully as possible, any given interface. For example, diffuse scattering is very dependent on the speci- men preparation techniques. The reasons for using these techniques can be appreciated by noting that the amor- phous layer, which may be present at the interface, may be only 1 nm wide. The complexity of image interpretation when examining thin (1–>5 nm wide) GB films makes computer analysis and simulation necessary. We can use image simulation programs to simulate the formation of Fresnel fringes, taking into account the possibility of GB grooving at both surfaces. 14.11 GBs IN THIN FILMS Why are we interested in this topic? Ceramic thin films are becoming increasingly important in the electronics industry for their novel magnetic and electrical properties. Often these films are neither amorphous nor single crystal, so GBs become relevant. There will be TJs in the FIGURE 14.35 A cautionary tale: the “glass” in the faceted GB is film and at the substrate/film interface (even if the sub- actually material deposited in surface grooves during sample strate is amorphous). The TJ can form a pit (a 3D groove) preparation. at the surface, but it will generally not groove at the substrate. Figure 14.36 is a dark-field TEM image from recrystal-  The type of oil used in the diffusion pump of the ion- lized anorthite glass on sapphire. The substrate appears miller (old ion-millers may use a silicone-based diffu- dark and the anorthite grains have faceted edges. sion pump oil since it is less expensive and more resistant to cracking than are Si-free oils).  The cleanliness of the system used to carbon coat the thinned TEM specimen.  The ion-thinning process also preferentially removes the lighter atoms and may deposit what it removes somewhere else on the sample.  Ion thinning can implant Ar into loose, or open, struc- tures (like GBs).  Ion thinning may thus both preferentially thin the GB (forming a groove) and then deposit material in that groove. (Figure 14.35 shows the problem.) It is always best to use bicrystals for model experi- ments to relate the chemical profile of an interface to its structure since we can then know the initial composition of the GB, but these are not “real” materials. The principal techniques are  The Fresnel-fringe technique  The diffuse-scattering technique  Direct lattice-fringe imaging where the geometry of the interface is suitable The diffuse scattering technique suggests amorphous- film thicknesses that are 50–100% larger than are found FIGURE 14.36 Example of GBs in thin films of anorthite on Al2O3 ; by high-resolution EM (HREM), i.e., at least part of the the three grains correspond to three epitactic orientations, but only image obtained from diffusely scattered electrons must be one shows the misfit dislocations in this TEM image. 264 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s The facets often meet at 60° or 120° angles. The three 14.13 MODELING orientation variants are shown as A–C. Two TJs between all three variants can be seen in the image. Variant A The extensive analysis of the structure of GBs in ceramic contains irregular contrast associated with the interfacial oxides using computer modeling does not appear yet to dislocation network; variants B and C show moiré explain the experimental observations. One limitation of fringes. the modeling approach is that the GB plane is fixed in the calculation. Furthermore, computer modeling of asym- metric interfaces is not routine—constructing the unit cell 14.12 SPACE CHARGE AND for asymmetric GBs is difficult. Most of this computer CHARGED BOUNDARIES modeling has been directed at understanding the structure of GBs in materials with a rocksalt structure. In these We introduce this topic now because it shows the funda- materials (primarily NiO and MgO), the oxygen-ion sub- mental relationship between point defects and interfaces. lattice is in an fcc arrangement whereas the cations are The concept of a space charge is special for ceramics. located at the octahedral sites. The situation is more Simply put, it is possible for an excess charge of one sign complex for most other oxides when different interstices to be present at the interface. This excess charge must be are occupied; as you know, in spinel two-thirds of the balanced by a space charge further away from the bound- cations occupy octahedral interstices while one-third ary. There is not much experimental data, but the concept occupies tetrahedral interstices. is widely accepted. We cannot assume that all the ions have found their Consider NaCl: ions on either sublattice can, in prin- “ideal” sites in sintered material, e.g., some Al3+ ions in ciple, move to a new site on the GB leaving a vacancy in MgAl2O4 may be on tetrahedral sites. The structure pre- the lattice. dicted by computer modeling for the {112} lateral twin interface in NiO contains a rigid-body translation. Such a translation is not observed experimentally for the same Na Na → V′Na + NaGB • (14.4) type of interface in spinel, which has the same oxygen ClCl → Cl′GB + VCl • (14.5) sublattice. It may be that the reason for this difference is that the translation-free configuration is what is present on In general, the energy required to form these point a migrating GB and this becomes “frozen in” when the defects at the GB is not the same as it is in the bulk and sample is cooled. The structure predicted by minimum differs for the two ions. We therefore get more of one than energy calculations is a stationary structure. the other at the grain boundary. Overall, the crystal is The disagreement between experiment and modeling neutral, hence there must be a space charge in the bulk. may be also due to the difficulty in preparing ideal clean Now add CaCl2 to the NaCl crystal. The impurities (or interfaces in ceramic materials. For example, the Σ = 5 GB dopants) give charged point defects. in NiO can be stabilized by adding Schottky defects to the interface, i.e., by decreasing the density at the GB while CaCl2 → Ca•Na + V′Na + ClCl (14.6) keeping it “pure.” Experimental observations do show that the density at interfaces is generally lower than that of the bulk material. We are adding the positively charged Ca2+ ion and are thus Most programs use a cell that repeats the structure of increasing the concentration of vacancies on the Na sites. the GB and, hence, most calculations have been carried We know that out for low-Σ GBs. null ↔ V′Na + VCl • (14.7) 14.14 SOME PROPERTIES • So, adding CaCl2 to the bulk decreases [VCl ] in the bulk (because it increases [V′Na]). Since we have increased [V′Na] GBs are everywhere in ceramics. The formation of GBs • in the bulk, [NaGB ] must decrease in the GB, which implies will be discussed in Chapter 24 since this is the initial that [Cl′GB] increases in the GB. Hence the GB potential product of the sintering process. The movement of GBs is is negative. There is a complication: what about Ca•Na? the necessary process allowing grain growth to occur and What if it all goes to the GB? The radii of the Ca2+ and will also be discussed there. GBs influence the behavior Na + ions are about the same (∼0.1 nm). We do not know of polycrystalline ceramics—both bulk materials and thin the radius of the Ca ion on the Na site. We have also not films. We will discuss their properties extensively in later considered the possibility of forming a defect complex chapters. Here we just list a few examples so you can see such as (Ca•Na, V′Na); the binding energy is quite large, their importance. ∼0.4 eV. The idea of the GB space charge is therefore important, but far from simple, and there is not much Example 1: GBs are probably the most important defect experimental data. in ceramic superconductors. They can dramatically 14 .14 S o m e P r o p e r t i e s .................................................................................................................................................. 265  (B) (C) (A) FIGURE 14.37 HRTEM image of the 45° GB in YBCO and the diffraction pattern. reduce critical currents (Jc). The idea is that the GB In metals, GBs control mechanical properties when the acts as if it is a second phase. This sheet is not a super- grain size is small as seen from the Hall–Petch equation conductor—it may act like a sheet of insulator inside the superconductor. If the GB is very thin then it is B σ y = σ0 + (14.8) possible to use its weak-link nature to fabricate a d1/2 Josephson junction. Figure 14.37 is an HRTEM image of a near Σ = 29 GB in a YBCO thin film. The GB is The yield strength (σy) is expressed in terms of the yield narrow, abrupt, and facetted. We will revisit this topic stress, σ0 (σ0 is related to the intrinsic stress, σi, resisting in Chapter 30. dislocation motion) and the grain size, d. When this rela- Example 2: GBs in AlN can reduce the thermal conductiv- tionship was deduced, it applied to a situation in which ity if they are not clean. Because AlN is difficult to the grains were deformed by plastic deformation and the sinter to high density without the use of a liquid phase GBs acted as barriers to dislocation motion. This model (the bonding is mainly covalent), the GBs often contain is unlikely to be valid in general for ceramics since defor- a second phase, which always has a lower thermal mation by dislocation glide is not common. However, the conductivity (Chapter 34). Yttria may be added to relationship between d and σy does hold as we saw for react with oxide in the GBs to form YAG at the triple polycrystalline MgO in Figure 1.2. junctions: a GB-dewetting process. Example 3: GBs in ZnO are processed intentionally to include a glass film. This film allows the ceramic to be used as a varistor (voltage-dependent resistor), a device that protects circuits from high-voltage spikes ZnO (Chapter 30). Figure 14.38 illustrates an IGF of varying CSL1 CL CSL2 RG1 RG2 thickness in ZnO and how this film controls the resistance. RSL1 RL RSL2 ~ 1 μm Example 4: GBs in Si3N4 invariably contain glass films as shown earlier. At high temperatures they can lose their mechanical strength when the films soften (Chapter Bi2O3-rich 10 ~ 100 nm 18). IGF Example 5: GBs in magnetic ferrites affect the initial Bi-enriched 2 ~ 10 nm GB permeability, μ. The permeability of Mn-Zn ferrite increases from about 0.8 × 10−3 up to 3.5 × 10−3 when Bi2O3-rich the grain size is increased from 5 μm to 15 μm (Chapter IGF 33). Although porosity has a role, it has been deter- CS CL mined that grain size is more important. Grain 1 Grain 2 Example 6: GBs affect the scattering of light in transpar- RG CsÕ ent materials. Light scattering is greatest when the RS RL grain size is close to the wavelength. In addition, IGFs Bi2O3-rich triple junction RsÕ produce a change in refractive index as light passes through a material (Chapter 32). FIGURE 14.38 Modeling IGFs in ZnO varistor materials. 266 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s  CHAPTER SUMMARY GBs in ceramic materials are important in almost all applications of these materials since ceramics are usually polycrystalline. GBs have a thickness—we can think of them as thin films even if they are structured. This means that a polycrystalline material is really a composite one. An added difficulty is that essentially every GB “film” is different, but we can think of an average GB, which is especially good if there actually is an amorphous film (IGF) at the interface. The most important point to remember is the relationship between GB energy and GB (interface) tension, which includes the idea that there is a pressure difference across a curved GB just as there is across a curved surface. You should be able to define the words twist, tilt, mixed, and twin and to understand the concept of Σ (and Γ), how it relates to struc- ture, and why it can be related to GB energy. Triple junctions and the space charge at GBs are very important, but we know little about them. There are two special features for ceramics: the space charge and IGFs. IGFs are special for ceramics because glass is easily formed and maintained, especially when the ceramic contains at least small concentrations of Si. PEOPLE IN HISTORY Bollmann, Walter was a pioneer in explaining the O-lattice concept. Friedel, G. and Friedel J. were early contributors to the development of the CSL. Matthews, John was best known for his work on misfit, epilayer growth, and MgO smoke. Mullins, William W. explained and predicted observations on GB grooving. He died in 2002. GENERAL REFERENCES Grain boundaries have been extensively reviewed in several recent books. These texts cover all crystalline materials, but you will still need to go to the original papers to learn more about GBs in ceramics. Bollman, W. (1970) Crystal Defects and Crystalline Interfaces, Springer-Verlag, New York. The original book giving the analysis of Σ, O lattice, etc. Howe, J.M. (1997) Interfaces in Materials: Atomic Structure, Thermodynamics and Kinetics of Solid/Vapor, Solid/Liquid and Solid/Solid Interfaces, John Wiley & Sons, New York. A very readable book with a practical emphasis. Hull, D. and Bacon, D.J. (2001) Introduction to Dislocations, 3rd edition, Butterworth-Heinemann, Philadelphia, A review of the basics. Kelly, A., Groves, G.W., and Kidd, P. (2000) Crystallography and Crystal Defects, John Wiley & Sons, New York. Not broad or up-to-date but an excellent basic text. Read, W.T. and Shockley, W. (1950) “Dislocation models of crystal grain boundaries,” Phys. Rev. 78(3), 275. A classic readable paper with great diagrams. Smith, D.A. and Pond, R.C. (1976) “Bollman’s 0-lattice theory: a geometrical approach to interface structure,” Inter. Met. Rev. 205, 61. Very readable discussion of the background to the GBs. Stokes, R.J. and Evans, D.F. (1997) Fundamentals of Interfacial Engineering, John Wiley & Sons, New York. Bob Stokes retired from Honeywell and joined the University of Minnesota part time. Sutton, A. and Balluffi, R. (1996) Interfaces in Crystalline Materials, Oxford University Press, Oxford, UK. Wolf, D. and Yip, S. (Eds.) (1992) Materials Interfaces: Atomic-Level Structure and Properties, Chapman & Hall, London. SPECIFIC REFERENCES Amelinckx, S. (1958) “Dislocation patterns in potassium chloride,” Acta Met. 6, 34. Seeing GBs in KCl by decoration. Chaudhari, P. and Matthews, J.W. (1971) “Coincidence twist boundaries between crystalline smoke particles,” J. Appl. Phys. 42, 3063. Original description of the MgO smoke experiment for GBs Zhu, Y. and Granick, S. (2001) “Viscosity of interfacial water,” Phys. Rev. Lett. 87(9), 096104. The idea is that the viscosity of water can be very different if it is constrained to be a film in a silicate grain boundary. EXERCISES 14.1 Using the idea of capillarity and relating it to a triple junction, what happens as the temperature increases (so that viscosity decreases)? 14.2 Consider a 1-cm cube of a 100% dense ceramic that contains 5% glass that can wet the crystal grains. If the grain size changes from 100 nm to 10 mm due to heat treatment, how does the distribution of the glass change? Be careful to summarize your assumptions and list as many variables as you can. C h a p t e r S u m m a ry .......................................................................................................................................................... 267  14.3 Consider two small-angle (2°) tilt grain boundaries in MgO, both having a [001] tilt axis. For one the bound- ary plane is nearly (100) while for the other it is (110). Discuss the structure of these two grain boundaries. 14.4 The structure of the spinel, MgAl2O4, projected onto the (110) plane in shown in Figure 7.1b. Spinel twins on {111} planes. Draw all the different allowed structures for the coherent (IT) plane and discuss which of them is most likely to occur giving clear reasons. Consider how your analysis might change if the spinel was not equimolar. 14.5 If the surface energy for (001) MgO is 1 J/m 2 what is that in electron volts per oxygen ion on the surface. How does this number compare to the formation energy of the Schottky defect? How would this number be different if the material were NaCl instead of MgO? 14.6 Dislocations in a tilt boundary on the (011) plane in silicon lie 200 nm apart. What is the misorientation of the two grains. Would the etch-pit method be a good way to examine this boundary? Explain your answer. 14.7 (a) For the TJ shown in Figure 14.34 derive a relationship between γGB, γSL, and the dihedral angle, φ, which is the angle subtended by the liquid. (b) Assuming that γSL is 700 mJ/m 2, determine γGB. 14.8 Construct a model for a Σ = 7 twin boundary in sapphire that is also a tilt boundary with a [0001] rotation axis. 14.9 Consider what might happen to the grain boundary charge when MgO is added to Al2O3. 14.10 A tilt boundary in olivine lies on the (100) plane with a [001] rotation axis. The dislocations are all the same Burgers vector and are 100 nm apart. What is the rotation angle? 268 ........................................................................................................................................ I n t e r fac e s i n P o lyc ry s ta l s  15 Phase Boundaries, Particles, and Pores CHAPTER PREVIEW This chapter is both an extension of the chapters on surfaces and grain boundaries (GBs) and essential preparation for those on sintering and phase transformations. The theme of the chapter could be reworded as interfaces between ceramics and different materials; the material can be crystalline, amorphous (glassy), liquid, or gaseous (pore). Hence the topics include three critical areas for ceramics: phase boundaries (PBs), particles, and pores. Examples of PBs include ceramic/metal interfaces, crystal/crystal interfaces, and crystal/glass interfaces. Because we also include any interfaces that interact with pores it is a very large and important topic. By definition, PBs are the essential feature of composite materials. Solid-state reactions and reactions involving liquids and gases all occur by the movement of these interfaces, but the details of how this motion occurs are often even less well understood than the interfaces themselves. 15.1 THE IMPORTANCE to control the grain morphology or because going to the melting temperatures would be too expensive. Particles of In ceramic materials, as in other materials systems, inter- different phases join together to form PBs. faces are the most important region of the material because that is where most of the action takes place. Phase bound- Moving PBs aries are particularly important because they are the inter- faces between dissimilar phases. New phases form by a solid-state reaction when ceramic powders are reacted. The new phase grows at the expense  Phase transformations take place by the movement of of the starting phases: the reaction occurs by PBs moving. PBs. We will examine these reactions in Chapter 25; here we  Growing one material on a different material generates will concentrate on the interfaces themselves. a PB (a heterojunction).  Bonding one material to another generates a PB. Properties of PBs  Most commercial and natural ceramics contain two or Whether the PBs separate thin films from a substrate or a more phases and thus many PBs. bulk grain of one composition from one of another com- position, the properties of the interface determine the use- Forming PBs—Film Growth fulness of the material. There are innumerable examples of why PBs are important to ceramics: seals on Na-vapor Increasingly, we are growing thin films of ceramic materi- lamps are the most likely source of failure; loss of adhe- als on substrates, coating glass, coating metals, etc. A PB sion of thermal barrier coatings (TBCs) leads to failure separates a ceramic film from the substrate. The behavior when the coating separates from the metal; GaAs on Si is and properties of that PB will determine the usefulness of not as widely used as was once hoped because the films the thin film. This is not a new field—the electronics indus- do not align perfectly at the interface and they would be try has been built on the ability to deposit layers of SiO2 unlikely to remain perfect during cooling from the growth and Si3N4 on Si. The high-Tc superconductors in thin-film temperature. form are made this way. GaN is revolutionizing the light- ing industry with thin films grown on Al2O3 and SiC. 15.2 DIFFERENT TYPES Forming PBs—Processing Clearly there are many types of PB. We have already We usually process ceramic materials in the solid state considered the solid/vapor and liquid/vapor PBs in Chapter (although small amounts of liquid may be present) either 14; we also touched on the solid/liquid PB. Here we will 1 5 . 2 D i f f e r e n t Ty p e s ................................................................................................................................................... 269  TABLE 15.1 Examples of PBs in Multiphase Ceramics 15.3 COMPARED TO OTHER MATERIALS PB Material How are ceramics different from metals? Metals can be Glass/ceramic Crystallization of a glass to form a glass- very clean. If particles are wanted they can often be pre- ceramic Fiber composite Ceramic fiber (e.g., SiC) with metal, ceramic, or cipitated by moderate heat treatments. In ceramics, parti- polymer matrix cles are more likely to result from inclusion of insoluble Geomaterial Granite contains quartz along with other impurities than from precipitation. minerals such as orthoclase and microcline; there are multiple PBs Impurities are common in all ceramics except in pure Cement A ceramic matrix composite; cement is the matrix and aggregate (sand and small semiconductors. pebbles, or historically pumice) is the Heat treatment may change the oxidation state of the con- reinforcement stituent ions. Porous ceramic A very large developing topic, e.g., bioceramics, where we want controlled pore size for tissue Alumina with 0.1 mol% impurities would be regarded ingrowth as being a pure alumina; many commercial aluminas contain less than 98% alumina. In metals, we use precipi- tates to pin dislocations. In such materials, the aim is to optimize the number and spacing of the particles while controlling the total content. This is not usually done in ceramics—we do not need to pin the dislocations because discuss the solid/solid PB and use earlier concepts on the they are not moving anyway. However, particles in ceram- solid/gas PB. ics have become more useful in preventing the movement We will examine two types of particles and the PBs of cracks—they help to toughen the ceramic. We can use between these and the matrix. ion implantation to harden ceramics (including glass). The process does produce particles, but again the defects that  Particles are a distinct second phase. Some could dis- are impeded are cracks not dislocations. This technique is solve in the matrix if the temperature were high clearly restricted to the near-surface region. enough; some may never be able to dissolve until Historical note. For many years, pores dominated the we exceed the melting temperature. They can be ceramics literature because of sintering—we wanted to equiaxed, platelets, or needles. Note that in metals, remove them to make dense material. Now we may want the particles are often precipitates and the two to keep them or we may simply avoid them in the process- words are used interchangeably. Particles in cer- ing route. Intergranular phases are really special for amic materials are less likely to have formed by ceramics and can be extremely useful, or disastrous, or precipitation. both, but they are much more common than in metals.  Pores are essentially negative particles, but there are Particles are becoming more than just accidental inclu- some big differences: (1) there is a gas/solid PB, (2) sions present in impure materials as we start to use them there are no solid-state reactions at the interface, and in ways that are special for ceramics (e.g., in toughening). (3) kinetics of point defect motion are fastest at the The mechanical strength of pores is not great(!) but surface of the pore (the PB). pores can affect the mechanical properties in different ways. If the pore is small, it actually may be difficult to The idea of the pore as a particle may seem to be deform it. stretching the point at first. We will justify including this topic by showing that pores behave like particles and are a major component of many ceramic systems, including 15.4 ENERGY composites. Thin interfacial phases can also lie along PBs just as they do along GBs. When the intergranular films In the same way that GBs have an associated energy, an at a GB or triple junction become thicker than ∼10 nm, it interface between two different phases has a PB energy: is already a second phase and there are two PBs instead the energy necessary to form a unit area of a new PB. (Two of one GB. We discussed intergranular films (IGFs) in of these PBs were treated in Chapter 13 on surfaces.) If Chapter 14 because the GB is essential to their existence this interfacial energy is not less than the sum of the sepa- (by definition). rate surface energies of the two phases the two phases will Because PBs are everywhere in oxide minerals this not join. is an enormously varied topic. We discuss this topic A low-energy geometry arises by minimizing the in more detail in Chapter 19, but for now a summary surface energy. In general, the interfacial energy between of some systems is given in Table 15.1. A point to keep chemically similar phases is low compared with the sum in mind is that today’s minerals are tomorrow’s of the surface energies. Thus, liquid metals or oxides on ceramics. sapphire (or other solid oxides) generally have a small 270 ................................................................................................................ P h a s e B o u n da r i e s , Pa r t i c l e s , a n d P o r e s interface energy. The interface energy is also low when there is a strong chemical attraction, i.e., when the two materials are likely to react readily. Although new approaches have been developed for creating these interfaces, it has always been difficult to control the initial interface. In this example the structure is well known but the energy is usually still a mystery. 15.5 THE STRUCTURE OF PBs Phase boundaries can be like GBs where the adjoining two grains may not only be rotated relative to one another but will also (or instead) be structurally and/or chemically different; of course, one or both phases may be a glass, 25 nm which means the interface is not structured. As with heterojunctions, the word “hetero” is implied when we say FIGURE 15.1 Image of an Fe2O3 film on an Al2O3 substrate “phase boundaries.” Semiconductor heterojunctions are showing both Σ = 1 and Σ = 3 PBs. The inset shows the hexagonal examples of PBs; “heterojunction” usually indicates that dislocation network. we are talking about flat interfaces and a thin-film geo- metry. As is the case with GBs, almost all the detailed studies have been concerned with “special” PBs. We can these different dislocations have a direct relevance to the summarize this idea and compare some PBs to GBs. movement of any phase boundary and hence to the mecha- nisms of solid-state reactions because they are associated The “Σ = 1” PB is particularly important since it is often with steps in the PB. The latter point is not usually con- associated with epitactic growth. sidered when discussing heterojunctions in semiconductor NiO grows on MgO with both grains aligned so that cor- systems since the location of the interface is usually fixed responding planes and directions in the two crystals before the growth of the epilayer. are nearly parallel. The difference in lattice parameter Phase boundaries between ceramic oxides are particu- (Δa) will be accommodated by a square array of misfit larly complex because the structure, the lattice misfit, and dislocations. the different cations can each be influenced by external conditions, particularly the oxygen activity. The model When two phases have similar or related structures system AO/AB2O4 /B2O3 allows all of the above variables and are in close alignment, the mismatch due to differ- to be considered; A is a divalent cation and B is a trivalent ences in the lattice parameter may be accommodated by cation. There is an extensive, although by no means com- arrays of misfit dislocations. Such dislocations have been plete, database for both the thermodynamic and kinetic extensively studied in semiconductor systems and in some aspects of such systems. The growth of spinel into alumina oxide systems. The image of Fe2O3 on Al2O3 in Figure 15.1 can take place by the movement of interfacial steps rather is complex because the Σ = 1 and the Σ = 3 interfaces exist than dislocations as we will see in Chapter 25. Structur- side by side (the Fe2O3 films contain twin boundaries). In ally different variations of the same “chemical” interface the Σ = 1 PB, Δa is accommodated by a hexagonal array can exist as illustrated in Figure 15.2; new interfaces such of dislocations with Burgers vector –31 <112̄0>; these are the as that in Figure 15.2b can be thought of as high-angle displacement-shift-complete lattice (DSCL) vectors for PBs. This particular PB can also be thought of as a plane- this interface. In the Σ = 3 PB, the misfit dislocations are matching boundary, which has been recognized as a –31 <101̄0> (so they are closer together and more difficult to special form of GB (see Section 15.14). image). At the interface between NiFe2O4 and NiO, which is shown in Figure 15.3, the oxygen sublattice is undisturbed The Σ = 3 PB often occurs in thin-film growth on {111} by the presence of the interface. The distribution of the or (0001) substrates: it is the PB version of the twin cations has changed in a way that is analogous to the boundary. stacking fault in spinel in that only the cations are shifted. Since there is actually a lattice-parameter difference, as If the corresponding planes [e.g., in the (001) NiO / this particle grows larger, dislocations must be nucleated (001) MgO interface] are rotated about an axis that lies in at the interface. The resulting misfit dislocations are illus- the plane, then the interfacial dislocations must have a trated in Figure 15.3b. component that is normal to the plane of the interface. Two notes: (1) PBs are more likely to be structured if Again, this situation has been demonstrated for both semi- the particles form by precipitation than if they form by conductors and oxides. The presence and distribution of inclusion during two-phase sintering. (2) Particles and 1 5 . 5 Th e S t ru c t u r e o f P B s ........................................................................................................................................ 271  The coalescence process, which is similar to the sinter- Spinel ing of two particles that we discussed in Chapter 24, depends on the size of the particle. The phenomenon is known as Ostwald ripening—large particles grow while small particles shrink. The difficulty is that the initial joining of the particles must involve diffusion through the lattice unless there are defects connecting the particles. Particles of NiO that have grown in Ni titanate spinel are shown in Figure 15.4. The particles have grown following nucleation, but there is a thin layer of spinel separating the particles. This is similar to observations in Ni-based superalloys. Shape: An example of spinel particles growing in an NiO matrix is given in Figure 15.5. The particles have an interesting shape consisting of six dendrites extending along <001> directions as they grow. This shape is deter- Al2O3 mined by the soft elastic directions in the matrix and not (A) by the gradients of the diffusing Fe3+: so the shape is Spinel determined by the orientation. When the same particle is NiO (B) Al2O3 FIGURE 15.2 HRTEM images of crystallographically two different (A) Spinel spinel/Al2O3 PBs (a and b). White lines show the {111} planes in the spinel. powders have a common feature—both are contained within another phase. NiO 15.6 PARTICLES Two particles that are located within the matrix can always lower the total surface energy by coalescing to form a single particle with the same volume but less surface; we ask the following questions: what is the driving force, how long will it take (thermodynamics and kinetics), and what (B) Spinel is the influence of crystallinity? FIGURE 15.3 The spinel/NiO PB. (a) HRTEM image of lattice- matched PB; (b) dislocations are present at the interface after For particles, we need to consider size, shape, and relaxation to accommodate lattice misfit. The inset is from the orientation. arrowed region. 272 ................................................................................................................ P h a s e B o u n da r i e s , Pa r t i c l e s , a n d P o r e s  annealed after using all the available Fe3+ ions, the shape changes from kinetics controlled to energy controlled and becomes the octahedron enclosed by the low-energy {111} planes. (More details on internal oxidation and reduction of ceramics are given in Chapter 25.) These processes are similar to those affecting isolated powders. Nanoparticles of inert materials can be extremely reactive because of the driving force for reactions and growth caused by their high surface-to-volume energy ratio. One low-energy PB: Some examples of particles formed by precipitation are summarized in Table 15.2. The particles of β⵳-Al2O3, which can grow in a relatively pure (99.8%) α-alumina matrix, tend to grow parallel to the basal plane of the β⵳-Al2O3 no matter what the orien- tation of the surrounding grain or grains as illustrated in Figure 15.6a. Figure 15.6b shows two types of precipitates in a garnet matrix. The large particles of ilmenite are randomly oriented, but the rutile needles are aligned with the matrix. The rutile particles gives us the star garnets FIGURE 15.4 Lattice-matched particles of NiO in Ni–Ti spinel. (like star sapphire, but rarer), which we discuss in Chapter Dark-field TEM image was formed by using a spinel reflection (that 36. The β⵳-Al2O3 particles have grown as platelets because was not also an NiO reflection). FIGURE 15.5 Spinel particles changing shape in NiO due to heat treatment. (The image is formed as for Figure 15.4.) (A) Looking along [011]: 30-minute heat treatment between images: (B) 800°C, (C) 825°C, (D) 850°C, (E) 875°C, (F) 900°C. The shape change is summarized in the schematics (G–I). The 3D figures shows the original shape. 1 5 . 6 Pa r t i c l e s ................................................................................................................................................................ 273  [111] S GB [111] GB GB [011] [111] [111] [100] [011] (G) (H) {111} S GB (A) {110} (I) FIGURE 15.5 Continued TABLE 15.2 Examples of Particles in Ceramics Material Situation (B) FIGURE 15.6 Particle in a matrix. (a) TEM image of a second- Spinel in NiO Nucleation and growth phase β-Al2O3 growing along a GB in α-Al2O3. The insets show ZrO2 in Al2O3 Toughening (ZTA) spinel (S) growing up the GBs. (b) VLM of rutile needles growing TiO2 in Al2O3 The gem stone, star sapphire in a garnet grain. Y2O3 in AlN Sink for oxygen, forms garnet (YAG) at the triple junctions Xe in MgO Ion implantation; Xe is immiscible with MgO there is a good lattice match along one plane; the rutile in the low-angle GB. Figure 15.8b is a little complex. Here particles are needles because the match is really good only the Fe3+ ions have precipitated out onto large NiFe2O4 along one direction. spinel particles that were present at high temperature. As Particles need not be crystalline as is illustrated in the sample was cooled, the misfit dislocations around Figure 15.7 where a particle of glass has been grown in a these large particles could not move because such move- thin-film matrix of α-Al2O3. The particle has a shape that ment requires defects on the oxygen sublattice. Hence the is determined by the crystallography of the matrix. spinel particles grow out between the dislocations—the Figure 15.8 shows two examples of precipitate-free spinel grows into the NiO. zones (PFZ). Figure 15.8a is the classical PFZ at a GB. Finally, you can recognize several triple junctions During cooling from the processing temperature, the Fe3+ (TJs) in the images shown in this chapter. For example, ions in the doped NiO have segregated to the dislocations the spinel is forming at one TJ in Al2O3 in Figure 15.6 and 274 ................................................................................................................ P h a s e B o u n da r i e s , Pa r t i c l e s , a n d P o r e s  FIGURE 15.7 Glass “particles” in a thin film of α-Al2O3 before and after additional heat treatment. (B) FIGURE 15.8 Precipitate-free zones in Fe-doped NiO. (a) At a low-angle GB (with precipitation along the GB); (b) at particles of (A) spinel after oxygen diffusion has ceased. 1 5 . 6 Pa r t i c l e s ................................................................................................................................................................ 275 β⵳-Al2O3 is forming at the other two. Clearly the new If a polycrystalline sample of α-Al2O3 containing phase is not wetting the Al2O3 GB. particles of ZrO2 is heating during consolidation to a temperature at which the ZrO2 is in the tetragonal phase, the matrix can stabilize the high-temperature phase as the sample is cooled. This is the concept used to toughen 15.7 USE OF PARTICLES α-Al2O3 in Chapter 18. What are the properties of PARTICLES IN RELATED FIELDS 15.8 NUCLEATION particles in ceramics and You will find many of these processing techniques AND GROWTH can we make use of them? applied to particles in pharmaceuticals, cosmetics, pig- OF PARTICLES Examples of the uses of ments, paints, etc. ceramic particles in a In metals we often form matrix (rather than as a NUCLEATION OF A SPHERE particles by precipitation powder) include the use of The free energy for a spherical particle depends on the from a solid solution as a glass beads for hardening surface area and the volume: result of heat treatment. The rubber for tires and adding particles can adopt differ- kaolin to paper to make it 4 3 Δ G = 4 π r 2 γ + π r ΔG Box 15.1 ent shapes and set up differ- smoother and easier to r sl 3 V ent strain fields in the print on. The properties The two energy terms balance when matrix during cooling. We depend not only on the can follow the same pro- particle but also on the PB ∂ ( ΔGr ) cess in ceramics or we that encloses it. Particles =0 Box 15.2 ∂r can add particles to the are used to seed crystalli- The critical particle radius is matrix during processing. zation and other phase We actually have an extra transformations. Hematite γ sl variable—we can change particles can be used to r * = −2 Box 15.3 ΔGV the oxygen activity and thus seed the growth of α-Al2O3 The critical value of ΔG* is then change the oxidation state at temperatures lower than of an ion. This process is the usual phase transfor- 4 16 γ 3sl illustrated in Figure 15.5. mation so that the grain ΔG* = πr * γ sl = π 2 Box 15.4 3 3 ΔGV2 size can be kept small. This is now the basis of the Nucleation widely used technique of crystal templating as illustrated in Figure 15.9. The principle involved is the use of parti- The formation of nuclei requires the formation of an inter- cles for nucleating phase transformations so as to control face between the two phases (e.g., between a liquid and a the grain size during subsequent processing. In Chapter solid). Thus, the formation of very small par-ticles gener- 26 we will use nanoparticles to seed crystallization in ally increases the total free energy of the system. glass ceramics and in other specialty glasses such as Vycor. Growth Once such particles reach a sufficiently large size, the interface energy increase is small compared with the volume energy decrease so that the total free energy begins to decrease as the particle size increases. The classic example of precipitate nucleation in metals is the formation of GP zones in Al–Cu alloys. In ceramics, analogous examples include spinel in NiO, rutile in sapphire, or platelets of nitrogen in diamond. When par- ticles are very small, the surface energy dominates. The calculation in Eqs. Box 15.1–Box 15.4 is instructive. Remember that the calculation is for a spherical nucleus and it ignores kinetics; kinetics are actually important as we saw in Figure 15.5. Assuming a spherical nucleus, the total energy required for the formation of a nucleus of radius r is ΔGr, which is FIGURE 15.9 Templating grain growth. The seed is the elongated a combination of two terms. The first term relates to the grain in the center. energy required to create the solid/liquid interface; γsl is 276 ................................................................................................................ P h a s e B o u n da r i e s , Pa r t i c l e s , a n d P o r e s  NiO grain 1 not so important in metals because they tend to collapse to form dislocation loops unless they contain a gas that cannot dissolve in the metal. Pores or voids? We generally use the term pore since the term void suggests that the pore is empty. Most pores in ceramics are created during processing and most GB processing does not occur in a vacuum. Hence, in ceram- ics most pores contain at least some amount of gas. PB These volume defects can have very important effects on the properties of crystalline solids and clearly relate closely to Chapter 13. Examples of these defects follow. D NiO grain 2  Pores in the matrix: Isolated pores and surfaces  Pores at grain boundaries and other grain junctions FIGURE 15.10 Growth of a particle along a GB. The particle is topotactically aligned with one NiO grain (along PB at grain 2) but We often start with very porous material so the “concen- not the other (grain 1). D shows a dislocation at the coherent tration of pores” may be large. We will extend this discus- interface. sion in Chapter 24 (sintering). We may want a porous material (e.g., MCM-41). Pores interact with grain bound- the solid/liquid interfacial energy. This term dominates aries, phase boundaries, etc. for small particles. The second term relates to the energy Does the pore have an equilibrium shape? The shape liberation associated with the volume change; ΔGv is the of the pores is determined by the surface energies. Facet- free-energy change per unit volume for the new phase. ted pores are shown in Figure 15.11. A technique has been The second term dominates when the particle size developed to study systematically the annealing of pores increases, so that once the particles reach some critical size further growth leads to an increasingly lower free energy and hence a more stable system. We can deduce the size of the particle that has the maximum free energy, and that on further growth leads to a continuous decrease in free energy, by differentiating ΔGr in Eq. Box 15.2. The critical value of r is given by Eq. Box 15.3 and implies there is a critical value of ΔG*. When the particles have r < r* we call them clusters or embryos; nuclei are the stable particles with r > r*. Heterogeneous Nucleation If particles nucleate at GBs or at surfaces they generally require less energy since an interface is already present. This is illustrated in Figures 15.8a and 15.10. The plate of spinel growing along the NiO GB has a topotactic align- (A) ment with one grain but not with the other since it is a high-angle GB. The presence of such particles in grain boundaries can change the properties of the material. For example, since β⵳-Al2O3 is a fast ion conductor, such particles in polycrystalline Al2O3 provide short-circuit paths for rapid diffusion of Na, which can accelerate the degradation of Na-vapor lighting products. 15.9 PORES Pores are very important in ceramics, in part because powder processing automatically creates them. The prop- erties of pores are related to the surfaces that define them, but because the surfaces are usually curved they are not well understood. In ceramics, pores are everywhere and always contain some gas, although for simplicity we often (B) think of them as surfaces enclosing a vacuum. Pores are FIGURE 15.11 A faceted pore in UO2. 1 5 . 9 P o r e s ........................................................................................................................................................................ 277  FIGURE 15.12 A method for systemati- cally studying voids. (a) Grooves lying along different crystallographic directions break up to form pores at different rates. (b) The break up of one channel pore can be followed over time. (A) (B) and the effect of dopants on this process. Channels or tasks of the cement industry. Here, one way of minimizing pores can be created in a Σ = 1 or high-angle GB by porosity is to minimize the amount of water used in the joining together two flat plates after patterning the surface cement. With suitable use of plasticizers and so-called of one grain using lithography as illustrated in Figure microsilica, compressive strengths of >100 N/mm2 and 15.12. The formation of such pores will occur when two tensile strengths of ∼15 N/mm2 can be achieved. The plas- nearly flat plates are joined, but will not be controlled. The ticizers used for this are water soluble and mainly improve technique has been extensively used to study pore anneal- the packing density, thus decreasing pore content. Inciden- ing and the effect of dopants on this process in Al2O3, but tally, cement can also be reinforced with up to 5% glass could easily be extended to other materials including fiber and concrete may be reinforced with polypropylene glass. (See also the discussion of Figure 14.33.) fiber and of course steel “fibers.” Pores can coalesce just as particles can. (Think of them as inverse particles.) The driving force is the same, namely, reduction of the total energy by reducing the area 15.10 MEASURING POROSITY of the interface. The difference is that in order to shrink, the pore must nucleate a vacancy first. This vacancy must We are interested in three quantities: (1) the size of the diffuse away through the lattice, along a dislocation or pores, (2) the distribution of the porosity, and (3) the total along an interface. amount of porosity in the sample. Usually the actual shape What is the effect of gas in pores? You can not remove of the pores is less important, although there may be situa- the gas easily once the pore has separated from an inter- tions in which the shape would be a critical factor. We face because you then have to move a neutral atom through can see pores in transmission electron microscopy (TEM), the lattice. Pores can move through the matrix as we will scanning electron microscopy (SEM), and atomic force discuss in Section 24.15, but this process is likely to be microscopy (AFM). If they are large enough, we will also slow and involves surface diffusion from one side of the see them in visible light microscopy (VLM). None of these pore to the other; as for a bubble rising in a liquid, we observations will give a statistical measurement of the need a driving force. amount of porosity. Pores are also the prin- The total amount of cipal defect in cement and PORE PARAMETERS porosity can be estimated concrete (see Section 2.7), Some closely related topics include pore size, particle quite accurately if you which makes controlling size, total surface area, active surface area, and total know the phases present in porosity one of the main material density. the sample. You estimate 278 ................................................................................................................ P h a s e B o u n da r i e s , Pa r t i c l e s , a n d P o r e s  This type of void is not what we mean by the term pore since these voids are an essential component of those crys- talline structures. They may become filled with gas or liquid, but this is more closely analogous to an impurity occupying an interstice in other crystal structures as He can, for example, in the fluorite-structured UO2. The new mesoporous materials have extremely high surface-to-volume ratios. An example of these materials is MCM41, which was invented by DuPont. A simple struc- ture that can be manufactured in the laboratory is illus- trated in Figure 15.14. The structure initially contained a periodic array of polymer spheres. When close packed, these spheres leave 26% of the volume empty. We can then infiltrate a liquid into these pores, burn out the spheres, and convert the liquid to a polycrystalline ceramic. Another synthesized porous ceramic is the cordierite honeycomb structure used to support the Pt catalyst in automobile catalytic converters. In this case the cylindrical pores are introduced mechanically in the extrusion process. Pumice is a natural porous ceramic. It is produced by volcano eruptions and the gas is trapped inside the solid as it rapidly cools. The matrix is mainly glass, but it can contain small crystals. Synthetic ceramic foam is illus- trated in Figure 15.15. Uses for ceramic foam are sum- FIGURE 15.13 A commercial porosimeter. marized in Table 15.3. One of the best-known applications for a porous ceramic is the space shuttle tile. An SEM the theoretical density, deduce the actual density, and thus image of such a tile is shown in Figure 15.16. Notice that estimate the porosity. The other two quantities are much in this case, the ceramic consists mainly of fiber (pressed more difficult to determine. We can infiltrate a liquid and not woven), so the principle is the same as for ceramic apply mercury-intrusion porosimetry. The principle is that (glass) fiber for house insulation. the capillary pressure depends on the radius of the pore. If The structures shown in Figure 15.17 illustrate the we vary the pressure on the Hg, it will fill pores down to a result of computer modeling of foams. A thin membrane different size. If we then increase the pressure, more pores connects the structural ribs, as in a soap bubble in a wire will be filled. The drawback to this approach is that we frame. Since this film is amorphous, its surface energy is only measure the pores that are connected to the exterior. uniform and the film will be flat. The structure, of course, Commercially available equipment for measuring porosim- etry is illustrated in Figure 15.13. A related technique uses nuclear magnetic resonance (NMR) to measure the time taken by a liquid to fill the pores. It measures the relaxation times of the liquid filling the pores and relates this relaxation time to the thickness of the liquid and hence determines a surface-to-volume ratio for the pores. It is also possible to obtain information on the porosity using electron paramagnetic resonance (EPR), but neither EPR nor NMR is widely used for this purpose. There are many other uses of porosity measurements; the oil exploration industry is a major example. There is clearly a strong link to powders: in some applications surface area may be more important than pore/particle size, but the two are not independent. 15.11 POROUS CERAMICS We discussed the structure of zeolites in Chapter 7. The special feature of the crystal structure is the large void that is surrounded by a silicate cage but linked to other voids. A related void is that found in C60 and the other buckyballs. FIGURE 15.14 An ordered mesoporous material. 1 5 .11 P o r o u s C e r a m i c s ................................................................................................................................................. 279  TABLE 15.3 Uses for Ceramic Foam Foam material Application Sieves Molten metal filters Sieves, microporous Gas filters Catalyst supports Catalytic converter Thermal insulators Space shuttle tiles Artificial opal Optical FIGURE 15.15 Sintered alumina foam made using a soap-nut slurry with a 40 volume % ceramic. looks very similar to the glass films between grain bound- aries, at triple junctions and at 4-fold junctions as dis- cussed in Chapter 14, but all the “grain boundaries” are now flat (because the grains are pores). 15.12 GLASS/CRYSTAL PHASE BOUNDARIES Crystals have been grown in glass matrices for hundreds of years. The luster glaze used on some medieval pottery FIGURE 15.16 The porous material used to make insulating tiles owes its sparkle to nanoparticles of copper in the glass. for the space shuttle. The silica fibers are 2–4 μm in diameter. Kelvin cell Weire-Phelan foam (A) (B) φ = 0.001 φ = 0.01 φ = 0.01 (0.95) φ = 0.05 Wet Kelvin cell φ = 0.01 Wet rhombic dodecahedron φ = 0.05 φ = 0.11 (C) (D) (E) FIGURE 15.17 IGFs without grains. (a and b) Models of the Kelvin cell and a Weaire–Phelan foam used to describe soap bubbles; (c–e) how these relate to the structure of TJs and QJs. 280 ................................................................................................................ P h a s e B o u n da r i e s , Pa r t i c l e s , a n d P o r e s  TABLE 15.4 Observed Microstructures in Some Ceramic Eutectic Systems System Teut (°C) Growth Rate (cm/hour) Comments PbO–Pb2Fe2O4 (12.8 wt% Fe2O3) 730 0.5–2 Broken lamellar, two-phase matrix PbO–Pb3Nb2O8 (6.85 wt% Nb2O5) 835 2 Lamellar V2O5 –Pb2V2O7 (5.7 wt% V2O5) 760 Cast Lamellar Pb4GeO6 –Pb3Ge2O7 (15.0 wt% GeO2) 707 1.45 Circular rod WO3 –BaWO4 (18.5 wt% BaO) 935 Cast Water soluble V2O5 –BaV2O6 (32.2 wt% BaO) 550 Cast Glassy Bi4Ge3O12–Bi14GeO24 (10.3 wt% GeO2) 880 Cast Unbranched dendrites V2O5 –ZnV2O6 (14.2 wt% ZnO) 640 Cast Coarse unbranched dendrites V2O5 –NiV2O6 (9.2 wt% NiO) 650 Cast Coarse unbranched dendrites V2O5 –MnV2O6 (9.10 wt% MnCO3) 660 2 Coarse unbranched dendrites PbO–Pb2WO5 (17.6 wt% WO3) 725 Cast No fine two-phase areas seen Bi2O3 –Bi26Zn2O38 (1.24 wt% ZnO) 750 2 Circular rod, spheroidized BiFeO3 –Bi40Fe2O63 (1.14 wt% Fe2O3 790 0.5–2.5 Ciruclar rod, matrix may be faceted Li2WO4 –WO3 (19.1 wt% WO3) 695 Cast Porous, very soluble in water V2O5 –CuV2O6 (12.7 wt% CuO) 620 Cast No fine two-phase areas seen V2O5 –CaV2O6 (2.74 wt% CaO) 618 Cast No fine two-phase areas seen Bi2O3 –Bi2Mn2O9 (12.2 wt% Mn2O3) 790 Cast Lamellar Bi2O3 –Bi8TiO4 (0.53 wt% TiO2) 835 Cast Lamellar WO3 –CaWO4 (7.46 wt% CaO) 1135 Cast Triangular rods WO3 –SrWO4 (17.1 wt% SrCO3) 1075 Cast Triangular rods WO3 –MgWO4 (12.6 wt% MgCO3) 1120 2 Lamellar “Chinese script” La 2O3 –LaFeO3 (28.5 wt% La 2O3) 1430 ∼2 Triangular rods Fe2O3 –YFeO3 (15.9 wt% Y2O3) 1455 Coil Lamellar/rod, matrix forms three-pronged webs Gd2O3 –GdFeO3 (15.0 wt% Gd2O3) 1500 Cast Lamellar/rod, matrix forms three-pronged webs BaTiO3 –BaTiSiO5 (9.9 wt% SiO2, 1260 2 Rodlike 90.1 wt% BaTiO2) BaTiO3 –BaTiO4 (41.9 wt% TiO2) 1563 2 Lamellar and rod Zn2TiO4 –TiO2 (43.0 wt% ZnO) 1418 2 Lamellar Al2O3 –ZrO2 (Y2O3) (55 wt% Al2O3, 1890 0.5–10 Circular rod, matrix may be faceted 38.3 wt% ZnO2) Household window glass will eventually form crystals of they can in metal systems. Eutectic structures are well devitrite, an orthorhombic crystal with a formula like known in metals, but have not been exploited in ceramics. Na2Ca3Si5O16; these crystals usually form at the surface One reason for this is that eutectics are associated with first. Crystalline glazes, which can make a pot look so solidification of a liquid phase and we do not usually spectacular, actually rely on spherulites consisting of many process ceramics using a liquid phase; this also means that willemite (Zn2SiO4) crystals, with each acicular crystal processing temperatures are generally higher. In the exam- growing in the [001] direction, to achieve the effect. (More ples listed in Table 15.4, one column gives the morphology on this topic in is presented in Section 21.11.) of the respective phases. The minority phase can be sheets, When two crystalline oxides are joined together to rods, or particles; which of these actually occurs is deter- form a GB or PB, they are often thought of as being ionic mined in part by the energy of the PBs and the way in materials even though the bonding may have a relatively which the sample is cooled from the eutectic temperature. large covalent component. Glass is usually viewed in the Directional solidification is generally required to optimize opposite way. Clearly we should take the nature of the rods and platelets. bonding and the possibility of an interface space charge In the CoO/ZrO2 eutectic solid, the two ceramics are into account when we examine the glass/crystal interface. both cubic, but they have very different structures. They This point is particularly relevant to an understanding of grow in the cube-on-cube orientation, which means that all glass-ceramic materials. directions and planes in one material are parallel to the same directions and planes in the other material. As a pos- sible application of such a material, oxygen diffuses rapidly 15.13 EUTECTICS in ZrO2. It can then react with the CoO to produce a layer of Co3O4 at the interface between the two materials, result- Is there anything special about ceramic eutectics? Not ing in the structure illustrated in Figure 15.18. Notice how really (although they are very interesting), but it is some- uniform this spinel layer is: the growth is controlled by the times a bit of a surprise that they can be formed just as reaction, not diffusion of O through the ZrO2. 1 5 .1 3 E u t e c t i c s .............................................................................................................................................................. 281  500 nm [001] [010] Z S C S Z S C Z FIGURE 15.18 A CoO/ZrO2 eutectic after solidification and subsequent oxidation. Z, ZrO2; C, CoO; S, Co3O4 (spinel). FIGURE 15.19 Particles of W on SiC. When crossed fringes are present (because of the lattice misfit), the alignment is excellent, otherwise; the islands are tilted relative to the substrate. 15.14 METAL/CERAMIC PBs Metal/ceramic PBs are not only the most important feature alignment and lattice mismatch of the two phases can be in ceramic-reinforced metal-matrix composites, but they appreciated from the moiré fringes in the image. also occur when metals are oxidized or when oxides are High-resolution TEM (HRTEM) has now shown more reduced to the metal or when a metal film is grown on a details on such interfaces. The position of the misfit dis- ceramic substrate (or vice versa). In Figure 15.19 particles location actually depends on the elasticity parameters of of W have grown on a single-crystal thin film of SiC. The the two materials. The schematic diagram in Figure 15.20 [101] [121] FIGURE 15.20 Schematic of stand-off dislocations accommodating lattice misfit between Nb and Al2O3. 282 ................................................................................................................ P h a s e B o u n da r i e s , Pa r t i c l e s , a n d P o r e s  TABLE 15.5 PBs in Applications Bond Material Brazing Join a ceramic to a metal Metal–matrix composites Make a two-phase material Electronic interconnects Bonding metal to a semiconductor Oxidation of metal Form an oxide from metal Catalysis Support catalyst particles illustrates the dislocation BRAZING AlN bonding two materials stand-off, which is seen at Using an active metal such as Zr, we can get an idea together, we do not always the Nb/Al2O3 interface. about the possible reactions by using the Ellingham want to produce strong The dislocations preferen- free-energy diagrams. Figure 15.21 is a plot of the free bonds; some applications tially sit in the metal so as energy of formation of selected nitrides as a function of may prefer that the bond be to lower the energy of the temperature. The lines represent the reaction weak (for example, in fiber dislocation (remember, E composites). The forma- depends on the elastic con- 2 Zr(s) + N2 (g) = 2 ZrN(s) tion of the bond has some stants not just b) while still requirements. accommodating the misfit Thus, when AlN is combined with Zr at high tempera- between the materials. tures the reaction  Intimate contact be- tween the two materi- Zr + AlN → ZrN + Al als—the obvious 15.15 FORMING requirement for a PBs BY JOINING is favored. At 1123 K the free energy for this reaction is strong bond. −83.3 kJ/mol.  Formation of a chemical We form PBs whenever we bond—covalent bond- join dissimilar materials. ing would be strong and Table 15.5 summarizes some applications of joining proc- van der Waals bonding esses and the type of PB that is formed. Note that when would be weak. 600 ΔF°f kJ/g-mole N2 (s) 2 3N ) Ca 2 (s (g) )= 400 3N NH 3 (s) (g g =2 e 8N M 2 N (g ) 2F )= + N = 2 (g 2 (g) ) )+ a(g (g N +N 2 ) 3C 3H 2 N(s + (l) 2Fe 4 l) Fe g( 16 )= N 2(g 3M rN (l) + 2C 8Fe 200 M 1 Si N M B 2 3 4 2Fe 4N (s) M 2V N N(s) 2CrN N B 2 Fe 8 M 2Cr 2 lN (s) 2A 0 Mo 2N g) )=2 N H 3( N 2(g B M 2B 2N 4Mo(s) + ) (s CrN M B )=2 N 2(g s) + M 2Cr( rN ) (s ) = 2C 2 + N 2(g (s) 4Cr(s) N B -200 g) = 2 V N(s ) N 2( 2Ta )+ M g) = 2 V (s N 2( (s ) + N M (s) e N2 2Ta 2C Ca 3 N2 )= M Mg 3 N 2( g )+ (s ) e (l M BN 2C -400 (g ) =2 M s ) + N2 ( s ) M 2 B( 2A lN ) = (g + N2 ) l(s) N(s 2A 2Ti g) = N 2( s) -600 2Ti (s ) + =2 Zr N ( M = Melting point of metal (g) + N2 B = Boiling point of metal (s) 2Zr 0 500 1000 1500 2000 2500 T (°C) FIGURE 15.21 The Ellingham diagram. The lower line is used when brazing Zr. 1 5 .1 5 F o r m i n g P B s b y J o i n i n g .................................................................................................................................... 283   For a lasting bond, there must be a way to accommo- approaches have been used to braze nonoxide ceramics. date interfacial stresses. Zr may be a suitable candidate for an active metal for brazing of AlN ceramics. In making electronic interconnects it is often neces- The interfacial stresses may arise due to thermal sary to metallize the surface of Al2O3 (in ceramic packag- expansion mismatch generated during cooling, or after ing for integrated circuit applications). We describe how fabrication, or because of temperature changes in opera- metallization is accomplished using thick-film processing tional conditions. in Chapter 27. The development of an interlocking glass/ Brazing is joining a metal to a ceramic. The technique ceramic and glass/metal structure is required for good is well illustrated by considering metallization processes adhesion because it provides mechanical interlocking in for AlN. There are several possible routes for forming the addition to chemical bonding between phases. To achieve interfaces. the required microstructure at the conductor–substrate interface it is necessary for the glass to have the appropri-  Apply the metal in a liquid form ate surface tension and viscosity during the firing process,  Deposit either material from the vapor phase and for it to wet the substrate.  Use a solid-state reaction involving oxidation or In thin-film metallization by evaporation or sputtering reduction of thin metal films onto a ceramic surface (Chapter 28), it has been demonstrated that a sequence of layers of dif- ferent metals is required for optimum film properties. The Liquid metals have much higher surface energies than first layer is usually a refractory metal such as Ti, Cr, or most ceramic oxides, and the PB energy is also high. The NiCr; this layer provides adhesion to the ceramic. These result is that liquid metals do not readily wet a ceramic elements are reactive and bond through redox reactions and spread, unless special precautions are taken. Two with the substrate. The second layer acts as a diffusion approaches have been used for the development of barrier. The barrier material will usually be a noble metal, metal brazes for oxides. In one method, active metals preferably Pt or Pd. The top layer will be the metal such as Ti or Zr are added to the metal; these effectively of choice for the particular application, for example, reduce the interfacial energy because the additives have a Au for wire-bonding applications and Ni or Ag–Pd for strong chemical attraction to the oxide and hence they solderability. enhance wetting behavior. The active metal is essentially A schematic for the process of anodic bonding is shown acting as a surfactant! A braze must react with both in Figure 15.22. The concept is that two materials are the metal and ceramic components that you are joining joined together by heating them while applying a voltage and reach chemical equilibrium at the interfaces. across the assembly (hence it is also known as field-assisted Metal systems are generally compatible, resulting in bonding). The temperature is typically between 300°C and wetting; the braze can then bond (by solution or diffusion) 450°C while the applied voltage is ∼80 V. Glass can be to the metal component. bonded to glass or to Si with this process. In principle, the Braze alloys for Al2O3-based ceramics might be limiting factor is being able to polish the abutting surfaces Ag–Cu, Au–Ni, or Ag– to a roughness of <100 nm. Cu–Zn, but these alloys Glass works particularly generally do not wet METALLIZING ALUMINA well because the cations are ceramics. The oxidation A commercial process for metallizing debased alumina quite mobile. potentials of Cu and Ag uses Mo or W; the alumina grains in the debased alumina Some final examples of are less than that of Al, so are held together by a glassy phase binder. The Mo PBs are given. In catalysis, they do not react with the is applied to the surface as a powder, often mixed it is usually not possible ceramic. If a small per- with manganese oxide, and fired in a reducing atmos- to examine the interface centage of an active metal, phere with a controlled dew point so that the Mn between the support and e.g., Ti, is added, then the is present as MnO and Mo as the metal. The MnO the catalyst particle. An high oxidation potential reacts with both the alumina grains and the liquid glassy example of catalyst parti- of the Ti causes it to phase. The glassy phase from the Al2O3 migrates into cles on a silica nanowire is undergo a redox reaction the metal powder under the influence of capillary forces shown in Figure 15.23. with the ceramic (Al2O3). and bonds the metal particles to each other and to the We will discuss composite The result is the spread- Al2O3 surface, producing a wettable surface layer. In the materials in more detail ing of the braze because case of pure Al2O3 and oxides without binder phases, it later, but we note that the an oxide that is compati- is necessary to add glasses to the metallizing mixtures. filler material (fiber or ble with both phases The Mo coating is generally electroplated with Ni to particle) and the matrix forms at the interface; provide a clean and continuous surface as well as one can be glass, crystalline a chemical bond forms on which an applied braze would easily spread. A similar ceramic, or another (see at the interface. Similar process is applied for W metallization. Chapter 20). 284 ................................................................................................................ P h a s e B o u n da r i e s , Pa r t i c l e s , a n d P o r e s  — Pyrex glass HVpower supply Si wafer + Hot plate Probe Al plate (with insulated ceramic top) stand Vs — + + — + — Metal Silicon cathode + — anode + — (B) 7740 Glass Vs Applied Voltage t=0 t=∞ FIGURE 15.22 (a) Set-up for the anodic bonding of glass to Si Position and (b) an example of a glass/Si/glass sandwich produced using (A) this process. FIGURE 15.23 Au catalyst particles on a ceramic nanowire. CHAPTER SUMMARY There are several key ideas in this chapter. PBs are present wherever we have a second phase, particle, or precipitate in a matrix; we treat pores as a special particle. (The surface is actually a special PB.) Like GBs, PBs are everywhere in ceramics; we could develop a notation similar to the Σ for GBs but rarely use it. When a phase transforma- tion occurs, the mechanism is the movement of a PB. Particles can be different in structure and/or composition in a ceramic matrix; precipitates are particles that have developed by a specific process. Pores are present in most ceramics and play important roles in determining properties. We have developed special methods for characterizing porosity and ceramics in which the pores are actually the major phase—porous ceram- C h a p t e r S u m m a ry .......................................................................................................................................................... 285  ics. We just touch on some special PBs, namely glass/crystal interfaces and metal/ceramic interfaces; we will see much more of the former in later chapters. GENERAL REFERENCES The details of nucleation and growth theory are given in many standard textbooks on kinetics and phase transformations: see the books on interfaces in Chapter 15 and on phase transformations in Chapter 25. SPECIFIC REFERENCES Dhara, S., Pradhan, M., Ghosh, D., and Bhargava, P. (2005) “Nature inspired novel processing routes for ceramic foams,” Adv. Appl. Ceram. 104(1), 9. Formenti, Y. and Druitt, T.H. (2003) “Vesicle connectivity in pyroclasts and implications for the fluidisation of fountain-collapse pyroclastic flows in Montserrat (West Indies),” Earth Plan. Sci. Lett. 214, 561. Gibson, L.J. and Ashby, M.F. (1999) Cellular Solids: Structure and Properties, 2nd edition, Cambridge University Press, Cambridge. Gibson, L.J., Ed. (2003) “Cellular solids,” MRS Bull. 28(4). Halperin, W.P., D’Orazio, F., Bhattacharja, S., and Tarczon, J.C. (1989) “Magnetic resonance relaxation analysis of porous media,” in Molecular Dynamics in Restricted Geometries, Wiley, New York, p. 311. Korda, G. and Kang, Y. (1991) “Three-dimensional electron paramagnetic resonance imaging technique for mapping porosity in ceramics,” J. Am. Ceram. Soc. 74, 709. Montanaro, L., Jorand, Y., Fantozzi, G., and Negro, A. (1998) “Ceramic foams by powder processing,” J. Eur. Ceram. Soc. 18, 1339. Penner, S., Rupprechter, G., Sauer, H., Su, D.S., Tessadri, R., Podloucky, R., Schlogl, R., and Hayek, K. (2003) “Pt/ceria thin film model catalysts after high-temperature reduction: a (HR)TEM study,” Vacuum 71(1–2), 71. Perkowitz, S. (2000) Universal Foam, Walker, New York. Pumice is on p. 128: this text puts it in perspective. Suvaci, E., Oh, K.-S., and Messing, G.L. (2001) “Kinetics of template growth in alumina during the process of templated grain growth (TGG),” Acta Mater. 49, 2075. EXERCISES 15.1 Given the information in the text, determine the orientation of the samples. 15.2 What is the crystallographic relationship between the two grains shown in Figure 15.2a? How does it differ from that of the interface shown in Figure 15.2b? 15.3 Using reasonable values of the solid/liquid interface energies and ΔGv, estimate r* for spinel in MgO versus Cu in Si. 15.4 Do you expect the conduction of Na + ions in an ionic conductor to depend on crystallography? If so, why, and what are the implications? 15.5 How would you propose characterizing nanoparticles in the glaze on a priceless pot? Breaking the pot, even a little bit, is not allowed. 15.6 In Section 15.14 we note that dislocations can be present at metal/ceramic interfaces. When is this most likely; when is it least likely? How will the interfacial energies and strengths differ? 15.7 What is the relationship between the methods used to form the images in Figures 15.4 and 15.8? Explain why this technique works. 15.8 Assuming the interfaces labeled in Figure 15.7 are all viewed edge on, what is the viewing direction (the direction defined with respect to the sapphire crystal)? 15.9 Suggest reasons for the shape of the particle shown in Figure 15.5. How does this explanation compare with that for the shape of the particle in Figure 15.11? 15.10 List the possible applications for zeolites and mesoporous ceramics. 286 ................................................................................................................ P h a s e B o u n da r i e s , Pa r t i c l e s , a n d P o r e s  Part V Mechanical Strength and Weakness  16 Mechanical Testing CHAPTER PREVIEW The concepts of stress and strain and the elastic moduli should already be familiar. Where ceramics differ from most metals and polymers is that at room temperature most of them are brittle. Flaws play a major, often dominating, role in the mechanical behavior of ceramics. As a result, obtaining properties such as elastic moduli is often more difficult than it would be for metals: preparing the sample can lead to the introduction of flaws. Stress–strain curves for ceramics are usually obtained using a bending test rather than a tensile test. We need only to make our ceramic into a rectangular block. The brittle behavior of ceramics gives them low fracture toughness, a property that can most conveniently be obtained from indentation testing. A key point from this chapter is that when we use ceramics in load-bearing applications we need to understand the importance of flaws and how to incorporate them into our design approach. 16.1 PHILOSOPHY It will be important to keep these ideas in mind when you read older texts. We are not going to provide a treatise The classical view of ceramic materials includes the on mechanical properties of ceramics. There are many following: existing books that do and some of these are listed at the end of the chapter. What we will do is look at what is 1. They are brittle. special for ceramics. 2. Dislocations are not important because they do not The general need is to understand the response of a move. material to an applied stress. The stress may be applied 3. They are polycrystalline and fracture along grain externally or induced by altering other parameters such as boundaries. temperature (which can cause a phase transformation). The fundamental idea is the link to bonding. In Chapter Once again the classical view of ceramics and many 4 we described how the Young’s modulus is related directly of our preconceived ideas of how they behave are not to the bond-energy curve. In Chapter 12 we described the always correct. nature of dislocations in ceramics. So the following three chapters have three special  We can bend a sheet of silicon into a tube. themes  We can bend an alumina fiber into a circle.  Dislocations move ahead of crack tips, are present at  Mechanical testing—how to do it plus the fundamen- heterojunctions, and can be produced in large numbers tals of elastic constants, etc. during single-crystal growth.  Plastic deformation and how it is accommodated  Single-crystal ceramics also fracture (Figure 16.1  Fracture and how to control it shows an Nd-doped YAG single-crystal boule that fractured during growth). The starting point for most discussions of mechanical The modern view of ceramics is therefore very properties of materials is a stress–strain (σ–ε) curve for different: a material in tension. Figure 16.2 shows σ–ε curves for three different materials at room temperature. 1. We may be using the ceramic as a thin film where stresses may be very high. Material I: This has a high Young’s modulus, high failure 2. Deformation at high temperatures may be important. stress, low ductility, low toughness, and fractures 3. In some special “new” ceramics, displacive transfor- without significant plastic deformation. This behavior mations become important. is characteristic of many ceramics. 16 .1 P h i l o s o p h y .............................................................................................................................................................. 289  External Fabrication Texture Strength factors Raw Chemical materials composition Phase Flow Processing distribution and Temperature, grain size stress environment and test Pores and Fracture conditions Firing cracks stress Surface Finishing condition FIGURE 16.3 Factors affecting the mechanical properties of ceramics. limited toughness. This behavior is characteristic of many elastomers. The strength of ceramics is affected by many factors, and this complexity is illustrated in Figure 16.3. The com- 1 cm position and microstructure are particularly significant and mechanical properties depend strongly on these char- FIGURE 16.1 Cracking in an Nd-doped YAG boule. acteristics. Figure 16.4 shows two specific examples that Material II: This has moderate strength, moderate ductil- ity, deforms plastically prior to failure, and is the toughest of the three. This behavior is characteristic 4 of many metals. 200 Density Material III: This has a low Young’s modulus, is very g/cm3 ductile, and has low ultimate tensile strength and Strength (MPa) 2 100 σ Material I 0 0 0 0.5 1.0 Material II (A) Fractional Porosity MOR (MPa) 140 70 35 Material III 20 50 100 200 ε (B) Mean Grain Diameter, μm FIGURE 16.2 Idealized stress–strain curves for different materials FIGURE 16.4 (a) Effect of porosity on the strength of polycrystal- classes. line Al2O3. (b) Effect of grain size on the strength of BeO. 290 ...................................................................................................................................................... M e c h a n i c a l Te s t i n g  Grain Size, G (μm) high-temperature capabilities, and hardness) with the 100 50 20 10 4 2 1 ability to carry a significant tensile stress. The majority of Flexure Hot-pressed and press-forged Al2O3, 22 °C the high-performance ceramics are based on silicon Strength (MPa) nitride, silicon carbide, zirconia, or alumina. Structural 600 Kirchner 3 ceramics come in many forms—monoliths, composites, -196 °C coatings, fibers, and whiskers. 4 5 11 7 7 400 Charles 2 Rice survey 16.2 TYPES OF TESTING 6 (22 °C) 2 2 3 7 Ideally, before we use a ceramic in a load-bearing applica- 5 4 3 tion we would like to have the following information 3 200 4 about it: 3 4 3 5 5 Davidge & Tappin Hot pressed: 4 p ~ 6% Linde A } Rice  Young’s modulus Linde B Dewith (p ~ 0) Crandal et al.  Average strength and Weibull modulus Single crystal Press-forged Heuer & Roberts Rhodes et al.  Toughness 0  Crack propagation rate 0 20 40 60 80 100 (Grain Size, G)-1/2 (cm-1/2)  Cyclic fatigue resistance  Creep curves FIGURE 16.5 Compilation of strength data as a function of grain size for polycrystalline Al2O3.  Stress rupture data We would also like to know these parameters as a function of temperature, in particular, over the tempera- illustrate the role of microstructure on the strength of ture range at which our ceramic component is going to be ceramics. In Figure 16.4a the strength of a porous poly- used. Many different types of tests are used to obtain crystalline alumina is shown to decrease much more the mechanical properties of ceramics. There are major rapidly than its density. The reason is that pores act to differences between how metals are tested compared to concentrate stress, which will not be uniform throughout ceramics: the ceramic. The strength of nonporous ceramics decreases with increasing grain size as illustrated for the case of  It is often difficult to do tension tests on ceramics BeO in Figure 16.4b. Again, the observed behavior is due because of the possibility of introducing flaws. to flaws in the material that act as stress concentrators. In  Ceramics are stronger in compression than they are in large grains there can be larger flaws. The effect of grain tension because of how cracks propagate. size is often more complicated than that shown in Figure  For ceramics, we need to be concerned with statistics 16.4b when we consider ceramics in which the grain size because we don not know where the largest flaws is just a few micrometers. Figure 16.5 is a compilation of are. flexural strength results for polycrystalline alumina at room temperature as a function of grain size. Despite the Because some mechanical properties depend on how considerable scatter in the data, there are clearly two dis- the material was tested, it is important and necessary to tinct regions. In both cases strength is proportional to the establish specified test methods. Standard test methods reciprocal square root of the grain size (d −1/2) with differ- have been adopted for ceramics. In the United States ent constants of proportionality. The reason for this behav- ASTM International (originally the American Society for ior is that in addition to the preexisting flaws causing Testing and Materials, ASTM) is the primary organization brittle fracture, there is a competing fracture mechanism developing standards for materials testing. ASTM Com- that links dislocations and crack nucleation to subsequent mittee C-28 on Advanced Ceramics has completed several failure. standards and ones related to mechanical properties and It is therefore essential that when the mechanical prop- testing are listed in Table 16.1. Specialized subcommittees erties of a ceramic material are listed, some details of the work on specific areas within the field of advanced ceram- microstructure are also provided. As you can see from ics. Committee C28.01 is involved with standards related Figure 16.3 the measured value of a mechanical property to mechanical properties and performance of monolithic may be affected by the test method. This is particularly ceramics. Committee C28.02 deals with reliability issues. true in the case of hardness. The National Institute of Standards and Technology High-performance structural ceramics combine the (NIST) has established several free databases that list traditional advantages of ceramics (chemical inertness, mechanical properties of ceramics. 16 . 2 Ty p e s o f Te s t i n g ................................................................................................................................................... 291  TABLE 16.1 ASTM Standards on Mechanical Properties and Testing of Ceramics Mechanical properties and performance C1161-02 Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperaturea C1198-01 Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Advanced Ceramics by Sonic Resonance C1211-02 Test Method for Flexural Strength of Advanced Ceramics at Elevated Temperatures C1259-01 Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio for Advanced Ceramics by Impulse Excitation of Vibration C1273-95 Test Method for Tensile Strength of Monolithic Advanced Ceramics at Ambient Temperature C1291-95 Test Method for Elevated Temperature Tensile Creep Strain, Creep Strain Rate, and Creep Time-to-Failure for Advanced Monolithic Ceramics C1326-99 Test Method for Knoop Indentation Hardness of Advanced Ceramics C1327-97 Test Method for Vickers Indentation Hardness of Advanced Ceramics C1361-01 Practice for Constant-Amplitude, Axial, Tension-Tension Cyclic Fatigue of Advanced Ceramics at Ambient Temperature C1366-97 Test Method for Tensile Strength of Monolithic Advanced Ceramics at Elevated Temperatures C1368-01 Test Method for Determination of Slow Crack Growth Parameters of Advanced Ceramics by Constant Stress-Rate Flexural Testing at Ambient Temperature C1421-01 Test Method for the Determination of Fracture Toughness of Advanced Ceramics C1424-99 Test Method for Compressive Strength of Monolithic Advanced Ceramics at Ambient Temperatures C1465-00 Test Method for Determination of Slow Crack Growth Parameters of Advanced Ceramics by Constant Stress-Rate Flexural Testing at Elevated Temperature C1499-02 Test Method for Monotonic Equi-biaxial Flexural Strength Testing of Advanced Ceramics at Ambient Temperature C1525-02 Test Method for Determination of Thermal Shock Resistance for Advanced Ceramics by Water Quenching Reliability C1175-99 Guide to Test Methods for Nondestructive Testing of Advanced Ceramics C1212-98 Practice of Fabricating Ceramic Reference Specimens Containing Seeded Voids C1239-95 Practice for Reporting Uniaxial Strength Data and Estimating Weibull Distribution Parameters for Advanced Ceramics C1322-02 Practice for Fractography and Characterization of Fracture Origins in Advanced Ceramics C1336-96 Practice for Fabricating Non-Oxide Ceramic Reference Specimens Containing Seeded Inclusions C1495-01 Test Method for Effect of Surface Grinding on Flexure Strength of Advanced Ceramics a Standards for both three-point and four-point bending; −••, year of current version of standard, e.g., −01 is 2001. 16.3 ELASTIC CONSTANTS AND ν = −εT/εL (16.2) OTHER “CONSTANTS” For many ceramics and glasses it is in the range In this section we will define some of the parameters that 0.18–0.30. describe the mechanical behavior of materials. Some of 3. m—Shear modulus is the ratio of shear stress to these parameters are constants, like Young’s modulus E. shear strain. Some, like hardness, are not. Hardness depends on how the material was tested. μ = τ/γ (16.3) Table 16.2 lists four elastic constants for different ceramics. These are the four that are most common. 4. B—Bulk modulus is the ratio of stress to strain for 1. (or Y, but be careful because Y is also used hydrostatic compression. in our expression for stress intensity factor)—Young’s modulus (also referred to as the elastic modulus) is a B = −P(ΔV/V) (16.4) material constant defined by Eq. 16.1 for a linear elastic material under uniaxial tensile or compressive Although these constants are related directly to stress. bonding forces between atoms, in real ceramics they are affected by microstructure, e.g., porosity and the σ = Eε (16.1) presence of second phases. Because strain is dimension- less, elastic moduli have the same dimensions as those It is therefore the slope of a σ–ε curve where only elastic of stress: force per unit area (N/m 2) or in the SI classifica- deformation occurs. tion Pa. 2. n—Poisson’s ratio is the negative ratio of the trans- Some texts use a pair of related elastic constants l and verse strain (εT) to longitudinal strain (εL). m. These are known as the Lamé constants. We already 292 ...................................................................................................................................................... M e c h a n i c a l Te s t i n g  TABLE 16.2 Elastic Constants of Selected Polycrystalline Ceramics (20°C) Material Crystal type m (GPa) B (GPa) n E (GPa) Carbides C Cubic 468 416 0.092 1022 SiC Cubic 170 210 0.181 402 TaC Cubic 118 217 0.270 300 TiC Cubic 182 242 0.199 437 ZrC Cubic 170 223 0.196 407 Oxides Al2O3 Trigonal 163 251 0.233 402 Al2O3 ·MgO Cubic 107 195 0.268 271 BaO·TiO2 Tetragonal 67 177 0.332 178 BeO Tetragonal 165 224 0.204 397 CoO Cubic 70 185 0.332 186 FeO·Fe2O3 Cubic 91 162 0.263 230 Fe2O3 Trigonal 93 98 0.140 212 MgO Cubic 128 154 0.175 300 2MgO·SiO2 Orthorhombic 81 128 0.239 201 MnO Cubic 66 154 0.313 173 SrO Cubic 59 82 0.210 143 SrO·TiO2 Cubic 266 183 0.010 538 TiO2 Tetragonal 113 206 0.268 287 UO2 Cubic 87 212 0.319 230 ZnO Hexagonal 45 143 0.358 122 ZrO2–12Y2O3 Cubic 89 204 0.310 233 SiO2 Trigonal 44 38 0.082 95 Chalcogenides CdS Hexagonal 15 59 0.38 42 PbS Cubic 33 62 0.27 84 ZnS Cubic 33 78 0.31 87 PbTe Cubic 22 41 0.27 56 Fluorides BaF2 Cubic 25 57 0.31 65 CaF2 Cubic 42 88 0.29 108 SrF2 Cubic 35 70 0.29 90 LiF Cubic 48 67 0.21 116 NaF Cubic 31 49 0.24 77 Other halides CsBr Cubic 8.8 16 0.26 23 CsCl Cubic 10 18 0.27 25 CsI Cubic 7.1 13 0.27 18 KCl Cubic 10 18 0.27 25 NaBr Cubic 11 19 0.26 28 NaCl Cubic 15 25 0.25 38 NaI Cubic 8.5 15 0.27 20 RbCl Cubic 7.5 16 0.29 21 Note: All values were calculated from single-crystal data. defined μ, so only λ is new. The expressions that relate original geometry considered by Griffith); for a surface elastic moduli are given in Table 16.3. crack under similar loading Y = π / 2 ). The units of KI KI —Stress intensity factor is a combination of flaw are MPa · m1/2. size, c, and applied stress, σ. The subscript refers to the type of loading geometry. There are three fundamental deformation modes that can be important for crack propagation. These modes are illus- K1 = σY c (16.5) trated in Figure 16.6. Y in Eq. 16.5 is a dimensionless parameter that depends  Mode 1 opening. This is the most important for crack on the crack and loading geometries. For a simple interior propagation in brittle solids. It can be achieved by an crack of length 2c and tensile loading Y = π (this is the applied uniaxial tension. 16 . 3 E l a s t i c C o n s ta n t s a n d O t h e r “ C o n s ta n t s ” ................................................................................................. 293  TABLE 16.3 Expressions for Various Isotropic Elastic Moduli; Various Pairs of Moduli Independent pair of moduli Moduli E, m B, m B, n l, m E E 9Bμ/(3B + μ) 3B (1 − 2ν) μ(3λ + 2μ)/(λ + μ) μ μ μ 3B (1 − 2ν)/2(1 + ν) μ B Eμ/3(3μ − E) B B λ + (2μ/3) ν (E/2μ) − 1 (3B − 2μ)/(6B + 2μ) ν λ/(2λ + μ) λ (E − 2μ)μ/(3μ − E) B − (2μ/3) 3νB (1 + ν) λ  Mode 2 sliding 16.4 EFFECT OF MICROSTRUCTURE ON  Mode 3 tearing ELASTIC MODULI KIc —Critical stress intensity factor or fracture tough- In Chapter 4 we showed that Young’s modulus is a prop- ness. Fracture of a material in tension occurs when erty that is directly related to the bonding forces between KI ≥ KIc. atoms. We also showed that it varies as a function of tem- H—Hardness. There are different types of hardness. perature. In real ceramics we have to consider the fact that Why? Because the value of a material’s hardness depends we often have more than one phase present. The overall on how it is tested. The hardness of a material is its modulus is then going to be a combination of the proper- resistance to the formation of a permanent surface impres- ties of each of the phases; it lies somewhere between the sion by an indenter. You will also see it defined as resist- high- and low-modulus components. ance of a material to deformation, scratching, and erosion. Analytical expressions that represent the upper So the geometry of the indenter tip and the crystal orienta- and lower bounds for Young’s modulus include the tion (and therefore the microstructure) will affect the following. hardness. In ceramics, there tends to be wide variations in hardness because it involves plastic deformation and cracking. Table 16.4 lists hardness values on the Mohs’ Voigt Model hardness scale, a scratch test that can be used to compare hardness of different minerals. For example, quartz has a Assumption: Strain in each constituent is the same. It Mohs’ hardness of 7, which made flint (a cryptocrystalline represents the upper bound of Young’s modulus. quartz) particularly useful in prehistoric times for shaping bone (the mineral component is apatite with hardness 5) and shell (the mineral component is calcite with hardness E = V2E2 + (1 − V2) E1 (16.6) 3). Mohs’ hardness scale was not the first scratch hardness technique. As long ago as 1690, Christian Huygens, the famous astronomer, had noticed anisotropy in scratch hardness. Brittleness—Although not widely used, the brittleness TABLE 16.4 Mohs’ Hardness index (BI) has been used to quantify the brittleness of a Ridgeway’s ceramic where BI = H/KIc. Hardness extension of Knoop hardness number Mohs’ scale Mohs’ scale expanded scale 1 Talc Talc 2 Gypsum Gypsum 32 3 Calcite Calcite 135 4 Fluorite Fluorite 163 5 Apatite Apatite 430 6 Orthoclase Orthoclase 560 7 Quartz Vitreous silica — 8 Topaz Quartz or stellite 820 9 Corundum Topaz 1340 10 Diamond Garnet 1360 11 Fused zirconia — (A) (B) (C) 12 Fused alumina 2100 13 Silicon carbide 2480 FIGURE 16.6 The three deformation modes for fracture: (a) Mode 14 Boron carbide 2750 I opening. (b) Mode II sliding (in-plane shearing). (c) Mode III 15 Diamond 7000 tearing (antiplane shearing). 294 ...................................................................................................................................................... M e c h a n i c a l Te s t i n g  TABLE 16.5 Relations between Porosity, P, and Young’s Modulus, E = E 0 (1 − aP) Linear decrease in Young’s modulus with porosity when P is small, a ∼ 4 E = E 0 (1 − aP + bP 2) For a low concentration of spherical pores (a ∼ 1.9, b ∼ 0.9) E = E 0 (1 − aP) b For solid foams with very high porosity P > 0.7 (a = 1, b = 2) E = E 0 [(1 − P) 2 /1 + (a − 1)P] a is a shape factor with values depending on porosity: a = 2.5 for interconnected porosity (1/a = 0.4) a = 3.3–1.4 for porosity that resembles ribbons (1/a = 0.3–0.7) a = 0.6–1.0 for isolated pores (1/a = 0.6–1.0) (1/a is known as the Nielson shape factor) E = E 0 exp(−aP) Empirical for oxides with porosity in the range 0–40% (a ∼ 4) Reuss Model to account for the change in Young’s modulus with porosity, P. These are shown in Table 16.5 where the Assumption: Stress in each phase is the same. It represents “constants” a and b are often empirically determined; E 0 the lower bound of Young’s modulus. is the Young’s modulus of the dense material. 1 V2 (1 − V2 ) = + (16.7) E E2 E1 16.5 TEST TEMPERATURE Hashin and Shtrikman (HS) developed a narrower, Mechanical properties often show strong variations with more useful, set of bounds using basic elasticity energy temperature. We already considered in Chapter 4 how theorems. The HS bounds have been shown to be best for temperature affects Young’s modulus. For some mechani- the bulk modulus and are given by cal properties the change with temperature may be more −1 abrupt than the gradual decrease in E with increasing B − B1 V ( B − B1 ) ⎤ = V2 ⎡⎢ 1 2 (16.8) temperature. The ductile-to-brittle transition, which occurs B2 − B1 ⎣ B1 + H ⎥⎦ with decreasing temperature, is an important topic in metals. The significance of this phenomenon really came where H = 4μ2 /3 or H = 4μ1/3. Young’s moduli can be to light during World War II when there were reports of obtained from B if ν is known and reasonable fits with serious fractures in some of the Liberty ships (mass-pro- experimental data can be obtained as shown in Figure 16.7 duced vessels of predominantly welded construction). One for alumina-tetragonally stabilized zirconia (Al2O3 –ZrO2) of the most striking instances of this type of fracture was composites. the T2 tanker S.S. Schenectady built in Portland, Oregon, If the second phase is porosity, as is often the case in which suddenly broke into two sections at 10.30 pm on polycrystalline ceramics, then intuitively we realize that January 16, 1943. The reason was that the steel alloy used there will be a decrease in the elastic modulus. A pore has to construct the hull had undergone a ductile-to-brittle zero stiffness. Several relationships have been developed transition at a temperature of 4°C. This event gave particu- lar impetus to the study of fracture in brittle materials. Do ceramics experience a ductile-to-brittle (or the con- 400 verse) transition and is it important? Ceramics can exhibit Y-Stabilized both types of behavior over different temperature ranges. Young’s Unstabilized Figure 16.8 illustrates the temperature dependence of modulus (GPa) strength for ceramics. HS Average  Region A: the fracture is brittle and the fracture strain 300 Voigt is ∼10−3. There is no significant plastic deformation prior to failure and the strength varies little with temperature. Reuss  Region B: the fracture is again brittle but slight plastic deformation occurs prior to failure. The failure strain is usually in the region 10−3 –10−2 and strength falls 200 with increasing temperature. 0 50 Volume % ZrO2 100  Region C: Appreciable plastic flow occurs, with strains FIGURE 16.7 Comparison of predicted values of Young’s modulus of the order of 10−1 prior to failure. This behavior is for an Al2O3 tetragonally stabilized ZrO2 composite with experimen- rarely observed in ceramics, even in ductile polycrys- tal data. talline ceramics. 16 . 5 Te s t Te m p e r at u r e ................................................................................................................................................. 295  800 Fracture TA 5 wt. % Stress Stress 10 wt. % Stress (MPa) 2.5 wt. % TB 20 wt. % 600 1400 °C ε = 1.5 × 10–4 s–1 TC 400 30 wt. % A B C 200 TAB T TBC Strain Machine compliance FIGURE 16.8 Illustration of the effect of temperature on fracture 80 wt. % stress for a ceramic. The key temperatures are TAB and TBC. 0 0 1 2 3 Strain (%) FIGURE 16.9 Stress–strain curve for Si3N4 at 1400°C for various amounts of silica. The machine compliance is the inherent The critical temperatures, TAB and TBC, vary greatly for displacement within the instrument. different ceramics. For polycrystalline MgO the brittle-to- ductile transition occurs at ∼1700°C (0.6 Tm). There is no plastic deformation in β-SiC below 2000°C. Talc, MoS2, and graphite all deform at room temperature. MoS2 and graphite are widely used as solid lubricants. 16.7 TESTING IN COMPRESSION The transition can be important in structural ceramics AND TENSION (particularly nonoxides like silicon nitride) when they are used in high-temperature applications. Densification in The tensile test is the most frequently used procedure to these ceramics is often achieved using a second phase that determine the tensile strength of a metal. However, it is not forms a glass at grain boundaries and triple points. At used as widely for ceramics because of their inherent brittle- temperatures near the glass softening temperature very ness. It is difficult to make the typical “dog-bone”-shaped extensive plastic flow occurs. Figure 16.9 shows σ–ε samples, where the cross-sectional area is reduced in the curves for silicon nitride at 1400°C containing different gage length. We could do this with a ceramic, but the amounts of silica. For silica contents >20 wt% macro- machining needed to give this shape is likely to introduce scopic plastic deformation occurs. At high silica contents surface flaws. In many tensile test instruments the sample it is believed that the glassy phase is no longer constrained under test is connected by means of a screw thread. This is at the triple points. often tricky to machine with a ceramic and it may also break in the grips. Finally, because ceramics fail after only about 0.1% strain, the specimens under test must be perfectly 16.6 TEST ENVIRONMENT aligned or bending stresses will be introduced, which will complicate things. In some cases the environ- In some practical situa- ment to which the ceramic RINGER’S SOLUTION (PARTS BY VOLUME) tions we require ceramics is exposed is a very im- NaCl solution 0.9% 94 to support a tensile load. portant consideration. For KCl solution 1.15% 4 Consider the growth of example, you will often CaCl2 solution 1.22% 3 silicon single crystals by see that mechanical tests KH2PO4 solution 2.11% 1 the Czochralski process, on bioceramics are per- MgSO4 solution 3.82% 1 which involves pulling the formed either in vivo or NaHCO3 solution 1.3% 14 crystal from the melt. The in vitro. Tests performed in NaHPO4 solution 1 M 13 crystal is supported entirely the body are referred to as by a narrow region called in vivo. Tests performed outside the body, often in condi- the neck, about 3 mm in diameter. It is possible to support tions that seek to replicate or approximate the physiologi- a total crystal weight of about 200 kg. This requirement cal environment, are referred to as in vitro. ISO Standard determines the maximum overall volume of a silicon 6474 for alumina bioceramics specifies a bend strength boule. The diameter is controlled by our ability >450 MPa after testing in to produce dislocation- Ringer’s solution. Ringer’s free crystals as described solution is a model liquid RULE OF THUMB in Chapter 29. Steel- that resembles human body Compressive fracture strength is 10–15 times greater reinforced concrete and fluid. than tensile fracture strength. safety glass are two exam- 296 ...................................................................................................................................................... M e c h a n i c a l Te s t i n g  TABLE 16.6 Ratio of Compressive Strength σcc to Bending ing of a mixture of stone and sand (called the aggregate) Strength, sc in a cement matrix. The aggregate provides the strength Ceramic Grain size (mm) s cc /s c and the cement provides the workability. When concrete is used in construction it must always be loaded in com- TiB2 20–50 4–6 pression. As shown in Figure 16.10 cracks behave dif- ZrB2 20–50 4–6 ferently in compression than they do in tension. In B 4C 1 7 WC 1–6 4–6 compression, cracks twist out of their original orientation Al2O3 1–100 4–30 and propagate stably along the compression axis. The MgAl2O4 1 7 result is that the sample will crush rather than fracture. ThO2 4–60 13–17 Fracture is not caused by rapid unstable crack propagation UO2 20–50 5–18 as it is in tension. In tension we are concerned with the largest crack, the “critical flaw,” particularly if it is on the surface. In com- pression we are concerned with the average flaw size, cav. ples in which a ceramic is prestressed in compression to We can estimate the compressive stress to failure by sub- increase its ability to support a tensile load. stituting cav into Eq. 16.5 and using a multiplier between Stress–strain curves for metals look very similar and 10 and 15. Teeth are ceramic composites: they survive for provide similar results whether the testing is carried out years even when many cracks are present. in tension or compression. Ceramics are generally stronger in compression and can tolerate high compressive loads. Some examples are given in Table 16.6. However, reliable 16.8 THREE- AND FOUR-POINT BENDING compressive strength data are limited for ceramics. Note that the Young’s modulus will be the same because the To avoid the high expense and difficulties of performing curves will have the same slope. tensile tests on ceramics, tensile strength is often deter- One ceramic that is widely tested in compression is mined by the bend test. There are two geometries and concrete. Concrete is a ceramic-matrix composite consist- these are illustrated in Figure 16.11. The main advantage of the bend test, other than its lower cost, is that we use simple sample geometries. The specimens have either a rectangular or cylindrical geometry. The four-point bend σTS σTS test is preferred because an extended region with constant bending moment exists between the inner rollers. σTS T T Type B cracks P P D 2 2 D h σTS σTS P P L 2 2 σC C σC PL T 2 C T P Type B h cracks P P 2 L 2 PL σC σC 4 FIGURE 16.10 Illustration of unstable and stable crack propaga- tion for a brittle material in tension (T) and compression (C), respectively. Stable crack propagation will lead to crushing. FIGURE 16.11 The geometries for three- and four-point bending. 16 . 8 Th r e e - a n d F o u r - p o i n t B e n d i n g ...................................................................................................................... 297  The maximum tensile MODULUS OR RUPTURE EQUATIONS size differences between stress in the surface of the the samples are clearly one beam when it breaks is 3PL of the factors contributing called the modulus of Three-point bend: σ r = 2 to this variation. 2 BW rupture (MOR), σr. For an The main disadvantage elastic beam it is related to 3PD of the bend test is that the the maximum moment in Four-point bend: σ r = stress distributions can be BW 2 the beam, M complex and nonuniform. The consequence is that 6 Mr under certain conditions, particularly when the largest σr = (16.9) flaws in the sample are located in the interior of the speci- BW 2 men, the strength of the ceramic will be overestimated. W is the height of the beam and B is its thickness. For the case of bend testing a ceramic this equation is applicable only when the distance between the inner rollers is much 16.9 KIc FROM BEND TEST greater than the specimen height. Other terms are also There are several tech- used including flexural SENB AND CN SPECIMENS niques to determine KIc for strength, fracture strength, Typical dimensions: a ceramic. The two main and bend strength. The approaches are to use bend test is also known as B = 3 mm, W = 4 mm indentation or bending. In a flexure test and the resist- the bend test a notch is ance of a beam to bending S2 = 20 mm, S1 = 40 mm introduced, usually using is known as its flexural a diamond-tipped copper rigidity. The terminology Crack depth c/W ∼ 0.5 cutting wheel, into the can be a little confusing, Total specimen length 50 mm tensile side of the speci- but this test is important men as shown in Figure because it is widely used 16.13. In Figure 16.13a the and probably the best studied strength test for ceramics. Examples of data from such tests are shown in Figure 16.12 S2 for polycrystalline alumina. The main comment that can be made is that there is a wide variation in the values! Grain 1 Lucalox Crandall et al: W 600 (~40 μm) 3μ, 20μ Flexure Charles Spriggs et al: Davidge & Tappin Strength 95% Al2O3, p ~ 7%, G ~ 8 μm 1-2 μm 10-15 μm Crack (MPa) 40-50 μm 80-100 μm B 500 40-50 μm 3 1 Authors data: S1 Subscripts: ~G (in μm) (A) 400 10 S2 300 3 20 10 200 W 40 Lucalox 20 (~9 μm) Parikh 40 Crack 100 Wesgo 995 B Davidge & Tappin (~45 μm) 95% Al2O3, p ~ 5%, G ~ 40 μm Parikh S1 0 0 400 800 1200 1600 2000 Test T (°C) (B) FIGURE 16.12 Flexural strength of polycrystalline Al2O3 as a FIGURE 16.13 Geometries for (a) SENB and (b) CN specimens function of test temperature. used to determine KIc. 298 ...................................................................................................................................................... M e c h a n i c a l Te s t i n g notch is flat (single-edged notched beam, SENB), whereas in Figure 16.13b it is chevron-shaped. The specimen is loaded, usually in four-point bend, until it fails at FMax and 20 Vickers hardness KIc is calculated. Indentation For the SENB stress (GPa) Hertz (elastic) 3 c ( S1 − S2 ) ξFMax K lc = (16.10) 2 BW 2 10 Experimental data c is the length of the initial crack that we introduced and ξ is a calibration factor. The advantage of the SENB test is that it is quite simple, although it tends to overestimate KIc because the crack is often not atomically sharp. For 0 0 0.05 0.10 0.15 ceramics having very fine grain sizes the notch must be Indentation Strain very narrow. FIGURE 16.14 Indentation stress versus indentation strain. For the chevron notched (CN) specimen ( S1 − S2 ) ξ * FMax K lc = 3 (16.11) BW 2 projected area of the impression. The hardness is then determined by dividing the applied force, F, by this area. where ξ* is a compliance function. Sometimes you will The processes that happen under the indenter tip can be see Eq. 16.11 written in such a way that all the geometric quite complex. We often see a deviation from what is terms are grouped together as a single geometric function called “Hertzian” behavior where the indentation stress is Y*. Then we have proportional to the indentation strain (Figure 16.14). The deviation is due to plasticity beneath the indenter as illus- trated in Figure 16.15. We discuss this more in Chapter 17. F K lc = Max Y * (16.12) Cracking can also occur on indenting and this can be used B W as a means of determining fracture toughness. There are many differ- The value of Y* is then ent hardness tests and each necessary for different CAUTION gives a different number. specimen geometries and Fracture toughness values for different ceramics may The common hardness different notch geometries. depend on technique used to measure them. tests are listed in Table Two approaches can be 16.7 and the geometries of used to obtain Y* (see Specific References). the impression are shown in Figure 16.16. It is possible to The advantage of the CN geometry is that we do not convert between different hardness scales, but the conver- need to worry about introducing a sharp precrack. Our sion depends on both the material and its microstructure. original notch is made by two saw cuts to produce a tri- The most reliable data are for steels because most of the angularly shaped cross section. A crack is easily initiated work has been done on these alloys. Detailed conversion at the tip of the chevron, but the increasing cross section tables for metals and alloys are available in ASTM Stand- of the crack front causes crack growth to be stable prior ard E 140, “Standard Hardness Conversion Tables for to failure. Further crack extension requires an increase in Metals.” There are different regimes of hardness based on the applied load and it is possible to create an atomically the load used as shown in Table 16.8. These divisions are sharp crack before the specimen fails. Also you can see somewhat arbitrary, but they are commonly accepted. from Eq. 16.11 that we do not need to know the actual crack length. In fact, we do not need to know any of the materials properties. 16.10 INDENTATION C A B D z Measuring the hardness of a ceramic is important and this Region of plastic flow is usually done using an indentation test. The basic idea E is that a permanent surface impression is formed in the FIGURE 16.15 Plasticity under the indenter (the shaded area) material by an indenter. We then measure the actual or causes the deviation from Hertzian behavior. 16 .10 I n d e n tat i o n .......................................................................................................................................................... 299  TABLE 16.7 Details of Common Hardness Tests Test Indenter Description Equation Notes Brinell Hardened Brinell hardness number BHN = F/πDt Spherical indenters not steel ball (BHN) is applied force used for ceramics divided by surface area of indentation Meyer hardness number MHN = 4F/πd 2 (MHN) uses projected area Vickers Square Vickers hardness number VHN = 1.854F/a 2 The ceramics community pyramid (VHN) using contact area uses mainly the number VHN using projected area VHN = 2.000F/a 2 calculated using the projected area; need to be careful when comparing data from different sources Knoop Elongated Knoop hardness number KHN = 14.2F/L2 pyramid (KHN) Rockwell Various Dimensionless number and Widely used for metals but indenter various hardness scales not often for ceramics types/loads except cemented carbides Hertz The critical stress intensity factor is obtained by assum- 1896 Knoop ing that the applied stress intensity caused by the load is Rockwell 1922 1939 Berkovich equal to the critical stress intensity for crack propagation. Vickers 1950 1 Brinell 1916 Hodge Winchell DSI ζ (E / H ) 2 P 1900 1934 1945 Tabor 1954 1980s K Ic = 3 (16.14) c2 ζ is a dimensionless constant, which for ceramics has an 1900 1950 2000 average value of 0.016 ± 0.004. The use of indentation FIGURE 16.16 The evolution of common hardness tests and the techniques for determining KIc has been the subject of corresponding indenter shapes. many studies since being introduced by Lawn and Wilshaw (1975). The most commonly used variant, termed the indi- TABLE 16.8 Hardness Regimes rect method, uses indentation followed by determination Applied of the strength after indentation using bend testing. The Regime load (N) Comments main concern is to ensure that the crack does not grow between indentation and bend testing. To minimize effects Microhardness 0.0098–1.96 Hardness value decreases as load increases Possibility for very large Plastic variations in values Indentation 2a zone depending on technique 2c used and microstructure Surface effects may dominate Low load 1.96–98.1 hardness Standard >98.1 Hardness independent of hardness applied load and microstructure. Median/radial cracks (A) 16.11 FRACTURE TOUGHNESS FROM INDENTATION We can obtain the fracture toughness from indentation tests. The basic idea is illustrated in Figure 16.17. We get an indent and radial cracks. The hardness is then H = P/αa2 (16.13) α is a numerical factor that depends on the shape of the indenter. For a Vickers indenter α = 2. P is the load in (B) newtons. FIGURE 16.17 Cracks at an indent allow determination of KIc. 300 ...................................................................................................................................................... M e c h a n i c a l Te s t i n g  FIGURE 16.18 Load-displacement data on the 1.8 mN indentations of CAS films on three different alumina substrates. (C) FIGURE 16.17 Continued plastic deformation. When the load applied to the indenter of reactive species such as water a drop of oil may be is released the material attempts to return to its original placed on the indent. Tests seem to give reproducible shape. The slope of the elastic unloading region (dP/dh) values for KIc. can be used to determine the modulus and hardness. There are several different equations depending on the tip geom- etry. If the material is plastically deformed it cannot return 16.12 NANOINDENTATION to its original shape and there is a resi-dual impression, hr. The magnitude of hr will be greater for a metal such The nanoindentation technique was developed in the as steel than for a ceramic such as sapphire. 1980s because of the need to determine the mechanical Nanoindentation is a powerful technique because the properties of thin films and surfaces that had been modi- shape of the load-displacement curve can be used to iden- fied, for example, by ion implantation. To avoid the influ- tify effects such as phase transformations, cracking, and ence of the substrate the penetration depth of the indenter film delamination during indentation. It is also important must be less than 10% of the film thickness. Consequently in studying the mechanical properties of nanomaterials, penetration depths are on the order of nanometers rather such as carbon nanotubes. There is reference now to a than millimeters, which is common for conventional picoindenter, which is a combination of a nanoindenter indentation tests. and an atomic force microscope (AFM). Nanoindentation is also used to test small volumes of material. The low loads used mean that the extent of cracking is much smaller than in conventional indentation 16.13 ULTRASONIC TESTING methods. Two parameters are often of most interest in nanoin- The basic principle of this method is that the velocity of an dentation testing: ultrasonic wave through a material is related to its density  Elastic modulus and elastic properties. This is one example of a dynamic  Hardness method for determining elastic constants, such as Young’s modulus and shear modulus. Dynamic methods are more Load (P) versus depth of penetration (h) curves, also accurate than static methods with uncertainties of <0.5% called compliance curves, are the output from a nanoin- (±10% would be more typical for static methods). dentation test. The curves are obtained as load is applied To determine the shear modulus and Poisson’s ratio we to the indenter tip up to need the velocity of the some maximum value TRANSVERSE WAVE VELOCITIES longitudinal and trans- and then back to zero. Al2O3 Al verse waves, νL and νt. Figure 16.18 shows a The equations are general compliance curve μ 163 GPa 25 GPa for a material that under- ρ 3970 kg/m3 2710 kg/m3 goes both elastic and νt 6.4 km/s 3.0 km/s μ = ρνt2 (16.15) 16 .13 U lt r a s o n i c Te s t i n g ............................................................................................................................................ 301  1 − 2 ( vt / v L ) 2 v= (16.16) 2 ⎡⎣1 − ( vt / v L ) ⎤⎦ 2 1 E = 2μ(1 + ν) (16.17) Ps(VO) Conversely, if we know the elastic moduli we can Median strength determine the magnitude of the sound velocities. For ceramics with high moduli and low density the sound velocities will be much higher than many metals. The 1 propagation of sound waves through ceramics is particu- 2 1 larly important during earthquakes. The earth’s crust is e composed primarily of silica and aluminosilicates. Using Eqs. 16.15 and 16.16 we can show for SiO2, the primary constituent of rocks such as granite, that the longitudinal waves are the first shocks to arrive after an earthquake, followed by the transverse waves; νL = 6.04 km/s and νt = 0 4.1 km/s for quartz. The surface waves are the last to σO σ arrive, having a velocity <4 km/s, but these often have the FIGURE 16.19 The Weibull distribution function. most devastating effect. Ultrasonic testing is widely used in the concrete industry σ0 = the characteristic strength for which the survival to determine the presence or absence of voids, cracks, and probability is 0.37 (1/e). other imperfections and to measure deterioration that might σmin = the stress level below which the probability of have occurred due to age or through fire or frost damage. failure is zero. Because there is always a possibility, albeit slight, of 16.14 DESIGN AND STATISTICS our component having a very large flaw, we usually set σmin = 0. This leads to the two-parameter form that is used When we measure the strength of a series of equivalent for ceramics. ceramic specimens we typically find considerable scatter ⎡ ⎛ σ⎞ ⎤ m in the results. The reason is due to the size distribution of PS = exp ⎢ − ∫ ⎜ ⎟ dV ⎥ (16.19) ⎣ V σ0⎝ ⎠ ⎦ flaws that are responsible for failure. This behavior is very different from that of metals. Consequently we have to If the full volume is under uniform uniaxial tension then adopt different design approaches when we use ceramics. we can write Eq. 16.19 as When we design components using metals we deter- ⎡ ⎛ σ⎞ ⎤ m mine the maximum stress that will be present in the com- PS = exp ⎢ − ⎜ ⎟ ⎥ (16.20) ponent and then select a metal that has a larger strength. ⎣ ⎝ σ0 ⎠ ⎦ A reasonable safety margin is often included. This For other geometries we need to include the loading factor approach is referred to as deterministic design. It does not L F. This takes into account the stress distribution. For work with ceramics because of the large scatter. Rather uniaxial tension L F = 1; for other loading geometries see we have to use a probabilistic approach in which we rep- Table 16.9. The product (L FV) is often termed the effective resent this scatter in a quantitative way so that these mate- volume, Veff, as it indicates how “effectively” the body is rials can be used safely. The most popular method is to being stressed. use Weibull statistics, which are based on the weakest link Taking the natural logarithm of both sides of Eq. 16.20 approach. The analogy is to consider a chain the strength we get of which is determined by the weakest link. ⎛ 1⎞ ⎛ σ⎞ m The Weibull distribution function is shown in Figure ln ⎜ ⎟ = ⎜ ⎟ 16.19 and gives the probability of survival (PS), or, alter- ⎝ PS ⎠ ⎝ σ 0 ⎠ natively, the probability of failure (P F), of a stressed If we take natural logarithms again we get volume V. TABLE 16.9 Examples of Loading Factors a ⎡ ⎛ σ − σ min ⎞ ⎤ m PS = 1 − PF = exp ⎢ − ∫ ⎜ ⎟ dV ⎥ (16.18) ⎣ V ⎝ σ0 ⎠ Geometry Loading factor, LF ⎦ Uniaxial tension 1 The Weibull distribution function contains three Pure bending 1/[2(m + 1)] parameters: Three-point bending 1/[2(m + 1) 2] Four-point bending (mLi + Lo)/[2Lo (m + 1) 2] m = Weibull modulus, which indicates how rapidly the strength falls as we approach σ0. a Li, inner span; Lo, outer span. 302 ...................................................................................................................................................... M e c h a n i c a l Te s t i n g  99 1 Ps (Vo) m=10 98 Survival m=20 Probabilty m=5 (%) 95 90 80 70 60 0 σO σ 50 40 FIGURE 16.21 Illustration of the effect of m on survival probability. 30 When m changes PS changes. 20 10 3. A plot −lnln(1/PS) versus ln σ, the slope, which can be 5 determined by a least-squares fit, gives m. In ceramics there is a volume dependence of the 1 strength. This can be illustrated quite easily using a stick 250 300 350 of chalk. As the chalk becomes smaller it becomes stronger. Fracture Stress (MN m-2) The reason is again due to flaws. There is an increased FIGURE 16.20 Weibull plot showing probability of failure as a probability of finding a larger flaw in a larger body as function of fracture stress. illustrated in Figure 16.22. This effect can be expressed mathematically as ⎡ ⎛ V ⎞⎛ σ ⎞ ⎤ m ⎛ σ⎞ m ⎡ ⎛ 1 ⎞⎤ PS = exp ⎢ − ⎜ ⎟ ⎜ ⎟ ⎥ ln ⎢ ln ⎜ ⎟ ⎥ = m ln ⎜ ⎟ = m ln σ − m ln σ 0 ⎣ ⎝ P ⎠ S ⎦ ⎝ σ0 ⎠ ⎣ ⎝ V0 ⎠ ⎝ σ 0 ⎠ ⎦ Now if we plot −lnln(1/PS) versus ln σ we will get a where V = nV0. An example of the size effect is shown in straight line of slope −m as shown in Figure 16.20. The Figure 16.23 for Si3N4 springs. The springs have different higher the Weibull diameters of the wire and modulus the lower is the STRENGTH AND VOLUME of the coil and different variability of strength. The strength of metal samples does not depend on numbers of coils were Values for ceramics are volume. measured. often in the range of 5–20 (compared, for example, to steels, which have values of about 100). Figure 16.21 σTS shows how the Weibull modulus affects the survival probability. The Weibull modulus, which is the parameter often of most interest, is obtained experimentally by testing a batch of samples. We need a large number of specimens 2a 2a to get an accurate value of m. Usually a minimum of 30 samples is required, which will typically give m within Small sample 20%. Up to 100 samples is not uncommon, which will give m with a greater than 90% confidence. The following sequence of steps is used to determine A B smaller flaws m from a set, N, of measured strengths: (on average) 1. Rank the specimens in order of increasing strength. 2. Determine PS. For the jth specimen this is often given Largest σTS as the approximation PS (j) = 1 − j/(N + 1). A more flaw accurate expression that may be used instead is FIGURE 16.22 The largest flaw will be the weakest link and the PS = 1 − [(j − 0.3)/(N + 0.4)]. source of failure. Smaller samples have smaller flaws. 16 .14 D e s i g n a n d S tat i s t i c s ....................................................................................................................................... 303  V/V0=1000 1 2 100 10 500 lnln 1 1-F Strength 0 (MPa) -2 400 -4 -6 300 4.5 5 5.5 6 6.5 10 100 3 1,000 ln (σC) Veff (mm ) (A) FIGURE 16.23 Fracture stress as a function of volume for Si3N4 springs. (1) (2) 2 lnln 1 1-F 0 Complications arise if we have different flaw popula- -2 tions, for example, we may have pores and inclusions introduced during sintering and surface flaws introduced during grinding. The different flaws may lead to different -4 Weibull distributions and different Weibull moduli. Figure 16.24a illustrates the superposition of two flaw types and -6 Figure 16.24b for a sample containing surface and volume 4.5 5 5.5 6 6.5 flaws. And we have new equations. ln (σC) For two different surface flaw types: (B) FIGURE 16.24 (a) Different flaws lead to different values of m. (b) ⎡ σ σ ⎤ m1 m2 PS = exp ⎢ − ⎛⎜ c ⎞⎟ − ⎛⎜ c ⎞⎟ ⎥ Weibull plot for a sample having both surface and volume flaws. ⎣ ⎝ σ1 ⎠ ⎝ σ2 ⎠ ⎦ For flaw type 1 we have σ1 and m1; for flaw type 2 we have of confidence in the remaining components withstanding σ2 and m2. any stress < σPT. For two different types of volume flaws: CARES (Ceramics Analysis and Reliability Evaluation of Structures) is a public-domain program from the ⎡ V ⎛σ ⎞ Veff2 ⎛ σ c ⎞ ⎤ m1 m2 PS = exp ⎢ − eff1 ⎜ c ⎟ − National Aeronautic and Space Agency (NASA) that ⎜ ⎟ ⎥ ⎣ V0 ⎝ σ v1 ⎠ V0 ⎝ σ v 2 ⎠ ⎦ incorporates Weibull statistics. The program was formally known by the less friendly acronym SCARE (Structural As you now realize it is impossible to design a ceramic Ceramics Analysis and Reliability Evaluation). where the probability of failure is zero. Table 16.10 gives The NASA CARES program can be found at http:// some examples of what might be considered acceptable www.grc.nasa.gov/WWW/LPB/cares/life/refs.html. probabilities of failure. The following considerations and assumptions apply Proof testing can be used to truncate the extreme tail to the use of Weibull statistics: of the Weibull distribution. Components are tested up to a certain proof-test stress, σPT (Figure 16.25), for a short TABLE 16.10 Suggested Failure Probabilities period of time. The weakest ones obviously fail and can be weeded out. We then have increased confidence in the Possible consequences remaining components. We often have to proof test stresses PF of failure Example close to the design stress. For a ceramic with m = 10, 0.3 Slight inconvenience Sticks of chalk reducing the risk of rupture from 0.1 to 0.05 requires that 10 −2 Inconvenience and small Ceramic cutting tool the component be proof tested to 93% of the design stress. expense To reduce the probability of failure by an order of magni- 10 −6 Injury Window on a vacuum system 10 −8 Loss of life and significant Ceramic protective tile on tude, down to 0.02, the part must be proof tested to 99% expense space shuttle of the design stress (Figure 16.26). We have a good level 304 ...................................................................................................................................................... M e c h a n i c a l Te s t i n g  f (x) m = 12 f (x) m=5 σPT m=2 σ σ σ0 Failed σ0 components (A) (B) FIGURE 16.25 (a) Probability distributions for different values of m. (b) Proof testing up to σPT removes the weakest components from the distribution.  There is a need to ensure that the conditions under 16.15 SPT DIAGRAMS which we are testing match those in service. For example, flaws in a component may appear during Stress–probability–time (SPT) diagrams incorporate the service as a result of oxidation or corrosion that might time dependence of strength into failure statistics. They not be present in the test sample. give lifetime predictions. An illustration of the use of SPT  There is a complex distribution of flaws. diagrams is in bioceramrcs.  More than one type of flaw may be present. An important requirement for any implant material is how long it will last. Because of the nature of failure of ceramic components it is not possible to provide a specific 0.1 and definite lifetime for each individual implant. Rather 20 we have to express failure in terms of probabilities. Figure Risk of 16.27 is an applied stress versus probability of time to Rupture 10 failure (SPT) diagram for medical grade alumina. It shows m=5 that for a 30-year survival period with failure of no more 0.08 than 1 in 100 components the maximum tensile stress that can be applied is limited to <200 MPa. If stresses of 0.06 99 Ps (%) 98 0.04 3 years 95 survival 0.02 90 80 30 years survival 0 0 0.2 0.4 0.6 0.8 1.0 0 250 300 σPT/σdesign σ (MPa) FIGURE 16.26 Plot showing the risk of rupture after proof testing FIGURE 16.27 SPT diagram for medical grade Al2O3. The survival to the ratio of proof-test stress to design stress. probability decreases with increasing stress and longer times. 16 .1 5 S P T D i ag r a m s ....................................................................................................................................................... 305  TABLE 16.11 Average Annual Wear Rates of Articulating distributions, makes it possible to design ceramic compo- Surfaces in Total Hip Prosthesis nents that have very low probabilities of failure during the Materials Wear rate (mm/year) lifetime of the patient. Numerous clinical studies have been performed on patients receiving total hip replace- Co–Cr–Mo alloy/UHMWPE 200 ment. One of the main problems that have been encoun- Alumina/UHMWPE 20–130 tered is that of wear between the head (ball) and the Alumina/alumina 2 socket. Although there is considerable variation in the data, it is generally found that the wear rate for systems 250 MPa are applied to the ceramic component, within 3 with metal balls is much higher than the rate with alumina years 4% of the implants is likely to fail and by 30 years balls. And alumina balls in alumina sockets produce the 7% will probably fail. Use of SPT diagrams such as these, least wear of any materials combination as indicated in together with finite element analysis of local stress Table 16.11. CHAPTER SUMMARY Flaws dominate the mechanical properties of ceramics. They determine how we test them and how we design components from them. Flaws are also the reason why ceramics are stronger in compression than tension. In this chapter we described the methods used to measure mechanical properties of ceramics. The important ones are bend testing, compression testing, and indentation. To determine the mechanical properties of small volumes we use nanoindenta- tion. This technique is especially important for thin films, surfaces, and nanomaterials. An understanding of statistics is particularly important when using ceramics in load-bearing appli- cations. The Weibull approach is the one most widely used for ceramics. PEOPLE IN HISTORY Mohs, Fredrich (1773–1839) was a German mineralogist. His original paper on the scratch test and the eponymous hardness scale was published in Grundriss der Mineralogie in 1822. Poisson, Siméon Denis (1781–1840) was a French mathematician. He was more suited to mathematics than medicine because of his clumsiness. This was not an impediment for a mathematician! In 1837 he pub- lished a paper on probability, which described the Poisson distribution. During his career Poisson pub- lished more than 300 mathematical works and was reported to have said “Life is good for only two things, discovering mathematics and teaching mathematics.” Ringer, Sidney (1835–1910) was a British physician and physiologist. His original salt solution was developed in 1882 and used to prolong the survival time of tissue taken from a frog’s heart. The solution used to test biomaterials differs in composition from that developed for amphibians. Young, Thomas (1773–1829) was an English physician physicist. He could read fluently by age two and pre- sented his first paper to the Royal Society at the young age of 20. By 1801 he was a professor at the Royal Institution in London. He was probably best known for his classic double slit experiment, which demon- strated the wave nature of light. Weibull, E.H. Waloddi (1887–1979) was a Swedish engineer. The original paper describing his statistical analysis was published in 1939, “A Statistical Theory of the Strength of Materials,” Ingeniöersvetenskaps- akademiens Handlingar 151, 1–45. Weibull was a frequent visitor to Wright Patterson Air Force Base in Ohio and lectured at the Air Force Institute of Technology. In 1972 he was awarded the American Society of Mechanical Engineers gold medal for his achievements. King Carl Gustav XVI of Sweden presented Weibull with the Great Gold medal from the Royal Swedish Academy of Engineering Sciences in 1978. GENERAL REFERENCES Cook, R.F. and Pharr, G.M. (1994) “Mechanical properties of ceramics,” in Materials Science and Technol- ogy, edited by R.W. Cahn, P. Haasen, and E.J. Kramer, VCH, Weinheim, p. 339. Davidge, R.W. (1979) Mechanical Behavior of Ceramics, Cambridge University Press, Cambridge, UK. A brief introduction. Engineered Materials Handbook, Volume 4, Ceramics and Glasses (1991) ASM International (Materials Park, OH. A useful reference. Fischer-Cripps, A.C. (2002) Nanoindentation, Springer, New York. Gordon, J.E. (2002) The New Science of Strong Materials, or Why You Don’t Fall Through the Floor, 2nd edition, Penguin, London. An excellent introduction to mechanical properties of materials; the original was published in 1968. 306 ...................................................................................................................................................... M e c h a n i c a l Te s t i n g  Green, D.J. (1998) An Introduction to the Mechanical Properties of Ceramics, Cambridge University Press, Cambridge, UK. Lawn, B. and Wilshaw, T.R. (1975) “Indentation fracture—principles and applications,” J. Mater. Sci. 10, 1049. The paper that showed how to derive K1c from indenter experiments. McColm, I.J. (1990) Ceramic Hardness, Plenum Press, New York. Munz, D. and Fett, T. (1999) Ceramics: Mechanical Properties, Failure Behavior, Materials Selection, Springer, Berlin. Richerson, D.W. (2006) Modern Ceramic Engineering, Properties, Processing and Use in Design, 3rd edition, Taylor & Francis, Boca Raton, FL. Chapter 18 describes design approaches for ceramics. Sines, G. and Adams, M. (1978) “Compression testing of ceramics,” in Fracture Mechanics of Ceramics, Vol. 3, Plenum Press, New York, p. 403. Wachtman, J.B. (1996) Mechanical Properties of Ceramics, Wiley, New York. SPECIFIC REFERENCES Blum, J.J. (1975) “Slice synthesis of three dimensional work-of-fracture specimens,” Eng. Fract. Mech. 7, 593. The slice model for determining Y*, the geometric “constant” in KIc measurements (cf. Munz et al.). Hashin, Z. and Shtrikman, S. (1963) “A variational approach to the theory of the elastic behavior of multiphase materials,” J. Mech. Phys. Solids 11, 127. Lawn, B.R. and Marshall, D.B. (1979) “Hardness, toughness, and brittleness—indentation analysis,” J. Am. Ceram. Soc. 62, 347. Defines the brittleness index (BI). Munz, D.M., Shannon, J.L., and Bubsey, R.T. (1980) “Fracture-toughness calculation from maximum load in 4 point bend tests of chevron notch specimens,” Int. J. Fracture 16, R137. The straight-through crack assumption approach to determination of Y*. the geometric “constant” in KIc measurements (cf. Blum et al.). Ridgeway, R.R., Ballard, A.H., and Bailey, B.L. (1933) Trans Electrochem. Soc. 63, 267. Syed, S.A., Wahl, K.J., and Colton, R.J. (2000) “Quantitative study of nanoscale contact and pre-contact mechanics using force modulation,” Mat. Res. Soc. Symp. Proc. 594, 471. Developed the picoindenter—a combination of a nanoindenter and an AFM. Thoman, D.R., Bain, L.J., and Antle, C.E. (1969) “Inferences on the parameters of the Weibull distribution,” Technometrics 11, 445. Used numerical methods to determine m. Weibull, W. (1951) “A Statistical Distribution Function of Wide Applicability,” J. Appl. Mech. 18, 293. WWW NIST Structural Ceramics Database (http://www.ceramics.nist.gov/srd/scd/scdquery.htm) NIST Fracture Property Data Summaries: Oxide Glasses (http://www.ceramics.nist.gov/srd/summary/glsmain.htm) NIST Fracture Toughness Data for Ceramics (http://www.ceramics.nist.gov/srd/summary/ftmain.htm) NIST Property Data Summaries: Sintered Alumina (http://www.ceramics.nist.gov/srd/summary/scdaos.htm) NIST Property Data Summaries: Silicon Carbide (http://www.ceramics.nist.gov/srd/summary/scdscs.htm) EXERCISES 16.1 In Figure 16.7 the experimental data for the unstabilized samples deviate from the predicted values for Young’s modulus. (a) What do we mean by “unstabilized.” (b) How can you account for the difference in the predicted values and experimental values? 16.2 Is Young’s modulus affected more by the presence of an intergranular glass phase or an equal amount of porosity? Justify your answer with a suitable calculation. 16.3 Ten rectangular test specimens of MgO were tested in three-point bending. The bars were 1 cm wide and 0.5 cm high and were tested over a 5-cm span. The failure loads for each are given in ascending order: 140, 151, 154, 155, 158, 165, 167, 170, 173, and 180 kg. Calculate the MOR for each sample and the average MOR for this group of samples. 16.4 A commercially available polycrystalline alumina is tested using three different methods: three-point bend, four-point bend, and uniaxial tension. The resulting MOR values are 550, 410, and 175 MPa, respectively. What conclusions can you make about the material from these data? 16.5 The soda-lime silicate glass sample shown in Figure 16.17 was indented with a load of 20 N. Estimate (a) hardness and (b) fracture toughness. (c) How else might you obtain the fracture toughness? C h a p t e r S u m m a ry .......................................................................................................................................................... 307  16.6 For the data shown in Figure 16.20 determine the Weibull modulus. 16.7 The following data were obtained in a series of tensile strength tests on polycrystalline silicon carbide speci- mens (in MPa): 334, 289, 232, 294, 252, 337, 256, 339, 308, 365, 311, 341, 286, 314, 274, 285, 382, 379, 282, 324, 316. (a) Determine the Weibull modulus for these samples. (b) Would you expect the value of m for a set of steel specimens to be higher or lower than the value you calculated in part (a). Assuming that these SiC specimens were made by hot pressing, would you expect m for a series of SiC made by sintering to be higher or lower? 16.8 Calculate using the Voight and Reuss models the bounds for Young’s modulus of MgO–Al2O3 composites as a function of volume fraction. 16.9 Explain briefly why there is a size dependence for the strength of ceramics but not for metals. 16.10 Sketch stress–strain plots for polycrystalline MgO at (a) 25°C, (b) 1000°C, (c) 1700°C, and (d) 2800°C. 308 ...................................................................................................................................................... M e c h a n i c a l Te s t i n g  17 Deforming: Plasticity CHAPTER PREVIEW In this chapter we are concerned with the deformation of ceramics leading to a permanent shape change. This is known as plastic deformation and is both nonrecoverable and irreversible. There are several mechanisms that are responsible for plastic deformation in crystalline mate- rials: dislocation motion, vacancy motion, twinning, and phase transformation. In metals at room temperature dislocation motion is the most important of these mechanisms. In Chapter 12 we already noted that dislocations do not move easily in ceramics and this is the reason for their inherent brittleness. Nevertheless, dislocation motion is observed in ceramics under spe- cific loading conditions. In general, plastic deformation of ceramics requires high temperatures and this is important because  We often process ceramics at high temperature.  Many potential applications for ceramics, such as in fuel cells and engines, require them to be stable at high temperature. We know that glass flows and that we can produce complex shape changes in glass. There are no dislocations in glass so how does plastic deformation occur? And does the plastic defor- mation of glass always require a high temperature? Selecting ceramics for use at high temperatures or under applied load requires consideration of their long-term stability. Time dependent deformation is known as creep, and creep resist- ance is a critical design parameter. Even if creep does not lead to failure, a change in shape or size may render a component useless. The mechanism responsible for creep depends on temperature, stress, and the microstructure of the ceramic. 17.1 PLASTIC DEFORMATION recall that for metals we see a wide range of values, e.g., for a low-strength aluminum alloy σy = 35 MPa and for a The onset and extent of plastic deformation are often high-strength steel σy > 1400 MPa. We usually say yield measured when the σ–ε behavior of a material is being strength rather than yield stress. Strength is a material determined. We showed some general σ–ε curves in property; stress is a measure of the applied load. Chapter 16. In Figure 17.1 σ–ε curves obtained for crystals Fracture strength, σF, is the stress at a fracture. Because of KBr and MgO tested in bending are shown. From these ceramics are often tested in bending we do not see any curves we can identify several parameters that may already reduction in cross-sectional area during the test as we be familiar to you from the discussion of the mechanical often see in a tensile test with a metal. As a result we properties of metals. would not expect to see a maximum in the σ–ε curve cor- The proportional limit P corresponds to departure responding to the tensile strength or ultimate tensile from linearity and is defined as the onset of plastic defor- strength. mation. If the transition from elastic to plastic deformation Figure 17.2 shows a σ–ε curve for LiF that illustrates is gradual it may be difficult to determine precisely where an abrupt elastic–plastic transition. Plastic deformation P is and sometimes it is better avoided. begins at the upper yield point and there is a decrease in The yield strength σy is the stress determined by stress. At the lower yield point deformation continues at drawing a line parallel to the linear part of the σ–ε curve lower stress levels. This type of behavior is similar to that at some specified strain offset. We usually use a strain of of some low-carbon steels as well as aluminum oxide and 0.002. To compare the values of σy in Figure 17.1 you may magnesium oxide at high temperatures. 17.1 P l a s t i c D e f o r m at i o n ........................................................................................................................................... 309  Stress Bending Stress MgO Fracture (MPa) Moment Upper yield (MPa) (mm.kg) 8 150 Yield stress 15 6 100 10 Lower yield 4 KBr 50 5 Fracture 2 Yield stress 0 0 0 0.25 0.5 Deflection (mm) FIGURE 17.1 Stress–strain curves for KBr and MgO crystals 0 0.05 0.10 tested in bending. Deflection (mm) FIGURE 17.2 Stress–strain curve for a LiF single crystal. 17.2 DISLOCATION GLIDE the additional consideration of electrostatic interaction between ions. We can illustrate these considerations by Dislocation glide (or slip) is a primary mechanism for looking at the familiar rocksalt structure (structure of plastic deformation in crystals. Slip takes place discon- NaCl and MgO). This is an interesting example to choose tinuously in bands as illustrated in Figure 17.3. Although to start with because the first studies of crystal plasticity, we often think of dislocations in ceramics as immobile, which were conducted by Reusch in 1867, were conducted they can glide as shown in Figure 17.4a. In this case a using sodium chloride. He concluded that the slip system crystal of LiF has been plastically bent and the disloca- for NaCl is {110}<11̄0>. tions revealed by etching. Figure 17.4b is a dark-field The choice of slip plane has often been explained by transmission electron microscopic (TEM) image that considering the position of ions during slip. Figure 17.5 shows a glide band in spinel. The dislocations are visible compares the ion positions during slip on {100} and {110}. in the dark-field image as bright lines against a dark The key difference is that slip on {100} would increase background. the distance between oppo- Both the direction of site ions. However, during SLIP SYSTEM slip and usually the slip slip on {110} oppositely A slip system is a plane and a direction and is repre- plane have a definite crys- charged ions are brought sented as {hkl}<uvw>. tallographic orientation, closer together. The overall which together are known effect is that slip on {110} as a slip system. Slip systems for several ceramics would lead to a decrease in the electrostatic interaction are given in Table 17.1. Primary slip systems are those energy. Clearly this is not the complete story as we men- for which slip is easiest; it is more difficult on secondary tioned in Section 12.5. Not all crystals with a rocksalt slip systems and these are usually activated at higher structure share the same slip system as shown in temperature. What determines the slip system for Table 17.2. The primary glide plane depends on the atoms ceramics? present. For PbS and PbTe the primary glide plane is The slip direction is usually the direction having the {100} not {110}. The explanation proposed back in 1930 smallest spacing between atoms or ions of the same type by Buerger is based on the polarizability or “deformabi- (the highest linear density). In metals, the slip plane is lity” of the ions. As the sum of the polarizability of both often the closest packed plane (the highest planar density). ions increases there is increasing ease of slip on {100} and In ceramics, we consider planar density, but there is often increasing plasticity. 310 .................................................................................................................................................. Deforming: Plasticity  Slip Crystal axis (A) Slip (B) FIGURE 17.3 Illustration of slip bands: (a) macroscopic appearance; (b) showing atomic movements. FIGURE 17.4 (a) Glide bands in LiF revealed by etching. (b) “Glide” bands in spinel: (top) 200°C; (bottom) 950°C. 17. 2 D i s l o c at i o n G l i d e ................................................................................................................................................ 311  TABLE 17.1 Slip Systems for Several Ceramics Activation Slip systems temperature (°C) Crystal Material structure Primary Secondary Primary Secondary Al2O3 Hexagonal {0001}<112̄0> Several 1200 BeO Hexagonal {0001}<112̄0> Several 1000 MgO Cubic (NaCl) {110}<11̄0> {001}<110> 0 1700 MgO·Al2O3 Cubic (spinel) {111}<11̄0> {110}<11̄0> 1650 β-SiC Cubic (ZnS) {111}<11̄0> >2000 β-Si3N4 Hexagonal {101̄0}<0001> >1800 TiC, (ZrC, HfC, etc.) Cubic (NaCl) {111}<11̄0> {110}<11̄0> 900 UO2, (ThO2) Cubic (CaF2) {001}<110> {110}<11̄0> 700 1200 ZrB2 (TiB2) Hexagonal {0001}<112̄0> 2100 C (diamond) Cubic {111}<11̄0> C (graphite) Hexagonal {0001}<112̄0> β-SiO2 Hexagonal {0001}<112̄0> CaF2 (BaF2, etc.) Cubic {001}<110> CsBr Cubic (CsCl) {110}<001> TiO2 Tetragonal {110}<11̄0> {110}<001> WC Hexagonal {101̄0}<0001> {101̄0}<112̄0> 17.3 SLIP IN ALUMINA the oxygen ions the close-packed direction is actually <11̄00>; this is not the slip direction because we need to The slip system for α-alumina (corundum) is given in consider what happens to the aluminum ions, which Table 17.1. The primary slip plane is the basal plane, occupy only two-thirds of the octahedral interstices. Slip (0001); the slip direction is <112̄0>. The arrangement of along <112̄0> preserves the stacking sequence of the alu- atoms on the slip plane was shown in Figure 12.12. For minum ions. Temperatures around 1300°C are needed before significant plastic deformation is observed in single- crystal alumina. At even higher temperatures other slip systems become activated as summarized in Table 17.3. [001] TABLE 17.2 Comparison of Primary Glide Planes in Crystals Having a Rocksalt Structure D Polarizability (10−30 /m3) Lattice A Primary constant B Crystal glide plane Anion Cation Total (nm) [110] C LiF {110} 0.03 1.0 1.03 0.401 (A) [110] MgO {110} 0.09 3.1 3.19 0.420 NaCl {110} 0.18 3.7 3.88 0.563 PbS {100} 3.1 10.2 13.3 0.597 [001] PbTe {100} 3.1 14.0 17.1 0.634 a TABLE 17.3 Slip Systems in a-Alumina (Corundum) 2 B [110] System name Slip system Remarks A a 2√2 (C) Basal (0001)1/3<21̄1̄0> Dominant system (B) under shear superimposed on 1-atm pressure D Prismatic {12̄10}<101̄0> {12̄10}<101̄1> Occurs above 1600°C under shear [110] superimposed on C 1-atm pressure Pyramidal {11̄02}<011̄1> {101̄1}<011̄1> Occurs above 1600°C (D) (E) under shear superimposed on FIGURE 17.5 (a–e) Schematic comparing slip in the rocksalt 1-atm pressure structure on {100} and {110} planes. 312 .................................................................................................................................................. Deforming: Plasticity  Because of the large Burgers vector involved the F combined motion of partial dislocations may lead to A slip. The background to this argument was presented in Chapter 12. Graphite is another hexagonal ceramic in which slip has been found to occur by the motion of partial ψ φ dislocations. Plane normal 17.4 PLASTIC DEFORMATION IN Slip SINGLE CRYSTALS direction There are many mechanisms that can lead to plastic defor- mation in single crystals, but the most important is slip. Slip The two things that we need to consider are the inherent plane resistance to the movement of dislocations provided by the periodicity of the lattice and the orientation of the crystal with respect to the applied stress. F Lattice Resistance FIGURE 17.6 Geometry used to determine the critical resolved The stress, τf, needed to move a dislocation along the slip shear stress. plane is known as the Peirels–Nabarro (or frictional) stress and is given by τ f = m exp ⎛ − 2p w⎞ (17.1) ⎝ b ⎠ The stress, which is clearly a function of the crystal case, dislocation motion does not occur and the crystal structure and bonding, depends on b and w. You will recall will not plastically deform at stresses below the theoretical from Chapter 12 that dislocation widths in covalent solids lattice strength. For example, in MgO τr is zero when σ is are quite narrow (w ∼ b) compared with those in face- applied along <111>. Under these loading conditions at centered cubic (fcc) metals (w ∼ 10b). elevated temperatures (>300°C) slip may occur on the secondary slip system: {001}<110>.  For metals τf ∼ 10 MPa ∼ 10−4 μ, these stresses are The critical resolved shear stress, τcrss, is the minimum fairly small and dislocations can move freely. The shear stress required to initiate slip for a particular slip yield stress is determined primarily by interactions system defined when σ = σy: between dislocations and other defects such as impurities. τcrss = σy(cos φ cos ψ) (17.3)  For simple ionic ceramics (e.g., NaCl and CaF2) τf ∼ 10–100 MPa ∼ 10−4 μ–10−3 μ. Figure 17.7a shows the stress–strain behavior for a  For complex ionic (e.g., Al2O3) and covalent ceramics single crystal that is favorably oriented for plastic flow. (e.g., SiC) τf ∼ 1000 MPa ∼ 10−2 μ. Dislocations have This type of behavior is seen in MgO and other ceramics low mobility and lattice resistance is the main with a rocksalt structure. There are three distinct stages: obstacle.  Stage I: Easy glide of dislocations with the possibility Orientation of large strains (∼20%)  Stage II: Interaction of dislocations on intersecting slip Plastic deformation depends not only on how easy it is for planes resulting in work hardening the dislocations to glide on their slip plane but also the  Stage III: Cross-slip orientation of the slip plane and the slip direction with the applied stress. If we consider a single crystal subject to The value of τcrss depends on test conditions such as uniaxial tension as illustrated in Figure 17.6 the shear temperature and strain rate as shown schematically in stress, τr, acting on the slip plane in the slip direction is Figure 17.7b. We can again identify three distinct behaviors: τr = σ cos φ cos ψ (17.2)  Region I: τcrss decreases with increasing temperature For some structures it is possible to orient the crystal and decreasing strain rate. Thermal fluctuations so that τr on all operative slip systems is zero. If this is the enhance dislocation motion. 17. 4 P l a s t i c D e f o r m at i o n i n S i n g l e C ry s ta l s ...................................................................................................... 313  Work σ hardening σ (MPa) 0 20 40 30 1700 °C Easy glide e (%) I II III 20 1650 °C ε 1800 °C (A) 10 1750 °C I II III 1600 °C τC • 0 μ γ1 • FIGURE 17.8 Stress–strain curves for polycrystalline MgO as a γ2 function of temperature. • γ1 • γ2 17.5 PLASTIC DEFORMATION IN POLYCRYSTALS 0 0.5 T 1 Tm.p. Plastic deformation is more difficult in polycrystals than (B) in single crystals because now we have to consider what FIGURE 17.7 (a) Stress–strain curve for a crystal suitably oriented happens at the grain boundaries. Grain boundaries act as for plastic flow. (b) Temperature dependence of the normalized barriers to dislocation motion and if adjacent grains are critical resolved shear stress for two strain rates, where γ1 > γ2. not favorably oriented for slip to continue, dislocations will pile up at the boundary. A polycrystal needs five independent slip systems before it can undergo an arbitrary strain. This requirement is known as the von Mises criterion. A slip system is  Region II: τcrss is independent of temperature and strain independent if the same strain cannot be produced from rate. There is interaction between dislocations and a combination of slip on other systems. From Table 17.4 between dislocations and other defects. you can see why MgO might be ductile when stressed as  Region III: τcrss again decreases with increasing a single crystal but in polycrystalline form it is brittle temperature and decreasing strain rate. At high except at high temperature where secondary slip systems temperatures diffusion processes can become operate. For polycrystalline MgO the brittle-to-ductile important. transition occurs at ∼1700°C as shown in Figure 17.8. TABLE 17.4 Independent Slip Systems for Some Ceramics Lattice type Crystal Slip system Number of independent systems Rocksalt MgO, NaCl, LiF, NaF {110}<11̄0> 2 Rocksalt MgO, NaCl, LiF, NaF {110}<11̄0> 5 at high temperature {001}<11̄0> {111}<11̄0> Fluorite UO2 and CaF2 {001}<11̄0> 3 TiC and UC {111}<11̄0> 5 Spinel MgAl2O4 {111}<11̄0> 5 {110}<11̄0> Fluorite UO2 and CaF2 {001}<11̄0> 5 at high temperatures {110}<11̄0> {111}<11̄0> Hexagonal Al2O3, C (graphite), BeO {0001}<112̄0> 2 Hexagonal Al2O3, C (graphite), BeO {0001}<112̄0> 5 at high temperatures {12̄10}<101̄0> {12̄10}<101̄1> {11̄02}<011̄1> {101̄1}<011̄1> Sphalerite ZnS, β-SiC (111}<11̄0> 5 314 .................................................................................................................................................. Deforming: Plasticity  20(μm) 100(μm) 25(nm) 10(nm) 5(nm) B 6 Theory, Porosity-0 Compressive Theory, Porosity-6% A stress Theory, Porosity-11% (GPa) Experiment, Porosity-6% 5 Experiment, Porosity-11% P 4 3 2 FIGURE 17.9 Illustration of slip propagation from grain A to grain B. 1 0 Some cubic materials, e.g., TiC and MgAl2O4, do have 0 0.1 0.2 0.3 0.4 enough independent slip systems, but the Peierls–Nabarro Grain Size (nm-1/2) stress is high making dislocations immobile except at high FIGURE 17.11 Compressive yield stress as a function of grain size temperature. for nanocrystalline TiO2 at three levels of porosity. The Hall–Petch relation (Eq. 14.8) indicates the effect of grain size, d, on the stress required to make the disloca- tion move in a polycrystalline sample. The origin of the relation is that the stress to operate a Frank–Read source increases as the size of the source decreases. If the grain So the grain size of a polycrystalline ceramic is impor- size decreases, then the maximum size of the Frank–Read tant in determining the yield strength and the fracture source also decreases. The result is the famous d1/2 strength of ceramics. Figure 17.9 illustrates the back- relationship. ground to Eq. 14.8. Slip starts in the most favorably oriented grains. If the material is to plastically deform then slip must propagate from one grain to the next. Grain Size, μm Stress concentrations are built up at the grain boundary 500 100 25 10 5 at P and these are greater when the length of the slip Yield band, or the grain size, is large. For deformation to Stress MPa continue the stress must be sufficient to start dis- 30 location motion in an adjacent grain, which will be easier for large grained samples. The increase in strength of polycrystalline KCl as the grain size decreases (an illustration of the Hall–Petch phenomenon) is shown in Figure 17.10. In some cases the Hall–Petch equation appears to 20 hold when the grain size is on the order of several nanom- eters. In these cases deformation cannot be due to disloca- tion glide and perhaps Eq. 14.8 is best thought of as a scaling law. Figure 17.11 shows a Hall–Petch plot for TiO2 over a wide range of grain sizes. At the very smallest grain 10 sizes studied the behavior is inverse or negative Hall– Petch. The reasons for this transition are not well under- stood and the transition does not appear to occur for all nanomaterials. 0 0 0.2 0.4 0.6 17.6 DISLOCATION VELOCITY Grain Size, -1/2μm-1/2 AND PINNING FIGURE 17.10 Grain size dependence of yield strength for KCl. The solid circles are for pure material with a <100> texture; the Figure 17.12 shows the stress dependence of dislocation open circles are for pure material with a <111> texture. The velocity for CaF2. At low stresses the relationship has the crosses are for Sr-doped KCl. form 17. 6 D i s l o c at i o n Ve l o c i t y a n d P i n n i n g ................................................................................................................. 315  10-2 75°C 25°C V Screw cm/sec2 Edge 10-3 Screw Edge 10-4 Etch pits Initial (001) position (100) Final position Stress 10-5 Stress Glide direction [101] (101) (010) FIGURE 17.13 Etch pits showing the motion of a dislocation loop 10-6 in single-crystal LiF. 0.6 0.7 0.9 1.0 1.3 1.5 1.8 2.2 2.6 3.2 τA (kg/mm-1/2) FIGURE 17.12 The stress dependence of dislocation velocity. p city has been done using the etch-pit technique as illus- ⎛t ⎞ v=⎜ ⎟ (17.4) trated in Figure 17.13 for LiF. ⎝ t0 ⎠ Dislocations in ceramics can be pinned by solute atoms just as they can in metals as shown in Figure 17.14. The Both τo and p are material constants: τo is the shear stress dislocations are impeded because of their interaction with for unit dislocation velocity and p is the velocity stress the stress field around the impurity. This effect has long exponent that describes the stress dependence of the dis- been used to strengthen metals. location velocity. Values are given for some materials in Table 17.5. At very high stresses Eq. 17.4 does not hold, as the maximum dislocation velocity in a crystal equals the velocity of sound. Determination of dislocation velo- % ~ Mole % NiO 6.0 6.2% Compressive Yield Stress 9.7% 27.2% 102 kg/cm2 4.4% 14.5% 15.2% TABLE 17.5 Values of the Constants in Eq. 17.4 for Some 4.0 Materials (RT Except for Ge) Material t o (MPa) p Zn 0.03 1 2.0 Pure MgO Cu 0.03 1 Mo 64.8 7 Nb 48.3 16 Fe+3%Si 193.1 30 NaCl 1.45 8 0 LiF 11.7 25 ε 1% Ge (440°C) 965 GPa 1 FIGURE 17.14 Illustration of solute hardening in MgO. 316 .................................................................................................................................................. Deforming: Plasticity 17.7 CREEP 0.08 Rupture Creep is time-dependent permanent deformation that is Creep often due to diffusion processes rather than dislocation strain motion. Engineers need to consider creep in cases in which ceramic components will be used in load-bearing applications at high temperature. It is necessary to specify Primary creep Tertiary a particular maximum strain that is acceptable during the 0.04 Secondary creep anticipated lifetime of the component. creep In general, creep behavior of ceramics is similar to that of metals. However, in ceramics it usually occurs at higher temperatures, typically >0.5 Tm. In com- parison, creep is a consideration in aluminum alloys at Elastic extension 100°C and in polymers at room temperature. Creep is 0 particularly important in ice, which creeps extensively 0 200 400 t (h) 600 at low temperatures. The creep of ice is responsible for FIGURE 17.15 Creep curve illustrating three distinct regimes. the movement of glaciers and the spreading of the Antarctic ice cap. Figure 17.15 shows a general creep curve. There are three regimes: simplest approach a load is attached to the sample,  Transient or primary creep: Following a spontaneous which is heated, and the deformation is measured as a elastic strain the creep rate (also referred to as the function of time. Because of the problems we mentioned creep strain rate) decreases with time from an initially earlier in performing tensile tests on ceramics the load is high value. This stage of creep is often represented by usually applied by bending. The disadvantage of bending an equation of the form tests is the inhomogeneous stress state that changes during creep deformation. The creep behavior of ceramics is different if the load is applied in tension or compression ε = βT m (17.5) and compressive creep tests may, although rarely, be performed. β is a constant and m varies from 0.03 to 1.0 depending There are three mechanisms for creep and we will on the material, stress, and temperature. In some describe each of these in the following sections. ceramics (e.g., SiC fibers) this may be the only stage shown. 17.8 DISLOCATION CREEP  Steady-state or secondary creep: Strain increases lin- early with time, the creep rate is constant, and defor- In this mechanism creep occurs by dislocation motion, mation may continue for a long time. This is the most i.e., glide and climb. For the climb-controlled process the important regime. The equation for secondary creep creep rate can be expressed as is n a D L mb ⎛ s ⎞ e = ⎜ ⎟ (17.7) ε = Kt (17.6) kT ⎝ m ⎠ K is a constant that depends on stress and temperature. which we can simplify by taking all of the “constants” The mechanisms for this stage are discussed in the next into a temperature-dependant constant Γ: sections. . ε = Γσ n (17.8)  Tertiary creep: a rapid increase in creep rate just before failure. This stage is often missing for ceramics. This is a simple power law equation and when n > 1 we refer to it as power The creep behavior of a law creep. For climb n is ceramic is determined by STRAIN AND CREEP in the range 4–5; for . measuring the stain rate as Elastic strain: ε0 = σ/E Creep rate: ε c = dεc /dt εc is the a glide-controlled process a function of load. In the creep strain. n = 3. 17. 8 D i s l o c at i o n C r e e p ................................................................................................................................................ 317 17.9 DIFFUSION- TERMS IN CREEP EQUATIONS  Because of the d−2 depend- CONTROLLED α a constant ence the creep rate will CREEP DL lattice diffusivity increase with decreasing k Boltzmann’s constant grain size (shorter diffu- In this mechanism creep b Burgers vector sion distance). is due to atomic diffusion. T absolute temperature  The creep rate is pro- There is no dislocation σ applied stress portional to the applied motion. If we consider the μ shear modulus stress (at least for lower single crystal shown in m grain size exponent stresses). Figure 17.16 Nabarro n stress exponent  There is a linear depend- (1948) showed that vacan- ϕ atomic volume ence between strain rate cies would move from the d grain size and stress. faces under tension to Dgb grain boundary diffusivity those under compression. δ grain boundary width At lower temperatures There will be a counter- A dimensionless constant and for fine-grained ceram- flow of atoms and we D diffusion coefficient ics grain boundary diffu- obtain a permanent shape sion may be the dominant change as a result. path. In these situations For Nabarro–Herring creep the creep rate is given by the process is termed Coble creep (Coble, 1963) and the creep rate is a DLs Ω e = (17.9) d 2 kT 150ΩdDgbs e = (17.10) In this case the constant, α, depends on the extent of pd 3 kT grain-boundary sliding as determined by Herring (1950). For simple tension test measurements under steady-state The important points to note from Eq. 17.10 are that conditions α = 13.3. We assume the following:  Creep rate varies as d −3; hence it is important for very fine-grained ceramics.  The main source and sink for vacancies are grain  Dgb > D L, so Coble creep is favored at lower boundaries. temperatures.  We are in equilibrium.  There is no cavitation. Nabarro–Herring and Coble creep can take place in The following important points apply to Nabarro– parallel so that actual creep rates will involve both Herring creep: components and both diffusion coefficients. In ceramics we also have a situation in which both anions and  The temperature has to be high enough to allow sig- cations are diffusing adding further complications to nificant vacancy diffusion. the creep rate equations. If there is a large difference  Diffusion is considered to occur through the bulk of in the diffusion rates then the creep rate is controlled by the material. the slower diffusing species along the faster diffusing path. σ σ Creep 17.10 GRAIN-BOUNDARY SLIDING extension Some ceramics have an intergranular film (IGF) formed σ d σ σ d σ during fabrication, often due to the addition of a sintering aid. If this phase softens at high temperature then we get creep by grain-boundary sliding. The glass viscosity, η, which is a function of temperature, controls the creep rate. σ σ As the temperature increases the viscosity decreases, and Direction of this is usually represented by an empirical relation known vacancy flow as the Vogel–Fulcher–Tammann (VFT) equation or some- FIGURE 17.16 Illustration of Nabarro–Herring creep. times simply the Fulcher equation: 318 .................................................................................................................................................. Deforming: Plasticity  This latter mechanism is similar to what happens σ during liquid-phase sintering (see Chapter 24). The requirements include the following:  Thep solid must have a certain amount of solubility in the liquid.  The liquid must wet the solid. The composition of the IGF is important in determining (A) σ overall creep behavior. For example, using Y2O3 as a sin- tering aid for silicon nitride ceramics has been found to be superior to using MgO. Other important aspects of the σ microstructure are the grain size and the volume fraction of liquid present. 17.11 TERTIARY CREEP AND CAVITATION (B) σ Tertiary creep represents the final stage of creep defor- FIGURE 17.17 Illustration of the dissolution–precipitation mecha-mation and involves an acceleration of the creep rate nism that could be operative in ceramics containing a glassy phase at the GB. followed by failure of the component. This stage does not occur in all ceramics, and as previously noted certain ceramics exhibit only primary creep. Tertiary creep involves the formation of cavities that lead to crack formation, often along grain boundaries. The B cracks can propagate rapidly, particularly under tensile lnh = A + (17.11) loading. T − T0 Although the nucleation of cavities does not seem to be well understood at present it is clear that cavitation A, B, and T0 are constants for a particular glass. The VFT depends on microstructure. Porosity and second-phase equation works very well except at temperatures close to particles, which are sources of stress concentration (see the glass transition temperature, Tg. Chapter 18), can act as nucleation sites for cavitation and There are several mechanisms that can result in a per- subsequent crack growth. Remember pores can be found manent change in shape. In one mechanism the glass is in most ceramics; even “pore-free” materials such as hot- squeezed out of the boundaries during compression pressed alumina may contain small pores. Cavitation also flowing to those under tension. Proof of this mechanism occurs in ceramics with IGFs. Nucleation of the cavities comes from high-resolution TEM, which can be used to will usually occur at regions where the IGF is not homo- directly measure the thickness, w, of the IGF. In these geneous, e.g., nonwetted regions, gas bubbles, and impu- cases rity particles. Figure 17.18 shows aw 3s e = (17.12) VISCOUS FLOW cavity size distribution h0 d 3 data for two polycrystal- Newton’s law: line aluminas. One is Another proposed Lucalox (there is no glassy mechanism is that of disso- τ = ηdγ/dt phase) and the other is lution and reprecipitation, 99% pure alumina with a which is illustrated in Figure 17.17. Here grains dissolve glassy phase. The data were obtained using small-angle in the liquid at points of high stress, and this solute then neutron scattering. For Lucalox the number of pores diffuses through the liquid and precipitates at regions of increases with increasing creep strain but their size does low stress. In this case the creep rate is not increase—nucleation is the dominant process. For the 2 alumina with a glassy phase both the number and size of aws Ω 3 e = (17.13) the pores increase with creep strain—we are getting both h0 d 3 nucleation and growth. 17.11 Te r t i a ry C r e e p A n d C av i tat i o n ..................................................................................................................... 319  5 100 Normalized N(D) Stress -1 nm • m -3 Lucalox alumina 10-1 (τ/μ) x 10-15 Dislocation glide 4 Theoretical 10-2 shear strength 10-3 Dislocation creep 3 Peierls 10-4 stress 10-5 2 10-6 Coble Nabarro-Herring ε = 7.75% creep creep ε = 2.7% 10-7 1 ε = 0% 10-8 0.0 0.2 0.4 0.6 0.8 1.0 Homologous Temperature T/Tm.p. 0 (A) 0 50 100 150 200 250 (A) Diameter (nm) Alumina Al2O3 T (°C) d = 100 μm 5 N(D) 200 600 1000 1400 1800 nm-1• m-3 AD99 Alumina 10-1 Normalized Plasticity Strain x 10-16 rate/s 4 Shear -10 Stress -2 10 /s 1 /s 10 3 O diffusion 10-1 through 10-3 lattice Power-law 10-2 2 creep 10-3 10-4 ε = 0.10% ε = 7.72% 10-4 1 10-5 10-6 ε = 0.08 0 10-5 10-7 0 40 80 120 160 200 Al diffusion Al diffusion (B) Diameter (nm) along GBs through lattice FIGURE 17.18 (a) Cavity-size distribution as a function of creep 10-6 0 0.2 0.4 0.6 0.8 1.0 strain in alumina without a glassy phase (Lucalox). (b) Cavity-size Homologous T (T/Tm.p.) distribution as a function of creep strain in alumina with a glassy phase (AD99). (B) FIGURE 17.19 (a) Schematic of creep deformation map for a polycrystalline ceramic. (b) Creep deformation map for Al2O3. TABLE 17.6 Creep Equation Exponents and Diffusion Paths for Various Creep Mechanisms Creep mechanism m n Diffusion path Dislocation creep mechanism Dislocation glide climb, climb controlled 0 4–5 Lattice Dislocation glide climb, glide controlled 0 3 Lattice Dissolution of dislocation loops 0 4 Lattice Dislocation climb without glide 0 3 Lattice Dislocation climb by pipe diffusion 0 5 Dislocation core Diffusional creep mechanisms Vacancy flow through grains 2 1 Lattice Vacancy flow along grain boundaries 3 1 Grain boundary Interface reaction control 1 2 Lattice/grain boundary Grain boundary sliding mechanisms Sliding with liquid 3 1 Liquid Sliding without liquid (diffusion control) 2–3 1 Lattice/grain boundary 320 .................................................................................................................................................. Deforming: Plasticity  characteristic that is both beneficial and deleterious, but unavoidable at high temperature. Under most conditions oxide glasses behave as New- tonian fluids, i.e., the strain rate, dγ/dt, is a linear function of the applied shear stress, τ. An important consequence of this behavior is that when we draw glasses, such as during the formation of optical fibers, the cross section reduces at a constant rate. In other words, we do not get necking of narrow sections of the fiber. At high stress levels non-Newtonian behavior, which is common in poly- mers, may be observed in oxide glasses. Models of viscous flow include the following: Absolute-rate theory: Viscous flow is a thermally acti- vated process involving a high-energy activated state. Viscosity follows an Arrhenius expression with activa- FIGURE 17.20 Detail from a glass sculpture by Dale Chihuly. tion energy for viscous flow, Ev. The preexponential term has a weaker dependence on temperature than the exponential term. This theory is applicable only over a narrow range of temperatures. 17.12 CREEP DEFORMATION MAPS Free-volume theory: Molecular motion involves the avail- ability of vacancies. The vacancy volume is the free From the previous sections you can see that there are a volume, VF, of the liquid, approximately the difference large number of creep mechanisms. These can be expressed in volume of the liquid, VL, and crystalline, Vc, forms. by one general equation: VF is a function of temperature. D is a constant close m n to unity. The Williams–Landel–Ferry (WLF) equation AD mb ⎛ b ⎞ ⎛ s ⎞ e = ⎜ ⎟ (17.14) uses a similar approach in which fg is the fraction of kT ⎝ d ⎠ ⎝ m ⎠ free volume at Tg, about 0.025, and βL and βC are the volumetric thermal expansion coefficients of the liquid The various creep mechanisms give rise to different and solid, respectively. values of the exponents, m and n, as shown in Table 17.6. Excess-entropy theory: There is a decrease in the configu- For a given ceramic a specific creep mechanism may rational entropy, Sc, of a liquid when it is cooled dominate at certain temperatures and stresses. This can down—fewer molecular arrangements are possible. be represented on a creep This makes deformation deformation map as illus- more difficult. Es is pro- trated in Figure 17.19a for EQUATIONS FOR VISCOUS FLOW portional to the potential a general case and in Arrhenius: energy barrier for mole- Figure 17.19b for the spe- h = h0 exp ⎛ v ⎞ E cular rearrangement. cific case of Al2O3. These ⎝ RT ⎠ maps are based on a large The Vogel–Fulcher– amount of experimental Turnbull and Cohen: Tammann (VFT) equation data. DVc ⎞ h = h0 exp ⎛⎜ is an empirical expression ⎝ VF ⎠ ⎟ relating η to T and can be interpreted in terms of 17.13 VISCOUS Williams–Landel–Ferry (WLF): the different models. The FLOW ⎡ D ⎤ VLT expression is accurate h = h0 exp ⎢ ⎥ over a wide range of Viscous flow is an impor- ⎣ fg + ( b L − bC ) (T − Tg ) ⎦ temperatures and is widely tant mechanism for perma- Adams–Gibbs: used in many practical nent deformation in glasses. applications. It allows us to form h = h0 exp ⎡ Es ⎤ The viscosity of a spe- complex shapes such as ⎣⎢ TS ⎦⎥ cific glass depends on tem- shown in Figure 17.20. perature as shown in Figure Viscous flow is also a Vogel–Fulcher–Tammann (VFT): 17.21. Glass blowing is mechanism by which often performed at viscosi- ⎡ C ⎤ ceramics containing IGFs h = h0 exp ⎢ ties of ∼10 MPa·s. This is undergo creep. So it is a ⎣ T − T0 ⎥⎦ at the top end of the 17.13 Vi s c o u s F l o w ........................................................................................................................................................ 321  15 Log Viscosity (Pa s) Strain point 12 Annealing point 9 Softening point 6 Flow point 3 Working point 0 200 600 1000 1400 T (°C) FIGURE 17.21 Temperature dependence of viscosity for a soda- lime-silica glass. working range, which extends from 1 kPa·s to 10 MPa·s. Figure 17.22 shows a microblown feature formed in a silica scale on oxidized SiC at 1800°C, which for pure silica corresponds to the softening point. If the viscosity was at the fining temperature (∼5 Pa·s) the gas would have been able to escape easily. If the viscosity were too high FIGURE 17.22 Microblown silica shape formed on oxidized SiC. the glass would not have been able to deform in this way. There is also time dependence to the viscosity, particu- larly near Tg and above. At these temperatures structural σ relaxation occurs. 17.14 SUPERPLASTICITY σ Superplasticity is the ability of a material to sustain very large strains. From our discussions so far on the mecha- FIGURE 17.23 Model showing how grain switching can produce a nical properties of ceramics you may think it unlikely that shape change. any ceramic would exhibit superplasticity. But superplas- ticity has been observed in, for example, tetragonal ZrO2 stabilized with Y2O3. Elongations of 800% were observed is no appreciable change in grain shape. Several models for ceramics stabilized with 3 mol% Y2O3 and 1038% for have been proposed. The one illustrated in Figure 17.23 tetragonal zirconia stabilized with 2.5 mol% Y2O3 con- involves grain switching and accounts for the constancy taining 5 wt% SiO2. The general requirements are that the of grain shape during deformation, but cannot account for grains should be the increase in surface area resulting from plastic defor- mation. Other models involve grain boundary sliding, but  Small (typically < 1 μm) again do not appear to fully account for the process.  Equiaxed Although superplasticity is a useful forming process for metals it tends not to work for ceramics because of The mechanism for superplasticity in ceramics must the problem of cavitation and the requirement of high clearly be different from that in metal alloys because there temperatures. CHAPTER SUMMARY Although we often think of the mechanical properties of ceramics entirely in terms of their brit- tleness, in this chapter we showed that plastic deformation is also important. The main differ- ence between plasticity in ceramics and in metals is that for ceramics the primary mechanism 322 .................................................................................................................................................. Deforming: Plasticity  of plastic deformation may not be the motion of dislocations. If dislocations are involved then we are invariably at high temperatures. Plastic deformation is a key engineering design consid- eration in the use of ceramics in structural applications. Consequently, understanding creep behavior is essential, which means we have to understand point defects (Chapter 11) and in many cases the role of IGFs (Chapter 15). As an illustration of why we devoted an entire chapter to this topic remember the example from the final section; elongations in excess of 1000% have been observed in some ceramics. This is clearly not the conventional wisdom when it comes to ceramics and probably something that you would not have expected prior to reading this chapter. Unfortunately, we have not been able to come up with a clear explanation for this property. PEOPLE IN HISTORY Herring, W. Conyers, an exception to our rule, is Emeritus Professor of Applied Physics at Stanford University. He has won many major awards and was elected to the National Academy of Sciences in 1968. Nabarro, Frank Reginald Nunes (1916–2006) is another exception to our rule. He studied at Oxford and Bristol University. During World War II he worked on the explosive effect of shells and was made a member of the Order of the British Empire (OBE). In 1953 he became head of the physics department at the Uni- versity of the Witwatersrand in South Africa. He is perhaps best known for Nabarro–Herring creep and the Peierls–Nabarro force. von Mises, Richard (1883–1953) was born in Lemberg, Austria-Hungary, which is now Lviv, Ukraine. A mathematician and engineer he worked in a number of areas including statistics, probability theory, and mechanics. He died in Boston. GENERAL REFERENCES Cannon, W.R. and Langdon, T.G. (1983) “Creep of ceramics: Part 1,” J. Mater. Sci. 18, 1–80; (1988) “Creep of ceramics: Part 2,” J. Mater. Sci. 23, 1. Chan, K.S. and Page, R.A. (1993) “Creep damage development in structural ceramics,” J. Am. Ceram. Soc. 76, 803. A review of creep behavior. Cook, R.F. and Pharr, G.M. (1994) “Mechanical properties of ceramics,” in Materials Science and Techno- logy, Vol. 11, edited by M. Swain, VCH Publishers, Weinheim, p. 339. Davidge, R.W. (1979) Mechanical Behaviour of Ceramics, Cambridge, University Press, New York. Green, D.J. (1998) An Introduction to the Mechanical Properties of Ceramics, Cambridge University Press, Cambridge UK. Nieh, T.G. and Wadsworth, J. (1990) “Superplastic ceramics,” Annu. Rev. Mater. Sci. 20, 117. Poirier, J.-P. (1985) “Creep of crystals: High-temperature deformation processes,” in Metals, Ceramics and Minerals, Cambridge University Press, Cambridge, UK. Sprackling, M.T. (1976) The Plastic Deformation of Simple Ionic Crystals, Academic Press, London, UK. Wachtman, J.B. (1996) Mechanical Properties of Ceramics, Wiley-Interscience, New York. SPECIFIC REFERENCES Buerger, M.J. (1930) “Translation-gliding in crystals of the NaCl structural type,” Am. Mineral. 15, 174 and 226. Coble, R.L. (1963) “A model for boundary diffusion controlled creep in polycrystalline materials,” J. Appl. Phys. 34, 1679. Gilman, J.J. (1959) “Plastic anisotropy of LiF and other rocksalt-type crystals,” Acta. Metall. 7, 608. Hall, E.O. (1951) “The deformation and aging of mild steel: III. discussion of results,” Proc. Phys. Soc. B64, 747. Herring, C. (1950) “Diffusional viscosity of a polycrystalline solid,” J. Appl. Phys. 21, 437. Nabarro, F.R.N. (1948) in Report of a Conference on Strength of Solids, The Physical Society, London, 75. The conference was held at Bristol University in the UK in 1947. Petch, N.J. (1953) “The cleavage strength of polycrystals,” J. Iron Steel Inst. (London) 173, 25. Reusch, E. (1867) “Ueber eine besondere Gattung von Durchgängen im Steinsalz und Kalkspath,” Ann. Phys. Chem. 132, 443 and 449. EXERCISES 17.1 An MgO single crystal is loaded in uniaxial compression with the [001] direction parallel to the compression axis. Assuming that dislocation motion occurs on the primary slip system when the applied stress is 30 MPa, what is the inherent lattice resistance to dislocation motion? 17.2 The lattice parameter of MgO is a = 0.4211 nm. Calculate the distance between Mg2+ and O2− ions prior to slip (Figure 17.5a and c) and at the midpoint position (Figure 17.5b and d) during slip on {100} and {110} planes. C h a p t e r S u m m a ry .......................................................................................................................................................... 323  17.3 Figure 17.14 shows the hardening effect of NiO additions to MgO. Based on what you know about these two ceramics would you expect the NiO/MgO system to show a complete range of solid solubility? You must justify how you arrived at your answer. 17.4 Figure 17.22 shows a microblown silica shape formed on SiC. What gas do you think would be formed at the SiO2 /SiC interface and lead to the shape shown? Would the gas be different at different temperatures? 17.5 For each of the ceramics listed in Table 17.1 will a tensile stress applied parallel to the c axis give a nonzero resolved shear stress? 17.6 The following dislocation reaction has been proposed for dislocation motion in graphite: a/3 [21̄1̄0] = a/3 [11̄00] + a/3 [101̄0] Is the reaction favorable as written? Justify your answer and state any assumptions that you make. 17.7 The addition of impurity atoms can pin dislocations in single crystals. The addition of small amounts (0.002%) of NdF3 to CaF2 can be very effective at increasing the yield stress because of the formation of point defect complexes. Using Kröger–Vink notation show that adding NdF3 to CaF2 can result in the forma- tion of a defect complex. 17.8 Creep is a concern for structural ceramics at high temperatures. Discuss possible creep mechanisms for SiC and Si3N4. 17.9 A major multinational company hires you as a consultant because of your knowledge of ceramics. You are asked to recommend a ceramic that will have the maximum possible creep resistance at an operating tem- perature of 1200°C. What material would you select and why? Also consider how you would process it. 17.10 Using the data in Figure 17.21 determine the activation energy for viscous flow in the soda-lime-silica glass. Based on your knowledge of glass structures would you expect the activation energy to be higher or lower for a pure silica glass? Briefly justify your answer. 324 .................................................................................................................................................. Deforming: Plasticity  18 Fracturing: Brittleness CHAPTER PREVIEW The previous two chapters on mechanical properties described how we test ceramics, their elastic response, and how under certain conditions they can permanently deform. In this chapter we describe why and how ceramics break. The main topics are  Fracture  Toughening  Fatigue Some of these topics may already be familiar from classes on metals. The exception is probably toughening. Ceramics are not tough. Toughening makes the material absorb energy during fracture by mechanisms such as local phase transformations, plastic deformation near the crack tip, or crack bridging behind the crack tip. Fracture requires cracks. In fatigue crack growth occurs as a result of cyclic loading—even at small loads. We begin this chapter by showing some of the key equations. The most important work is that of A.A. Griffith, the “Father of Fracture Mechanics.” Griffith showed the importance of flaws, which act as stress concentrators. Because it is almost impossible to make ceramics without flaws they often are the dominant cause of failure. So there is a link between this chapter and Chapter 16. 18.1 THE IMPORTANCE OF BRITTLENESS provides an additional mechanism for absorption of energy before the projectile exits the final layer. Table 18.1 gives Most ceramics are brittle at room temperature. That is the kinetic energy of several different types of handgun they fracture with very little plastic deformation. Many bullets. archeologists believe that our very existence depended on The brittle behavior of ceramics is critical to the the brittleness of ceramics, particularly flint. The fracture successful operation of ceramic armor. In addition to of flint, like cubic zirconia, diamond, and glass, is termed brittleness the basic requirements are that it be conchoidal, producing shell-like fracture surfaces. These surfaces are very sharp and were utilized in early stone  Hard tools to cut and shape wood and to butcher animals  Lightweight required for food. The hides were used for clothing and were attached to wooden frames to make shelters. Stone The first ceramic used in this application was alumina tools were necessary to cut vegetation and cultivate plants, backed with a laminate of fiberglass and polyester resin allowing a change from a food-gathering economy to one called “Doron.” Boron carbide (B4C) ceramic armor was of food production, which happened around the eighth developed during the Vietnam War and used in the mid- millennium bce in southwestern Asia. This revolutionary 1960s for both helicopter and infantry armor. It provides change from hunting to farming laid the foundation for the same protection as alumina, but with a 20% savings civilization. in weight. A quarter-inch (0.64-cm) plate of B4C can stop Bulletproof glass, which is a laminate of glass and a 30-caliber armor-piercing projectile (one containing a polycarbonate, is a dramatic illustration of the utilization tungsten carbide core). Boron carbide is being used during of brittle fracture. The glass absorbs the energy of the the current conflict in Iraq. Small arms protective inserts projectile either in elastic changes or ultimately in the are made of boron carbide. They will stop up to a 7.62-mm creation of new surfaces when it fractures. The polymer round with a muzzle velocity of ∼850 m/s. 18 .1 Th e I m p o r ta n c e o f B r i t t l e n e s s s ...................................................................................................................... 325  TABLE 18.1 Kinetic Energy of Handgun Projectiles It is important to remember that metals and polymers can Missile velocity also fracture in a brittle manner. But brittle fracture often Hand gun size Missile size (g) (m/s) Energy (J) occurs only at temperatures below room temperature. 0.38 10 243 295 0.22 2.6 305 133 0.45 15 259 503 18.2 THEORETICAL STRENGTH: 0.357 10 381 725 THE OROWAN EQUATION 9 mm 8 332 440 We will consider brittle fracture at the atomic level where we are separating two planes of atoms as shown in Figure 18.2a. In many crystalline materials fracture occurs Brittle fracture is used for shaping and machining along crystallographic planes that are relatively densely ceramics after they have been fired. Ceramics can be packed. These planes are known as cleavage planes. In modified to make them machinable: this is controlled MgO {100} is the cleavage plane. (It is interesting that fracture and is the approach we adopt with machinable {111} is the growth plane for MgO and that fluorite is glass-ceramics such as Macor (Chapter 26). Of course, exactly the opposite!) In glasses and in some crystals many ceramics already are machinable and can be shaped (diamond and cubic zirconia, for example) fracture is into intricate and beautiful forms as illustrated in the noncrystallographic. carved marble sculpture shown in Figure 18.1. Figure 18.2b shows a plot of stress versus distance. In many of the applications in which we use or would Note we are using X for distance (rather than r as we did like to use ceramics their brittleness can be a serious in Chapter 3) because we are now thinking about planes limitation: of atoms rather than individual atoms. The curve is the  Space shuttle tiles are made of silica glass. We need to be concerned about the impact of space debris.  Radomes are made of fused silica and silicon nitride. They have to be transparent to infrared (IR) and radio waves and resist the impact of atmospheric particles.  Ceramic bearings are used in low-load applications (watch bearings of ruby or sapphire “jewels”), but for high-load and high-speed use metals are often pre- ferred because ceramics have low fracture toughness. a0 (A) σ σth σ = σth sin (2πX/λ) 0 X a0 λ/2 (B) FIGURE 18.1 Marble sculpture in a fountain outside the Pantheon FIGURE 18.2 (a) Model of a crack tip. The interplanar spacing is in Rome. a 0. (b) Stress versus distance plot. 326 ............................................................................................................................................. F r ac t u r i ng : Br i t t len e s s same; it is only the notation that changes. If a stress is TABLE 18.3 Comparison of Theoretical Strength and applied that exceeds the theoretical strength, σth, then the Actual Strength ceramic will fracture. This is the strength of the ceramic Estimated Measured Measured if there is no plastic deformation and there are no defects. theoretical strength of strength of It is “theoretical” because we can rarely, if ever, achieve strength fibers polycrystalline it. We would like to be able to obtain an expression for Material E (GPa) (GPa) (GPa) specimen (GPa) σth and there are several different approaches we can use. Al2O3 380 38 16 0.4 The one we have selected is simple, works well, and SiC 440 44 21 0.7 gives values similar to those obtained by more complex methods. The part of the σ–X curve near to the equilibrium Combining Eqs. 18.5 and 18.6 gives interplanar spacing, a 0, can be approximated as being sinusoidal and we can write 2πσth /λ = E/a 0 (18.7) σ = σth sin(2πx/λ) (18.1) By substitution of Eq. 18.3 we get the Orowan equation where x is the displacement of the planes beyond their σth = (Eγ/a 0)1/2 (18.8) equilibrium value and λ is the wavelength of the sine wave. Theoretical strength thus depends on The two new surfaces created during fracture—the fracture surfaces—have a total energy 2γ, which must be  Surface energy equal to the work required to separate the two planes of  Young’s modulus atoms (i.e., it is the area under the curve or the integral of  Lattice spacing Eq. 18.1 between 0 and λ/2): Putting in reasonable values for γ (see Chapter 13) and l /2 a 0, we find that σth ≈ E/5 to E/10. This is a useful relation- 2γ = ∫s th sin (2 πx / λ ) dx = λσ th / π (18.2) ship to remember. Values of σth for some materials calcu- o lated using the Orowan equation are given in Table 18.2. These values are possible only in very special forms such Rearranging Eq. 18.2 gives as silica fibers with pristine surfaces. Whiskers and fibers of sapphire and silicon carbide have been made with σth = 2πγ/λ (18.3) measured strengths of about σth /2 (Table 18.3). For most polycrystalline ceramics, measured strengths For low stresses the material will be elastic, Hooke’s law are in the range of E/100 to E/1000 or even less. Why is will be obeyed, and we can write the Young’s modulus there such a large discrepancy between theoretical and as measured strengths? The reason is the presence of pre- existing cracks on the surface or inside the ceramic and E = σa 0 /x (18.4) sharp corners that may be introduced during processing. The presence of cracks does not mean that samples will and fracture spontaneously; our teeth are full of cracks. dσ/dx = E/a 0 (18.5) 18.3 THE EFFECT OF FLAWS: For small displacements we can make the approximation THE GRIFFITH EQUATION sin x ∼ x and from Eq. 18.1 write To explain the discrepancy between theoretical strength dσ/dx = 2πσth /λ (18.6) predicted by Eq. 18.8 and experimental data A.A. Griffith (1920) suggested that preexisting flaws in the materials act to concentrate stress. Figure 18.3 shows data obtained by TABLE 18.2 Values of Theoretical Strength Griffith for the tensile strength of glass fibers as a function of their diameter. As the fibers get smaller the probability Material Direction E (GPa) g (J/m2) s th (GPa) of having a crack decreases and the size of the largest α-Fe <111> 132 2 30 crack also decreases. Consequently, they get stronger. Si <111> 188 1.2 32 This is the basis of the “weak link” approach adopted in NaCl <100> 44 0.25 6.3 Weibull statistics that we described in Chapter 16. So there MgO <100> 245 1.2 37 is a direct relationship between flaws and probability of Al2O3 <0001> 460 1 46 failure. 18 . 3 Th e E f f e c t o f F l aw s : Th e G r i f f i t h E q uat i o n ............................................................................................. 327  5 E Es Es 4 Tensile Strength Etot (GPa) 3 ccrit ccrit 2 Etot 1 Ee Ee Crack Length, c c 0 (A) (B) 0 20 40 60 80 100 120 Fiber Diameter (μm) FIGURE 18.4 Plots of energy versus crack length. Etot is the sum of Es and Ee. The right plot corresponds to a greater applied stress FIGURE 18.3 Tensile strength of a glass fiber as a function of (on this scale the stress is greater by 2 and c crit is correspond- fiber diameter. ingly reduced by a factor of 2). Griffith’s approach is SCRIBING For an atomically sharp an energy balance: A crack A simple illustration of the effect of surface flaws is the crack of length 2c, as illus- will propagate when the ease with which a sheet of glass can be “cut” after light trated in Figure 18.5, the additional energy created scribing using a diamond tip. energy balance approach by the formation of the shows that fracture surfaces, Es, is offset by a decrease in the stored elastic energy, Ee, in the σf = (2Eγ/πc)1/2 (18.12) stretched bonds (this is the area under the stress–strain curve). The Griffith energy balance condition can be Equation 18.12 is often called the Griffith equation and expressed as shows that fracture stress depends on the following: dEe dEs = (18.9)  Young’s modulus (a property of the material) dc dc  Surface energy (a property of the material)  Crack length Note that we are using E for energy to avoid any confusion with Young’s modulus (E). The elastic energy term is Griffith confirmed this equation using experimental data on glass as shown in Figure 18.6. Although the energy Ee = πσ2 c2 /E (18.10) balance approach works well, kinetic effects may also be present during fracture as demonstrated for the fracture The surface energy term is of mica flake. Es = 4cγ (18.11) Because Es scales linearly with c and Ee scales quadrat- ically with c there is a maximum in the total energy Etot of the system, which corresponds to the critical crack size, ccrit. This balance can be represented graphically as shown 2c in Figure 18.4.  A crack smaller than ccrit is stable, therefore the surface energy dominates.  A crack larger than ccrit is unstable, therefore the released strain energy dominates. FIGURE 18.5 The “Griffith” crack of length 2c. 328 ............................................................................................................................................. F r ac t u r i ng : Br i t t len e s s Tensile σf = (Eγ/8c)1/2 (18.15) Strength (MPa) 6 The fracture process, although not far from ideal in ceramics, can be quite complex. Real cracks differ from those assumed in the model in that there is often no dis- 5 tinct crack edge. There will be attractive interactions between atoms on opposite sides of the crack when the 4 spacing is quite small. 3 18.5 STRESS INTENSITY FACTOR We introduced the stress intensity factors in Chapter 16. 0.3 0.4 0.5 0.6 0.7 1/√c 0.8 These are a combination of c and σ for different loading FIGURE 18.6 Verification of Eq. 18.12. The tensile strength of geometries with respect to crack position. glass as a function of crack length. The most important geometry for ceramics is mode I, the opening mode. The mode I stress intensity factor is K Ι = sY c (18.16) 18.4 THE CRACK TIP: THE Y is a dimensionless term that depends on crack configura- INGLIS EQUATION tion and loading geometry. For a simple interior crack of length 2c and tensile loading Y = π (this is the original In our discussions of fracture so far we have assumed that geometry considered by Griffith); for a surface crack the crack looks much like that shown in Figure 18.2a. The under similar loading Y = ( π / 2 ) . crack separates planes of atoms, is atomically sharp, and The critical stress intensity factor for mode I loading, the only deformation is elastic ahead of the crack tip. This KIc, at which the crack will propagate and lead to is the situation encountered in many ceramics at room fracture is known as the temperature. fracture toughness (some- The maximum tensile AI ALLOYS times denoted as T). Table stress at the crack tip, for Fracture toughness is ∼40 MPa·m1/2. 18.4 lists some values for the geometry in Figure 18.5, is TABLE 18.4 Fracture Toughness for Several Ceramics σm = 2σ(c/ρ)1/2 (18.13) Ceramic K Ic (MPa·m1/2) where ρ is the crack tip radius. The ratio σm /σ is called the stress concentration factor. As an illustration of how Al2O3 2.0–6.0 large the stress concentration factor can be we will con- Al2O3 (single crystal, 101̄2) 2.2 Al2O3 (single crystal, 0001) >6.0 sider an example of a ceramic with a flaw size c of 50 μm. MgO 2.5 The stress concentration at the crack tip is about 1200. MgAl2O4 1.9–2.4 For fracture to occur in an ideal brittle material, the Mullite (fully dense) 2.0–4.0 maximum stress must reach the theoretical strength of the ThO2 1.6 material to provide a mechanism for fracture, i.e., σm = Y2O3 1.5 ZrO2 (cubic) 3.0–3.6 σth. If we set the applied stress (σ) equal to the fracture ZrO2 (partially stabilized) 3.0–15.0 stress (σf ) then we obtain SiC (hot pressed) 3.0–6.0 SiC (single crystal) 3.7 ⎛ Eg r ⎞ 1/2 sf =⎜ ⎝ 4c a 0 ⎟⎠ (18.14) Si3N4 (hot pressed) 3.0–10.0 TiC 3.0–5.0 WC 6.0–20.0 From Eq. 18.14 you can see why sharp cracks are so de- CaF2 0.80 leterious to the strength of ceramics. For metals there is KCl (single crystal) ∼0.35 often a plastic zone ahead of the crack tip, which is due MgF2 1.00 SrF2 1.00 to dislocation motion. This leads to blunting of the crack Aluminosilicate glass (Corning 1720) 0.96 tip and a corresponding decrease in stress concentration. Borosilicate glass (Corning 7740) 0.75 A crack in a brittle material passes between adjacent LAS (glass-ceramic) 2.00 planes of atoms and a reasonable estimate for the tip Silica (fused) 0.80 radius is half the atomic spacing, therefore we can sim- Silica (96%) 0.70 Soda-lime silica glass 0.82 plify Eq. 18.14: 18 . 5 S t r e s s I n t e n s i t y Fac t o r ..................................................................................................................................... 329  TABLE 18.5 Theoretical and Measured Values of Gc for KI Some Materials Theoretical G c = 2g Measured G c Material (N/m) (N/m) R curve Glass 3.5 14 Plexiglass 11.4 480 KI ∞σ2c1/2 σ2 MgO 14.9 17.5 High-strength steel 22.8 53,000 KIc KI ∞σ1c1/2 High-strength aluminum 7.0 17,000 initial High-strength titanium 10.5 105,000 σ1 c FIGURE 18.7 A material showing R curve behavior (bold curve) ceramics. You can see that the values are generally low exhibits a region of stable crack growth and flaw tolerant behavior. and a significant amount of research has been undertaken The lighter curves σ1 and σ2 represent typical Griffith behavior. over the past 40 years or so to increase KIc. We will look at some of the approaches that have been used a little later in this chapter. The R curve, which is a plot of fracture toughness versus If the material is not perfectly brittle, i.e., there are crack length, relates the crack resistance to crack length energy dissipating mechanisms in addition to the creation as shown in Figure 18.7. The fracture toughness increases of new surfaces, then we introduce a term Gc, which is an as the crack grows. We can explain the shape of these energy (its units are J/m2) representing crack extension by curves by considering what happens in the wake of the all the available processes. You will find Gc referred to as crack. If there is a mechanism that bridges the crack then total work of fracture, crack extension force, and strain the energy required for crack propagation will increase. energy release rate. There are several mechanisms that can be envisaged, for For plane stress (the sample is a thin plate) example, a phase transformation associated with crack propagation, or ligaments that bridge the crack after the K Ic = (E Gc ) (18.17) crack tip has passed. Both these mechanisms will be described when we discuss how we actually try to toughen For plane strain (the sample is a thick block) ceramics. Eventually a plateau is reached beyond which fracture E Gc K Ic = (18.18) toughness will not increase. This is the steady-state condi- (1 − ν2 ) tion. The following implications apply to ceramics that show R curve behavior: When fracture occurs we can write  Strength degradation is less dependent on flaw size Gc = dEs /dc = R (18.19) (illustrated in Figure 18.8).  Reliability is increased. There is a region where the R is the crack resistance of the material and is called the strength is insensitive to crack size. crack resistance “force.” The material will fracture when  Fatigue resistance is decreased. Gc = R, i.e., the crack extension force is equal to the crack  There is better thermal shock resistance. resistance force. If the fracture is entirely brittle, the energy is only required to create new surfaces, then R = 2γ. (Note: The surface energy term used here differs from that in Eq. 18.11 by a factor of two because Gc is associ- Strength Ceramic with ated with a single crack tip.) R curve Table 18.5 compares some measured values of Gc to some theoretical values based on surface energies. You can see that for MgO the two values are in good agree- ment. This is not the case for the metal alloys. Ceramic without R curve 18.6 R CURVES The crack resistance R is related to fracture toughness Flaw Size, c as we just described. It was assumed that R and T are FIGURE 18.8 Effect of R curve behavior on strength. There is a independent of crack length. But this is not necessarily so. region in which the strength is insensitive to flaw size. 330 ............................................................................................................................................. F r ac t u r i ng : Br i t t len e s s 18.7 FATIGUE AND STRESS varying relative humidity. We can identify three distinct CORROSION CRACKING regions: Region I: Crack growth is The cracks that we have sensitive to KI and CORROSION AND FAILURE been describing so far The corrosion rate of silica glass in water is 10−17 m/s. follows a relationship lead to rapid fracture. We of the form The rate of stress corrosion cracking (SCC) is call these “critical cracks.” 10−3 m/s. Ceramics may contain ν = A* exp αKI (18.20) many other cracks, called “subcritical cracks,” that can lead to time-dependent A* and α are fitting parameters. From an engineering fracture. Static fatigue, also known as stress rupture, is point of view this is the most important region. where subcritical cracks grow under an applied load. Region II: Crack growth is independent of KI. Failure occurs gradually, is often unexpected, and may Region III: Very rapid crack growth leads to fracture. occur after a component has been in service for many years. For many materials there exists a threshold value of KI The slow growth of cracks is often the result of a below which the crack will not grow. This value is not combination of stress and corrosion. This is the field of seen in Figure 18.9 because of the experimental difficul- stress corrosion cracking (SCC), which is important ties in measuring very small values of crack velocity. in metals such as gold jewelry alloys and many Figure 18.10 illustrates the process that is happening ceramics. Figure 18.9 shows experimentally measured at the crack tip. The corresponding reaction, which involves crack velocities in soda-lime glass tested in nitrogen of breaking of Si–O bonds, is shown below: Crack Velocity (m/s) 100% 10-4 30% 10% 10-5 III 1.0% H2O(I) 0.2% 10-6 Si Si Si O 0.017% H O O H H -7 H O 10 H II H O O Si I Si Si 5.0 6.0 7.0 8.0 Stress Intensity Factor, KI (N/m3/2 x 105) FIGURE 18.9 Crack velocity in soda-lime glass as a function of KI, FIGURE 18.10 Environmental effects at the crack tip. A water the stress intensity factor. The percentages indicate the relative molecule diffuses to the crack tip, chemisorbs, and rotates such humidity and the Roman numerals indicate the three regions of that the lone pairs on the oxygen are aligned with the unoccupied crack propagation. electron orbitals of the Si atom. 18 .7 Fat i g u e a n d S t r e s s C o r r o s i o n C r ac k i n g ....................................................................................................... 331  Crack -5 Kmax Cyclic 10 Mg-PS GrowthRates Crack (TS) m/cycle 2090 Km DK Growth -6 TS1 Al dc 10-5 Rate 10 Mg-PSZ (over-aged) Si3N4 dN Kmin (m/cycle) Pyrolytic 300 M 10-7 carbon Alloy Time da steel dN SiC 10-7 10-8 dc Region = B(DK) Slope q III dN 10-9 10-9 Ti3SiC2 Region II KIc 10-10 R = 0.1 Region 25 hz I KO room air 10-11 10-11 0.5 1 10 50 Log ΔK, MPa • m 1/2 (A) Stress Intensity Range, ΔK1 (MPa m1/2) (B) FIGURE 18.11 (a) Log–log plot of crack growth rate versus K, which is defined in the inset. (b) Cyclic-fatigue crack growth rates for several ceramics and metal alloys as a function of applied stress intensity range, ΔK. Si–O–Si + H2O → 2Si–OH Region III: At high ΔK values crack growth is very rapid and fracture would be characteristic of normal static Other small polar molecules such as methanol (CH4OH) failure. and ammonia (NH3) can promote SCC in glass. The main requirement is that they are small enough to fit into the Figure 18.11b shows examples of cyclic fatigue plots crack, <0.3 nm. for several ceramics. The curves are linear and very steep Ceramics can also fail by cyclic fatigue. The mecha- implying a high value of q in Eq. 18.22 and that fracture nisms are complicated and not well understood. Fatigue is rapid. The fatigue fracture we see in metals is rare in failure in metals is pervasive and due to dislocation ceramics. motion. Because fatigue is due to propagation of cracks it will be related to K. During a fatigue cycle K will vary, so what 18.8 FAILURE AND FRACTOGRAPHY we are actually interested in is ΔK, the difference between K at the maximum load (Kmax) and K at the minimum load Here we discuss the appearance of different surfaces (Kmin). formed when a ceramic fractures; this is the topic of frac- tography and is always a postmortem analysis. Fractogra- ΔK = Kmax − Kmin (18.21) phy is used not only to determine the failure mechanism but also the origin of fracture. Examples of where frac- Figure 18.11a shows a schematic log–log plot of the crack tography is used include growth rate (dc/dN), N is the number of cycles, against ΔK. We can identify three distinct regions:  Dentistry, e.g., examination of teeth to improve survivability Region I: The lower limit to the curve ΔKT is the threshold  Liability cases, e.g., hip implants to determine who is stress intensity factor range for crack growth. In this to blame range crack growth with cyclic loading is negligible,  Disasters, e.g., space shuttle tiles to make sure prob- if indeed it occurs at all. lems do not reoccur Region II: The plot is linear and the crack growth rate can be described by the following equation (sometimes Figure 18.12 illustrates two different crack paths called the Paris–Erdogan equation): through a material. In Figure 18.12a the crack passes between grains and the fracture is termed intergranular. dc/dN = B(ΔK) q (18.22) Intergranular fracture is most likely when the grain boundaries are weak. A striking example of intergranular B and q are materials constants, which are determined fracture is shown in Figure 18.13a. The ceramic is AlN, empirically. which was prepared by sintering with Y2O3 added as a 332 ............................................................................................................................................. F r ac t u r i ng : Br i t t len e s s  σ Surface pore direction of crack propagation σ (A) (A) (B) FIGURE 18.12 (a) Illustration of intergranular cracking. (b) Illustration of transgranular cracking. sintering aid. The individual grains, which are faceted, can be clearly seen in the scanning electron microscopy (SEM) image. In transgranular (or cleavage) fracture the crack passes through the grains as illustrated in Figure 18.12b. The (B) fracture surface may be smooth or show steps, which form FIGURE 18.13 (a) The fracture surface of polycrystalline AlN. (b) as the crack front moves for one plane to another. Figure The fracture surface of polycrystalline SiC. 18.13b shows transgranular fracture in polycrystalline SiC. In conchoidal fracture there are no distinct cleavage planes. As mentioned earlier, conchoidal fracture occurs Origin Origin in flint, cubic zirconia, diamond, and glass. When fracture surfaces are examined, in addition to determining the failure mechanism we also are often interested in the origin of fracture, which in turn might 180° L help identify the cause. By reassembling the pieces and looking for where cracks come together as illustrated in Bending Figure 18.14 it is possible to determine crack initiation sites. These may be associated with flaws (e.g., pores or Point inclusions) introduced during processing. loading The extent of crack branching provides information about the amount of energy associated with crack propa- gation. There will be more branching if the applied stresses Origin 90° are large or if there are large residual stresses that are released as the crack advances. The latter principle is uti- Origin lized in tempered glass. Extensive crack branching occurs 15° causing the glass to eventually break into many small pieces. In glasses it is often quite easy to determine the origin Internal of fracture as shown in Figure 18.15. We can identify three Torsion pressure distinct regions on the fracture surface: FIGURE 18.14 Determination of crack origin and failure mecha- nism by postmortem examination of glass fragments. 18 . 8 Fa i l u r e a n d F r a c t o g r a p h y ................................................................................................................................ 333  FIGURE 18.15 Fracture surface of a glass rod and corresponding schematics illustrating the distinct regions of the surface. (A) Source of failure Hackle Mist Mirror N 2rh 2rm 2b N a Hackle region Mist region Smooth mirror region (B) (C) (D) Mirror: The region around the crack origin. The crack Hackle: Crack branches forming larger ridges, further travels in a single plane accelerating as it goes. The increasing the roughness of the fracture surface. By fracture surface is smooth and highly reflective. This tracing the hackle lines backward we can usually can be seen in polycrystalline ceramics, but reflectivity determine the origin of fracture. is lower. Mist: The crack deviates either because it reaches a Hackle is also referred to as river patterns because the critical velocity, intersects an inclusion, or there is appearance is similar to a river branching into tributaries. a change in the internal stresses in the glass. The Figure 18.16 illustrates river patterns on the fracture fracture surface is rougher and less reflective. This surface of an Nd-doped YAG single crystal that fractured region is often difficult to see in polycrystalline during growth. The irregular shaped voids seen in the ceramics. image are where failure originated. 334 ............................................................................................................................................. F r ac t u r i ng : Br i t t len e s s  Ultimate Stress strength, σm σ Matrix cracking, σ0 Fiber pullout EC 1 Strain, ε FIGURE 18.17 Schematic stress–strain curve for a tough fiber- reinforced ceramic matrix composite. FIGURE 18.16 SEM image of the fracture surface of Nd-doped reinforcing the ceramic matrix [e.g., a lithium aluminosili- YAG. River marks are indicated by arrows. cate (LAS) glass ceramic] with fibers (e.g., SiC) produced the desired toughening. The resulting fracture surface would look like that shown in Figure 18.18. Toughening is achieved by bridging of the crack surfaces behind the crack tip by the strong reinforcing phase. The stress intensity at 18.9 TOUGHENING AND CERAMIC the crack tip is reduced, which slows crack propagation. MATRIX COMPOSITES The fibers absorb energy as the crack front advances. An additional energy-absorb- Ceramics usually have low TOUGHENING ing process that often fracture toughness. For We want to increase Gc to toughen the ceramic. accompanies crack bridg- many engineering applica- ing is fiber pullout away tions we must increase the from the crack plane as toughness. The desire to toughen ceramics is not new. illustrated in Figure 18.19. Toughening of brick using straw was known in 9000 bce. The following factors contribute to the fracture tough- The basic idea is how to stop crack movement thereby ness of a composite: increasing the amount of energy required for crack propagation. The toughening mechanisms for ceramics are summa- rized in Table 18.6. A stress–strain curve for a toughened ceramic is shown in Figure 18.17. In this particular case, TABLE 18.6 Classification of Toughening Mechanisms in Ceramics General mechanism Detailed mechanisms Crack deflection Tilt and twist out of the crack plane around grains and second-phase additions Crack bowing Bowing in the crack plane between second-phase crack-pinning points Crack branching Crack may subdivide into two or more roughly parallel cracks Crack tip shielding by Microcracking process zone activity Transformation toughening Ductile yielding in process zone Crack tip shielding by Second-phase brittle fibers with partial crack bridging debonding Frictional and ligamentary grain bridges FIGURE 18.18 SEM image showing fiber pullout on the fracture Second-phase ductile ligament bridging surface of AlPO4-coated alumina/mullite fiber/Al2O3 CMC, hot pressed at 1250°C for 1 h. 18 . 9 To u g h e n i n g a n d C e r a m i c M at r i x C o m p o s i t e s .............................................................................................. 335  For the specific case in which toughening is due to r elastic deformation of a partially debonded reinforcement xDB with no interfacial friction, KIc has been determined to be umax K Ic = {E c Gm + σ 2f [ (rVf E c γ f ) / (12E f γ i ) ]} (18.23) l DB The subscripts c, m, and f refer to the composite, matrix, λ Fc and reinforcement, respectively. Increases in fracture toughness are predicted by  Increasing Vf  Increasing Ec /Ef  Increasing γf/γi The last bullet implies that toughness is enhanced when the interface between the fiber and the matrix is weak. u The crack will then pass around the fiber as shown in Figure 18.21. An important toughening mechanism involves a phase transformation in zirconia (ZrO2). The best-known FIGURE 18.19 Illustration of a crack bridging mechanism with example is zirconia-toughened alumina (ZTA), which debonding and fiber pullout. contains 10–20 vol% of fine ZrO2, particles. At elevated temperatures the equilibrium structure of ZrO2 is tetrago- nal (t) and at low temperatures it is monoclinic (m). On  Volume fraction of reinforcement. Figure 18.20 shows cooling ZTA from the high temperatures required for fab- how fracture toughness increases for SiC whisker- rication the t → m transformation may occur in the zir- reinforced ceramics as a function of increasing whisker conia particles. This transformation is accompanied by content. an increase in volume of about 3%.  Young’s modulus of matrix and reinforcement. If a The transformation is athermal, i.e., it is not time matrix is reinforced with high modulus, high strength dependent and proceeds very rapidly. If the transformation fibers then more of the stress can be carried by the takes place in the ZrO2 particles during fabrication of ZTA fibers. ceramics, then the 3% volume change produces stresses  Strength of the matrix/reinforcement interface. In in the alumina matrix around the transformed particle fiber-reinforced composites a strong interface can lead leading to microcracking. These microcracks increase the to transfer of the stress from the matrix to the fibers; toughness of the ceramic by their ability to deflect and a weak interface can lead to debonding and crack deflection. Composite Alumina K1c 8 1 MPa.m 2 Mullite 4 Glass 0 0 20 40 SiC whisker content (vol.%) FIGURE 18.21 SEM image showing crack propagation around a FIGURE 18.20 The effect of SiC whisker content on toughness sapphikon (Al2O3) fiber in a calcium aluminosilicate (CAS) enhancement in different matrices. glass-ceramic. 336 ............................................................................................................................................. F r ac t u r i ng : Br i t t len e s s  Wake of Original metastable process region Plastic tetragonal region zirconia particle w Process region rc Martensitically transformed zirconia particle Wake of plastic region S Compressive stress field around crack tip FIGURE 18.22 Illustration of transformation toughening in a ceramic matrix containing ZrO2 particles. bifurcate a propagating crack. Control of the extent of the It is important to note that in contrast to ZTA microcracking determines the increase in toughness. The toughened by microcracking, transformation toughening optimum conditions are when the particles are large can lead to an improvement in both toughness and enough to transform but only small enough to cause strength and, consequently, is the preferred toughening limited microcrack development. If microcracking mechanism. becomes extensive then the cracks can interact resulting The effectiveness of the different toughening mecha- in a decrease in strength. Zirconia particle size is control- nisms for structural ceramics appears to decrease in the led by following order:  Milling prior to sintering  Continuous fiber reinforcement—most effective  Aging after sintering  Metal dispersed particles  Transformation toughening If a stabilizing oxide, say 3 mol% Y2O3, is added to the  Whiskers/platelet/particle reinforcement zirconia then it is possible to suppress the t → m transfor-  Microcracking—least effective mation on cooling from the fabrication temperature. The ZrO2 particles can be retained in the metastable tetragonal form at room temperature. Whether the transformation Some examples and associated toughness values are takes place depends on the amount of stabilizing oxide given in Table 18.7. It is worth remembering that although and the particle size. The presence of the alumina matrix the values are higher, in some cases by an order of mag- makes it difficult for the volume expansion associated with nitude, than for single-phase polycrystalline ceramics, the transformation to be accommodated. The constraint is they are still much lower than most engineering metal such that small particles are less likely to transform than alloys. large particles. With a suitable combination of amount of stabilizing oxide and particle size it is possible to obtain a dispersion of metastable tetragonal particles. Under the influence of the stress field at a cracktip TABLE 18.7 The Effect of Different Toughening these particles will transform athermally to the mono- Mechanisms clinic state. This leads to transformation toughening and Highest value Exemplary the toughening increment ΔKT that can be achieved by this Mechanism achieved (MPa·m1/2) systems mechanism is Continuous fiber >30 SiC–SiC; glass–SiC ΔKT = AVZrO2 εT Em w1/2 (18.24) reinforced >25 Glass-ceramics–SiC ∼16 Si3N4 –SiC Metal dispersed ∼25 Al2O3 –Al; Al2O3 –Ni A is a constant with a value close to unity, Vzirc is the Transformation ∼20 ZrO2 (MgO) volume fraction of the metastable particles, εT is the Platelet ∼14 Si3N4 –SiC volume strain accompanying the transformation, Em is Whisker ∼11 Si3N4 –SiC Young’s modulus of the matrix (often alumina), and w is ∼8.5 Al2O3 –SiC Particle ∼8 Si3N4 –SiC the width of the process zone around a crack containing Microcracking ∼10 Al2O3 –ZrO2 transformed particles (shown in Figure 18.22). 18 . 9 To u g h e n i n g a n d C e r a m i c M at r i x C o m p o s i t e s .............................................................................................. 337  18.11 WEAR Wear resistance is the ability of a material to resist mechanical (or chemical-mechanical) abrasion. There are two main mechanisms that lead to removal of material from the surface of a ceramic:  Grain pullout: In polycrystalline ceramics with weak grain boundaries  Cracking: Fracture due to abrasion, gouging, or erosion Wear resistance is usually closely associated with hard- ness and corrosion resistance. For example, Table 18.9 shows how erosion resistance correlates very directly with hardness. Erosion usually specifies wear of a material by FIGURE 18.23 The fracture surface of Macor ®. an abrasive in a fluid, the type of situation encountered when ceramics are polished. Although ceramics are generally characterized as being wear resistant their commercial use as wear parts is 18.10 MACHINABLE GLASS-CERAMICS less than 10% of the overall market. Alumina is the most commonly used wear-resistant Machinable glass-ceramics (MGCs) rely on controlled ceramic. One of the early applications was in seal faces fracture. In Macor®, a commercial MGC made by Corning, for rotary water pumps for automobiles. Alumina is par- the crystalline phase is fluorophlogopite mica. The mica ticularly suitable because it is resistant to engine cooling forms as randomly oriented grains in a borosilicate glass fluids. Another application for alumina, which we men- matrix. During machining cracks propagate along the tioned in Chapter 16, is in total hip prosthesis. In terms of glass–mica interface (intergranular) and material is wear rates at the contact surfaces between the ball and removed. Figure 18.23 shows the fracture surface of socket, alumina is far superior to alternative metal and Macor® where the mica crystals, which look like packs of polymer systems. cards, can be clearly seen. MGCs can be machined using Alumina and toughened zirconia ceramics are used either high-speed steel or tungsten carbide cutting tools. in the wire drawing industry as capstans, pulleys, and They can be used at high temperatures (up to 1000°C) and guides. Improved product quality, longer component because of their high chemical resistance they are used for service life, and lower manufacturing costs have been precision valves and nozzles in the chemical industry. attributed to the use of ceramics. For example, ceramic Table 18.8 lists the composition of Macor® and some of capstans last up to 10 times longer than carbide-coated its properties. capstans. As with other mechanical properties there are standard tests to measure wear resistance. The main method is described in ASTM G99, which uses a pin-on-disk appa- TABLE 18.8 Composition (wt%) and Properties of Macor ® MGC ratus. This test is used to measure sliding wear of ceramics and ceramic coatings. SiO2 Al2O3 B 2O 3 K2O MgO F 46 16 7 10 17 4 Property Value TABLE 18.9 Erosion Resistance versus Hardness for Coefficient of thermal expansion (ppm/°C) 7.4–12.6 Several Ceramics Thermal conductivity (W m−1 °C−1) 1.46 Material (in order of increasing Continuous operating temperature (°C) 800 erosion resistance) Knoop hardness (kg/mm2) Maximum no-load temperature (°C) 1000 Density (g/cm3) 2.52 MgO 370 Young’s modulus at 25°C (GPa) 66.9 SiO2 820 Poisson’s ratio 0.29 ZrO2 1160 Shear modulus at 25°C (GPa) 25.5 Al2O3 2000 Knoop hardness, 100 g load 250 Si3N4 2200 Modulus of rupture at 25°C (MPa) 94 SiC 2700 Compressive strength (MPa) 345 B 4C 3500 Fracture toughness (MPa·m1/2) 1.53 Diamond 7000–8000 338 ............................................................................................................................................. F r ac t u r i ng : Br i t t len e s s  Abrasive polishing Pressure grains Workpiece Resilient pad Adhesive Polishing wheel FIGURE 18.24 Illustration of the polishing process using abrasive grains held in a soft pad. This method is the one most often used in university metallography laboratories. TABLE 18.10 Hardness of Selected Abrasives Used in the Polishing of Ceramics Abrasive Mohs hardness Knoop hardness Zirconia 8 1160 Garnet 8 1360 Calcined alumina 9 2100 Silicon carbide 9–10 2480 Boron carbide 9–10 2750 Cubic boron nitride 10 4500 Diamond 10 7000 18.12 GRINDING AND POLISHING Grinding and polishing both use controlled fracture. Abrasives are the basis of an important ceramic industry. FIGURE 18.25 SEM image of ceria particles in a modern polishing For example, the abrasive used in Emory paper is SiC; cloth. sand paper uses SiO2. The historically important abrasive was jeweler’s rouge (hematite). Now ceria (CeO2) is often preferred for glass and ceramics and colloidal silica (e.g., Chemical/mechanical polishing (CMP) may also be SytonTM) is used for Si. Abrasive particles are almost used. In this case an abrasive is used together with a always ceramics (usually oxides, carbides, or diamond). chemical (usually either an acid or a caustic solution) that The polishing action actually involves an interaction will produce an etching action. CMP is actually very between two surfaces with the second surface being the complex and still not fully understood. Final CMP may abrasive particle. Figure 18.24 illustrates mechanical pol- involve an abrasive that is softer than the materials being ishing using abrasive grains held in a soft pad. Table 18.10 polished. lists some of the common abrasives used for polishing An example of a modern commercial polishing cloth ceramics together with their hardness. is shown in Figure 18.25. The pyramids are particles of The abrasive is often applied as a slurry onto a soft ceria bound in a polymer on a flexible cloth. This type of pad. A series of polishing steps are used, with abrasives fixed abrasive has an advantage over a slurry in that the with decreasing particle size (eventually down to as low abrasive is well controlled and can be easily changed/ as 4 nm). The final step produces a smooth specular renewed and there is always a clear channel for the elec- surface, which is good enough for film deposition. trolyte to reach the polishing site. CHAPTER SUMMARY Although we often think of the brittleness of ceramics as a distinct disadvantage, the very existence of our civilization depended on this property. We make use of brittleness in many applications, such as sculpture and in polishing, but for reliable structural uses we often need better fracture toughness. One way to achieve this is to form a composite by adding some fibers to a ceramic matrix. The fibers provide additional mechanisms for energy absorption during fracture. The key work in understanding brittle fracture goes back to that of Griffith. He showed C h a p t e r S u m m a ry .......................................................................................................................................................... 339  that flaws act as stress concentrators, which lead to measured strengths significantly lower than those predicted by theory. The work of Griffith is the link to the Weibull statistics described in Chapter 16. By examining fracture surfaces, a process called “fractography,” we can often determine how and why a brittle material failed. This information can be useful in guiding processing methods to avoid stress concentrators such as porosity and inclusions. PEOPLE IN HISTORY Griffith, Alan Arnold (1893–1963), was known as “The Father of Fracture Mechanics” and “Bubble Griffith,” the first for his classic work in fracture mechanics and the role of flaws and the second for his work on soap films. He was a British aeronautical engineer who worked at Rolls-Royce from 1939 to 1960 design- ing turbojet engines. Inglis, Sir Charles Edward (1875–1952), professor of Engineering at Cambridge University, was best known for his wok on stress in metal plates when cracks are present. Orowan, Egon (1901–1989) was born in Budapest, Hungary and died in Cambridge, Massachusetts. In addi- tion to his work on fracture, he showed the importance of dislocation in plastic deformation. He joined MIT as a professor in 1950. GENERAL REFERENCES Davidge, R.W. (1979) Mechanical Behaviour of Ceramics, Cambridge University Press, Cambridge, UK. Green, D.J. (1998) An Introduction to the Mechanical Properties of Ceramics, Cambridge University Press, Cambridge, UK. Hull, D. (1999) Fractography, Cambridge University Press, Cambridge, UK. Lawn, B. (1993) Fracture of Brittle Solids, 2nd edition, Cambridge University Press, Cambridge, UK. Tabor, D. (2000) The Hardness of Metals, Oxford University Press, Oxford, UK. Reprint of the 1959 classic. Very readable. Wachtman, J.B. (1996) Mechanical Properties of Ceramics, Wiley-Interscience, New York. SPECIFIC REFERENCES Garvie, R., Hannick, R.H.J., and Pascoe, R. (1975) “Ceramic steel?” Nature 258, 703. First description of transformation toughening. Griffith, A.A. (1920) “The phenomenon of rupture and flow in solids,” Phil. Trans. R. Soc. Lond. A221, 163. (1924) “The theory of rupture,” Proc. 1st Int. Cong. Appl. Mech. p. 55. Inglis, C.E. (1913) “Stresses in a plate due to the presence of cracks and sharp corners,” Trans. Inst. Naval Archit. A127, 219. The Inglis equation (Eq. 18.13). Johnson, J.W. and Holloway, D.G. (1966) “On the shape and size of the fracture zones on glass fracture sur- faces,” Phil. Mag. 14, 731. Also “Microstructure of the mist zone on glass fracture surfaces,” Phil. Mag. 17, 899. Obreimoff, J.W. (1930) “The splitting strength of mica,” Proc. R. Soc. Lond. A127, 290. Early study of the fracture of mica (Section 18.3). Orowan, E. (1949) “Fracture and strength of solids,” Rep. Prog. Phys. 12, 185. EXERCISES 18.1 Carbon nanotubes have been proposed as a material for the next generation of ceramic armor. (a) What are the properties of carbon nanotubes that make them of interest for this application? (b) Are there practical limitations that are currently preventing their widespread use? 18.2 Calculate the theoretical strength of MgO. Are there any conditions under which this value would be attainable? 18.3 A sharp notch 0.1 mm long is introduced into the surface of a fused silica plate. The plate is then loaded to 100 MPa in tension normal to the notch. (a) Will the plate fracture? (b) If not, what is the applied stress that would lead to fracture? (c) If the plate was made of an LAS glass-ceramic what applied stress would lead to fracture? 18.4 A soda-lime silica plate failed at 100 MPa. (a) Estimate the flaw size and state any assumptions you make. (b) If the plate were made of fused silica and contained the same flaw size what is the maximum applied stress it could withstand without breaking? Assume the glass has E = 70 G Pa. 18.5 A manufacturer of silicon nitride jet engine parts found that a recent batch of samples became damaged during processing and had surface flaws about 50 μm deep. The normal average flaw size in these parts is about 10 μm. (a) Estimate the tensile strength of these samples. (b) Estimate the compressive strength of these samples. 340 ............................................................................................................................................. F r ac t u r i ng : Br i t t len e s s  18.6 You have been hired as a consultant and asked to choose the best ceramic for a load-bearing application. A vendor has offered you the following options; which one would you take and why? Are there any other factors that you need to consider before you make your final recommendation? Maximum flaw size Average flaw size Ceramic (μm) (μm) Si3N4 20 15 SiC 30 18 MgO 10 7 Al2O3 5 3 18.7 In Table 18.6 we list different toughening mechanisms for ceramic–matrix composites (CMCs). Illustrate each mechanism using a sketch and, where appropriate, indicate the differences between using particles, platelets, and fibers as the reinforcement. 18.8 Explain how the addition of zirconia particles can lead to toughening of a ceramic. Suggest other additions that might produce similar toughening effects. 18.9 Draw sketches similar to Figure 18.10 to indicate how (a) ammonia and (b) methanol might lead to stress corrosion cracking in glass. 18.10 Figure 18.13a shows the fracture surface of polycrystalline AlN. Can you see any evidence of transgranular failure? C h a p t e r S u m m a ry .......................................................................................................................................................... 341 Part VI Processing  19 Raw Materials CHAPTER PREVIEW In this chapter we look at several important raw materials used in the ceramics industry. Obtaining the necessary raw materials is the first step in the fabrication of ceramic components. This topic used to be addressed by many Departments of Mining and Mineral Engineering. It is no less important today, but few such departments still exist. There are two basic sources for these raw materials:  Naturally occurring minerals  Synthetic minerals For naturally occurring minerals we will describe, in general terms, their origin, the loca- tions in which they can be found, and their relative abundance. Naturally occurring minerals require extraction, which is often a regional industry located close to abundant quantities of the natural deposit. Most minerals need to go through some form of physical or chemical pro- cessing before use. The collective term for these processes is beneficiation. When you under- stand how oxides are manufactured, it will be clear why they are often impure and why Si, Na, Ca are the major impurities. Materials that do not occur in nature or are rare must be synthesized (so calling them minerals is a misnomer) and we describe the processes used for their synthesis. Carbides, nitrides, and borides are becoming more common, but are generally expensive and require special processing environments. For many nonoxides the main impurities are often compo- nents of the starting material that have not reacted, e.g., Al in AlN or Si in Si3N4. There are many other raw materials that play important roles in specific ceramics, but rather than providing a comprehensive discussion about every raw material, we focus on representa- tive examples of naturally occurring minerals and synthetic ones. There are two ways of looking at this topic: the mineral we start from and the material we want to form. Here, we mix the two approaches. 19.1 GEOLOGY, MINERALS, AND ORES and Fe silicates, free Fe, and minor Fe sulfides. Minerals in the mantle (and the core) are presently not accessible; Figure 19.1 shows a schematic cross section of the earth. for this reason we will not discuss them further. However, The earth has a mean radius of about 6370 km and consists geologists can identify rocks that have moved from the of three distinct concentric layers. The outermost layer is mantle to the crust by natural processes. An ore is defined known as the crust and is relatively thin. The continental as a mineral from which a constituent can be profitably crust ranges in thickness from about 20 to 60 km, averag- mined or extracted. Examples include hematite (Fe2O3), ing approximately 30 km. It is the minerals that occur here which is the major ore of Fe, and ilmenite (FeTiO3), which that are important to us as raw materials for ceramics. is the major ore of Ti, but is also an Fe-containing mineral. The continental crust is composed primarily of the Pyrophanite (MnTiO3) is neither a Ti nor Mn ore, but is silicates of Mg, Fe, Al, and Ca, and the alkali metals plus actually a rare mineral. Al and free SiO2. Table 19.1 lists the abundance of the major elements in the continental crust. From this you can see that O, Si, and Al together account for almost 90 wt% of the elements in the crust. 19.2 MINERAL FORMATION Beneath the earth’s crust is the mantle. This Minerals are the constitu- thick layer is thought to be MINES ents of rocks, which make composed of Mg silicates The deepest mine is ∼5 km deep. up the entire inorganic, 19. 2 M i n e r a l F o r m at i o n ............................................................................................................................................. 345  Crust 30 km ρ=2.2x103 kg.m-3 TABLE 19.2 Major Oxides in Igneous Rocks and Their P=1 atm Ranges of Composition Rocky Mantle Constituent (oxide) Concentration (wt%) 25 °C 2900 km SiO2 30–78 Core Al2O3 3–34 Fe2O3 0–5 P=136 GPa 5200 km FeO 0–15 Inner Liquid MgO 0–40 Core Fe,S Plastic CaO 0–20 Mg,Fe r=6370 km Al,Si,O Na 2O 0–10 Solid Fe K 2O 0–15 ρ=12.8x103 kg.m-3 P=329 GPa 1000 °C 4300 °C 3700 °C FIGURE 19.1 Schematic cross section of the earth. solid portion of the earth. IGNEOUS ROCK Figure 19.2. Olivine and Rocks are usually not com- Granite: magma cooled near the earth’s surface Ca feldspar form at high posed of a single mineral; Rhyolite: fine grain granite temperatures and may sep- rather they are an aggre- Obsidian, pumice and scoria: volcanic origin arate early from the melt. gate of two or more miner- Basalt: very small grains of usually rapidly cooled lava Other minerals solidify as als. Broadly speaking, Gabbro: like basalt, but has larger grains the temperature falls. The geologists divide rocks into Mafic: dark igneous (e.g., basalt) last minerals to crystallize three types: igneous, meta- Intermediate: e.g., diorite; Mg and Fe rich are K feldspar, muscovite morphic, and sedimentary. Felsic: light igneous (e.g., granite); quartz rich mica, and quartz, the major Igneous rocks form constituents of granite. when magma cools and Finally, water in the magma solidifies. Magma is a complex molten material that origi- carries metals and S in solution through cracks in the sur- nates deep within the earth. The word igneous comes from rounding rock and deposits them as sulfides in veins. the Latin word ignis, which means “fire”; igneous rocks Metamorphic rocks have undergone structural and/or then are “formed from fire.” Magma is rich in the elements chemical transitions (metamorphism or metamorphosis) Si, O, Al, Na, K, Ca, Fe, and Mg. Table 19.2 shows the composition ranges for the major elements (expressed as oxides) in igneous rocks. These are the elements that when combined with SiO2 form the silicate minerals. A limited Complex silicate solution number of silicate minerals accounts for over 90% of all (Magma) igneous rocks. Mafic No Fe/Mg All silicate minerals contain tetrahedral silicate [SiO4] Olivines groups. Classification of the silicate minerals is based BOWEN’S Ca feldspars Isolated SiO4 REACTION upon the way in which these groups combine, as described SERIES in Chapter 7. The specific mineral crystallizing from magma depends Pyroxenes Ca/Na feldspars both on the composition and temperature of the magma. Single chains Framework silicates The order of crystallization of the main silicate minerals 1400 °C is given by Bowen’s reaction series, which is shown in Amphiboles Na/Ca feldspars Double chains Increasing Na TABLE 19.1 Abundances of the Major Elements in the Continental Crust Biotite mica Na feldspars Element wt% at% vol% of ion Sheets Oxygen 47.2 61.7 93.8 Silicon 28.2 21.0 0.9 Potassium feldspars Aluminum 8.2 6.4 0.5 Muscovite mica Quartz Total Iron 5.1 1.9 0.4 Calcium 3.7 1.9 1.0 800 °C Sodium 2.9 2.6 1.3 Aqueous solutions of sulfur, Potassium 2.6 1.4 1.8 transition metals, semimetals, Magnesium 2.1 1.8 0.3 and silica Hydrogen trace 1.3 0.0 FIGURE 19.2 Bowen’s reaction series. 346 ................................................................................................................................................................ R aw M at e r i a l s from their original form as a result of high temperatures Igneous Rocks are formed by cooling and solidifica- and pressures deep beneath the earth’s surface. These tion of magma. transitions occur in the solid state without melting and Metamorphic Rocks have undergone structural and/or result in the formation of new minerals, such as kyanite, chemical transitions. staurolite, sillimanite, andalusite, and some garnets. Other Sedimentary Rocks are formed when smaller particles minerals, such as some of the igneous minerals, may be become cemented. present in metamorphic rocks, although they are not nec- essarily the result of metamorphism. The word “metamorphic” has a Greek origin coming 19.3 BENEFICIATION from meta meaning “change” and morphe meaning “shape.” Beneficiation is the process through which most minerals Sedimentary rocks are formed when small particles need to go before they can be used to produce ceramics. or precipitated crystals become cemented together. Physical beneficiation includes crushing and grinding of Sedimentary rocks are classified as either clastic or coarse rocks. The particle size of the raw material may chemical. affect subsequent steps in the production process. An Clastic sedimentary rocks form when rock particles example that we use is producing alumina from bauxite, produced by mechanical and chemical weathering are a process that involves a chemical reaction. transported by water, ice, and wind to new locations where Chemical beneficiation includes processes of separat- they become cemented together. ing the desired mineral from unwanted waste products, for Chemical sedimentary rocks form when highly soluble example, by dissolution in a suitable solvent followed by ions, such as Na + , K+ , Ca2+ , Mg2+ , Cl−, F−, (SO4) 2−, (CO3) 2−, filtration. The Bayer process for producing alumina is also and (PO4)3−, from existing rocks are dissolved in water a good example of chemical beneficiation. Bauxite con- and subsequently precipitate forming layers in oceans and tains many impurities. lakes where they become cemented together. The composi- The purity of the raw materials will be reflected in tion of sedimentary rocks depends on the the composition of the final product. For many ceramics careful control over purity is required. For these applica-  Composition of the original source rocks tions the raw materials are synthesized. Furthermore,  Chemical and mechanical resistance of each mineral several important ceramics do not occur naturally in component mineral form and must be fabricated chemically. Synthe-  Distance traveled sis of ceramic powders can have advantages not only in purity but also in allowing the generation of fine particle- Resistant minerals such as quartz are common con- sized powders having a well-defined morphology. We will stituents of sedimentary rocks, and some more rare miner- show in Chapter 24 the importance of particle, size on the als (e.g., garnet, rutile, and zircon) have similar properties. densification of a ceramic component by sintering. Feldspar is less resistant, but is so common that it is a major constituent of many sedimentary rocks. Precipitated minerals include the carbonates (e.g., calcite and dolo- 19.4 WEIGHTS AND MEASURES mite), sulfates (e.g., gypsum and anhydrite), chlorides, and chalcedonic silica (e.g., chert and flint). The SI unit of mass is the kilogram (kg), which is interest- The three rock types are compared below; Figure 19.3 ing for a few reasons. It is the only basic SI unit defined shows what is called the rock cycle. with a prefix (kilo) already in place, and it is the only one defined by reference to a physical object—a mass of platinum-iridium held at Sevrès in France. To express the Molten Rock large quantities of material that we encounter in the extraction and processing of ores it is usual to use the Melting metric ton (sometimes written tonne: symbol t): Melting Cooling 1 t = 1 Mg = 103 kg Igneous Heat & Metamorphic Rock Pressure Rock Possible confusion exists because of special British and Weather U.S. units that are still in use in these countries. Weather Erosion Erosion Heat & Pressure 1 t = 0.984 UK (long) ton Weather Sediments Erosion Sedimentary 1 t = 1.103 US (short) ton Rock Compaction & Cementation The situation is even more complicated in the FIGURE 19.3 Simplified diagram of the rock cycle. UK where the short ton is often used in mining 19. 4 We i g h t s a n d M e a s u r e s ....................................................................................................................................... 347 metal-containing ores, but the long ton is used in coal TABLE 19.3 Abundance of Minerals in the Earth’s Crust mining. We will use the metric ton (written simply as ton) Mineral groups vol% unless specifically stated otherwise. You can see that for “ballpark” estimates of mass it really does not make much Feldspars 58 difference. When we discuss single crystals in Chapter 29 Pyroxenes, amphiboles 13 Quartz 11 we will introduce units of mass that are used to describe Micas, chlorites, clay minerals 10 very small quantities of a material. Carbonates, oxides, sulfides, halides 3 Determining the quantity of all commercial minerals Olivines 3 produced is straightforward. The United States Geological Epidotes, aluminosilicates, garnets, zeolites 2 Survey maintains updated information on their website in the form of Mineral Commodity Summaries and the Minerals Yearbook. These sources provided most of the such as a certain grain size or shape, the geographic market numbers given in this chapter. Obviously, like all com- of a plant rarely extends beyond 200 miles. This is because modities, the production of minerals may vary from year of the high transportation cost relative to the price of the to year based on many different factors such as supply, materials and the extensive location of mines. demand, and reserves. The problems at the end of this In recent years, environmental regulations have been chapter will help you think about some of those factors placed on the mining of silica sand due to health risks for specific minerals. associated with this product. Quartz, the principal silica mineral, is a constituent of igneous rocks such as granite. It is also found in most 19.5 SILICA metamorphic rocks, comprising a major portion of the sandstones, as well as in the pure form in veins running Silica (SiO2) is an important raw material for ceramics. through other rocks. Optical quality quartz crystals are The major use (accounting for about 38% of U.S. produc- quite rare, but there are economically viable methods to tion) is in glass manufacture. For example, incandescent produce quartz crystals as we will see in Section 29.11. lamp bulbs are made of a soda-lime silicate glass contain- ing about 70 wt% SiO2. The SiO2 content of high-quality optical glasses can be as high as 99.8 wt%. 19.6 SILICATES A major source of silica is sand. Industrial sand and silica sand are two terms used by the ceramics industry We discussed the silicates in Chapter 7. Here we discuss for sands that have a high percentage of SiO2. In some of the use of these materials to form commercial ceramics. the high-quality silica sand sources mentioned below the SiO2 content is >99.5%. Feldspar 70% is used for glass. Sand is defined by the American Society for Testing Kaolin It is used in fine china, paper, and rubber. and Materials (ASTM) as granular rock particles that pass Mica Over 200,000 t of low-quality mica is used through a No. 4-mesh (4.75-mm aperture) U.S. standard each year. sieve, are retained on a No. 200-mesh (75-μm aperture) Mullite 600,000 t is used each year for refractory sieve, and result from the natural disintegration or com- furnace blocks. minution of rock. Sands are also produced by physical beneficiation of rocks by crushing. These sands have Feldspar various chemical compositions, determined by the type of rock being mined. Feldspars constitute an abundant mineral group and make The United States is the largest producer of industrial up an estimated 60% of the earth’s crust, as shown in sand in the world. The states of West Virginia, California, Table 19.3. They are present in many sedimentary deposits Illinois, Pennsylvania, Ohio, and New Jersey supply about and are found in almost all igneous and metamorphic 80% of all the high-quality silica sand used domestically. rocks. In Illinois and Missouri, practically all the glass-grade The glass industry uses most of the feldspar produced. silica is derived from the St. Peter sandstone formation. Feldspar is a source of Al2O3, which improves the mechani- Other quality deposits are the Oriskany sandstone cal properties of glass such as its scratch resistance and deposits in West Virginia and Pennsylvania. Deposits its ability to withstand thermal shock. It is also used in are usually found in dune forms or in deposits lying 20– whiteware bodies as a flux, which produces a glassy phase 30 m under layers of silts, clays, and shales. during firing increasing the strength and translucency of The mining of indus- the body. trial silica is, in general, The Republic of Korea a regional market. Unless SILICA PRODUCTION is the largest producer of the material possesses Annual production of silica in the United States is feldspar in the world. unique characteristics, approximately 30 Mt, valued at around $700 million. Annual feldspar produc- 348 ................................................................................................................................................................ R aw M at e r i a l s tion in the United States is about 800,000 t with a value are distinguished by their composition, plasticity, color, of about $45 million. The largest producing states are and firing characteristics. North Carolina, Connecticut, and California. The typical Mechanical and chemical weathering of feldspars in procedure for processing feldspar deposits is igneous and metamorphic rocks forms kaolin, a key ingre- dient in China clay. It may be disintegrated in situ or  Drilling and blasting at the quarry transported by water or wind and redeposited elsewhere.  Transporting to a mill for crushing and grinding (phys- Primary kaolin deposits are located at the site of the origi- ical beneficiation) nal rock. These typically contain large amounts of quartz  Froth flotation separating the minerals according to and mica, which also formed during weathering. Large, their relative wettability in aqueous solution (chemical primary kaolin deposits are found in southwest England, beneficiation) the Ukraine, and China.  Drying Secondary kaolins were washed from the original  Grinding to a No. 20 mesh (841 μm aperture size) for weathering site, naturally beneficiated, and redeposited in glassmaking and below a No. 200 mesh (aperture size large areas of pure kaolin. The major commercial deposits 74 μm) for most other ceramic applications of secondary kaolin in the United States were formed 50 In the froth flotation process, air is bubbled through a million years ago and occur as a continuous belt stretching water suspension containing the crushed minerals to form along the ancient coastline from Alabama northeast to a foam or froth. The wetted particles (those that are hydro- North Carolina. philic) remain in the water suspension, whereas hydropho- bic particles collect at the air bubble/water interface and Mica can be removed from the liquid. Various agents, such as amino acids (having a high molecular weight), can be used The mica group consists of 37 minerals, known as phyl- to enhance the relative wettability of the solids in a losilicates, which have a layered or platy texture. The mixture; these agents are Greek word “phyllon” adsorbed selectively on the means leaf. Some of the MICA mica minerals are listed in surface of certain species The commercially important mica minerals are musco- in the mixture. The process Table 19.5 together with vite and phlogopite. the location of their princi- is carried out in stages: pal sources. The micas are 1. Remove mica classified as either true or brittle. 2. Remove iron-bearing minerals, especially garnet True micas contain univalent cations (e.g., Na + or K+) 3. Separate feldspar from a residue consisting mainly of between each set of layers and show perfect basal cleav- quartz age, allowing the crystals to be split into thin sheets. The cleavage flakes are flexible and elastic. In brittle micas, the interlayer cations are divalent (e.g., Clays and Kaolin Ca2+). The bond is stronger and although the layered struc- Clay is the primary ingredient in traditional ceramics ture still imparts basal cleavage they are more brittle. and is the general name given to the layer silicates with a Brittle micas are uncommon minerals and not of any real grain size < 2 μm. Any of the layer silicates could interest. qualify as a clay mineral. There are six types of Muscovite is the principal mica used because of its commercial clays and these are listed in Table 19.4. They abundance and superior electrical properties. Phlogopite TABLE 19.4 Commercial Clays, Their Main Uses, and Annual U.S. Production Type Main uses Annual U.S. Production (Mt) Comments Ball clay Floor and wall tiles 1.3 Also called “plastic clay” because it improves workability Sanitary ware Bentonite Foundry sand bond 4.4 The United States imports bentonite from Absorbents Canada Common clay Bricks 26 Also called “brick clay” Cement Red color comes from iron Fire clay Refractories 0.3 Fireclay refractories contain 25–45% alumina Fuller’s earth Absorbents 3.2 Textile workers (or “fullers”) cleaned raw wool by kneading it in a mixture of water and fine earth, which adsorbed oil, dirt, and other contaminants Kaolin Paper 7.2 Kaolinite is a hydrous aluminum silicate; kaolin is a white firing clay, primarily composed of kaolinite 19. 6 S i l i c at e s ................................................................................................................................................................. 349  TABLE 19.5 Principal Sources and Occurrence of Mica Minerals Mineral Chemical formula M, H, or O Type Source Muscovite KAl2 (Si3Al)O10 (OH) 2 M True United States, India, Brazil, Russia Phlogopite KMg3 (AlSi3O10 )(OH,F) 2 M,H True Madagascar, Canada, Mexico, Sri Lanka Paragonite NaAl2 (Si3Al)O10 (OH) 2 M True United States, Switzerland, Italy Biotite K(Mg,Fe) 3 (Al,Fe)Si3O10 (OH,F) 2 M,H True United States, Canada, Ireland, Scotland Lepidolite K(Li,Al) 3 (Al,Si) 4O10 (F,OH) 2 M,H,O True United States, Canada, Brazil, Sweden Zinnwaldite KLiFeAl(AlSi3)O10 )(F,OH) 2 M True United States, Brazil, Scotland, Germany Margarite CaAl2 (Al2Si2O10 )(OH) 2 M Brittle United States, Scotland, Italy, Austria Clintonite Ca(Mg,Al) 3 (Al3Si)O10 (OH) 2 M Brittle United States, Italy, Finland, Russia is stable at higher temperatures and is used in applications The largest producer of mica is Russia, which produces in which a combination of high heat stability and electrical about one-third of the world’s annual supply of 300,000 t. properties is required. Both are used in sheet and ground The United States produces about 75,000 t of scrap and forms. flake mica each year. Although historically the United Micas occur in igneous, sedimentary, and metamor- States was a producer of sheet mica, domestic reserves phic rocks in a great many contrasting geological environ- have declined to zero and commercial production is all ments. The reason for this range of occurrence is their scrap and flake. wide thermal stabilities. Figure 19.4 shows a pressure– The principal use for ground mica is as a filler and temperature diagram for muscovite mica. At very high extender in gypsum wallboard joint compounds where it temperatures (>600ºC) it becomes unstable, breaking produces a smooth consistency, improves workability, and down in the presence of quartz to give potassium feldspar prevents cracking. It is also found in paints, molded rubber and sillimanite. products including tires, and toothpaste. Mica flakes are being used as a replacement for asbestos in brake linings KAl2[Si3AlO10](OH)2 + SiO2 → KAlSi3O8 + Al2SiO5 + H2O and clutch facings. India is the largest producer of muscovite sheet mica. Muscovite Quartz K-feldspar Sillimanite Madagascar is the principal supplier of phlogopite sheet mica. The prices for sheet mica range from less than $1/kg Muscovite occurs in low-grade metamorphic rocks for low-quality material to more than $2,000/kg for the where it forms from pyrophyllite (Al4 [Si8O20](OH) 4) and highest quality. High-quality muscovite mica is used as a illite (K1–1.5Al4 [Si7–6.5Al1–1.5O20](OH) 4). It also occurs as a dielectric in capacitors. primary crystallizing mineral in igneous rocks, such as granites and pegmatites, and is a common constituent of sedimentary rocks, especially the arenites. Muscovite Mullite mica is locally common in many parts of the United States. Mullite (3Al2O3 · 2SiO2) does not exist in nature in large quantities and must be produced synthetically. It has many properties that make it suitable for high-temperature appli- 400 cations. Mullite has a very small coefficient of thermal Fluid expansion (giving it good thermal shock resistance) and Pressure Muscovite (MPa) K-feldspar is creep resistant at high temperature. Most importantly, + corundum +L it does not react readily with molten glass or with molten 300 metal slags and is stable in the corrosive furnace atmo- sphere. Hence it is used as a furnace lining and other refractory applications in the iron, steel making, and glass industries. 200 There are two commercial approaches to producing mullite: 100  Sintering  Fusing Sintered mullite may be obtained from a mixture of 0 kyanite (Al2OSiO4), a naturally occurring mineral found 400 500 600 700 800 900 in metamorphic rocks, bauxite, and kaolin. This mixture T (°C) FIGURE 19.4 Pressure–temperature phase relations for the bulk (in the correct ratio) is sintered at temperatures up to about composition K 2O · 3Al2O3 · 6SiO2–2H2O. 1600ºC. The sintered quality contains 85–90% mullite 350 ................................................................................................................................................................ R aw M at e r i a l s with the balance being mainly glass and cristobalite (a crystalline polymorph of SiO2). South Africa is the major producer of kyanite, about 165,000 t/year. The United States has the largest resource of kyanite and these are located mainly in the Applachian Mountains region and in Idaho. Andalusite and sillimanite are other aluminosili- cate minerals, similar to kyanite, that can be used as a raw material for mullite. By fusing the appropriate amounts of alumina and kaolin together in an electric-arc furnace at about 1750ºC a higher purity mullite can be made. The fused product contains >95% mullite, the rest being a mixture of alumina and glass. 19.7 OXIDES The raw materials used for oxide ceramics are almost entirely produced by chemical processes to achieve a high chemical purity and to obtain the most suitable powders for component fabrication. The important oxides are sum- marized in Table 19.6 and are discussed individually. FIGURE 19.5 Alcoa refinery in Wagerup, Western Australia that supplies 15% of the world’s alumina. Alumina Aluminum oxide (Al2O3, alumina, corundum) is the most Digestion: The coarsely ground bauxite is treated with widely used inorganic chemical for ceramics and is pro- a sodium hydroxide (NaOH) solution at 150–160ºC and duced from the mineral bauxite using the Bayer process. 0.5 MPa total pressure. Most of the hydrated alumina goes Bauxite is a mixture of hydrated aluminum oxide with into solution as sodium aluminate: iron oxide (Fe2O3), silica (SiO2), and titania (TiO2) impuri- ties. It results from the decay and weathering of aluminous Al(OH)3 (s) + NaOH (aq) → Na + (aq) + Al(OH) 4 − (aq) rocks, often igneous, under tropical conditions. Like kaolin, bauxite occurs as both primary deposits and sec- Filtration: The solid impurities, mainly SiO2, TiO2, ondary deposits. and Fe2O3, remain undissolved and are separated by The Bayer process produces a nominal 99.5% Al2O3 filtration. product. The alumina can be prepared in a range of grades Precipitation: After cooling, the filtered sodium alu- to suit specific applications. The grades differ by the size minate solution is seeded with very fine gibbsite [a natu- and shape of the crystals and the impurity content. The rally occurring hydrated alumina, α-Al(OH)3] and at the dominant impurity, accounting for up to 0.5%, is Na 2O. lower temperature the aluminum hydroxide reforms as the The crystal size can be adjusted to measure between 0.1 stable phase. Reducing the pH by bubbling CO2 through and 25 μm. Figure 19.5 shows a refinery that produces the solution encourages precipitation. alumina from bauxite using the Bayer process. Washing: The precipitate is filtered and washed to The steps in the Bayer process are as follows: reduce the sodium content. Physical beneficiation: The bauxite from the mine is Calcination: The powder is calcined at temperatures first ground, fairly coarsely, to a particle size of <1 mm. in the range 1100–1200ºC to convert the hydroxide to the Grinding increases the total surface area of the particles, oxide: leading to a reduction in the processing time for the chem- ical reaction in the following step. 2 Al(OH)3 (s) → Al2O3 (s) + H2O (g) TABLE 19.6 Oxide Raw Materials At this stage the alumina is in the form of agglomerates of small grains about 5–10 μm in diameter. Alumina Refractories, abrasives, substrates Ceria Catalysts, fuel cells, polishing (CMP) Milling: The powder is then milled to give the desired Ferrites Magnets particle size and particle size distribution. The alumina Magnesia Refractories produced in this way contains ≥99.5% Al2O3 and, as Rutile and anatase Paints mentioned earlier, the major impurity is Na2O. The Zincite Rubber, adhesives, varistors powder may also contain small amounts, on the order of Zirconia Additives, furnace components 0.001%, SiO2. This level of purity is sufficient for many 19.7 O x i d e s ...................................................................................................................................................................... 351  TABLE 19.7 Composition of Calcined Aluminas High-purity aluminas can also be prepared directly Normal Na2O (wt%) Low Na2O (wt%) Reactive (wt%) from aluminum metal, of which there are several routes as shown in Figure 19.6. Al2O3 98.9–99.7 99.5–99.8 >99.5 SiO2 0.02–0.05 0.07–0.12 0.04–0.08 Fe2O3 0.04–0.05 0.04–0.06 0.01–0.02 Magnesia Na 2O 0.3–0.6 <0.13 0.08 Magnesium oxide (MgO, magnesia) occurs naturally as the mineral periclase, a metamorphic mineral formed by the breakdown of dolomite, CaMg(CO3) 2, and other mag- applications. Careful control of the precipitation condi- nesium minerals. Occurrences of periclase are rare and tions, thorough washing of the precipitate, and control of are of no commercial importance. The principal commer- the calcination/milling conditions can give aluminas of up cial sources of MgO are magnesite (MgCO3) and magne- to 99.99% purity. The cost of normal calcined alumina is sium hydroxide [Mg(OH) 2]. about $0.60/kg and can go up to over $2.00/kg for higher Major deposits of magnesite occur in many countries purity calcined aluminas. The price for metallurgical- including China, Turkey, and Russia. The magnesite con- grade (suitable for conversion into Al) alumina is around tains varying amounts of impurities including silica, iron, $150/t. aluminum, manganese, and calcium, usually present in the Table 19.7 gives typical compositions of the main form of various minerals, for example, quartz, talc, mica, forms of calcined aluminas. The presence of Na2O can be and magnetite. After mining the ores must be beneficiated. unacceptable. For example, the Na + ion is mobile in an The methods for beneficiation vary, for example, crush- electric field and causes degradation of electrical insula- ing, screening, washing, magnetic separation, and froth tion. Also during high-temperature processing a sodium floatation. β-alumina (Na2O · 11Al2O3) phase can form that leads to After the impurities have been separated the magne- a reduction in density, strength, thermal shock resistance, sium carbonate is calcined. Calcining at temperatures and corrosion resistance of the final product. Table 19.8 between 800 and 900ºC produces a very reactive fine- shows the Na2O content required for various applications grained MgO called caustic magnesia. Sintered, or dead of calcined alumina prepared by the Bayer process. burned, magnesia is obtained by calcining the magnesium Australia is the world’s largest producer of bauxite, carbonate at temperatures above 1700ºC. During this producing almost 60 Mt per year. The major regional pro- process the reactive crystals grow and lose their activated ducer of bauxite in the United States is Arkansas, with state. smaller deposits in Georgia, Alabama, and Mississippi. Magnesia can be produced from seawater and Domestic mines supply less than 1% of the U.S. bauxite magnesium-rich brines. About 60% of the U.S. production requirement and hence the United States is a major importer of bauxite, importing over 10 Mt/year. Of all the bauxite mined about 95% is converted to alumina. World production of alumina is about 50 Mt/ Bayer Hydrate [Al(OH)3] year. The majority (about 90%) of the alumina is used for Multistage Acid Reaction Hydrothermal the production of aluminum; most of the rest goes into Water Leach to form Al Salt Extraction nonmetal uses such as specialty aluminas. It is this latter quantity that is of interest to us in ceramics. The primary suppliers of specialty aluminas in the United States are Calcine Alcoa, Alcan, Aluchem, LaRoche, and Reynolds. HIGH PURITY ALUMINA Calcine Gibbsite or Boehmite or Transition TABLE 19.8 Soda Contents Required of Calcined Aluminas Bayerite pseudoboehmite Al Salt Oxides in Commercial Applications Median crystal Na2O content Application size (mm) range (%) Aqueous Aqueous Hydro- React Direct Oxidation Oxidation thermal Hydrolyze with Oxidation Electronic ceramics <0.5–5 <0.02–0.1 with with Oxidation Acid Organic Mechanical Sodium vapor lamps <0.5 <0.02–0.1 Base or Structural ceramics <0.5–5 0.02–>0.4 Electrical Make Fused abrasives <0.5–1 0.2–>0.4 Alkoxide Ceramic fibers <0.5–1 0.2–>0.4 or Alkyl High-technology 0.5–3 < 0.1–0.25 refractories Aluminum Metal Spark plugs 2.5–>5 0.02–0.2 FIGURE 19.6 High-purity alumina production routes. 352 ................................................................................................................................................................ R aw M at e r i a l s of magnesium compounds is from these sources. Seawater titania. Baddeleyite deposits are mined commercially in contains about 1.28 g Mg2+ /kg. The most important process Brazil and South Africa. for the production of MgO from seawater is precipitation Zirconium ores all contain varying amounts of of magnesium hydroxide [Mg(OH) 2] from solutions of hafnium, typically 1.5–3 wt% of the Zr content. As a result magnesium salts by a strong base: of the chemical similarity of Hf to Zr, separation tech- niques are expensive. Unless specifically required separa- Mg2+ (aq) + 2(OH) − (aq) → Mg(OH) 2 (s) tion is not performed and technical grade zirconia is sold containing up to 3 wt% Hf. The Mg(OH) 2 precipitate is washed, filtered, and calcined to produce MgO. Another means of obtaining magnesia is from brines. Zincite This process is based on the decomposition of MgCl2 at Zinc oxide (ZnO) occurs naturally as the mineral zincite. 600–800ºC: Chemically pure ZnO is white. Zincite is red because it MgCl2 + 2H2O → Mg(OH) 2 + 2HCl contains up to 10% Mn; traces of FeO are usually also present. Naturally occurring sources of zincite are not World magnesia production capacity is about 10 Mt/year: commercially important. There are two production ∼9.0 Mt from natural magnesite and ∼1.5 Mt from seawater methods for forming zinc oxide: and brines. Prices for magnesia range from $150/t to more than $1200/t depending on purity.  Oxidation of vaporized zinc metal in air The major application for magnesia is as a refractory  Reduction of sphalerite (ZnS) with carbon and CO lining in furnaces. In lesser quantities, it is made into a Sphalerite is a naturally occurring mineral and the well-known milky solution and ingested. It is also used to most important ore of zinc. Large deposits are found in manufacture other ceramics such as chrome-free spinels. limestone of the Mississippi Valley, around Joplin, MO Nonchrome spinel is not available in nature on an indus- and Galena, IL. Significant deposits are also found in trial scale. At Asahi Glass, spinel is produced by electro- France, Mexico, Spain, Sweden, and the UK. fusing magnesia with alumina. The largest consumers of ZnO are the rubber and adhesives industries. Zinc oxide is also found in some Zirconia latex paints, tiles, glazes, and porcelain enamels, and is the most widely used material in the manufacture of Zirconium dioxide (ZrO2, zirconia) is principally derived varistors. from zircon, ZrSiO4, which occurs in igneous rocks such as granites and pegmatites. Decomposed pegmatites have Rutile and Anatase been worked for zircon in Madagascar and Brazil. Zircon is also a constituent of some metamorphic rocks and also Rutile (TiO2, titania) occurs as a constituent of igneous occurs as secondary deposits in beach sands in Australia, rocks such as granites and also in metamorphic deriva- Brazil, India, and Florida. In these secondary deposits, tives such as gneiss. It also occurs as fine needles in slates, which have been worked commercially, the zircon occurs biotite mica, quartz, and feldspar. Economically the most together with other minerals such as ilmentite, rutile, and important deposits are segregations in igneous rocks as monazite. found in Virginia, Canada, and Norway. Rutile is also an There are a number of commercial approaches to pro- important constituent of beach sands resulting from denu- ducing pure zirconia from zircon. Zircon dissociates above dation of rutile-bearing rocks, as in Australia, Florida, and 1750ºC into ZrO2 and SiO2. Injection of zircon sand into India. a plasma (at temperatures >6000ºC) results in dissociation Titania is also produced by reacting ilmenite FeTiO3 and melting. The zirconia solidifies first, in the form of with sulfuric acid at 150–180ºC to form titanyl sulfate, dendrites, and the silica solidifies as a glassy coating on TiOSO4: the zirconia. The silica may be removed by leaching in boiling sodium hydroxide solution. The residue is washed FeTiO3 (s) + 2H2SO4 (aq) + 5H2O (l) → and the zirconia is removed by centrifuging. FeSO4 · 7H2O (s) + TiOSO4 (aq) The main production method for zirconium oxide is Titanyl sulfate is soluble in water and can be separated electric arc melting of zircon between 2100 and 2300ºC. from undissolved impurities and the precipitated iron Dissociation still occurs at these lower temperatures, but sulfate by filtration. Hydrolyzing at 90ºC causes the solid zirconia is produced along with liquid silica. The hydroxide TiO(OH) 2 to precipitate: purity of the ZrO2 produced is about 99%. Another, although commercially less significant, TiOSO4 (aq) + 2H2O (l) → TiO(OH)2 (s) + H2SO4 (aq) source of zirconia is baddeleyite (impure monoclinic ZrO2). Baddeleyite is found in small deposits and usually The titanyl hydroxide is calcined at about 1000ºC to contains contaminants such as silica, iron oxide, and produce titania TiO2. 19.7 O x i d e s ...................................................................................................................................................................... 353 19.8 NONOXIDES Most of the important nonoxide ceramics do not occur naturally and therefore must be synthesized. The synthesis route is usually one of the following:  Combine the metal directly with the nonmetal at high temperatures.  Reduce the oxide with carbon at high temperature (carbothermal reduction) and subsequently react it with the nonmetal. In this section we look at several important nonoxide ceramics. To show the variety of nonoxide ceramics we have taken examples of carbides, nitrides, and borides. There are of course many other nonoxide ceramics that are of interest. FIGURE 19.7 SiC produced by the Acheson process. SiC Abrasives, harsh-environment electronic packing TiC Bearings, cutting tools AlN Electronic packaging, crucibles Si3N4 Future gas-turbine and diesel engine components purity green hexagonal SiC crystals suitable for electronic ZrB2 Crucibles and thermowell tubes (steel) applications. The purity of the SiC can be determined WC Abrasives, cutting tools based on the color of the crystals. C Graphite: solid lubricant; diamond: abrasive  Light green 99.8% pure  Dark green 99% pure Silicon Carbide  Black 98.5% Silicon carbide (SiC) is the most widely used nonoxide Around the core is a zone of lower purity (≥97.5%), ceramic. Its major application is in abrasives because of which is suitable for abrasives. The outer layer consists of its hardness (surpassed only by diamond, cubic boron a mixture of SiC, unreacted SiO2, and C that is reused in nitride, and boron carbide). Silicon carbide does not occur the next batch. Figure 19.7 shows examples of SiC crystals in nature and therefore must be synthesized. It occurs in produced by the Acheson process. two crystalline forms: the cubic β phase, which is formed The world’s largest producer of SiC is China, which in the range 1400–1800ºC, and the hexagonal α phase, produces about 450,000 t/year. The largest U.S.-based formed at >2000ºC. manufacturer for SiC is Exolon in Hennepin, IL, Silicon carbide is synthesized commercially by the which produces about 40,000 t of SiC annually. Figure Acheson process, which involves mixing high-quality 19.8 shows several of the furnaces at the Hennepin plant silica sand (99.5% SiO2) with coke (carbon) in a large in various stages of production. The cost for SiC pow- elongated mound and placing carbon electrodes in oppo- ders produced by the Acheson process is in the range site ends. Each mound, or furnace, consists of about 3000 t $10–$40/kg. of material. An electric current is passed between the electrodes resistively heating the coke in the mound to about 2200ºC. The total electrical energy consumed Titanium Carbide during a standard furnace run is about 2 million kWh Titanium carbide (TiC) is another nonoxide ceramic that (about 7 TJ). The average power input during the furnace is not available in nature. It is prepared either by the car- run is 9000–10,000 kW. bothermal reduction of TiO2 or by direct reaction between At the high temperatures the coke reacts with the SiO2 the elements titanium and carbon. As in many of these to produce SiC plus CO: reactions high temperatures are required. The carburiza- tion temperature is between 2100 and 2300ºC. SiO2 (s) + 3C (s) → SiC (s) + 2CO (g) Heating is continued (2–20 days depending on the size of Aluminum Nitride the transformer and the furnace) until the reaction is com- There are several large-scale methods for producing AlN, pleted on the inside of the mound. After cooling, the two of which are currently used in industry. One method mound is broken up and sorted. The core contains high- is direct nitridation of aluminum: 354 ................................................................................................................................................................ R aw M at e r i a l s  Silicon Nitride Silicon nitride (Si3N4) is another synthetic mineral. It occurs in two crystalline forms. The lower temperature α form is usually preferred as a raw material because the transformation to the β form during sintering favors the development of an elongated crystal structure. Several routes are available for the synthesis of Si3N4 powder, similar to those used to form AlN:  Nitridation of Si powder  Carbothermal reduction of silica in N2  Vapor phase reaction of SiCl4 or silane (SiH4) with ammonia Most commercially available powder is made by react- FIGURE 19.8 The Exolon plant in Hennepin, IL. This plant is ing silicon powder with nitrogen at temperatures from one of the newest SiC facilities in the world, producing both 1250 to 1400ºC according to the reaction high-quality metallurgical and crystalline SiC annually. It is North America’s only manufacturer of SiC. The plant features 16 furnaces 3Si (s) + 2N2 (g) → Si3N4 (s) operating off of four transformers. The powder generally consists of a 90:10 mixture of α- Si3N4 and β-Si3N4 polymorphs. Seeds of Si3N4 powder are often mixed with the silicon to hasten the reaction and Al (l) + 1/2N2 (g) → AlN (s) to help prevent the formation of the undesired β phase. Nitrided powder contains impurities such as Fe, Ca, and Al originally present in the Si or picked up during subse- Al powders are converted directly to the nitride at tem- quent milling. Higher purity Si3N4 powder can be made peratures above the melting point of the metal. Careful by carbothermal reduction in the range 1200–1550ºC: process control is necessary to avoid coalescence of the metal prior to nitridation. 3SiO2 (s) + 6C (s) + 2N2 (g) → Si3N4 (s) + 6CO (g) Reducing alumina using nitrogen or ammonia in the presence of carbon is another method to produce AlN: Although this process leads to powders with residual carbon and oxygen it produces high surface area powder 2Al2O3 (s) + 3C (s) + 2N2 → 4AlN (s) + 3CO2 (g) with a high α content. Si3N4 seeds may again be used to speed up the reaction. High-purity powders are also made via vapor phase The mixture of alumina and carbon is reacted with a reactions such as nitrogen-containing atmosphere above 1400ºC. Fine powders and extremely good control of mixing are required SiCl4 (g) + 6NH3 (g) → Si(NH)2 (s) + 4NH4Cl (g) to result in complete conversion to AlN. Si(NH)2 (s) → Si3N4 (s) + 2NH3 (g) In both processes the major impurities are O (∼1.0 wt%) and C (<0.07 wt%). Other impurities are silicon, iron, 3SiH4 (g) + 4NH3 (g) → Si3N4 (s) + 12H2 (g) and calcium, which typically occur at levels <50 ppm each. Powder from these reactions is amorphous, but the product The main vendors for AlN powders are Advanced on heating to 1400ºC is mostly α-Si3N4. Refractory Technologies (in the United States); H.C. Worldwide production of Si3N4 is about 500 t/year; Starck and Elf Atochem (Europe); and Toyo Aluminum Japan is the primary market. The cost for this powder is and Tokuyama Soda (Japan). The world market for AlN between $30/kg and $150/kg depending on the particle powder is about 200 t/year. Prices range from $20/kg to size and the quantity ordered. $180/kg depending on supplier, powder characteristics, Silicon nitride exhibits high strength at elevated tem- and quantity. peratures and excellent thermal shock, creep, and oxida- Many of the applications of AlN require it to be in tion resistance in hostile environments, which makes it consolidated in the form of substrates or crucibles. It is an ideal for gas turbine and diesel engine applications. The electrical insulator and has a high thermal conductivity SiAlONs are variations on this theme. For example, (better than Fe), which makes it attractive for use in elec- SiAlON is being combined with boron nitride (BN) to tronic packaging. Aluminum nitride crucibles are used to produce a composite material that is reported to have contain metal melts and molten salts. incomparable thermal shock resistance. 19. 8 N o n ox i d e s ............................................................................................................................................................... 355 Zirconium Diboride The graphite used in industry comes both from natural sources where it is mined in open pit and underground ZrB2 is useful as a crucible material for metal melts operations. The largest producers of natural graphite are because of its excellent corrosion resistance. It is also used China and India and total world production is around in Hall–Heroult cells (for Al production) as a cathode and 1 Mt/year. Graphite is not currently mined in the United in steel refining where it is used as thermowell tubes. States, although the United States does produce about Several different processes can be used to produce 300,000 t of synthetic graphite annually with a value of ZrB2; these are similar to those used to form carbides and almost $1 billion. nitrides. Commercially, either a direct reaction between There are several methods used to produce synthetic zirconium and boron graphite. Many of these involve heating nongraphitic carbons above 2500ºC. For example, a high-purity form Zr + 2B → ZrB2 (s) is produced by heating a calcined mix of petroleum coke and coal tar pitch to 3000ºC. The high temperature allows or carbothermal reduction of zirconia is used: the carbon atoms to order into the graphite structure. Synthetic graphite can also be obtained by chemical vapor deposition from hydrocarbons at lower temperatures 2ZrO2 + C + B4C → 2ZrB2 + 2CO2 (∼1800ºC). 2ZrO2 + 5C + 2B2O3 → 2ZrB2 + 5CO2 Most of the synthetic graphite produced in the United States (>60%) is used in the massive electrodes in carbon- All these reactions must be carried out at high temperature arc furnaces to melt steel and in much smaller battery in an inert atmosphere or in vacuum. The typical price of electrodes. Other major applications include lubricants ZrB2 powder is $60–$100/kg. and carbon raisers in steelmaking. Synthetic graphite is used in replacement heart valves, an application we describe in Chapter 35. Tungsten Carbide The largest uses for natural graphite are in refractories (45%) and brake linings (20%). Natural graphite costs Tungsten carbide is a wear-resistant material used in the around $500/t, whereas synthetic graphite costs over metalworking, mining, and construction industries for $2000/t. machine parts and dies that are subject to severe service The quantity of industrial diamonds produced in the conditions. It is produced by carburization of tungsten United States is much smaller than the amount of syn- powder. The United States uses about 5500 t of WC each thetic graphite. About 300 million carats or 60 t are pro- year. duced each year with major applications in stone cutting and highway/building repair. The fullerenes were discovered in 1985 and the related Carbon carbon nanotubes in 1991. Both are now available in com- Graphite is one of three crystalline forms of carbon, the mercial quantities, but at present they are very expensive others being diamond and fullerenes. Graphite is unlike and the applications are limited to specialty products such most of the nonoxide ceramics in that it occurs naturally as Nanodesu bowling balls, which use fullerenes as an in metamorphic rocks such as marble. additive in a polymer coating. CHAPTER SUMMARY This chapter described the processes used to obtain the raw materials necessary to make ceramics. The significant points to remember from this chapter as you continue your study of ceramics are as follows:  Where and how we get the raw materials will determine impurity concentrations in the final powder (e.g., Na is the major impurity in Bayer alumina).  The abundance of a mineral may affect the cost of the final ceramic component (e.g., SiO2 comes from sand; it is abundant and inexpensive. Glass bottles are cheap; the cost of an Si wafer is not related to the cost of sand).  If the raw materials are not oxides then they have almost certainly been synthesized [e.g., we use 0.5 Mt of SiC (mostly for abrasives), which must be synthesized. The cost of the powder depends on how pure it is].  Gemstones are found during mining, but are not abundant (e.g., about 200 mg of diamonds will come from 1 ton of ore; the market price of diamonds can justify this dilution). 356 ................................................................................................................................................................ R aw M at e r i a l s  PEOPLE & HISTORY Acheson, Edward Goodrich (1856–1931), was an American chemist who worked with Thomas Edison before establishing his own laboratory. He developed a process for producing silicon carbide while trying to make synthetic diamonds. In 1891 he founded The Carborundum Co. to produce SiC for abrasives and was granted a patent in 1893 for SiC. In 1926, the U.S. Patent Office named his patent for SiC one of the 22 patents most responsible for the industrial age. Bauxite is named after the small French town of Les Baux de Provence, which is near Arles. Bayer, Karl Joseph (1847–1904) was an Austrian chemist (born in (Bielitz) who described the Bayer process in 1888. Dana, James Dwight (1813–1895) was educated at Yale University and made contributions to the fields of geology, mineralogy, and zoology. He developed classification systems that are still in use in these fields today. Graphite. The word is derived from the Greek word graphein, to write. Graphite is used as the “lead” in pencils among many other applications. Kaolin refers to an area of Jiangxi province, which is why it is also called China clay. Moissan, Ferdinand Frédéric-Henri (1852–1907) is known in the field of ceramics for his unsuccessful attempts at diamond synthesis (he actually produced SiC). Moissan was awarded the 1906 Nobel Prize in Chemistry for isolating fluorine on June 26, 1886. It was in Moissan’s laboratory at the University of Paris in France that tungsten carbide was first made. Mullite is named after the Isle of Mull off the west coast of Scotland where the rare mineral is found. Muscovite mica was first used in 1850 by James Dwight Dana and is derived from the term “Muscovy glass,” by which it was previously known because of its widespread use as a window-glass substitute in the old Russian state of Muscovy. Phlogopite mica comes from the Greek word phologopos meaning fiery in reference to the reddish color seen on some specimens of this mica. GENERAL REFERENCES Annual Minerals Review published in the Bulletin of the American Ceramic Society gives an annual update on the production status of a wide range of ceramic raw materials. Evans, J.W. and DeJonghe, L.C. (1991) The Production of Inorganic Materials, Macmillan, New York. A readable description of how many metals and ceramics are produced. Gribble, C.D. (1988) Rutley’s Elements of Mineralogy, 27th edition, Unwin Hyman, London. Classic resource on mineralogy including detailed descriptions of properties and occurrences of a wide range of minerals. Mineral Commodity Summaries, published by the U.S. Department of the Interior, U.S. Geological Survey, provide extensive data on mineral production in the United States and the rest of the world. Reed, J.S. (1995) Introduction to the Principles of Ceramic Processing, 2nd edition, Wiley, New York. Chapters 3 and 4 describe the extraction and synthesis of various ceramic raw materials. SPECIFIC REFERENCES Bowen, N.L. (1922), “The reaction principle in petrogenesis,” J. Geol. 30, 177. Describes the eponymous reaction series. Martin, E.S. and Weaver, M.L. (1993) “Synthesis and properties of high-purity alumina,” Am. Ceram. Soc. Bull. 72, 71. Discussion of the pros and cons of different processes to produce alumina. WWW www.usgs.gov U.S. Geological Survey. The Mineral Commodity Summaries and the Minerals Yearbook are here, and so much more. EXERCISES 19.1 How many pounds of mullite are there in 1 ton of the material? How many kilograms? 19.2 What are the major impurities you would expect to find in high-quality deposits of silica sand? 19.3 Why do you think rock quartz is not used widely as a source of silica? 19.4 In the brief description of Edward Acheson we noted that the U.S. Patent Office named silicon carbide as one of the 22 patents most responsible for the industrial age. Why do you think this was such an important material? 19.5 What factors do you think contribute most to feldspar sales in the United States? C h a p t e r S u m m a ry .......................................................................................................................................................... 357  19.6 Why are magnesia sales related to steel production? 19.7 What is the difference between zircon and zirconia? Which of these, in single crystal form, is the diamond simulant? 19.8 A commercial supplier of ceramic powders sells 1 g of HfO2 (purity 99%) for about $2, but charges only 15 cents for the same amount of ZrO2 (purity 99%). Both powders come from the ore zircon. Explain the differences in the price. 19.9 Quartz, basalt, and obsidian are all formed when magma cools (they are all igneous). Relate the microstruc- ture of each of these materials to the expected relative rate of cooling of the magma. (We described obsidian in Chapter 2, you may need to look in a geology book for the microstructure of basalt.) 19.10 Synthetic graphite is used primarily for electrodes and as a carbon raiser in steel production, whereas the major applications of natural graphite are refractories and brake linings. Why does the source of graphite matter and what are some of the considerations end users might make in deciding where to buy their graphite? 358 ................................................................................................................................................................ R aw M at e r i a l s  20 Powders, Fibers, Platelets, and Composites CHAPTER PREVIEW The topic of this chapter is how to produce particles of a particular shape, chemistry, and size and then how to characterize them. We are going to describe the methods used to produce ceramic powders, from the traditional ball-milling technique to more recent vapor-phase approaches that can produce nanometer-sized particles. It is worth remembering that powder processing is used to produce some special metals (e.g., tungsten filaments for incandescent lamps), it is used in the pharmaceutical industry, for making catalysts, and it is used to prepare many food ingredients. Producing powders of a consistent quality and composition is an important industry. In the United States the total market for powders of advanced ceramics (e.g., electronic and structural ceramics) alone is around $1 billion per year. To specify powders for particular applications and products we need to be able to determine their physical and chemical characteristics, often with a high degree of accuracy and with sta- tistical significance. In this chapter we will describe the different analytical techniques used for particle characterization and also indicate which technique works best. In addition to powders there are other important dimensionally constrained forms of ceramics. Whiskers and fibers are long in one dimension but restricted in the other two. Ceramics in these forms are important reinforcement phases in composites, such as  C fibers in polymer–matrix composites (PMCs)  Al2O3 fibers in metal–matrix composites (MMCs)  SiC whiskers in ceramic–matrix composites (CMCs) If the particles are constrained in only one dimension, we have platelets. The amount of space we devote to platelets does not correlate with their commercial importance: remember that clay particles are platelets. The excuse is that most platelet particles are produced in nature while we are concentrating on particles we “design.” If we limit the size in two or three dimensions to less than 100 nm, we have nanomaterials. 20.1 MAKING POWDERS size is gradually reduced. The final step is known as milling, which produces particles of the desired size. Many methods are available for the preparation of ceramic Mechanical methods of powder production are used widely powders. These can be divided into just three basic in the production of traditional ceramic products where types: high purity powders are not required and cost is one of the most important requirements.  Mechanical Chemical methods, such as sol-gel processing, offer  Chemical several advantages over mechanical methods because they  Vapor phase allow exceptional control over particle morphology and purity. Chemical processes are used widely in the produc- Mechanical methods use coarse-grained materials that tion of advanced ceramic materials. have generally been derived from naturally occurring Vapor-phase processes can be used to produce ceramic minerals. They are subjected to a series of processes, col- powders. They tend to be expensive, but offer many advan- lectively referred to as comminution, in which the particle tages, such as the ability to produce particles of nonoxides. 2 0 .1 M a k i n g P o w d e r s ................................................................................................................................................... 359  TABLE 20.1 Desirable Powder Characteristics for Brownian motion. Consequently, colloidal particles Advanced Ceramics will settle very slowly. Powder characteristic Desired property  Aggregates are coarse constituents, >1 mm, in a mixture. The important example is the addition of Particle size Fine (<1 μm) gravel to cement to make concrete. In early concrete Particle size distribution Narrow structures such as the Pantheon in Rome, pumice was Particle shape Spherical or equiaxed State of agglomeration No agglomeration or soft agglomerates used as aggregate. Chemical composition High purity Phase composition Single phase 20.3 MECHANICAL MILLING Vapor phase techniques are also used to produce nano- For traditional raw materials like clay and the oxides pro- particles (particles with diameters of a few to 10s of duced from ores, it is often necessary to eliminate aggre- nanometers). gates and to reduce the particle size. Compound formation Table 20.1 lists the desirable powder characteristics for during firing and densification during sintering require advanced ceramics. For most processing methods we want diffusion between neighboring particles. Diffusional pro- a small particle size. The small size helps shape the cesses are proportional to the square of the particle size. product and during densi- The most common fication (sintering) at high method for reducing parti- temperature, allows higher POPULAR MILLING MEDIA cle size is ball milling. density bodies at lower Porcelain (ρ = 2.3 Mg/m3) A ball mill is a barrel firing temperatures. Alumina (ρ = 3.6 Mg/m3) (usually made of a ceramic, Zirconia (ρ = 5.5 Mg/m3) although for small-scale Steel (ρ = 7.8 Mg/m3) milling in the laboratory a 20.2 TYPES OF Tungsten carbide (ρ = 15.6 Mg/m3) small plastic bottle works POWDERS well) that rotates on its axis and is partially filled with a grinding medium (called Powders can have a complex structure; to describe this media) in the form of spheres, cylinders, or rods. Figure structure it is necessary to follow a consistent terminology. 20.1 shows a crosssection of a ball mill. The quantity of The terminology we use follows that used in the ceramic the media is such that the rotation of the mill causes it to processing industry. cascade, creating both shearing and crushing actions on the powder.  Primary particles are the smallest clearly identifiable The media should have a high density (ρ) as this pro- unit in the powder. Primary particles may be crystal- vides for the most effective collisions. The choice of media line or amorphous and cannot easily be broken down is also based on cost, wear resistance, and the possibility into smaller units. of introducing contamination into the powder.  Agglomerates are clusters of bonded primary particles. Soft agglomerates are easily broken up; hard agglom- erates, because of the stronger interparticle bonds, are more difficult to break up. Hard agglomerates should be avoided in ceramic powder processing as much as possible. Mill  Particles is a general term applied to both primary rotation particles and agglomerates. Some of the techniques that we refer to in the next section measure particle size often with no distinction between agglomerates and primary particles.  Granules are large agglomerates, usually 0.1–1 mm in diameter, that are formed by the addition of a granulat- ing agent (e.g., a polymer binder). The mixture is tumbled, producing large, nearly spherical granules that flow freely and can be used to fill complex molds and in automated processes.  Flocs are clusters of particles in a liquid suspension held together electrostatically.  Colloids are very fine particles (they can be as small FIGURE 20.1 Cross section of a ball mill showing the movement as 1 nm in diameter) held in fluid suspension by of the media as the mill rotates about its axis. 360 ......................................................................................................... P o w d e r s , F i b e r s , P l at e l e t s , a n d C o m p o s i t e s  TABLE 20.2 Possible Particles Sizes for Different There are many other mechanical methods that can be Milling Techniques used to achieve comminution. The possible particle size Jaw crushers to 5 mm range for each is compared in Table 20.2; we describe Cone crushers to 5 mm three of the methods in more detail below. Crushing rolls to ∼1 mm Fluid-energy milling, also called jet milling, achieves Hammer mill to ∼0.1 mm particle size reduction by particle–particle impact in a Jet mill 1 to ∼50 μm high-velocity fluid, usually either compressed air or super- Vibratory mill 1 to ∼50 μm Ball mill 0.5–10 μm heated steam. The powder is added to the fluid and injected Attrition mill 0.1–5 μm into the grinding chamber at sonic or near-sonic velocity. Roller mill 0.1–5 μm The design of the chamber maximizes particle–particle impact while minimizing particle–wall impact. Coating of the walls of the chamber, Depending on the MILLING e.g., with a polymer, can amount of powder to be The minimum particle size possible by ball milling is further reduce contamina- milled, the size of the mill, ∼0.1 μm. tion. Fluid-energy milling and the final particle size Vibratory milling is 10× faster than ball milling. can achieve controlled par- required, the media could ticle size (down to about range from more than 8 cm 1 μm) with a narrow size in diameter to 0.6 cm, which is used for fine grinding. The distribution. Table 20.3 shows examples of ceramic powder is often milled in a liquid with a surface-active powders formed by fluid-energy milling. The main draw- agent added. Ball milling eliminates aggregates and can back with this method is collecting the fine powder that is typically reduce the particle size down to 1 μm. mixed into the gas stream. The advantages of ball milling are that the equipment In vibratory milling the drum containing the media is and powder is vigorously shaken. The collisions between the media are much more violent than they are in ball  Simple (although experimentally straightforward, milling and this can shorten milling times. Polymer balls there are many theoretical aspects that are quite can be used as media and this means any contamination complex) can be burned off during subsequent firing.  Inexpensive (at least for small batch sizes) Attrition milling, or agitated ball milling, differs from conventional ball milling in that the milling chamber does The disadvantages of ball milling are that it not rotate. Instead, a slurry containing the particles and media is stirred continuously at frequencies of 1–10 Hz.  Cannot produce ultrafine particles The grinding chamber is aligned either vertically, as shown  Can add impurities to the powder from the media and in Figure 20.2, or horizontally, with the stirrer located in the inside of the mill the center of the chamber. The media consists of small  Is inefficient, less than 2% of the energy input goes spheres (0.2–5 mm) that make up between 60 and 90% of into creating new surfaces the available mill volume. Most attrition mills work on a continuous basis with the powder to be milled fed in at one You have seen polished stones of hematite, quartz, etc. end and the milled product collected at the other. Attrition These are obtained by tumbling in the same type of mill— mills are more energy efficient than the other methods the “particle” size is just bigger. The biggest “ball” mill we have described and can also handle higher solid is the seashore, where pebbles are eventually changed into contents in the slurry. The rapid milling time, because sand. of the use of small media, helps reduce contamination. TABLE 20.3 Examples of Ceramic Powders Produced by Fluid-Energy Milling Average particle Mill diameter Material feed rate size obtained Grinding Material cm in. medium kg/h lb/h mm in. Al2O3 20.3 8 Air 6.8 15 3 0.00012 TiO2 76.2 30 Steam 1020 2250 <1 <0.00004 TiO2 106.7 42 Steam 1820 4000 <1 <0.00004 MgO 20.3 8 Air 6.8 15 5 0.0002 Dolomite 91.4 36 Steam 1090 2400 <44 <0.0018 Fe2O3 76.2 30 Steam 450 1000 2–3 ∼0.0001 2 0 . 3 M e c h a n i c a l M i l l i n g ........................................................................................................................................... 361  Air disperser Drying Feed air Pump Rotary atomizer Controlled atmosphere Exhaust Drying air chamber Cyclone Powder (A) Product Co-current Air disperser Drying air Grinding medium Drying chamber Cutaway Exhaust Nozzle FIGURE 20.2 An attrition mill. air atomizer Cyclone Feed Lining the chamber with a polymer or a ceramic and Pump using ceramic stirrers and media can further reduce (B) Product Mixed flow contamination. FIGURE 20.3 Spray dryers: (a) Centrifugal atomizer with cocurrent air flow. (b) Nozzle atomizer using mixed-flow conditions. 20.4 SPRAY DRYING decomposition temperature. Chlorides and oxychlorides Spray drying is an example of powder production from are frequently used in industrial spray-drying operations solution. It is used widely for preparing ferrites, titanates, because of their high solubility in aqueous solutions. The and other electrical ceramics. Fine droplets produced by capacities of industrial spray dryers are up to several an atomizer are sprayed into a drying chamber and the hundred kilograms per hour. The spray drying process is powder is collected (Figure 20.3). There are different not limited to aqueous solutions; for example, alcohol types of atomizers. One uses ultrasonic atomization in solutions of alkoxides can be used. which the solution is passed over a rapidly vibrating piezo- Table 20.4 lists examples of salt precursors and their electric membrane. Droplet sizes in the range of 10 μm to decomposition temperatures. The decomposition of salts over 100 μm can be produced. to oxides is an example of a solid-state reaction. These In the drying chamber, the flow pattern of the hot air reactions are often referred to as calcination and are fre- determines the completeness of moisture removal and the quently governed by kinetics rather than thermodynamics. maximum temperature that the particles experience. As a consequence, they may be carried out at temperatures Finally the particles are carried out of the chamber in the much greater than those necessary based on thermody- air stream and captured in a bag or another form of col- namic calculations. A feature of the decomposition reac- lector. The particles produced by spray drying are often tions is that they often result in the production of extremely agglomerated with a primary particle size less than fine particles. 0.1 μm. The variables in spray drying are TABLE 20.4 Salt Precursors and Their Decomposition Temperatures in Air  Droplet size  Solution concentration and composition Precursor T (°C)  Temperature and flow pattern of the air in the drying Zn(NO3)⋅6H2O 360 chamber Ni(NO3) 2⋅6H2O 400  Chamber design Ni(CH3COO) 2⋅4H2O 350 Fe(NO3) 3⋅9H2O 200 MgSO4 1000 For small-scale laboratory experiments nitrates and Y2 (C2O4) 3⋅5H2O 500 acetates are often used because of their relatively low 362 ......................................................................................................... P o w d e r s , F i b e r s , P l at e l e t s , a n d C o m p o s i t e s  Evaporate Precipitate Dry Decompose Sinter Reaction 2: Condensation Vapor diffusion (C3H7O) 2–Al–OH + C3H7O–Al–(C3H7O) 2 → Solution Dv (C3H7O) 2–Al–O–Me–(O C3H7) 2 + C3H7OH (20.3) Ds α1 The remaining alkoxy groups (–OR) of the condensa- vapor αg Heat Precipitate Solution tion product can be hydrolyzed further to form a cross- transfer linked, three-dimensional network of metal–oxygen FIGURE 20.4 Stages in the spray pyrolysis process. bonds. The actual reactions that occur appear to be significantly more complex than those represented by Eqs. 20.2 and 20.3. There are several variables in the sol-gel process: A variation of the spray drying process, known as spray pyrolysis, uses a higher temperature and a reactive  Rates of hydrolysis and condensation (relative differ- (often an oxidizing) environment in the chamber. This ences in the rates can be used to modify the micro- allows the salts to be dried and decomposed directly. structure of the powder) Figure 20.4 shows the stages in the spray pyrolysis process.  Type of alkoxide (mixing of the alkoxides in the solu- In addition to producing powders this technique has been tion is achieved at a molecular level giving the powders used to produce thin films and fibers. a high degree of chemical homogeneity)  Reaction temperature (affects the degree of poly- merization of the gel) 20.5 POWDERS BY  Amount of water added (affects the degree of poly- SOL-GEL PROCESSING merization of the gel)  Solution pH (rates of hydrolysis and condensation can Sol-gel processing is one of the topics we describe in be increased by the addition of acids or bases, Chapter 22. It is best applied to the formation of films and respectively) fibers. We discuss the technique here because, although expensive, it can produce powders with a high surface Gelation times vary from seconds to several days. area, which allows sintering to nearly full density at much When the gel forms it may contain only about 5 vol% of lower temperatures than are normally required when the the oxide. The dried gel is calcined to completely convert particles have been made by other techniques. it to oxide. Powders produced by the sol-gel method In most sol-gel processes the reactants are solutions of are amorphous. A crystallization step is required to pro- metal alkoxy compounds. Alkoxides result from the reac- duce crystalline bodies, which is often performed after tion of metals (Me) with alcohols. The general reaction sintering. is nROH + Me → (RO) nMe + (n/2)H2 (20.1) 20.6 POWDERS BY PRECIPITATION where R is an organic group. For ethanol, R is the ethoxy To cause precipitation it is necessary to produce a super- group C2H5. Catalysts are often necessary to increase saturated solution. This can be achieved, for example, by reaction rates. For example, aluminum will react with changing the pH or the temperature. A larger quantity of isopropanol at 80°C in the presence of a small amount of a soluble component (for example, a metal salt) can be HgCl2. In this case the catalyst breaks down the protective dissolved in a solution at high temperature than at a lower oxide layer that forms on the aluminum. temperature. For example, not only does sugar dissolve A number of metal alkoxides are commercially avail- more quickly in hot tea than in iced tea, but more sugar able in high purity form. To make metal oxide powders dissolves. The relation between solubility and temperature from these organometallic precursors we start with a solu- for several ionic compounds is shown in Figure 20.5. tion (a “sol”) of the metal alkoxide in alcohol. (The alcohol There are some exceptions to prove the rule: cerium sulfate is usually the same one that was used for alkoxide forma- is less soluble at higher temperatures because its heat of tion.) Water is added to the alcohol solution. Two reactions solution is negative (ΔHsol < 0). then occur, which, using aluminum isopropoxide as an At a supersaturation that exceeds the concentration example, may be written as follows: threshold for homogeneous nucleation, a large number of nuclei form suddenly. Their formation lowers the solution Reaction 1: Hydrolysis concentration below the concentration at which nucleation occurs, but enough excess solute remains for the existing (C3H7O) 2–Al–OC3H7 + HOH → nuclei to grow. If the solution is kept uniform, growth of (C3H7O) 2–Al–OH + C3H7OH (20.2) all the particles proceeds at the same rate, producing 2 0 . 6 P o w d e r s b y P r e c i p i tat i o n ................................................................................................................................. 363  100 Ethylene Glycol NaNO3 KNO3 Solubility wt.% solute 100°C “Ti Solution” Ti n-Butoxide in H2O) Stir H2O 80 Citric Acid HNO3 Precipitate (NH4)2CO3 + H2O SrCO3 Wash, Filter Sr (NO3)2 + H2O 60 KCl “Ti Solution” “Sr, Ti Solution” Sr (NO3)2 + H2O (Dopants) 40 NaCl Batch H2WO4, H2O Solution NH4OH Dry 150°C 20 Glassy Char 250°C, Crush KClO3 Powder Resin Calcine 700°C Ce2(SO4)3 FIGURE 20.7 Flow chart for preparing SrTiO3 powders by the Pechini method. 0 0 20 40 60 80 T (°C) 100 FIGURE 20.5 Solubility (grams of solute in 100 g H2O) versus temperature for several ionic compounds. 80°C and precipitation occurs when the pH is increased to around 11 with ammonium hydroxide. A mixed hydro- xide precipitates, which powders with extremely PRECIPITATION is washed to remove the uniform size distribution. It is important to make sure that nucleation occurs residual sulfate and dried The variation of solute homogeneously. Good housekeeping is essential as to a powder with a particle concentration with time specks of dirt can act as nucleation sites causing hetero- size between 50 nm and during the nucleation and geneous nucleation. 1 μm. growth of particles from The Pechini method is solution is shown in Figure a commercial process for 20.6. This diagram is often referred to as a LaMer diagram the preparation of titanates and niobates for the capacitor after the work of LaMer and Dinegar. industry. With slight modifications, it is also referred to Precipitation of mixed oxides is possible. For example, as the “citrate gel” process or the “amorphous citrate” in the fabrication of nickel ferrite (a magnetic ceramic process. Figure 20.7 shows a flow chart for the preparation used for memories) a mixed aqueous solution of iron of strontium titanate powder. Metal ions from starting and nickel sulfates is used. The solution is kept at about materials such as carbonates, nitrates, and alkoxides are complexed in aqueous solution with α-carboxylic acids such as citric acid. When heated with a polyhydroxyl alcohol, such as ethylene glycol, polyesterification occurs. Nucleation threshold On removal of the excess liquid a transparent resin is c formed. The resin is heated to decompose the organic constituents, ground to break up large agglomerates, and finally calcined. The powders produced are not as uniform Solubility limit as those from the sol-gel process: they often contain hard agglomerates. Nucleation burst 20.7 CHEMICAL ROUTES TO NONOXIDE POWDERS Growth Many important engineering ceramics are nonoxides, e.g., Si3N4 and SiC. These often do not exist in nature or are FIGURE 20.6 Concentration versus time for a solution in which rare and so must be produced synthetically. In Chapter the concentration is first increased to the point of nucleation (e.g., 19 we described how nonoxide powders are obtained by evaporation) and then declines as a precipitate grows. by solid-state reactions, such as between SiO2 and C to 364 ......................................................................................................... P o w d e r s , F i b e r s , P l at e l e t s , a n d C o m p o s i t e s produce SiC. We also described direct nitridation pro- Liquid N2 cesses, such as the reaction between Al and N2 to produce AlN. Now we are concerned with liquid-phase reactions Scraper that lead to the formation of nonoxides. It is possible to produce submicron particles of α-Si3N4 by reacting silicon tetrachloride, a liquid at room tempera- ture, and ammonia. The reaction involves the formation of silicon diimide [Si(NH) 2] as an intermediate phase. 3Si(NH) 2 → Si3N4 + 2NH3 (20.4) This process is used commercially by Ube Industries in Japan to produce Si3N4. The particle morphology is con- A B trolled by the calcination time and temperature: Gas Evaporation inlet sources Funnel  Fine-grained equiaxed powders form at low temperatures  Needle-like and coarse-grained hexagonal particles To compactor form at temperatures >1500°C. FIGURE 20.8 Schematic of a gas-condensation chamber for nanoparticle synthesis. Another example of a liquid-phase reaction used to produce precursors for nonoxide powders involves reduc-  Versatility in producing powders of oxides and tive dechlorination of halide solutions. An example is the nonoxides reaction between silicon tetrachloride, carbon tetrachlo- ride, and sodium in heptane at ∼300°C: Figure 20.8 illustrates a gas-condensation chamber developed specifically for this purpose. Material is evapo- SiCl4 + CCl4 + 8Na → “SiC” + 8NaCl (20.5) rated from the two sources and condenses in the gas phase. The condensate is transported by convection to the liquid The amorphous precursor can be crysyallized by heating nitrogen cold finger. The clusters are scraped from the cold between 1400 and 1800°C in 5% H2 /Ar. This process has finger and collected via a funnel. It is possible to have the also been used to produce powders of TiB2 and B4C. particles transferred directly into a cold press where they can be compacted. With this technique ceramic powders 20.8 PLATELETS with very small particle size have been produced, e.g., TiO2 powders with an average particle size of 10–15 nm. Platelets are particles that are constrained in one dimen- Figure 20.9 shows a typical plasma reactor that can sion. They are commercially important because this is the also be used to produce ceramic nanoparticles. The shape of clay particles and mica. Another example of platelets previously encountered is SiC, which forms as RF power Gas inlet flat hexagonal crystals by the Acheson process. An in situ 13.56 MHz process has been developed to produce platelet-reinforced- intermetallic composites. The reaction is RF showerhead electrode Mo2C + 5Si → 2MoSi2 + SiC (20.6) The SiC is in the form of platelets in an MoSi2 matrix. 20.9 NANOPOWDERS BY Plasma VAPOR-PHASE REACTIONS Vapor phase processes are relatively expensive, but there are several good reasons for using them to prepare powders, Substrate Grounded particularly when we want electrode  High purity Vacuum  Discrete and nonaggregated particles  Nanoparticles with narrow size distributions FIGURE 20.9 Schematic of a plasma reactor. 2 0 . 9 N a n o p o w d e r s b y Va p o r - p h a s e R e a c t i o n s ...................................................................................................... 365  TABLE 20.5 Summary of Particle Size Analysis Techniques Method Medium Size (mm) wt (g) t Light microscopy Liquid/gas 400–0.2 <1 S-L Electron microscopy Vacuum 20–0.002 <1 S-L Sieving Air 8000–37 50 M Air 5000–37 5–20 M Liquid 5000–5 5 L Inert gas 5000–20 5 M Gravity sedimentation Liquid 100–0.2 <5 M-L Centrifuge sedimentation Liquid 100–0.02 <1 M Electrical sensing zone Liquid 400–0.3 <1 S-M (Coulter counter) Fraunhofer scattering Liquid/gas 1800–1 <5 S Mie scattering Liquid 1–0.1 <5 S Intensity fluctuation Liquid 5–0.005 <1 S X-ray line broadening Air <0.1 <1 S-M gaseous reactants are introduced into an argon plasma curved line is measured and from this information the where they are decomposed into free atoms, ions, and grain size is determined. It is possible to make these mea- electrons. Quenching of these highly excited species surements by hand using a ruler, but it would take a long results in the formation of ultrafine powders with sizes time to obtain a statistically relevant sample. Using image- typically less than 20 nm. analysis methods on a computer a large number of parti- cles can be measured quickly. The data are often then plotted as a histogram of frequency of occurrence versus 20.10 CHARACTERIZING POWDERS particle size. For submicron particles it is necessary to use an elec- There are several techniques that can be used to obtain tron microscope. For scanning electron microscopy particle size and particle size distribution and these are (SEM), and in particular transmission electron micro- compared in Table 20.5. The choice of technique depends scopy (TEM), the total amount of material that can be on several factors, such as applicable particle size range, examined is quite small, and so it is essential to make sure sample size required, and the analysis time. In addition, that the sample examined is representative of the entire we often have to consider instrument cost, availability, powder batch. ease of operation, and maintenance. The digital readout on a TEM is not more than ±10% Obtaining accurate and representative measurements accurate. To obtain more accurate measurements you must of particle size is not trivial. Beyond selecting the right first calibrate the magnification of the instrument. experimental method to use, you may have to perform a statistical analysis of the data to obtain meaningful results. 20.12 SIEVING Sieving is the oldest method to determine particle size dis- 20.11 CHARACTERIZING POWDERS tribution. Actually, sieving is used for sorting particles BY MICROSCOPY according to size rather than measuring their size. Typi- cally, sieves with decreasing mesh size are stacked with the The most direct way to determine the size of a particle is largest mesh at the top. The term “mesh size” denotes the to look at it. We described the various microscopy tech- number of openings per linear inch in the sieve screen. niques in some detail in Chapter 10. If the size of the NBS (now NIST) developed the sieve numbering system particle is >1 μm, then visible light microscopy (VLM) is based on the “fourth root of two” ratio; this series is known fine. Particle size measurements are made either directly as the ASTM E-11 standard. This ratio (= 1.189) means at the microscope or from micrographs (photographs that the sieve openings are an exact geometric series. taken using the microscope). The main challenge is in Table 20.6 lists the aperture (hole) size of standard determining the size of three-dimensional grains on the sieves; this size corresponds closely to the ISO standard. basis of planar images. Several procedures have been As you can see sieving is not applicable to the smallest employed for making these measurements. The Heyn particle sizes (<5 μm), which are often used in the fabrica- intercept method is one of the most useful approaches, and tion of components from advanced ceramics. But sieving is ideally suited for nonequiaxed grains. The number of is used in the traditional ceramics industry for size deter- grain or grain boundary intersections of a straight or mination of raw materials. It is particularly suited for 366 ......................................................................................................... P o w d e r s , F i b e r s , P l at e l e t s , a n d C o m p o s i t e s  TABLE 20.6 Aperture Size of U.S. Standard Sieves F = 3πηdv (20.7) Sieve number Aperture (mm) Sieve number Aperture (mm) where η is the viscosity of the liquid. Equating F to the effective weight of the particle (i.e., the downward force) 3.5 5,660 60 250 4 4,760 70 210 gives 5 4,000 80 177 6 3,360 100 149 v = d(ρs − ρl)g/18η (20.8) 7 2,830 120 125 where g is the gravitational constant and ρs and ρl are the 8 2,380 140 105 10 2,000 170 88 densities of the particle and the liquid, respectively. Equa- 12 1,680 200 74 tion 20.8 is Stokes’ equation from which we can determine 14 1,410 230 63 d by measuring the sedimentation rate. 16 1,190 270 53 The sedimentation technique is reliable for particle 18 1,000 325 44 size determination when d is in a size range of 2–50 μm. 20 841 400 37 25 707 600 30 The falling rate of smaller particles is affected by Brown- 30 595 1,200 15 ian motion resulting from collisions with the molecules of 35 500 1,800 9 the liquid and other interactions between particles. Stokes’ 40 420 3,000 6 law is valid only for laminar or streamline flow (i.e., when 45 354 8,000 3 there is no turbulence). The Reynolds number (Re) is a 50 297 14,000 1 measure of when the process transitions from turbulent to laminar flow: powders with particle size >56 μm. The particle size dis- Re = vρl d/η (20.9) tribution obtained by sieving is normally only approxi- Laminar flow is restricted to Reynolds numbers of less mate because it is often too time consuming to sieve for than 0.2. long enough periods to achieve the final distribution of If there is a narrow distribution of particle sizes then particles in the various sieves. sedimentation is experimentally very simple. A dilute sus- pension of the particles is shaken in a tall graduated cylin- der. After a few seconds the suspension becomes stagnant 20.13 SEDIMENTATION and the particles start to settle at a constant (terminal) velocity. A clear layer of liquid forms at the top of the cyl- A spherical particle of diameter, d, falling through a inder and grows as the particles continue to settle. The viscous liquid, soon reaches a constant velocity, v, where velocity of the downward movement of the interface between its weight is balanced by a frictional force, F, exerted by the clear liquid and suspension is v, which can readily be the liquid as shown in Figure 20.10. Stokes’ law gives the obtained using a stopwatch and the cylinder graduations. important relationship between F and v: The technique becomes more complicated if there is a distribution of particle sizes. In these cases it is more usual to measure the particle concentration at some point in the FUP fluid. One way of doing this is by determining the turbid- ity of the fluid (i.e., its clarity). We use either light or X- rays and measure the intensity of the transmitted beam as the powder settles. The ratio of the intensity of the the transmitted beam, I, to that of the incident beam, I0, is given by the Beer–Lambert law: I/I0 = exp(−KAcx) (20.10) where K is the extinction coefficient, A is the projected area per unit mass of particles, c is the concentration by mass of the particles, and x is the path length of the light through the suspension. For a dilute suspension containing roughly equal amounts of two particle sizes, Figure 20.11 shows the way turbidity changes with time at a distance, L, below the top of the liquid. Turbidity is usually expressed in terms of nephelometric turbidity units (NTu). This is in reference FDOWN to a specific type of measurement technique. A nephelom- FIGURE 20.10 Illustration of the force balance during settling of a eter specifically measures the light reflected into the particle in a Newtonian fluid with laminar flow. detector by the particles. 2 0 .13 S e d i m e n tat i o n .................................................................................................................................................... 367  either side of which an electrode is immersed. As a parti- cle passes through the orifice, it displaces an equivalent volume of electrolyte and causes a change in resistance, R. The magnitude of this change is proportional to the particle size. NTu The changes in R are converted to voltage pulses that are amplified, sized, and counted to produce data for the Large Small size distribution of the suspended particles. The peak particle particle height depends on the particle size as illustrated in Figure L L t= t= 20.12b. For peak A a larger particle passes through the Vt,l Vt,s orifice than for peak B. The peak width is a measure of t how long it takes the particle to move through the orifice. FIGURE 20.11 Result of sedimentation measurements using The Coulter counter can measure particles in a size range turbidity for two particle sizes in a solution; Vt is the terminal 0.5–100 μm. velocity. The particle size can be determined from Stokes’ 20.15 CHARACTERIZING POWDERS BY equation. Clearly, if the particle size distribution is broad, LIGHT SCATTERING the interpretation of turbidity measurements is not simple! Turbidity measurements are widely used to assess water When a beam of light strikes a particle, some of it is quality. In the United States the allowable turbidity in transmitted, some is absorbed, and some is scattered. drinking water is 1 NTu. Many drinking water utilities try When the particles are larger than the wavelength of the to achieve levels as low as 0.1 NTu. incident light they cause Fraunhofer diffraction. The intensity of the forward-scattered light (i.e., light traveling 20.14 THE COULTER COUNTER in roughly the same direction as the incident light) is proportional to d2. Figure 20.13 shows examples of the The Coulter counter, shown in Figure 20.12a, measures light scattered from two particles of different sizes. the number and size of particles suspended in an electro- lyte by causing them to flow through a narrow orifice on  Smaller particles scatter a small amount of light through a large angle.  Large particles scatter a greater amount of light but Meter through a smaller angle. The relationship between scattering angle (θ) and d is sin θ = 1.22λ/d (20.11) B Orifice θ A Large Laser particle A beam Detector R plane B θ Small particle t Laser FIGURE 20.12 Results of Coulter counter measurements for two beam particle sizes A and B. R is the resistance between the electrodes, shown as shaded squares. FIGURE 20.13 Scattering of light by large and small particles. 368 ......................................................................................................... P o w d e r s , F i b e r s , P l at e l e t s , a n d C o m p o s i t e s The light source is usually an He–Ne laser with λ = series of XRD profiles for the 111 peak (arising from dif- 0.63 μm. For this wavelength the reliable particle size fraction of the X-rays by the {111} planes) of a ZrO2 range is 2–100 μm. Light-scattering methods have the fol- powder doped with 3 mol% Y2O3. Higher calcination tem- lowing advantages: peratures lead to particle coarsening and a corresponding decrease in β.  Accuracy It is important to remember that when determining  Speed particle size in a powder by measuring the width of X-ray  Small sample size peaks it is actually the size of the individual crystals that  Can be automated are being measured. As a consequence, if the particles are agglomerated XRD will give the size of the primary par- ticles and not the agglomerate size. 20.16 CHARACTERIZING POWDERS BY Similarly, the reflections (spots) in an electron diffrac- X-RAY DIFFRACTION tion pattern will be broadened if the sample is composed of small crystals. There- In Chapter 10 we discussed PEAK WIDTH fore diffraction in the TEM X-ray diffraction (XRD) Depends on where it is measured relative to its maximum is not normally used to and how it can be used height. determine particle size to obtain crystallite size. Full width at half maximum. because the number of Because of the widespread Full width at tenth maximum. particles that can be exam- use of this technique and ined is fairly small and its applicability to very because it is better to just small particles we will reiterate some of the key points look at the image and make the measurements directly. as they apply to characterizing powders. The width of the diffraction peaks, β, is related to d by the Scherrer equation: 20.17 MEASURING SURFACE AREA (THE BET METHOD) d = 0.9λ/(β cos θ) (20.12) Surface-area methods rely on the adsorption of gases onto where λ is the X-ray wavelength and θ is the Bragg angle. a particle surface at low temperature. The mass of gas From Eq. 20.12 you can see that as d increases, β decreases. adsorbed is measured as a function of gas pressure at a When d is greater than about 0.1 mm the peaks are so fixed temperature (typically liquid nitrogen). narrow that their width cannot be distinguished from in- The method developed by Brunauer, Emmett, and strumental broadening. Consequently, XRD is most applic- Teller (BET) to estimate the particle size relies on deter- able to fairly small particle sizes. Figure 20.14 shows a mining the surface area of the powder, which is calculated from the N2-isotherm observed at the boiling point of N2. (111) peak The BET equation is P/[Va (P0 − P)] = (VmC) −1 + (C − 1)P/[P0VmC] (20.13) 25°C P is the gas pressure P0 is the saturation vapor pressure for the adsorbate at the adsorption temperature 1100°C Va is the adsorbate volume at relative pressure P/P0 Vm is the adsorbate volume per unit mass of solid for monolayer coverage 1200°C C is the BET constant Vm is determined in the relative pressure ranges P/P0 1250°C ∼ 0.05 and P/P0 ∼ 0.2; according to BET theory this is the amount of nitrogen necessary to form a monomolecular 1300°C layer on the particle. Since one nitrogen molecule requires a surface area of 0.162 nm2, the surface area of the particle can be easily estimated in m2 /g. 1500°C A plot of P/Va (P0 − P) versus P/P0 gives a straight line 29 30 31 2θ 32 from which Vm and C can be determined. The specific FIGURE 20.14 Illustration of X-ray line broadening for a ZrO2 /3 surface area, S, of the powder can then be calculated mol% Y2O3 powder prepared by hydrothermal synthesis. using 2 0 .17 M e a s u r i n g S u r fa c e A r e a ( Th e B e t M e t h o d ) ............................................................................................. 369  S = NAσVm /V′ (20.14) TABLE 20.8 Chemical Analysis of Powders Bulk techniques Comments where NA is Avogadro’s number, V′ is the molar volume = 22,410 cm3/mol, and σ is the cross-sectional area of the Emission spectroscopy (ES) Elemental analysis to the ppm adsorbate molecule (0.162 nm2 for N2). level, frequently used for For spherical particles the particle radius, a, can be qualitative survey analyses, 5 mg powder sample obtained from Flame emission Quantitative analysis of alkali and spectroscopy (FES) Ba to the ppm level, ppb a = 3/ρS (20.15) detectability for some elements, solution sample where ρ is the density. Atomic absorption Industry standard for quantitative spectroscopy (AAS) elemental impurity analyses; detectability to ppm level, solution sample 20.18 DETERMINING PARTICLE X-ray fluorescence (XRF) Elemental analyses, detectability COMPOSITION AND PURITY to 10 ppm, Z >11, solid/liquid samples Gas chromatography/mass Identification of compounds and In addition to knowing particle size and particle size dis- spectrometry (GC/MS) analysis of vapors and gases tribution of our powder we often need to know its compo- Infrared (IR) spectroscopy Identification and structure of sition and purity. Table 20.7 lists the composition of a organic and inorganic typical high-purity alumina powder. Industrial ceramic compounds, mg dispersed powders can contain over 30 detectable elements, but in powder in transparent liquid or solid or thin-film sample most cases less than 10 are present at levels greater than X-ray diffraction (XRD) Identification and structure of 0.01–0.05%. Many industries use wet chemical techniques crystalline phases, quantitative such as precipitation and titration for such analysis. These analysis to 1%, mg powder techniques are used because they are often simple to sample perform and give a quick result. For example, in the indus- Nuclear magnetic Identification and structure of resonance (NMR) organic and inorganic trial production of red lead (Pb3O4) it is necessary to compounds, sample to 5 mg for determine the amount of free Pb and litharge (PbO). This H and 50 mg for C analysis is typically done hourly and the results are used to modify the furnace temperature or throughput. In addition to using wet chemistry there are numerous analytical methods that can give us chemical composition Of these factors, cost is often the most important. and impurity levels and these are summarized in Table There are numerous choices: 20.8. The choice of technique depends on several factors:  X-ray fluorescence (XRF) would not be a good choice to determine the amount of low-Z elements present.  Type of material (is it readily soluble in common sol-  Flame emission spectroscopy (FES) is a good choice vents, is the powder agglomerated) if we have very small amounts of the alkali metals.  Amount of material (do we have milligrams or  Nuclear magnetic resonance (NMR) can be used to kilograms) determine H concentrations, but it is often expensive  Possible impurities (alkali metals, H, rare earths) to use and not as widespread as atomic absorption  Amount of impurities (ppm or percent) spectroscopy (AAS).  Availability and cost of instrument (do we need to use  For phase determination and phase proportions in a a national facility) powder mixture XRD is useful, allowing quantitative phase analysis down to ∼1% in a powder sample.  With a field-emission source in TEM, chemical analy- sis with atomic resolution is possible; the interaction volume can be as small as ∼10−8 mm3. TABLE 20.7 Composition of a High-Purity Alumina Powder (wt%) Oxide % 20.19 MAKING FIBERS AND WHISKERS Al2O3 99.8 Na 2O 0.06 Ceramic fibers and whiskers are used in the fabrication of MgO 0.05 composites where they are dispersed within a matrix, SiO2 0.03 which may be a ceramic, a polymer, or a metal. The choice Fe2O3 0.03 of matrix depends on the proposed applications for the com- U oxide ≤0.0005 posite. A primary consideration is the desired operating 370 ......................................................................................................... P o w d e r s , F i b e r s , P l at e l e t s , a n d C o m p o s i t e s temperature. Polymers are stable up to a maximum tem- Step 2. Spinning. The slurry is extruded through a perature of about 300°C, metals up to about 900°C, and spinnerette into “green” fibers and dried. A similar process ceramics are usable at temperatures >1800°C. Ceramics produces polymer fibers, such as nylon. can be used as the rein- Step 3. Firing. The forcement phase in all “green” fibers are fired ini- types of matrix. The major ALKYL CHAINS tially at low temperatures requirements are that they Straight chains are always designated as normal, and the to drive off the organic are strong and stiff. word is usually abbreviated to n-. So in n-butoxide the additives and convert the Whiskers are small alkyl chain is CH3CH2CH2CH2–]. aluminum oxychloride to single crystals a few tens the oxide. It is during this of micrometers in length with a diameter typically <1 μm. stage that shrinkage of the fiber is controlled. Firing at Whiskers have extremely high strengths, approaching the higher temperature causes sintering that results in solid theoretical strength, because of the absence of crystalline fibers with a controlled amount of porosity and grain size. imperfections such as dislocations. The resulting fiber is 99% α-Al2O3, 98% theoretical density, with a diameter of 10–20 μm and a grain size of ∼0.5 μm. The mechanical properties of these fibers at 20.20 OXIDE FIBERS room temperature are good, but the fibers are susceptible to grain growth at temperatures >1000°C, which leads to Oxide fibers have been commercially available since the a considerable fall in strength. 1970s. Control of the microstructure through careful pro- cessing is essential to obtain the desired properties, which Zirconia Fibers by Sol-Gel Processing for ceramic fibers for structural applications are Step 1. Sol formation. Zirconium n-butoxide [Zr(n-OBu) 4]  Low porosity is mixed with hydrogen peroxide (H2O2), nitric acid  Small grain size (for low-temperature applications) (HNO3), and a solution of yttrium nitrate [Y(NO3)3 · nH2O).  Large grain size (for high-temperature applications The zirconium n-butoxide undergoes hydrolysis produc- where creep is a concern) ing zirconium hydroxide and a molecule of alcohol.  High purity Zr(n-OBu) 4 + H2O → Zr(OH) 4 + n-Bu(OH) (20.16) Ceramic fibers cannot usually be produced by the techniques used to produce glass fibers because of the Step 2. Gelation. After mixing the solution is heated very high melting temperatures (often >2000°C) and to 60°C; at this temperature the alcohol evaporates. The the low viscosities when molten. There are four general viscous solution is passed through a spinnerette to produce methods to produce ceramic fibers: gel fibers. Step 3. Firing. The gel fibers are fired to produce a  From slurry ceramic. The zirconia is stabilized in a cubic fluorite  By sol-gel processing structure by the presence of yttrium in the structure. The  By chemical vapor deposition polycrystalline fibers are typically 5–10 μm in diameter.  From polymer precursors The grain size depends on the sintering temperature. At temperatures ≤1000°C the grain size is <0.1 μm. If the As you can see chemistry plays an important role and sintering temperature is 1500°C the grains are ∼1 μm in consequently there is overlap with Chapter 22. In this diameter. section we give one typical example of each of the methods, but bear in mind that it is possible to produce fibers of Silicon Carbide Fibers by Chemical many other ceramics by similar routes. Vapor Deposition Chemical vapor deposition often involves decomposition Alumina Fibers from Slurry of a volatile gas to produce a nonvolatile solid. The reac- A fiber developed in 1974 by DuPont and known as ‘Fiber tion usually proceeds at high temperature and the solid is FP’ was the first commercially produced alumina fiber. It deposited onto some form of substrate. In the case of fiber has now been discontinued, but the process is a good formation the substrate is a wire. SiC can be formed by illustration of the use of a slurry. decomposing methyltrichlorosilane, CH3SiCl3: Step 1. Slurry formation. The slurry is an aqueous solution containing aluminum oxychloride [Al2 (OH)5Cl] CH3SiCl3 (gas) → SiC (solid) + 3HCl (gas) (20.17) together with additions to stabilize the suspension (defloc- culents) and polymers to modify the viscosity. The viscos- The substrate or core in this case is a 10-μm-diameter ity must be adjusted such that the slurry is spinnable. tungsten wire. The deposit consists of fine crystals of 2 0 . 2 0 O x i d e F i b e r s ........................................................................................................................................................ 371 β-SiC oriented preferen- POLYCRYSTALLINE Si In the mid-1970s, a process tially with the {111} planes This is used by industry to manufacture Si boules. It is for obtaining SiC whiskers parallel to the fiber axis. prepared by decomposing silanes onto high-purity Si by pyrolyzing rice hulls These fibers, which are cores. was developed. Rice hulls sometimes called monofil- are a waste byproduct aments, have diameters in of rice milling. For each the range of 100–150 μm. It takes about 20 seconds in the 100 kg of rice milled, about 20 kg of rice hull is produced. reactor to obtain a monofilament of 100 μm. Because The rice hulls contain silica, which comes from the soil of their large diameter and high Young’s modulus, mono- and is closely mixed into the cellulose structure of the rice filaments are not flexible and, as a consequence, cannot hull in fortuitously near ideal amounts for producing SiC. be easily woven. The properties of the fiber are degra- The rice hulls are heated (called “coking”) in an oxygen- ded above about 1000°C because of the formation of W2C free atmosphere at 700°C and the volatile constituents are and W5Si3. driven off. The coked rice hulls, containing about equal amounts of SiO2 and free carbon, are further heated in an inert or reducing atmosphere (flowing N2 or NH3 gas) Silicon Carbide Fibers from between 1500 and 1600°C for about 1 hour to form SiC: Organic Precursors 3C + SiO2 → SiC + 2CO (20.18) These processes allow the production of fibers (10–20 μm in diameter) thinner than those produced by chemical About 10% of the product is in the form of whiskers and vapor deposition (CVD). the remaining product is in the form of particles, generally Step 1. Precursor synthesis. For SiC fibers the precur- platelets. The whiskers may be separated out to give a sor is polycarbosilane, a high-molecular-weight polymer 90–95% “pure” product. containing both Si and C. Polycarbosilane is synthesized SiC whiskers are used commercially in a number of by dechlorination of dimethylchlorosilane (a commer- different applications. Alumina reinforced with 25–30 wt% cially available organic compound) by reacting it with SiC whiskers is the material of choice for inserts used in sodium to produce polydimethylsilane. Thermal decom- high-speed cutting of nickel-based superalloys (for aero- position and polymerization of polydimethylsilane lead to space applications). However, whiskers do have a number polycarbosilane. The average molecular weight of the of disadvantages over particles. It is difficult to produce resulting polymer is about 1500. homogeneous dispersions as the whiskers tend to form Step 2. Melt spinning. The polymer is melt spun from entwined agglomerates and, even if well dispersed, some a 500-hole nozzle at about 350°C under N2 to obtain the orientation of the whiskers occurs leading to anisotropic so-called “preceramic continuous precursor fiber.” properties. Step 3. Firing. The precursor fiber is quite weak and must be converted to a strong SiC fiber by firing. The heat 20.22 GLASS FIBERS treatment involves several stages. Initially the precursor fiber is oxidized in air at 200°C to induce cross-linking of “Glass fiber” is a generic term like “carbon fiber” or the polymer chains. Heating is continued slowly in N2. “steel.” There are many types of glasses, but from the Above 200°C, the side chains containing hydrogen and point of view of composite technology only silica glasses methyl groups decompose. The conversion to SiC is com- are currently important. However, even within this group plete above about 850°C. of glasses the composition, and hence properties, vary The SiC is in the form of small (∼2 nm) crystals of β- considerably. The composition of three glasses commonly SiC. The fiber is not pure SiC as some oxygen remains used in fibers is given in Table 20.9. from the low temperature heat treatment and also excess The “E” in E glass is an abbreviation for electrical. E silicon and carbon are present. A typical composition is glass is a good electrical insulator and it has good strength 59% Si–31% C–10% O. TABLE 20.9 Approximate Chemical Compositions of Some Glasses Used in Fibers (wt%) 20.21 WHISKERS E glass C glass S glass SiC whiskers are the strongest materials known that are SiO2 55.2 65.0 65.0 produced in commercial volumes. There are two methods Al2O3 8.0 4.0 25.0 that are used: CaO 18.7 14.0 — MgO 4.6 3.0 10.0  Vapor–liquid–solid (VLS) process (this is described in Na 2O 0.3 8.5 0.3 K 2O 0.2 — — Chapter 29) B2O3 7.3 5.0 —  From rice hulls (described below) 372 ......................................................................................................... P o w d e r s , F i b e r s , P l at e l e t s , a n d C o m p o s i t e s and a reasonably high Young’s modulus. This glass is in the tank. The glass flows by gravity through the holes, based on the eutectic in the ternary CaO–Al2O3 –SiO2 with forming fine continuous filaments that are gathered some substitution of B2O3 for SiO2 and MgO for CaO. The together and passed around a fast rotating collet, followed B2O3 substantially lowers the liquidus temperature giving by drawing rapidly at a speed of 1–2 km/min. The dia- a longer working range and consequently makes fiber meter of the glass fibers depends on the diameter of the drawing easier. More than 90% of all continuous glass bushing orifice, the viscosity of the melt, which is a func- fiber produced is of the E glass type and is used mainly tion of temperature and composition, and the head of glass as a reinforcement in PMCs. in the hopper. Typically fibers produced in this way have S glass is based on the a diameter on the order SiO2–Al2O3 –MgO system; of 10 μm. A “size” consist- this fiber has higher stiff- E GLASS: E IS FOR ELECTRICAL ing of an aqueous polymer ness and strength (hence Most applications of E glass do not utilize its electrical emulsion is applied before the designation “S”) than properties. the fibers are wound onto a E glass. It also retains its drum. Sizing protects the mechanical properties to higher temperatures. However, S surface of the fibers from damage and also helps in han- glass is more difficult to draw into fibers due to its limited dling the fibers by binding them into a strand. working range and is therefore expensive. Because optical fibers require much more precise C glass has a high CaO content and this results in a control over composition and impurities than glass fibers glass with a high corrosion resistance in acid and alkaline for composites they are prepared by very different means; environments. we describe the methods for preparing optical fibers in Producing glass fibers is a well-established technol- Chapter 32. ogy. Figure 20.15 shows a schematic of the conventional procedure for forming glass fibers. The raw materials are 20.23 COATING FIBERS melted in a hopper and the molten glass is fed into electri- cally heated platinum-rhodium bushings; each bushing The interface between fiber (or whisker) and matrix is the contains 200 holes at its base. The bushing diameter is key to the overall mechanical properties of a composite. 1–2 mm. A constant head of molten glass is maintained A weak interface allows a propagating crack to be deflected, which increases the toughness of the composite. Molten glass (direct melt) A strong interface allows transfer of the load from the matrix to the fiber and produces an increase in modulus and stiffness of the composite. In CMCs we are usually Marble more interested in producing a weak interface so that feed debonding occurs, which often leads to fiber pull-out by frictional sliding and substantial absorption of energy. Bushing Figure 20.16 shows the effect of carbon coatings (resistance heating) of increasing thickness (Dc) deposited on NicalonTM (a Forming orifices 1000 10 τI Composite toughness G G Continuous Application filaments of sizing (MPa) (kJ.m-2) Filaments merged 100 1 into strand τI Strand traversed: Interfacial packaging shear strength 10 0.1 Package, 0 0.5 Dc (μm) 1 or cake, formed FIGURE 20.16 Effect of carbon coating thickness (D C) on the mechanical properties of NicalonTM fibers in an SiC matrix. Interfacial shear strength was measured by push-down testing and FIGURE 20.15 Fiber-forming process using either a glass melt or toughness from the area under the stress–strain curve during marble feed. loading along the fiber axis. 2 0 . 2 3 C oat i n g F i b e r s ................................................................................................................................................... 373  R –– Si X3 + H2O R –– Si(OH)3 + 3HX environments. Reaction with water can result in the for- (A) R R R mation of a weak porous surface on the fiber and to weak bonding between fiber and matrix. Coating a glass fiber HO Si OH HO Si OH HO Si OH with a coupling agent can lead to strong interfacial O O O bonding. There are many types of coupling agents, and H H H H H H the principles of how they work can be illustrated with O O O silane coupling agents. These have the general formula R–Si–X3, where X represents hydrolyzable groups such as M M M ethoxy (–OC2H5). The R group is chosen based on the Glass type of polymer used for the matrix. The processes leading (B) R R R to bond formation between a glass fiber and a polymer O Si O Si O Si O matrix via the use of a silane coupling agent are illustrated in Figure 20.17. O O O M M M Glass 20.24 MAKING CERAMIC–MATRIX (C) COMPOSITES Polymer network Monolithic ceramics generally have reasonably high R R R strength and stiffness but are brittle with low toughness. One of the main reasons for forming CMCs is to increase O Si O Si O Si O toughness. Naturally it is also hoped, and often found, that O O O there is a concomitant improvement in strength and stiffness. M M M Glass The development of CMCs has lagged behind MMCs and PMCs for two primary reasons: FIGURE 20.17 Illustration of the processes involved in joining a polymer and glass using silane coupling agents. (a) Hydrolysis of the silane to the corresponding silanol; (b) hydrogen bonding  Most of the processing routes for CMCs involve high between hydroxyls on the silanol and those attached to the glass; temperatures and can be employed only with high (c) polysiloxane bonded to the glass following condensation during temperature reinforcements. It was not until fibers drying; and (d) bonding between the functional group R and the and whiskers of ceramics such as silicon carbide polymer. were readily available that there was much interest in CMCs.  Differences in coefficients of thermal expansion, commercial SiC fiber produced from polymer precursors) α, between the matrix and the reinforcement lead fibers prior to composite formation. The interfacial shear to thermal stresses on cooling from the processing strength decreases with increasing coating thickness, but temperature. These stresses can lead to cracking of the macroscopic toughness increases. the matrix. When ceramic fibers are in contact with metals at ele- vated temperatures (e.g., during fabrication of MMCs) an The number of feasible methods for producing CMCs extensive reaction can occur that leads to interfacial crack- is limited and very few of these are commercially viable ing and degradation in the properties of the composite. at the present time. These reactions are particularly severe for titanium matri- ces, which are of interest for high-temperature applica- tions. Applying a protective coating (called a diffusion 20.25 CERAMIC–MATRIX COMPOSITES barrier) can reduce the extent of the reaction. These coat- FROM POWDERS AND SLURRIES ings must be This is simply an extension of the powder route for pro-  Thermodynamically stable ducing monolithic ceramics. A powder of the matrix con-  Nonpermeable to migrating reactants stituent is mixed with the toughening constituent, which  Robust is in particulate or whisker form, together with a binder. Although it is difficult to meet all these requirements, The mixture is then pressed and fired or hot pressed. particularly the first one, coatings that provide protection Difficulty can be experienced in obtaining a homoge- to ceramic fibers in titanium MMCs have been developed; neous mixture of the two constituents and high propor- examples include carbon and duplex C/TiB2. tions of the toughening phase cannot be easily achieved. Glass fibers, widely used as reinforcements in PMCs, Additional problems may arise with whiskers. Whiskers are often coated to improve their durability in aqueous tend to aggregate causing a significant reduction in the 374 ......................................................................................................... P o w d e r s , F i b e r s , P l at e l e t s , a n d C o m p o s i t e s packing efficiency. Also damage to the whiskers can occur matrix composites but can also be used for glass-ceramic during mixing and pressing, particularly when cold matrix composites. The advantage of matrix transfer pressing. molding is that it permits fabrication of components such Because of the difficulties encountered in obtaining as tubes, which are difficult to produce by other methods. homogeneous mixtures by conventional powder process- In tube production, a preform and a glass slug are inserted ing, wet processing is sometimes favored. It is essential into a cylindrical mold. Application of heat and pressure that the constituents remain deflocculated, i.e., well dis- forces the fluid glass into the pores in the preform and, persed, in the slurry. Deflocculation is achieved by control after cooling, the composite tube is ejected from the of the pH of aqueous solutions and by ultrasonic agitation mold. of the slurry. If a sol is poured over a preform it will infiltrate it The slurry process can also be used to produce com- because of its fluidity. The sol is then dried in a sub- posites by tape casting. An example is the fabrication of sequent heat treatment. The processing temperature is laminated SiC whisker-reinforced mullite composites. normally low, thus reducing the risk of damage to the preform, and complex shapes can be produced. However, 1. Mullite is mixed with an organic binder in a ball mill there are disadvantages of high shrinkage and low yield for 24 h. SiC whiskers, between 10 and 50 vol%, are and consequently repeated infiltrations are necessary to added and mixed for a further 24 h. increase the density of the matrix. Furthermore, for some 2. The mix is tape cast to produce sheets having a thick- materials temperatures higher than those needed just for ness of 50–200 μm. The whiskers are all oriented with drying are required to produce the desired ceramic, e.g., their long axes parallel and aligned to the edges of the Zr(OH) 4 needs to be calcined at about 550°C to give tape. ZrO2. 3. Several sheets (40–80) are laminated together at 80°C Infiltration can be done in the vapor phase using a and 35 MPa for 10 min. CVD process. In composite technology CVD is used, as 4. The binder is burned out by heating the laminate to we have already seen, to produce fibers. It is also used to 600°C at a rate of 2°C/min. The hold time at this coat fibers and to infiltrate porous preforms to form the temperature is 2 hours. matrix. In the latter case the process is called chemical 5. The laminate is hot pressed at 1550–1850°C for 30–70 vapor infiltration (CVI). minutes at a pressure of 35 MPa. An oriented SiC CVI is very similar to the CVD processes we have whisker composite is produced. already described. The gaseous reactants infiltrate the heated substrate positioned in the reactor. A chemical Another slurry-based process to form CMCs involves reaction occurs in the gaseous state and deposition of the passing the fibers (e.g., SiC) through a slurry of glass matrix takes place. The maximum deposition rate is about powder, water, and a binder. The bundles of fibers (called 2500 μm/h. tows) impregnated with the slurry are wound on a mandrel The best-established CVI process is for the production to form a monolayer tape. The tape is cut into plies that of carbon–carbon composites. It has also been employed are stacked into the required stacking sequence, e.g., uni- for the production of a wide range of ceramic matrices directional or cross-plied, prior to burnout of the binder. including carbides (e.g., B4C, SiC, TaC, and TiC), nitrides Hot pressing is used to consolidate the matrix. In glass- (e.g., BN and Si3N4), TiB2, and Al2O3. ceramic composite production some crystallization occurs The advantages of CVI are during hot pressing, but an additional heat treatment may be required to complete devitrification.  Complex shaped preforms can be coated.  Relatively low temperatures (800–1000°C) can be 20.26 CERAMIC–MATRIX COMPOSITES used. BY INFILTRATION  In situ fiber surface treatments can be made prior to densification. Melt infiltration techniques, although well established for MMCs, have met with only limited success for CMCs. The main disadvantages are that the process is time The main problems are consuming and expensive.  Reactions with the reinforcement due to the high melting temperatures of refractory ceramics and the reactivity of molten glasses 20.27 IN SITU PROCESSES  Low rates of infiltration resulting from the high viscosities The Lanxide process, developed by the Lanxide Corpora- tion, involves the formation of a ceramic matrix by the The most successful of the melt techniques is matrix reaction between a molten metal and a gas, e.g., molten transfer molding, which was originally developed for glass aluminum reacting with oxygen to form alumina. Growth 2 0 . 2 7 I N S I T U P r o c e s s e s ............................................................................................................................................... 375  of the ceramic occurs outward from the original metal Reinforcement surface and through a preform as illustrated in Figure 20.18. A preform is not a prerequisite. By simply placing powder particles above a liquid metal particulate rein- forced composites may be produced. In both cases the only requirements are that the fibers/particles do not react with the gas and are wetted by the ceramic. One of the big advantages of this type of process is that near-net- shape forming is possible. A number of novel techniques are being studied Growth Matrix barrier whereby the composite is formed in situ via a chemical growth reaction. One possible reaction is 2AlN + B2O3 → Al2O3 + 2BN (20.19) Molten alloy Such reactions have the potential to give good homo- Reinforced geneous distributions of the toughening phase, and the raw ceramic materials may be less costly than the products, e.g., BN is expensive. FIGURE 20.18 Illustration of the Lanxide process for making a shaped CMC. CHAPTER SUMMARY In this chapter we described ceramic particles and their use in making composite materials. We paid particular attention to how ceramic powders are produced. The important character- istics of ceramics powders are size and size distribution, shape, and chemical composition As is often the case, this is a big subject. For many traditional ceramic products cost is one of the overriding concerns; therefore the most inexpensive method of producing powders is often selected. For advanced ceramics products such as those used in the electronics industry, obtaining fine-grained uniform particles of high purity is often the dominant issue. For these applications chemical routes such as sol-gel are used for powder production. For nonoxide ceramics, such as Si3N4, vapor-phase routes are used to produce powders. A major advantage of vapor-phase routes is that we can produce nanoparticles with narrow size distributions. We also described the different analytical techniques used to characterize powders both in terms of their size and composition. To determine particle size it is necessary to choose a method that has sufficient sensitivity. Sieving is a low-cost method and is reliable when the particle size is greater than about 60 μm. But if the particles are smaller than this, as is often the case, then the use of light scattering or X-ray diffraction should be considered. In determin- ing both particle size and chemical composition it is essential that the specimen we choose for analysis is representative of the entire powder sample. Ceramics in the form of fibers and whiskers are often used as reinforcing phases in com- posites. We described the different methods used to produce whiskers and fibers and how they are incorporated into PMCs, MMCs, and, particularly for our interest, CMCs. One of the current directions in the production of CMCs is to produce the matrix and fiber in situ. PEOPLE IN HISTORY BET: Stephen Brunauer (1903–1986) was born in Budapest. Paul Emmett (1900–1985) was born in Portland, Oregon and was in the same Ph.D. class as Linus Pauling. Edward Teller, also born in Hungary (1908– 2003), is also known for his work in physics. Coulter, Wallace H. (1913–1998) was born in Little Rock, Arkansas. He patented the Coulter principle in 1953 and began production of the Coulter counter with his brother Joseph. The instrument was originally used to count blood cells. He established the Coulter Corporation in Miami Florida in 1961. 376 ......................................................................................................... P o w d e r s , F i b e r s , P l at e l e t s , a n d C o m p o s i t e s  Reynolds, Osborne (1842–1912) published his famous paper that described the Reynolds number in 1883. The paper, “An experimental investigation of the circumstances which determine whether motion of water shall be direct or sinuous and of the law of resistance in parallel channels,” was published in the Philo- sophical Transactions of the Royal Society. Stokes, Sir George Gabriel (1819–1903) was Master of Pembroke College, Cambridge, Lucasian Professor of Mathematics (a position once held by Sir Isaac Newton and now held by Stephen Hawking), and a former President of the Royal Society. Stokes was one of the foremost mathematicians of his time and established the field of hydrodynamics. GENERAL REFERENCES Allen, T. (1997) Particle Size Measurements. Volume 1: Powder Sampling and Particle Size Measurements. Volume 2: Surface Area and Pore Size Determination, 5th. edition, Chapman & Hall, London. Compre- hensive guides to particle size, surface area, and pore size measurements covering experimental methods and data analysis. Chawla, K.K. (1993) Ceramic Matrix Composites, Chapman & Hall, London. A detailed description of CMCs. Evans, J.W. and DeJonghe, L.C. (1991) The Production of Inorganic Materials, Macmillan Publishing Company, New York. Standard description of powder processing. Covers more than ceramics. Matthews, F.L. and Rawlings, R.D. (1994) Composite Materials: Engineering and Science, Chapman & Hall, London. A standard composite textbook. At a similar level to this text. Rahaman, M.N. (1995) Ceramic Processing and Sintering, Marcel Dekker, Inc., New York. A detailed description of ceramic powder processing. Reed, J.S. (1988) Introduction to the Principles of Ceramic Processing, John Wiley & Sons, New York. A detailed description of powder processing. Ring, T.A. (1996) Fundamentals of Ceramic Powder Processing and Synthesis, Academic Press, San Diego. Again with more detail on milling. Segal, D. (1989) Chemical Synthesis of Advanced Ceramic Materials, Cambridge University Press, Cambridge. SPECIFIC REFERENCES Brunauer, S., Emmett, P.H., and Teller, E. (1938) “Adsorption of gases in multimolecular layers,” J. Am. Chem. Soc. 60, 309. The original BET paper; cited almost 7000 times. LaMer, V.K. and Dinegar, R.H. (1950) “Theory, production and mechanism of formation of monodispersed hydrosols,” J. Am. Chem. Soc. 72, 4847. Messing, G.L., Zhang, S-C., and Jayanthi, G.V. (1993) “Ceramic powder synthesis by spray-pyrolysis,” J. Am. Ceram. Soc. 76, 2707. A comprehensive review of spray pyrolysis. Pechini, M.P. (1967) “Method of preparing lead and alkaline earth titanates and niobates and coating method using the same to form a capacitor,” U.S. Patent 3,330,697. Suryanarayana, C. and Norton, M.G. (1998) X-Ray Diffraction: A Practical Approach, Plenum, New York. In particular, experimental module 6 shows how to determine particle size and experimental module 7 shows the method used to determine phase proportions in a powder mixture using XRD. Vander Voort, G.F. (1984) Metallography: Principles and Practice, McGraw-Hill, New York, p. 435. Currently out of print. Although its title says it is for the metallurgist, it contains a detailed discussion of grain size determination that can be applied equally well to nonmetals. It gives a detailed description of the various methods and their pros and cons. WWW www.ube.com Ube Industries in Japan, a commercial manufacturer of Si3N4. There are currently no U.S. suppliers of Si3N4 powder. EXERCISES 20.1 (a) Explain briefly the differences between jet milling, vibratory milling, and agitated ball milling. (b) Which technique would you use if you wanted to obtain a particle size of <1 μm. (c) Which technique would you use if maintaining the purity of your powder was your primary concern. 20.2 Why does the sol-gel process allow outstanding control of purity and chemical homogeneity of ceramic powders? 20.3 In Section 20.6 we described the Pechini method for producing SrTiO3 powders. Other multicomponent oxide powders such as YBa2Cu3O7 (YBCO) have been made by a similar process. Identify suitable reactants to make YBCO powders by the Pechini method. C h a p t e r S u m m a ry .......................................................................................................................................................... 377  20.4 You have been employed as a consultant by a company making ceramic powders. Your first assignment is to recommend a technique for measuring particle sizes. An external analysis company has found that the powders typically have a size in the range of 5–30 μm. The powders are also sensitive to moisture. What technique(s) would you recommend and why? 20.5 You are given a sample of a whisker reinforced CMC. How would you go about determining the relative amount of whiskers in the composite and also the composition of the whiskers and matrix phases? 20.6 Compare the material costs involved in making a BN-reinforced Al2O3 CMC composite by (a) combining the individual constituents, and (b) using an in situ reaction involving AlN and B2O3. Would you expect the two composites to have similar microstructures? 20.7 What are the different forms of commercially available fiber that contain mainly alumina and silica? 20.8 Assuming that Figure 20.14 was recorded using Cu-Kα radiation, plot the change in particle size as a function of annealing temperature. 20.9 Are there any commercially available ceramic nanopowders? If so, what compositions are available and how much do they cost compared to a “conventional” powder of the same material? 20.10 Compare the use of scattering of visible light and that of X-rays to determine particle size distributions. 378 ......................................................................................................... P o w d e r s , F i b e r s , P l at e l e t s , a n d C o m p o s i t e s  21 Glass and Glass-Ceramics CHAPTER PREVIEW The structure of glass, particularly silica glass, was introduced at the end of Chapter 7. In this chapter we discuss the different types of glass and some of their various applications. Then, in Chapter 26, we will concentrate on processing glass and the wide variations in compositions. Only two chapters have been devoted to glass due to space limitations; do not take this as a reflection on its importance. Glass is arguably our most important material. It is used for windows, containers, lenses, optical fibers, insulators, glazing and enameling, surgical knives, spectacular art, and road signs! Glass is usually recyclable and environmentally friendly. The Egyptians were great glassworkers, but they were not the first. Glass was actually used much earlier and obsidian, a natural black volcanic glass, was important during Paleolithic times. We can say that glass has played a major role in shaping our civilization. However, there is some difficulty in defining a glass. We will discuss why the words glassy, vitreous, and amorphous are all used to describe glass and try to answer the question “what is glass”? Two thoughts should be kept in mind while studying this chapter:  The assertion by Sturkey: “glass at high temperatures is a chemical solution.”  If glass is a supercooled liquid, it is not a solid so it is not a ceramic (but it is). The mechanical, optical, and electrical properties of glasses are discussed in detail, along with other ceramics, in those topical chapters. 21.1 DEFINITIONS Alternative definition 1: Glass is a solid material that does not show long-range order. The classic definition of glass is based on the historical method of formation: this is a very unusual way of defin- “No long-range order” means not longer than, say, one or ing any material. The result is that glass is now defined in two or three times the basic building block of the glass. several different ways. This definition is consistent with experimental observa- tions [X-ray diffraction (XRD), transmission electron The classic definition: Glass is a supercooled liquid. microscopy (TEM), etc.] but it is clearly a little arbitrary since it depends on the size of the building block. The problem with this definition is that in some cases a Alternative definition 2: Glass is a liquid that has lost its ability particular glass can be prepared that never has been in the to flow. liquid state. This definition is consistent, but broader, than the one The American Society for Testing and Materials (ASTM) defi- given by ASTM and uses a mechanical property to describe nition: An inorganic product of fusion that has cooled to a rigid glass. It is actually close to the more modern physicist’s condition without crystallizing. view of glass. The main glasses we will discuss are the network This essentially says the same thing as the classic defini- oxide glasses, specifically the silicates. Then our defini- tion but excludes polymer glass. It is clearly not ideal to tion of such a glass is rely on the method of production to define a class of mate- rials. We would not consider doing this for crystalline Alternative definition 3: A solid assembly of vertex-sharing materials. tetrahedra lacking long-range order. 21.1 D e f i n i t i o n s ............................................................................................................................................................ 379 We are concerned only with ceramic glass, but you should Liquid V Glass know that there are metallic glasses and polymer glasses. transition How metallic glasses are formed provides a clue to why Liquid range they exist: they have complicated compositions to “frus- trate” crystallization when they are quenched quickly Fast f from the melt (a process known as splat quenching). For cooling the same reason, glycerin can be a glass below −90°C. f s With this understanding in mind, we can discuss the basic s Slow features of glasses. cooling Crystallize Structure Glasses are essentially noncrystalline (or amorphous) solids often obtained by freezing supercooled liquids. Long-range order (LRO) in the atomic arrangement does Crystal not exist over distances greater than, say, 1 nm. The regular arrangement resulting from the distribution over long dis- Tgs Tg Tm f tances of a repeating atomic arrangement (unit cell), which T is characteristic of a crystal, is missing. There is often evi- FIGURE 21.1 Plot of volume versus temperature for a liquid that dence of a short-range order (SRO) in glasses, which cor- forms a glass on cooling and one that forms a crystalline solid. responds to the atomic arrangement in the immediate The glass transition temperature, Tg, depends on the cooling rate vicinity of any selected atom. Numerous attempts have and is not fixed like Tm. been made to explain the formation or the nonfor- from a supercooled liquid mation of glasses. We have TERMINOLOGY The words “vitreous,” “amorphous” and “glassy” are not to a glass. Below Tg the two basic approaches: glass structure does not actually synonymous although they tend to be used interchangeably anyway. relax very fast because it is  Consider the structure Vitreous: from the Latin word for glass (vitrum) now a solid. In the region  Consider the kinetics Amorphous: means having no definite form (strictly of T g the viscosity is about of crystallization 10 13 dPa-s. The expansion speaking, shapeless from the Greek amorphos). Now the lack of ‘form’ implies ‘not crystalline.’ Liquids coefficient for the glassy In the first case, we examine state is usually about the the geometry of the con- are generally without form, so a ‘solid liquid’ is amorphous. same as that for the crys- stituent entities that make talline solid. If slower up the glass, the nature of cooling rates are used so the interatomic bonds, or the strength of the bonds. In the that the time for the structure to relax is increased, the second, we consider how the liquid transitions to a solid as supercooled liquid persists to a lower temperature, and the the temperature drops below the melting point. resulting glass may have a higher density as shown graphi- cally in Figure 21.1. Glass Transition Temperature The physics of glass examines the concept of fragil- ity; this is actually a property of glass-forming liquids We consider a plot of specific volume as a function of above Tg and is a measure of the strength of the intera- temperature as shown in Figure 21.1. This is a form of a tomic bonding. We will talk about water dissolving glass time–temperature–transformation (TTT) diagram for a or glass containers for water; what is less well know is glass. On cooling the liquid from a high temperature, two that you can freeze water into a glassy state by quench- phenomena may occur at the point of solidification, Tm. ing it into liquid ethane. It is a fragile glass, but it is thought that most of the water in the universe exists in  If the liquid crystallizes there is a discontinuous change this state! in V and a discontinuity in the rate of cooling (associ- ated with the heat of crystallization).  If no crystallization occurs the liquid passes into a 21.2 HISTORY supercooled state and V decreases at about the same rate as above Tm. In Chapter 2 we gave a brief history of glass. We will expand on that discussion here. Glass, like flint, is inti- At the glass transition temperature, Tg, the slope of the mately connected with human history because of the use curve decreases to become close to that of the crystalline of obsidian, which is a natural glass. Nobody knows for solid. This break in the cooling curve marks the passage sure when the first glass objects were made. The oldest 380 .......................................................................................................................................... Glass and Glass-Ceramics finds date back to ∼7000 bce, or possibly even earlier. Methods of manufacturing glass for its own sake, and not just as a glaze for pots, had already been discovered in Mesopotamia by approximately 4500 bce. The use of glass as the glaze in pottery dates back even earlier. Around 3000 bce Egyptian glassmakers systemati- cally began making pieces of jewelry and small vessels from glass. Glass had both a functional and a decorative role. Pieces of glass jewelry have been found on excavated Egyptian mummies; an example is the turquoise blue glass figure shown in Figure 21.2. By about 1500 bce Egyptian glassmakers during the reign of Touthmosis III had devel- oped a technique to make usable hollowware. A most FIGURE 21.3 Core-formed bottle shaped like a bulti-fish, 1390– striking example is the core-formed bottle in the shape of 1336 BCE. This example is unusual because it is in polychrome a bulti-fish shown in Figure 21.3. This vessel was made glass. The length is ∼14.5 cm. between 1352 and 1336 bce and was believed to be used to hold scented oil (based on the narrowness of the neck). The wave pattern is very typical of core-formed objects rested them on lumps on nitrum from their cargo. When these and was made by drawing a sharp object along the sof- became heated and were completely mingled with the sand on tened glass. the beach a strange liquid flowed in streams; and this, it is said, The Roman author Pliny the Elder (23–79 ce) explains was the origin of glass. the invention of glass in his encyclopedia Naturalis Historia: Nitrum is a naturally occurring soda, an important ingredient in both ancient and modern glasses. The ashes There is a story that once a ship belonging to some traders in of plants also provided the glassmaker with a rich source nitrum put in here [the coast of modern Lebanon] and that they of sodium. The plants saltwort and glasswort (known as scattered along the shore to prepare a meal. Since, however, no halophytes) were both used to supply sodium. stones for supporting their cauldrons were forthcoming, they Aside: Gerard’s Herbal (1633) says that ‘saltwort was called Kali by the Arabians’: hence the word alkali and the ashes are called soda. One of the most common methods used to form glass is glassblowing. Although this technique was developed over two thousand years ago, the glassblowing pipe has not changed much over time. The main development that has been made in glassblowing is the automated blowing processes that are used to produce glass containers and light bulbs and the technique of blowing the glass inside a mold. Most of the important milestones in the history of glass, particularly in the twentieth century, are associated with developments in manufacturing technology. These developments have led to the low-cost production of com- mercial glasses, for example, window glass, and the use of glass in new applications, such as optical fibers. Many of the topics summarized here have been redis- covered many times. Now that we have the tools, we can see that nature often preempted humans. Ancient History 50,000 bce to 1000 bce. Glass is used in potter’s colored glazes. 7000 bce to 1500 bce. Ancient glass artifacts (possibly as FIGURE 21.2 Glass head of a pharaoh (believed to be Amenophis early as 10,000 bce). II) as sphinx, 1400–1390 BCE. It was made by lost-wax casting and 2600 bce. Earliest actual dated glass. is ∼3.2 cm high. 1500 bce. Egyptians are manufacturing glass articles. 21. 2 H i s t o ry .................................................................................................................................................................... 381 1200 bce. Earliest glass molding. 1882) and named after the town in upstate New York 100 bce. Blown glass is invented with the glassblowing where it is still located. Houghton already owned the pipe (Romans in Syria). Brooklyn Flint Glass Works, but moved to Corning c100 bce. In Alexandria the introduction of manganese because real estate was cheaper there. oxide into the glass composition together with improve- 1881. Thomas Edison brought out his first incandescent ments in glass-melting furnaces resulted in the first electric lamps using glass bulbs made by the Corning successful production of colorless glass. Glass Works. 450 ce. Stained glass was used. 1884. Otto Schott (1851–1935), Ernst Abbe (1840–1905), Carl Zeiss, and Roderick Zeiss established the Glastechnisches Laboratorium Schott und Genossen, Beginning to Engineer Glass which later became the Jenaer Glaswerk Schott und 1200s. In Germany a new process was developed to make Gen and in 1952 the Schott Glaswerke. This company mirrors. The back of a piece of flat glass was coated is now the leading European glass company. with a lead-antimony layer to produce quality (“sil- 1893. The Enterprise Glass Company in the United States vered”) mirrors. The mirror format remains essen- developed a press-and-blow mold that led to the wide- tially unchanged today. spread production of wide-mouth containers. 1268. Eye glasses described by Bacon. These had convex 1903. The automatic bottle-blowing machine invented by lenses for the correction of near sightedness. the American Michael Owens (1859–1923) began pro- 1291. Murano, a small island near Venice, became a glass duction. A machine for drawing large cylinders of center. Glass workers on Murano were generally not glass that were then flattened into window glass was allowed to leave the island. developed by another American, John Lubbers. c1590. The first telescope lenses were made in Italy and 1913. Emile Fourcault, a Belgian, developed a flat-glass later, in 1604, in the Netherlands. machine for commercial operation. 1609. Glass was made in Jamestown, Virginia. 1917. Edward Danner at the Libbey Glass Company intro- 1612. Publication of the textbook L’Arte Vetraria by duced an automatic method for tube making. The Antonio Neri in Pisa. This was the first systematic company remains in operation today and is the largest account of the preparation of the raw materials for manufacturer of glass dinnerware in the United glassmaking. States. 1676. George Ravenscroft, an English glassmaker, devel- 1926. The Corning ribbon machine for high-speed auto- oped lead-crystal glass (also known as flint glass). The matic production of glass light bulbs was developed. addition of lead oxide to the glass formula yielded a glass of high brilliance and a pure ring. It is not crystal, Present Technology but it does contain a lot of lead and it is heavy. 1688. Bernard Perrot, a glassmaker in France under Louis 1957. Corning introduced the Pyroceram® brand of XIV, invented the plate-pouring process. This process glass-ceramics. allowed mirrors with a large surface area to be pro- 1959. Sir Alastair Pilkington’s float process for producing duced. Examples are the magnificent wall of mirrors flat glass worked. in the Galerie des Glaces at Versailles. 1960. Glass-ceramics were patented by S. Donald Stookey Late 1700s. Joseph von Fraunhofer (1787–1826), a German of Corning Glass Works. mirror maker and student of glassmaking technology, 1966. Optical fibers were developed. produced optical quality glasses for telescopes and 1975. Glass recycling became accepted/required. microscopes. (Fraunhofer diffraction and the Fraun- 1980. An acid-leaching process was introduced for pro- hofer Institutes are named in his honor.) ducing 99.6–99.9% silica fibers that resist devitrifica- tion up to 1370°C. These fibers were used as insulation for the space shuttle. Modern Times 1991. Schott produced an 8.2-m-diameter telescope blank 1857. William Clark of Pittsburgh patented a sheet-drawing from a glass-ceramic ZERODUR®, which had been process: a plate glass. introduced in 1968. 1861. A British patent was granted to C.W. Siemens and 1997. Corning produces glass for the Subaru Telescope F. Siemens. Their patent included a discussion of the mirror. Weighing 27 t and more than 26 feet across it application of the principle of regeneration to glass is one of the largest pieces of glass ever made. melting. Regenerative heating is still used in glass melting furnaces today. New and improved methods for processing glass are 1865. A U.S. patent was issued for a press-and-blow being developed. One of the main thrust areas for these process. activities is our concern for the environment. Reducing 1875. Corning Glass Works was incorporated. The energy costs and reducing polluting emissions are impor- company was founded by Amory Houghton Sr. (1812– tant in the modern glass industry. 382 .......................................................................................................................................... Glass and Glass-Ceramics 21.3 VISCOSITY, h the glass has a viscosity similar to that of honey at room temperature. For a typical soda-lime-silicate flat-glass Viscosity is a key property of glass. We need to know the composition this viscosity is achieved in the temperature viscosity of glass at different temperatures so that it can range 1015–1045°C. The other key reference value to be formed, shaped, and annealed. The concept of viscous remember is that a solid has a viscosity of >1015 dPa·s. flow was described (and illustrated) in Chapter 17 because The viscosity of glass varies dramatically with tem- this is the process by which permanent deformation occurs perature as shown in Figure 21.4a for various silicates. in glasses. Viscosity is a mechanical property. Consider The fictive temperature, Tf, is the temperature at which the the tangential force, F, required to slide two parallel plates liquid structure is frozen into the glassy state and is defined a distance d apart past one another when they are sepa- by the crossing of the extrapolated curves from high and rated by a layer of viscosity, η: low temperatures on the η against T plot. The fictive tem- perature like Tg is related to structural transformations in η = (Fd)/(Av) (21.1) glass; Tg is slightly lower. Figure 21.4b shows the The common area is A and temperature dependence VISCOSITY AND POISE of viscosity for the main the velocity of the planes If a force of 1 dyn is required to move an area of 1 cm 2 glass-forming oxides as a relative to one another is v. of liquid or gas relative to a second layer 1 cm away at function of temperature. Essentially, then, viscosity a speed of 1 cm s−1, then the viscosity is one P (poise). You will notice that from is a measure of the liquid’s response to a shearing. the slope of these lines we 1 P = 1 dPa·s can obtain the activation Liquids have viscosities measured in centipoises energy for viscous flow, Ev (cP) and gases have viscosities measured in micropoises (see Section 17.13). Table 21.3 gives some values for η and (μP). In the SI system we would say that liquids have some measured crystallization velocities, n. The latter viscosities in millipascal-seconds (mPa·s) while gas vis- term refers to the rate of movement of the solid/liquid cosities are tenths of micropascal-seconds (μPa·s) (so we interface. The very low n for SiO 2 is indicative of its excel- stick with the poise). lent glass-forming ability: it is very difficult to crystallize Table 21.1 lists some of the viscosity values that are a solidifying melt of SiO 2 . important for glass processing. The values given in Table There are several methods for measuring viscosity; 21.2 are used to define certain characteristics of a glass which is used depends on the expected value of the (again with an emphasis on processing). Many of the viscosity. values listed in this table of viscosities are “standards.” For example, ASTM C338-93(2003) is the “Standard Test Mergules viscometer ≤107 dPa·s Method” for determining the softening point of glass. Fiber elongation ≤107 to 109 dPa·s Beam bending ≤109 to 1014 dPa·s Determine the softening point of a glass by determining the temperature at which a round fiber of the glass, nominally The schematics in Figure 21.5 illustrate the first two 0.65 mm in diameter and 235 mm long with specified tolerances, approaches to measuring η. The viscometer is used for elongates under its own weight at a rate of 1 mm/min when the upper 100 mm of its length is heated in a specified furnace at the rate of 5°C/min. TABLE 21.2 Viscosity “Milestones” The viscosities of some common liquids are given in Viscosity Example Table 21.2 for comparison. Notice that at the working point 10 −2 dPa·s Water at 20°C 10 0 dPa·s Light machine oil 101 dPa·s Heavy machine oil 102 dPa·s Olive oil at 20°C TABLE 21.1 Viscosity Values for Glass Processing 104 dPa·s Runny honey at 20°C; some measure it to be Viscosity Example 102 dP-s 104 dPa·s Glass at its working point; begin working at 103 1.5 −2.5 107.6 dPa·s Shortening point (deforms under its own weight; 10 –10 dPa·s ASTM melting 103.7–103.8 dPa·s Casting plate glass softening at 107.7) a 103.8 dPa·s Seal glass to metal 108 dPa·s Upper limit for low viscosity 105.3 dPa·s Begin updrawing or downdrawing 1013 dPa·s Annealing point (ASTM) 10 6 dPa·s Sinter glass powder to produce a porous body 1013.4 dPa·s Glass at Tg 108 dPa·s Sinter glass powder to produce a solid body 1014.6 dPa·s The strain point of glass (ASTM) 1011.3 –1011.7 dPa·s Glass deforms under gravity >1015 dPa·s Solid 1012.7–1012.8 dPa·s Practical annealing range (stress relief in 1016 dPa·s Upper limit for measuring viscosity seconds) a The shortening point is also called the softening point. 21. 3 Vi s c o s i t y, η ........................................................................................................................................................... 383 logη T, °C 2500 2000 1500 1000 800 600 500 17 log η 12 15 13 SiO2 + 0.2% H2O 11 8 Alumina-silicate SiO2 GeO2 glass 8409 9 P2O5 7 Borosilicate glass 5 B2O3 4 3 4 8 10,000/T 12 Lead borate solder glass (B) Soda-lime glass 0 FIGURE 21.4 (a) Viscosity as a function of temperature (T) for several 0 400 800 1200 1600 silicate glasses: units of η are dPa · s. (b) Viscosity as a function of T (°C) temperature (1/T) for the main glass-forming oxides. Notice the effect that a (A) small amount of water has on the viscosity of silica glass. TABLE 21.3 Crystallization Velocities and Viscosities of Glass-Forming Liquids Glass Tm (°C) vmax (cm/s) Temperature for vmax (°C) Log h at Tm (dPa·s) Vitreous SiO2 1734 2.2 × 10 −7 1674 7.36 Vitreous GeO2 1116 4.2 × 10 −6 1020 5.5 P2O 5 580 1.5 × 10 −7 561 6.7 Na 2O·2SiO2 878 1.5 × 10 −4 762 3.8 K 2O·2SiO2 1040 3.6 × 10 −4 930 BaO·2B2O3 910 4.3 × 10 −3 849 1.7 PbO·2B2O5 774 1.9 × 10 −4 705 1.0 Viscometer Viscometer Furnace support Spindle Glass fiber Crucible Furnace Heating Molten elements glass Control thermocouple Pedestal LVDT assembly Sample thermocouple LVDT signal FIGURE 21.5 Schematic illustration of Weight instruments used to measure viscosity: (a) a viscometer; (b) the fiber elongation (A) (B) method. 384 .......................................................................................................................................... Glass and Glass-Ceramics low viscosities and the method is similar to the concentric removing the surface flaws (acid polishing or applying a cylinder viscometer used to determine the sol-gel transi- protective coating). Prince Rupert’s drops are an inter- tion that we describe in Chapter 22. The spindle is rotated esting and entertaining illustration of the effect of resid- at an angular velocity, ω, and the resistance to its motion ual stress on the mechanical properties of glass. Small is measured. gobs of molten glass are dropped into cold water to form For higher viscosities the fiber elongation method is tadpole-shaped drops. The surface cools much more used. A load is attached to a glass fiber, which can be rapidly than the center creating internal residual stresses heated to a range of temperatures. The strain rate of the and a very high surface tension. The solidified drops can fiber as it elongates is then measured. be hit with a hammer without breaking. But if the tail is broken off the entire drop shatters into powder. 21.4 GLASS: A SUMMARY OF ITS Some Electrical Properties of Glass PROPERTIES, OR NOT Glass usually has a high electrical resistivity because of We can summarize what we know about glass—and prob- the large band gap energy (see Chapter 30). In cases in ably be wrong. which they are conductive the charge is carried by ions, with alkali ions (e.g., Na +) being the fastest. Thus conduc- Glass is inert. This depends on the environment. It is tivity increases significantly as T is increased and it is nearly true if the glass is a silicate and essential if it different for silicate glasses, borate glasses, and phosphate is going to contain radioactive waste, but not all glasses glasses because the glass network is different. The mixed are inert. Bioglass® is designed not to be inert. alkali effect is an interesting phenomenon that occurs in Glass is homogeneous. This depends on how the glass was glasses that contain more than one different alkali ion. formed and its composition. We can process glass to The resulting conductivity has been found experimentally make it inhomogeneous. to be significantly lower than would be expected from Glass can be reshaped. This is generally true and is the simply adding their individual conductivities. This has reason why glass is so recyclable. Some glasses are applications in, e.g., high-wattage lamps. designed so that they can be modified by light, by dif- The dielectric constant of glass is quite high but not fusion, by irradiation, etc. high enough for some advanced memory applications such Glass has a small expansion coefficient. This is usually as dynamic random access memory DRAMS (see Chapter true, but not all glass is Pyrextm. 31). The capacitance is a measure of the amount of charge Glass is transparent. This is essential for optical fibers, stored and is related to the thickness of the dielectric. As but we can make it translucent or opaque (see Figure the layer gets thinner the capacitance increases, but elec- 21.2). Most early glasses were not very transparent trical breakdown can occur. SiO2 glass has a high dielec- because they contained impurities and inclusions. tric strength but not as high as some polymer dielectrics Glass is cheap. This is true for window glass since the such as phenolic resin. invention of the float-glass process. Thin films may be expensive. Some glass is colored red by doping it with Some Optical Properties of Glass Au. Some vases can cost >$50 k. Glass is a bulk material. This is true unless we grow it as Transmission in the ultraviolet (UV), visible, and infrared a thin film or it is present as an intergranular film (IR) depends on several factors including Rayleigh scat- (IGF) or pocket in, or on, a crystalline ceramic. tering, which is determined by impurities. The IR edge and the UV edge are the values where transmission of So the lesson is to beware of your preconceived ideas these frequencies cut off. A UV edge blocker removes the when thinking about glass. UV while a UV edge transmitter allows it through. The mechanical, optical, thermal, and electrical prop- Refraction depends on the refractive index and on dis- erties of glasses are discussed in detail, along with other persion. Reflection, which occurs at the surface, can be ceramics, in those topical chapters. Here we just give some internal. Because the optical properties of glass are so things to think about in relation to glass. important much of Chapter 32 is devoted to this topic. Some Mechanical Properties of Glass Some Thermal Properties of Glass The theoretical strength of silicate glass is around 10 GPa Expansion coefficients of glass are generally smaller than (using the criterion given in Section 18.2), but this is for metals. But often we want to make the following con- usually much reduced by the presence of surface flaws nections to metals: (cracks and seeds). Glasses are elastic but break in ten- sion. They can be strengthened by creating a compres- Glass-to-metal seals: an obvious important technological sive surface layer (by ion exchange or tempering) or by process 21. 4 G l a s s : A S u m m a ry o f I t s P r o p e r t i e s , o r N o t .............................................................................................. 385 SiO2: metal/insulator junctions for the electronics industry Graded seals: for example, a graded seal structure can be constructed by joining a series of glass pieces, each of which has a slightly higher thermal coefficient of expansion (α) Thermal conductivity is ∼1% of that of a metal. The implications and applications of this fact are obvious. 21.5 DEFECTS IN GLASS The idea is that although glass does not have a crystalline matrix, it can still contain point defects, precipitates, undergo segregation, and contain internal interfaces. Glass can be used to trap radioactive elements as point defects or as a “second phase.” The future value of this capability depends in part on how fast components can diffuse FIGURE 21.6 Region of liquid–liquid immiscibility for SiO2–Li2O. through glass. This applies to whether the radioactive Notice that these occur only in the silica-rich end of the phase material is diffusing out or other components are diffusing diagram. in (perhaps to leach out the trapped material). 21.6 HETEROGENEOUS GLASS segregation may be energetically less favorable than crys- tallization, but it is easier to accomplish because it requires Just because glass is a “supercooled” liquid does not mean only the segregation, not the correct rearrangement of the it must be homogeneous. Certain glasses can separate into atoms. As a general rule for silica, immiscibility is two phases, which need not be a crystallization process. increased by the addition of TiO2, but decreased by the When these two phases are both glassy, there may either addition of Al2O3. be no barrier to the separation (a spinodal decomposition) The Vycor process described in Chapter 8 uses the or, as in the case of liquid/liquid phase separation, there principle of phase separation. The resulting glass is 96% may be a nucleation step. In either case, diffusion is SiO2 and 4% pores and is used as a filter and a bioceramic important. where porosity is important. It can be densified (after The principle of immiscibility in glass is very impor- shaping) to allow processing of a pure SiO2 shape at a tant to today’s technology. For example, immiscibility lower temperature than for pure quartz glass. plays a role in forming glass-ceramics, making Vycor® and opal glass, and in the precipitation in glass. Many of the binary and ternary oxides with silica as a component 21.7 YTTRIUM–ALUMINUM GLASS show miscibility gaps. A miscibility gap is a region in the phase diagram in which a liquid separates into two liquids Yttrium–aluminum (YA) glasses can be formed in the of different composition (see Section 8.11). The following composition range ∼59.8–75.6 mol% Al2O3. With 59.8– are examples of systems exhibiting this effect: 69.0 mol% Al2O3, a two-phase glass forms with droplets of one phase in the other. The glass can spontaneously SiO2–Al2O3 SiO2–BaO SiO2–MgO crystallize to form YAG or a mixture of Al2O3 and YAlO3 Na2O–B2O3 –SiO2 Na2O–CaO–SiO2 (YAP; P = perovskite). These YA glasses show a phenom- enon known as polyamorphism, meaning that they exist Figure 21.6 shows the SiO2–Li2O phase diagram. In with different amorphous structures. the low-temperature silica-rich corner of the diagram one liquid phase separates into two chemically distinct, different liquid phases below the immiscibility dome. The dashed line represents the estimated region of 21.8 COLORING GLASS immiscibility. The difficulty in making these measure- ments is that phase separation occurs at a lower tem- Although many applications for glass require a colorless perature where the kinetics are slower. There is an product, for other applications colored glass is needed. interesting comparison with crystallization. Phase Windows in a church do not look as impressive when all 386 .......................................................................................................................................... Glass and Glass-Ceramics the glass is colorless. Glass is often colored by adding In a CdS-doped glass, adding more Se can result in transition-metal oxides or oxides of the rare-earth ele- “Selenium Ruby.” The details of all these colorings will ments to the glass batch. Table 21.4 lists the colors pro- depend on just what glass batch is used and the firing duced by some of the common glass colorants. We will conditions. look at how these additives actually result in the formation Corning makes microbarcodes (i.e., very small bar- of color in Chapter 32, but at this stage you should already codes) by doping glass with rare earths (REs); the REs know why glass bottles are often green. Bright yellow, have particularly narrow emission bands. Of 13 RE ions orange, and red colors are produced by the precipitation tested, four (Dy, Tm, Ce, and Tb) can be excited with UV of colloids of the precious metals. Au produces a ruby red radiation used in fluorescence microscopy but do not coloration, but it is not cheap. CdS produces a yellow interfere with other fluorescent labels. These microbar- coloration, but when it is used in conjunction with Se it codes can be used for biological applications since they produces an intense ruby red color. are not toxic; tags using quantum dots may be less benign. The questions are These bar codes can even label genes. The REs can be used together to give more color combinations.  How does coloring “work”? Special colored glasses include the following:  What causes the colors? Ruby and cranberry glass. Ruby glass is produced by  Is it the same as for crystals? adding Au to a lead glass with Sn present. Cranberry glass, first reported in 1685, is paler (usually a delicate Glass is intentionally colored by adding dopants (we pink) because it contains less gold. The secret of making are creating point defects in the glass). The color of the red glass was lost for many centuries and rediscovered glass depends on the dopant and its state of oxidation. The during the seventeenth century. explanation is the same as for coloring crystals, but because Vaseline glass or uranium glass. Uranium produces a the glass structure does not have LRO the absorption deep red when used in high-Pb glass. There are other spectra can be broader. uranium-containing glasses: the so-called “uranium Combinations of dopants can decolorize, mask, or depression-ware” glass (also called Vaseline glass), which modify the effect. For example, we can compensate for has a green color. True “depression ware” is actually the coloring effect of Fe by adding Cr; if too much Cr3+ is greener than Vaseline glass because it contains both iron added, Cr2O3 can precipitate out. When the glass is blown, and uranium oxides. What is special is that the glass these platelets of Cr2O3 can align to give “chromium aven- actually fluoresces when illuminated with UV radiation turine.” Cu was used to produce Egyptian Blue glass. Co (Vaseline ware more strongly because of the higher con- is present in some twelfth-century stained glass and, of centration of uranium). Since 1940 or so, only depleted course, was used in the glazes on Chinese porcelains in uranium has been used as a dopant and that is quite plenti- the Tang and Ming dynasties; the color it produces is ful, but for the previous 100 years, natural uranium was known as cobalt blue. used. Figure 21.7 shows an example of Vaseline ware. TABLE 21.4 Colors Produced by the Inclusion of Different Ions in a Glass Copper Cu2+ Light blue (red ruby glass for Cu nanoparticles) Cu + Green and blue (includes turquoise blue) Chromium Cr 3+ Green Cr 6+ Yellow Cr 3+ + Sn4+ Emerald green Manganese Mn3+ Violet (present in some Egyptian glasses) Mn2+ Weak yellow/brown (orange/green fluorescence) Iron Fe3+ Yellowish-brown or yellow-green Fe2+ Bluish-green FeS Dark amber Cobalt Co2+ Intense blue (especially if K + is present); in borates and borosilicates, pink Co3+ Green Nickel Ni2+ Grayish-brown, yellow, green, blue to violet, depending on glass Vanadium V3+ Green in silicates; brown in borates Titanium Ti3+ Violet (melting under reducing conditions) Neodymium Nd3+ Reddish-violet Praseodymium Pr 3+ Light green Cerium Ce3+ Green Ce4+ Yellow Uranium U Yellow (known as “Vaseline glass”) Gold Au Ruby (ruby gold, Au nanoparticles) 21. 8 C o l o r i n g G l a s s ..................................................................................................................................................... 387  21.10 PRECIPITATES IN GLASS Precipitation in glass is generally inevitable given time. The question is only how long it will take to occur, espe- cially if nucleation is homogeneous (i.e., no seeds are present). We may introduce seeds to produce particular effects. Nucleation of crystals in glass follows the classic theory. We will examine the topic more in Chapter 26 and see there that precipitates can also cause the coloring of glass. 21.11 CRYSTALLIZING GLASS FIGURE 21.7 Example of Vaseline ware produced by coloring with uranium. We will address processing these materials in Chapter 26. Here we will explain what a glass-ceramic is and relate it to other two-phase ceramics. We can crystallize a droplet of glass, as shown in Figure 21.9, or a complete film, as 21.9 GLASS LASER shown in Figure 21.10. We can also crystallize a bulk object almost completely to produce a glass-ceramic. The Rare-earth elements (e.g., Nd) are used to dope glass to basic idea is that there is sometimes a great advantage in create lasers and other optical devices (Figure 21.8). The processing a ceramic as a glass but producing the finished Nd-doped glass laser works like the ruby laser, although object as a polycrystalline body. there are some differences that relate to the glass. The Opal glass has a milky (opalescent) appearance caused laser rod is about –14 to –21 inch diameter and is usually by the formation of small crystallites. Even window pumped by a helical lamp to give a discharge length longer glass crystallizes; given time it devitrifies to form than from a linear lamp. The energy is stored in a capaci- devitrite. tor (e.g., 500 mF) with a charge voltage of ∼4 kV giving a The visible light microscopy (VLM) image shown in pulse duration of ∼0.8 ms. The Nd:glass laser gives effi- Figure 21.11 illustrates the growth of perfectly symmetric ciencies up to 2%, which is four times that of the ruby individual crystals inside a glass matrix. The crystals and laser, and the Nd:glass rod can be made even larger. the matrix are all transparent, so the full shape shown here Because the thermal conductivity of the glass is lower it schematically can be appreciated. The SEM images in requires more time to cool between firings. Figures 21.12 and 21.13 show that the glass and crystal Glass Crystal 2 μm FIGURE 21.8 Examples of phosphate laser glass. Individual laser rods vary from 0.6 to 1.2 mm in diameter. FIGURE 21.9 An example of crystallization in a glass droplet. 388 .......................................................................................................................................... Glass and Glass-Ceramics  FIGURE 21.12 SEM image of crystallized glass. The glass is a FIGURE 21.10 Spherulitic crystallization of an amorphous SiO2 binary Li–Be fluoride opal glass 40 mol% LiF, 60 mol% BeF2 film on SiC. The spherulites are crystobalite. containing small amounts of Ag and Ce (0.001 and 0.01 mol%, respectively). The glassy droplets (BeF2 rich) are surrounded by a crystallized matrix. (A) (A) o1 h h o o1 o1 h (B) FIGURE 21.13 SEM images of (a) Na–Be and (b) K–Be fluoride glass 15 mol% KF (or NaF), 85 mol% BeF2. This glass is cloudy: if (B) the droplets were smaller the glass would be clear. Replacing K by FIGURE 21.11 VLM image showing crystallization in a glass. Rb actually reduced the droplet size to 10–20 nm. 21.11 C ry s ta l l i z i n g G l a s s ......................................................................................................................................... 389  bined with a liquid to allow smooth application. The deco- rated pot is then typically coated with a clear glaze before it is fired. In the majolica technique, the pot is coated with an opaque white glaze first, then decorated, and then fired so that the colors bond to the white coating forming an in-glaze (rather than under) decoration. Glaze crawling. The glaze separates from the underly- ing pot—it dewets the pot surfaces during firing. Crackle glazes. If the coefficient of thermal expansion, α, of the glaze is greater than that of the underlying ceramic, the glaze may fracture as it cools; this crackling can easily be achieved using higher concentrations of Na or K in the glaze. In most technological applications this is not desirable. Some glazes, however, are designed to have a pattern of hair-like cracks for an artistic effect; these are then known as crackle glazes. Fast cooling pro- duces a finer pattern of crazes. Celadon, tenmoku, raku, and copper glazes are par- FIGURE 21.14 TEM image showing crystallization on a nanometer ticular glazes found in the ceramics art world. scale in an LAS glass-ceramic. Celadon glazes (first produced 3500 years ago) vary from light blue to yellow green and can be quite dark. The color is produced by iron (between 0.5 and 3.0 wt% Fe2O3 added to the glaze). The appear very different even FLUX AND MODIFIERS glazed pot is then fired a on a fractured surface. The flux in a glaze is a modifier in glass. The clear glaze second time at about Breaking a sample can is glass: i.e., silica and alumina with added modifiers. 1300°C. An example of quickly reveal a “grain” The clear glaze may contain lead but Pb should not be Korean celadon pottery is size down to ∼0.1 μm. To used for modern food containers. Strong colored glazes the small water container, probe the structure on a also often contain heavy metals. 23 cm tall, given to former near-atomic level with high U.S. President Harry spatial resolution, TEM Truman in 1946 by the can be used as shown in Figure 21.14, but its use has been government of Korea. It is now valued at $3 million. limited, in part because of the difficulties of preparing the Tenmoku glaze (from the Sung Dynasty) is dark brown TEM sample: the thickness of the sample tends to be or even black; 5–8 wt% Fe2O3 is included in the glaze to greater than the dimensions of the crystalline phase. produce the effect. An interesting variation of the tenmoku glaze is the oil-spot tenmoku where bubbles begin to form in the glaze as it starts to melt; if the potter catches them 21.12 GLASS AS GLAZE AND ENAMEL just in time, they leave spots all over the surface. If a tenmoku glaze is fired in reducing conditions, the Fe2O3 Glazes are everywhere, just as glass is. In this section we is partially reduced to FeO, which acts as a modifier summarize the topic of complete books, namely the glazes instead of an intermediate in glass terms. Hence this glaze on pottery and enamels. Glazing uses the viscous proper- behaves differently under oxidizing and reducing condi- ties of glass to form a (usually) smooth continuous layer tions, and the color will change. Copper glazes may use on a ceramic substrate (a pot); enameling does the same 0.5 wt% CuCO3 as the Cu source, but it breaks down to thing for a metal substrate. One thing that you will notice give CuO during firing, and this reacts with CO in the is that in general when it comes to ceramics, potters did furnace to give particles of Cu in the glaze. These parti- it first. The science of ceramics is often still unraveling cles of Cu provide the red color. just what they did. (In materials science, ceramists usually Raku glazes often appear metallic as if produced did it first.) by coating with a Ti metal. One modern method of raku First we summarize some terms in pottery. (The glazing involves firing the pots in the usual way, plunging processing of pottery was summarized in Chapter 2.) them into a reducing environment (like sawdust), and then Underglaze. When a pot [white bisqueware (also called quenching them before they can oxidize. These glazes are biscuit) is ideal] is decorated the first coating is the under- often the exception to the rule in that they can change with glaze. This is essentially a paint layer made by mixing time. This is simply because they oxidize when treated as oxide, carbonate, sulfate, etc., an opacifying agent to make other pots. The glaze is thus not as inert as others and is it opaque, and a flux to make it adhere better to the pot. used only for decoration. (However, see the historical note The mixture is calcined, ground, and then usually com- on Chojiro Rakuyaki.) 390 .......................................................................................................................................... Glass and Glass-Ceramics  Crystalline glazes. These are decorative glazes but are directly related to the formation of technologically impor- tant glass-ceramics. The crystals form by slowly cooling the glaze to allow a few large crystals to grow. The growth is interesting since the glaze is typically only ∼0.5 mm thick and the crystals must therefore form as platelets. A seed of TiO2 is usually used to nucleate the crystal in a low-viscosity glaze giving what is termed “rutile break- up,” which is actually the formation of PbTiO3. The chem- istry of the glaze is thus important, with SiO2 and Al2O3 being low and PbO between 8 and 10 wt%. The growing crystal tends to incorporate Fe from the glaze, but can also preferentially exclude other dopants. Modern potters tend to use Zn as the modifier and produce willemite crystals. [Willemite is a somewhat rare zinc mineral (except as kidney stones), but is abundant at Franklin, NJ.] The technique is tricky because the addi- tion of large amounts of Zn (a network modifier) to the glaze causes its viscosity to remain low even at low tem- peratures, so that it tends to run off the pot! The crystals appear to grow out from a seed as in the spherulitic growth seen by VLM in Figure 21.15. Each spherulite is actually FIGURE 21.16 Example of glaze color produced by nanoparticles. a mass of radiating crystals that is similarly aligned with respect to the center of the spherulite. Opaque glazes. If crys- tals are added to the molten SPHERULITES are produced by forming glaze it can be made Dana described spherulites in obsidian in 1863; these very small crystals (e.g., opaque. SnO2 was for long are the snowflakes in snowflake obsidian. In 1879 Rutley wollastonite for a “lime the standard, but zircon is noted that artificial glass may develop a spherulitic matt” and willemite, much cheaper; ZnO2 is structure. Zn 2 SiO 4 , for a “zinc matt”) used to make zircon glazes across the surface of the white. TiO2 is used less glaze. The wollastonite because larger rutile crystals are a golden color and thus can be formed by adding calcite (also known as whiting) make the glaze yellow. We can also make the glaze opaque to an SiO2-based glaze. An alternative is to add so much by forming crystals (e.g., wollastonite; CaSiO3) using a crystalline material to the glaze that it remains unchanged suitable thermal treatment, or by trapping gas (F2 or air), by the firing. A satin or vellum glaze, with smaller crystal or by causing a liquid/liquid phase separation. Matt glazes sizes, might contain 18% SnO2 or ZnO and 4% TiO2 in a high-lead glaze fired at 1000°C. Color in glass and glaze is the subject of much active research, with the realization that some colors are pro- duced by nanoparticles in the glass/glaze as for the luster- glazed plate in Figure 21.16. In general Ag and Au nanoparticles produce the gold color and Cu nanoparticles produce the red color; in the case of Cu especially, the ions may be reduced to the metal during processing. Explanations for the color of glazes are actually more complicated than for glass because the glaze is supported by a substrate and does not have to be transparent, so it can be a thin film or a multilayer and fired in a reducing or oxidizing environment. So this is a very large topic condensed into a paragraph! Cipriano Piccolpasso described luster preparation in 1557. Who says the use of nanomaterials is new! Colored glazes must use stable ceramic pigments if the color is to be consistent over repeated batches (e.g., for industrial production of sanitaryware, tiles, FIGURE 21.15 Illustration of spherulitic crystallization in a glass. etc.). Cheaper metal oxide colorants can be used when 21.1 2 G l a s s a s G l a z e a n d E n a m e l ........................................................................................................................... 391 variability is acceptable or desirable as in the pottery effect can actually be greater than for what we think of as crafts. Of course, many glaze colorants are the same as stronger acids (sulfuric, nitric, and hydrochloric acids we use for coloring glass (see Table 21.4). Co3O4 is a readily attack metals and skin). The Ca, Mg, and Al ions black powder but <1% gives a glaze a deep blue color, usually increase the chemical durability of a glass, but although it is usually added as the carbonate. Since Co2+ they will react with these “food” acids. The tannic acid is present when it dissolves, it changes the viscosity of the present in red wine and tea can have a similar effect. Thus glaze. Cr2O3 (2–3% can be added, but only 1.5% will Pb can be released from glass when the glass is in contact dissolve in the glaze) is intriguing because you expect with acid (even fruit juice). This means that we should not green but can produce red, yellow, pink, or brown. The use Pb in glazes either; however, this has often been done red can occur if Pb is present in the original glaze; if Zn because such glazes can be so brightly colored. is present, the glaze becomes brown unless Pb is also Silicate glass is strongly corroded by HF. The process present when the glaze becomes yellow. MnO2 (added as of “frosting” glass light bulbs was carried out for many the carbonate) gives a brown glaze but can produce red, years by blowing HF vapor into the glass envelope and purple, or even black; the color depends in part on how then evacuating it after a short period. much Na is present in the initial glaze. CuO is equally Glass dissolves in water, particularly at elevated tem- interesting: 1–2% added to an Na-rich glaze gives tur- perature and pressure: we use this fact to grow all the quoise whereas up to a 3% addition produces a clear quartz crystals used by industry. Dishwashers make glass green/blue. If even more CuO is added the glaze can have dull. Roman glass (Figure 21.17) is iridescent because the a metallic appearance like pewter. If the glaze (0.3–2% glass has reacted with acid in the soil. (The iridescence CuO) is fired in a reducing atmosphere, the classic copper was not present in Roman times.) The corrosion products red is formed. This color is caused by the presence of form several distinct layers and, hence, generate the inter- colloidal Cu. If you see the bright yellow glaze, this might ference known as iridescence. It can easily be duplicated be the CdS/CdSe yellow (also produces orange and red) as shown by Tiffany and others. glaze. If Pb is present, then PbS can form, which makes Not all glass is attacked as readily. As described in the glaze black. Zircon is used in industry to help stabi- Chapter 8, we leach one component of a phase-separated lize these Cd-based colors. In fact, (V,Zr)SiO4 (vanadium glass during the preparation of Vycor but leave the other zircon blue) and (Pr,Zr)SiO4 (praseodymium zircon intact. yellow) are most important in the whitewares industry. It is possible to minimize these reactions to some Uranium is added to glazes but tends to produce a dark extent by adding inhibitors, such as Zr or Be, to the glass. brown rather than the pale yellow found in Vaseline glass; This question of reactivity is closely related to the phe- it can be yellow or bright red/orange, but this depends on nomenon of ion exchange. the glaze composition. Salt glaze. The pot is reacted with salt in the furnace while at temperature. In practice, the potter actually throws salt over the pot when it is in the kiln. The tech- nique was used by early potters in Iran and by the English in the 1700s. You will see many examples in Germany where a blue coloring is often produced using metal oxides. The salt reacts with the clay forming a glass layer on the surface; essentially the process is high-temperature soda corrosion of the fired clay. The term enamel usually implies a glaze applied to a metal, but it can be a glaze applied on top of a glaze. The market for enamel is large varying from toilet fixtures (whitewares) to jewelry. Enamel is the ever-lasting paint with the organic component replaced by glass. 21.13 CORROSION OF GLASS AND GLAZE We think of glass as being inert. Citric acid and acetic acid (present in lemon and vinegar, respectively) can chelate with metal ions present in a glass and form water- soluble complexes. (A chelate is a complex compound with a central metal atom attached to a large molecule, a ligand, in a ring or cyclic structure like the claw of a crab.) The FIGURE 21.17 Example of iridescence in Roman glassware. 392 .......................................................................................................................................... Glass and Glass-Ceramics H + can replace alkali ions when glass is weathered. TABLE 21.5 Structural Elements in Glasses K+ can replace Na + and Na + can replace Li + when we want Silicates SiO4 to strengthen the surface of glass. Borates BO3 Ag + and Cu + can replace Na + to “stain” glass. Phosphates PO4 Fluorides F A special feature here is that we have point defects Chalogenides S (and large defects) in glass just as we do in crystals. Our challenge is to understand what determines the properties (e.g., diffusion) of such defects when we do not have a reference lattice. Lead Glass Generally the composition will be a lead-alkali silicate 21.14 TYPES OF CERAMIC GLASSES glass SiO2–PbO–R2O, so the PbO replaces the CaO in soda-lime glass. These glasses have a high resistivity, a Not all glass is based on the silica tetrahedron. The large α, a low softening temperature, and a long working structural units are summarized in Table 21.5 and some range. The reason that Pb glass has been used to make representation glass compositions are given in Table so-called lead crystal glass is that it has a high refractive 21.6. index. Besides being used in art objects, it is used for lamp tubing, TVs (the “bulbs”), and thermometer tubing. In a traditional English lead crystal the concentration of PbO Silicate Glass (Soda-Lime Glass) will be at least 30%: an EU directive required that glass This is based on SiO2–Na2O–CaO (usually containing must contain ≥24% to be considered lead crystal. Then MgO and Al2O3). It is relatively inexpensive and durable the EU had to exempt crystal glass from recycling laws! and is widely used in the building and packaging indus- Lead glass used for radiation shielding may contain as tries. It’s α is not negligible and it is not a good insulator. much as 65% PbO. Applications include TV tubes, The main uses are in sheet glass, bottles, tableware, and although Ba glass may be used in the face or panel of the in the light industry for envelopes (bulbs). The alkaline TV. (The electrons hitting the TV screen can create X-rays aluminosilicate glasses (SiO2–Al2O3 –RO, where R is the that the glass must then absorb.) Lead-borate glasses can alkali) have low αs, are durable, and are better electrical be used as glass solder—they contain little SiO2 or Al2O3 insulators. They also have a high strain point. Uses include and are quite inert. combustion tubing, envelopes for halogen lamps, and sub- Flint glass is a high-dispersion, lead-alkali silicate strates in the electronics industry. glass originally made by melting flint rock, which is a TABLE 21.6 Approximate Composition (wt%) of Some Commercial Glasses Glass SiO2 Al2O3 Fe2O3 CaO MgO BaO Na2O K2O SO3 F2 ZnO PbO B 2O 3 Se CdO CuO Container flint 72.7 2.0 0.06 10.4 0.5 13.6 0.4 0.3 0.2 Container amber 72.5 2.0 0.1 10.2 0.6 14.4 0.2 S-0.02 0.2 Container flint 71.2 2.1 0.05 6.3 3.9 0.5 15.1 0.4 0.3 0.1 Container flint 70.4 1.4 0.06 10.8 2.7 0.7 13.1 0.6 0.2 0.1 Window green 71.7 0.2 0.1 9.6 4.4 13.1 0.4 Window 72.0 1.3 8.2 3.5 14.3 0.3 0.3 Plate 71.6 1.0 9.8 4.3 13.3 0.2 Opal jar 71.2 7.3 4.8 12.2 2.0 4.2 Opal illumination 59.0 8.9 4.6 2.0 7.5 5.0 12.0 3.0 Ruby selenium 67.2 1.8 0.03 1.9 0.4 14.6 1.2 S-0.1 0.4 11.2 0.7 0.3 0.4 Ruby 72.0 2.0 0.04 9.0 16.6 0.2 Trace 0.05 Borosilicate 76.2 3.7 0.8 5.4 0.4 13.5 Borosilicate 74.3 5.6 0.9 2.2 6.6 0.4 10.0 Borosilicate 81.0 2.5 4.5 12.0 Fiber glass 54.5 14.5 0.4 15.9 4.4 0.5 0.3 10.0 Lead tableware 66.0 0.9 0.7 0.5 6.0 9.5 15.5 0.6 Lead technical 56.3 1.3 4.7 7.2 29.5 0.6 Lamp bulb 72.9 2.2 4.7 3.6 16.3 0.2 0.2 0.2 Heat absorbing 70.7 4.3 0.8 9.4 3.7 0.9 9.8 0.7 Trace 0.5 21.14 Ty p e s o f C e r a m i c G l a s s e s ................................................................................................................................ 393  adding fluorine ions to change the composition of the silica; this process allows transmission of wavelengths down to 157 nm. We have already discussed Vycor, which can be pure (porous) silica after we remove the second phase. Phosphate Glass Phosphate glasses are important because they are semi- conducting; one application is in the manufacture of elec- tron multipliers (hence amplifiers) using Er doping (with Er2O3). The cations here are usually V and P, but Oak Ridge National Laboratory (ORNL) developed a lead indium phosphate glass that has a high index of refraction, a low melting temperature, and is transparent over a wide range of wavelengths. Since it can also dissolve significant concentrations of rare-earth elements (it was designed to FIGURE 21.18 Crown glass with bull’s eye. be a container for radioactive waste), it is being explored for new optically active devices (e.g., fiberoptic amplifiers and lasers). Nd-doped (using Nd2O3) phosphate glasses are being used in solid-state lasers (1.054 μm wavelength). particularly pure form of silica. Note that this rock is now The typical composition is 60P2O5–10Al2O3 –30M2O (or calcined and is still used extensively in the pottery MO); the Nd concentrations is ∼0.2–2.0 mol%. Calcium industry. phosphate glass will be discussed more extensively in Crown glass based on soda-lime glass, has quite a low Chapter 35. dispersion. It is still made by initially blowing the glass, flattening it, and transferring it to the pontil (a solid iron Chalcogenide Glass rod rather than the blow pipe) where it is spun until it is in the form of a disc that could be 1.5 m in diameter Based on As, Se, and Te, these glasses are IR transparent. (Figure 21.18). The disk shows concentric ripples from the They are nonoxide semiconductors and are used in special spinning and has a bull’s eye at the center of the crown. electronic devices and lenses. The devices use the abrupt The disk can be very smooth having been flame annealed change in electrical conductivity that occurs when a criti- without mechanical polishing. Historically, windowpanes cal voltage is exceeded. The applications have to be special could be cut around the bull’s eye or could contain it. because these glasses are not durable and have low soften- ing temperatures. Borate Glass (Borosilicate Glass) Fluoride Glass The alkali borosilicates, SiO2–B2O3 –R2O (R is the alkali), are special for their low α. They are durable and have In general, halide glasses are based on BeF2 and ZnCl2 useful electrical properties. The cookware material and are used in optical waveguides (OWG) where the cost PyrexTM is a borosilicate. Borosilicate glass is widely used can be justified. in the chemical processing industry. Some borate glasses melt at very low temperatures (∼500 ± 50°C), so they can be used to join together other glasses. Zinc-borosilicate 21.15 NATURAL GLASS glass, known as passivation glass, contains no alkalis, so it can be used for Si electronics components. It surprises some people that not only does glass occur in nature, but it is relatively common. Tektites are formed within the impact craters of meteors. Moldavite is a green Fused Silica glass from Moldavia in the Czech Republic; Libyan Desert Being essentially pure SiO2, this is the silicate glass for Glass formed the same way but is yellow. Fulgarites are high-temperature applications. It has a near zero α [known fragile tubes of glass that can be formed when lightning as ultralow expansion (ULE) silica]. This is used for tele- strikes a sandy soil. Obsidian is the glass formed in scope mirrors and substrates. ULE® glass containing 7% volcano flows. The usual black color is due to impurities; TiO2 is being used for photolithography masks [for extreme green and red obsidian also occur. Obsidian was used to ultraviolet lithography (EUVL) at a wavelength of 13.4 nm, make tools during the Paleolithic period. The advantages extreme UV]. Another silica glass that can be used for of using glass for scalpels have only recently been redis- 157–nm lithography was made by removing the water and covered: the cut made by a glass knife is particularly even 394 .......................................................................................................................................... Glass and Glass-Ceramics  (B) (A) (C) FIGURE 21.19 SEM images of diatoms. so it heals fast. It has been proposed that the Aztec civili- has a skeleton that looks like a mesh of glassy silica fibers zation may not have developed metallurgy because it was (Figure 21.20). Each fiber actually consists of coaxial so adept at using obsidian and there are many sources of cylindrical layers with different optical properties. It is obsidian in the volcanic mountain ranges of Peru and reminiscent of the cladding used today on commercial Ecuador in particular. optical fibers, but nature did it eons earlier. The optical Pumice is another glass formed in volcanic eruptions. properties of the natural fibers are not as good as those of It can be very porous if it contains a high concentration human-made fibers but they are more resistant to break- of gas. Pumice is thus the porous form of obsidian. ing. Note that these layers are deposited at ambient water Trinitite is not really a natural glass but one that we temperatures! might say forms unintentionally. This glass has been found at the Trinity site where the nuclear bomb was exploded in New Mexico. Diatoms are included in this topic because they are both interesting and surprising. Not all living things on earth are based on carbon. Diatoms are small aquatic microorganisms, or one-celled plants, that live by ingest- ing silica that is dissolved in water; we usually think of seawater, but it can be a freshwater lake. The diatoms then use the silica to form and grow a pair of shells as illus- trated in Figure 21.19. The two shells resemble a pillbox. The shells come in many varieties—there are thousands of species of diatoms. When the microorganisms die, their siliceous skeletons have formed layers up to 3000 feet thick: they are not rare! The result is that there are regions in which deposits of silica have built up to form what is known as diatomite or diatomaceous earth. The compara- ble process for carbon-based creatures would be the formation of limestone and chalk. Diatoms do contain chlorophyll, so they are plant colored while alive. The Venus Flower Basket (Euplectella) is a sponge that lives in the deepest parts of the oceans in the tropics. It FIGURE 21.20 Sea sponge. 21.1 5 N at u r a l G l a s s .................................................................................................................................................... 395 21.16 THE PHYSICS OF GLASS We will now discuss glass from the physicist’s point of logη view. We have left this topic for last so as either to confirm Pa.s your excitement or not completely put you off the subject. 7 The idea is that glass is a condensed phase just as liquids and crystals are. The atomic interactions can be described by a potential energy function, φ. 3 If we describe the energy of a glass plotted against the coordinates of the glass, we would find a multidimensio- Strong -1 nal energy hypersurface, which is multiply dented with structured valleys. The glass structure corresponds to one Fragile of those valleys, but there may be another valley or a minimum not far away on the surface. Then we have the 0 0.4 0.8 Tg/T concept of polyamorphism, in which the glass can have FIGURE 21.21 Viscosity versus temperature for strong and fragile several distinct amorphous structures. (The comparison liquids. to crystalline materials is instructive!) The experimental observation is that the viscosity of some glasses decreases suddenly above Tg in a non- fast relaxation processes (known as β processes) and low- Arrhenius way. It is as if the structure of the glass col- frequency processes, which contribute to the dynamic lapsed because it was fragile (the term fragile refers only structure factor. In the glass’s vibrational spectra detected to the liquid, not the glass). Hence fragility is a property by Raman or neutrons, these features are known as the of some glass-forming liquids above Tg although we talk boson peak. The boson peak is large for strong glass about fragile and strong glasses. If we plot log η versus formers; low-frequency excitations in a glass suggest Tg/T (the reduced Tg as shown in Figure 21.21), then the intermediate-range order: so more order indicates a curve would be straight if it was for Arrhenius-like behav- stronger glass. ior. For SiO2 and other highly polymerized network glasses The molar heat capacity, cP, is a well-defined quantity. (strong glass formers), it is nearly straight. If the bonds At very low temperatures (T < 1 K: a temperature familiar are not directional, the plot deviates significantly from to physicists but less so to ceramists), glasses show a Arrhenius behavior; this is a fragile glass former. Two linear term in cP due to an anharmonic contribution. At approaches have been used to explain this behavior: T∼5–10 K, an excess vibrational (harmonic) contribution causes a bump in cP. The excess vibrational contribution  Free volume to cP at this bump (call it cP–cD) can be plotted against the  Configurational entropy fragility of the glass. The resulting correlation suggests that the excess vibration and the fragility have a related Each connects η to the macroscopic quantities of either origin. So SiO2, a particularly strong glass, has a large volume or entropy. A newer approach considers factors cP/cD, whereas a fragile glass like CKN [Ca0.4K0.6 (NO3)1.4] affecting the kinetics of the transformation. There are has a small cP/cD. CHAPTER SUMMARY This chapter has been placed after powders but before processing because we are still empha- sizing the material. Because glass is an extremely important material the history of this topic is particularly rich. Remember that glazes on pots and enamels on metals are essentially two variations on a single theme—protecting other materials by coating them with glass. The variety of glasses is large and we have touched on only a small range here. Remember that historically, silica-based glass was for a long time synonymous with the word glass. So, it has dominated our thinking about glass. New glasses are being developed that may contain no Si and the properties may be very different; there is not just one material called glass any more than there is one material called crystal. Glass will crystallize given time; although glass- ceramics were the new materials of the 1960s, they were already old friends to the potter. The basic science of glass is more difficult than for crystals because we have no “frame of refer- ence.” However, there are point defects in glass (remember the origins of color). Glass has both internal and external interfaces and does have special structural features. Of its many important properties, transparency and viscosity must be the most important, although for many applica- tions the small, or controllable, expansion coefficient is the key to the value of glass. 396 .......................................................................................................................................... Glass and Glass-Ceramics  As we explained from the beginning, glass appears throughout our discussion of ceramics. The processing of glass is treated in Chapter 26, mechanical properties are discussed in Chapter 18, and Bioglass is discussed in Chapter 35. The reason we treat glass separately is partly his- torical and partly because its behavior is often so different from crystalline ceramics, which emphasizes the point we made in Chapters 5 through 7, bonding and structure determine the properties and thus the applications. PEOPLE IN HISTORY Bacon, Roger, a Franciscan Friar, described reading glasses made using two lenses in 1268. Salvino D’Armate of Pisa is sometimes credited with the invention in 1284. Cassius, Andreas (1685) in the book “De Auro” describes how to produce this ruby red color, which thus became known as “Purple of Cassius.” La Farge, John (patent No. 224,831; February 24, 1880); a “Colored-Glass Window,” the original patent on opal glass, was followed shortly by Louis Comfort Tiffany’s patent (No. 237,417; February 8, 1881) with the same title, “Colored-Glass Window.” Lipperhey, Hans was a lens grinder in the Netherlands; he applied for a patent for the telescope in 1608. Pascal, Blaise (1623–1662) was born in Clermont-Ferrand, France and died in Paris. The SI unit of pressure (stress) is named after him. He argued against Descartes in favor of the existence of vacuum. Perrot, Bernard (1619–1709) was a well-known early French glassmaker. Poiseuille, Jean Louis Marie (1799–1869) was the French physician after whom we name the Poise. Prince Rupert of Bavaria (1619–1682) was the grandson of James I of England and nephew of Charles II. He introduced his drops to England in the 1640s, where they became party pieces in the court of Charles II. The famous diarist Samuel Pepys wrote about them in his diary on January 13, 1662. Rakuyaki, Chojiro (died 1859) was the first member of the family to begin the tradition of raku. Their home is now an exquisite museum illustrating tea bowls made by 15 generations. van Leeuwenhoek, Anton (1632–1723) was born in Delft, Holland and worked as a cloth merchant; he devised a simple microscope that succeeded so well because he was a skilled lens grinder. The microscope itself was invented in the 1500s and was used by Robert Hooke. Warren, Bertram Eugene (1902–1991; at M.I.T. 1930–1976) is known for his textbook on X-ray diffraction and his studies of the structure of glass and carbon black. These began small-angle scattering research into nonperiodic and nearly periodic structures. THE HISTORY OF GLASS Allen, D.(1998) Roman Glass in Britain, Shire Pub. Ltd., Bucks, UK. Boyd, D.C. and Thompson, D.A.(1980) Glass, 3rd edition (Kirk-Othmer: Encyclopedia of Chemical Technol- ogy, Vol. 11, p. 807). Bray, C.(2001) Dictionary of Glass Materials and Techniques, University of Pennsylvania Press, Philadelphia, PA. Douglas, R.W. and Frank, S.(1972) A History of Glass Making, Foulis & Co, London, UK. A very readable history of glassmaking with some super illustrations and photographs. Newby, M.S.(2000) Glass of Four Millennia, Ashmoleum Museum, Oxford, UK. Stern, E.M.(2001) Roman, Byzantine and Early Medieval Glass 10 BCE–700 CE, H. Cantz Publishers, Ost- fildern-Ruit, Germany. Stookey, S. Donald (2000) Explorations in Glass, American Ceramic Society, Westerville, OH. About 70 pages of essential reading. Zerwick, C.(1990) A Short History of Glass, H.N. Abrams Inc., New York. JOURNALS J. Non-Cryst. Solids; J. Chem. Phys.; J. Appl. Phys.; J. Mater. Sci. GENERAL REFERENCES Bach, H. and others (1998–) The Schott Series on Glass and Glass Ceramics, Springer, Berlin. Superb series from specialists at one of the leading glass companies. Bailey, M. (2004) Oriental Glazes, A & C Black, London. One of the Ceramic Handbooks series of texts aimed at the practicing potter. Brow, R.K. (2000) “Review: The structure of simple phosphate glasses,” J. Non-Cryst. Solids 263 and 264, 1. Creber, D. (2005) Crystalline Glazes, A&C Black, London. One of the Ceramic Handbooks series. Davies, J. (1972) A Glaze of Color, Watson-Guptill Pubs, New York. Very practical insights for the potter. C h a p t e r S u m m a ry .......................................................................................................................................................... 397  Doremus, R.H. (1994) Glass Science, 2nd edition, John Wiley & Sons Inc., New York. An essential text if you study glass. The discussion of definitions is very clear. Höland, W. and Beall, G. (2002) Glass-Ceramic Technology, American Ceramic Society, Westerville OH. The book on glass-ceramics. Dr. George Beall has the greatest number of patents (100 in 2004) granted to a single individual in Corning’s history. Ilsley, P. (1999) Macro-Crystalline Glazes: The Challenge of Crystals, The Crowood Press, Ramsbury, Wilts, UK. Beautiful illustrations from an experimentalist. Morey, G.W. (1954) The Properties of Glass, 2nd edition, Reinhold Publishing Co., New York. Includes a useful discussion of viscosity. Paul, A. (1982) Chemistry of Glasses, Chapman & Hall, London, UK. Pfaender, H.G. (1982) The Schott Guide to Glass, Chapman & Hall, London, UK. A small, enjoyable text with color illustrations. Rawson, H. (1967) Inorganic Glass-Forming Systems, Academic Press, New York. Another of the standards on glass. Shimbo, F. (2003) Crystal Glazes, 2nd edition, Digital Fire Co., Medicine Hat, Alberta, Canada. Stoemer, E.F. and Smol. J.P. (1999) The Diatoms, Cambridge University Press, Cambridge, UK. Concerned primarily with applications of these diatomaceous materials. Very comprehensive. Sturkey, S.D. (2000) Explorations in Glass, American Ceramics Society, Westerville, OH. A “must-read” for anyone interested in glass. Particularly nice discussion on opal glass. Taylor, J.R. and Bull, A.C. (1986) Ceramic Glaze Technology, Pergamon Press, New York. An excellent resource on glazes. Wiggington, M. (1996) Glass in Architecture, Phaidon Press, London. Zarzycki, J. (1991) Glasses and the Vitreous State, Cambridge University Press, Cambridge, UK. SPECIFIC REFERENCES Aizenberg, J., Weaver, J.C., Thanawala, M.S., Sundar, V.C., Morse, D.E., and Fratzl, P. (2005) “Skeleton of Euplectella sp.: Structural hierarchy from the nanoscale to the macroscale,” Science 309, 275. Angell, C.A. (1985) in Strong and Fragile Glass Formers in Relaxation in Complex Systems, edited by K.I. Ngai and G.B. Wright, National Technical Information Service, U.S. Department of Commerce, Springfield, VA, 3. Angell, C.A. (1995) “Formation of glasses from liquids and biopolymers,” Science 267, 1924. A particularly important review. Angell, C.A. (2002) “Liquid fragility and the glass transition in water and aqueous solutions,” Chem. Rev. 102, 2627. Much more relevant than it might appear. Bondioli, F., Manfredini, T., Siligardi, C., and Ferrari, A.M. (2004) “A new glass-ceramic pigment,” J. Eur. Ceram. Soc. 24, 3593. Kim, S.S. and Sanders, T.H., Jr. (2000) “Calculation of subliquidus miscibility gaps in the Li2O-B2O3-SiO2 system,” Ceram. Int. 26, 769. Knowles, K.M. and Freeman, F.S.H.B. (2004) “Microscopy and microanalysis of crystalline Glazes,” J. Microsc. 215, 257. Pye, L.D., Montenero, A., and Joseph, I. (2005) Properties of Glass-Forming Melts, CRC Press, Boca Raton, FL. A collection of chapters on current aspects of molten glass. Rössler, E. and Sokolov, A.P. (1996) “The dynamics of strong and fragile glass formers,” Chem. Geol. 128, 143. Strahan, D. (2001) “Uranium in glass, glazes and enamels: History, identification and handling,” Studies Conservation 46, 181. Tangeman, J.A., Phillips, B.L., Nordine, P.C., and Weber, J.K.R. (2004) “Thermodynamics and structure of single- and two-phase yttria-alumina glasses,” J. Phys. Chem. B 108, 10663. Vogel, W. (1971) Structure and Crystallization of Glasses, The Leipzig Ed., Pergamon Press, Oxford, UK. Zhu, D., Ray, C.S., Zhou, W., and Day, D.E. (2003) “Glass transition and fragility of Na2O–TeO2 glasses,” J. Non-Cryst. Sol. 319, 247. WWW www.bell-labs.com Bell Labs www.corning.com The site for the Corning Glass Company www.cmog.org The Corning Museum of Glass www.glass.org The site for the NGA (National Glass Association) 398 .......................................................................................................................................... Glass and Glass-Ceramics  www.pilkington.com The site for Pilkington Glass, a key developer of glass based in the UK www.schottglass.com The site for Schott Glass with descriptions of new glass developments www.focusmm.com/pasabahce/co_hi.htm Describes the history of the wonderful Pasabahce glass of Turkey www.doge.it/murano/muranoi.htm The history of Murano glass www.ortonceramic.com A source for testing equipment www.britglass.org.uk The site for the British Glass Manufacturers’ Confederation www.jlsloan.com/lct1.htm Julie L. Sloan’s site describing the rivalry between La Farge and Tiffany in developing opal glass EXERCISES 21.1 What causes refraction in glass? 21.2 Why is smoky quartz smoky? 21.3 If you increase the wavelength, how does the refractive index change? 21.4 What is dispersion and why does glass cause it? 21.5 If Pb were added to a typical lead crystal glass, what weight percent would be added? What atomic percent of Pb would the glass then contain? What is actually added in industrial practice and will this practice con- tinue in the future? 21.6 If you are given crystalline SiO2, quartz glass, silica gel, and a sample of liquid SiO2, how would you analyze the bonding of the Si in each case? Would you detect a difference? 21.7 How would you expect the properties of GeO2 glass to differ from those of SiO2 glass? Be as quantitative as possible. 21.8 We can make glass based on B and on P. What will the bonding characteristics of these two glasses be? Suggest three modifiers for each glass. Compare the densities you expect for these glasses. 21.9 Libyan Desert glass was produced naturally. Is pressure or temperature the more important factor? Explain your reasoning as quantitatively as possible. 21.10 Na is a network modifier for SiO2 glass. How would Li and K compare to Na in this role? Similarly Ca is present in soda-lime glass; if the Ca were replaced by an equal atomic percent of Mg or Ba, how would the properties of the glass change? C h a p t e r S u m m a ry .......................................................................................................................................................... 399  22 Sols, Gels, and Organic Chemistry CHAPTER PREVIEW Extensive research and development in the past decade have resulted in increasing awareness of the importance of chemical synthesis, particularly using organic precursors, in the process- ing and fabrication of ceramics. The sol-gel process is one method that is used commercially in many applications, such as forming coatings on window glass. It is also used, as we have previously described, for forming powders and fibers. The process gives us excellent control of product purity and composition for the simple reason that we start with pure materials. It allows us to deposit films and coatings on a range of different surfaces, enabling a flexibility that is not present in many vapor-phase methods. We can summarize the key advantages offered by the sol-gel process.  It uses relatively low temperatures.  It can create very fine powders.  It produces compositions not possible by solid-state fusion. There are some disadvantages of the sol-gel process.  The cost of the raw materials (the chemicals) may be high. As an example, MgO powder with a purity of 98% is available in small quantities for $30/kg. Magnesium ethoxide, a chemical source for making MgO, costs about $200/kg.  There is often a large volume shrinkage and cracking during drying (we have to remove the “organics”).  Organic chemistry often uses confusing terminology and is avoided by ceramists whenever possible. In Chapter 20 we described how sol-gel processing (and other chemical methods) is used to make ceramic powders and fibers. So, why do we need another chapter on this topic? There are two main reasons. First, to use sol-gel processing scientifically you must understand the chemistry (the terminology and the reactions). Second, chemical methods for making powders are going to be even more important in the future because they can be used to make nanopar- ticles and even to coat them. 22.1 SOL-GEL THE TERM SOL-GEL The process that occurs PROCESSING depends on the form of the It is convention to use the term “sol-gel” rather than sol, i.e., whether it is a “sol/gel,” although the latter might be more correct; The sol-gel process con- “sol” and “gel” are two independent concepts.solution or a suspension sists of two steps. First we of fine particles. A flow form a sol. Then we trans- diagram indicating each of form this into a gel. In ceramic synthesis, two different the processes is shown in Figure 22.1. sol-gel routes have been identified and depend on the gel In this chapter we are concerned only with the poly- structure. meric gel route because this is the approach that is most useful to ceramists. This  Particulate gel—using method has been success- a network of colloidal DEFINITION OF SOL AND GEL ful in preparing a range of particles Colloidal particles or molecules are suspended in a advanced ceramics such  Polymeric gel—using liquid or solution, a “sol.” The sol is mixed with another as lead zirconate titanate an array of polymeric liquid, which causes formation of a continuous three- (PZT) and the high-Tc chains dimensional network, a “gel.” oxide superconductors. 400 ......................................................................................................................... S o l s , G e l s , a n d O r g a n i c C h e m i s t ry  TABLE 22.1 Examples of Metal Alkoxides Solution of Metal Alkoxides Name Chemical formula Physical state hydrolysis & hydrolysis Aluminum S-butoxide Al(Os C4H9) 3 Colorless liquid, condensation TB ∼203°C Aluminum ethoxide Al(OC2H5) 3 White powder, Sol Sol TM 130°C (solution) (suspension: particles) Aluminum isopropoxide Al(Oi C3H7) 3 White powder, TM 118.5°C gelation gelation Antimony ethoxide Sb(OC2H5) 3 Colorless liquid, TB 95°C Barium isopropoxide Ba(Oi C3H7) 2 Off-white powder ‘Polymeric’ ‘Particulate’ Gel Gel Boron ethoxide B(OC2H5) 3 Colorless liquid, TB 117.4°C Calcium methoxide Ca(OCH3) 2 Off-white powder drying drying Iron ethoxide Fe(OC2H5) 3 TM 120°C Forming Iron isopropoxide Fe(Oi C3H7) 3 Brown powder network Silicon tetraethoxide Si(OC2H5) 4 Colorless liquid, Dried Gel TB 165.8°C Silicon tetraheptoxide Si(OC7H15) 4 Yellow liquid firing Silicon tetrahexoxide Si(OC6H13) 4 Colorless liquid Silicon tetramethoxide Si(OCH3) 4 Colorless liquid, TB 121–122°C Dense Product Titanium ethoxide Ti(OC2H5) 4 Colorless liquid, TB 122°C FIGURE 22.1 Flow chart comparing sol-gel processing using a Titanium isopropoxide Ti(Oi C3H7) 4 Colorless liquid, solution and a suspension of fine particles. TB 58°C Yttrium isopropoxide Y(Oi C3H7) 3 Yellowish-brown liquid The significant advantage of sol-gel processing of ceramic powders is that homogeneous compositions can Methoxide R = CH3 Example is B(OCH3)3 be prepared at temperatures lower than required for con- Ethoxide R = C2 H 5 Example is Si(OC2H5) 4 ventional powder processes. Furthermore, the reactants Propoxide R = C3H7 Example is Ti(OiC3H7) 4 used in sol-gel processing are available in very high puri- (n- and iso-) ties, which allows the formation of high-purity powders Butoxide R = C 4H9 Example is Al(OsC4H9)3 of crystalline ceramics and glasses. (n-, iso-, sec-, and tert-) A commonly studied approach for synthesizing oxides has been to hydrolyze the appropriate metal alkoxides. In these molecular formulas, the superscripts n, t, s, There are several advantages to using metal alkoxides as and i refer to normal, tertiary, and secondary or isoalkyl precursors for ceramic powders. Most of the alkoxides of chains, each of which is illustrated for the butoxide group interest can be easily prepared or are commercially avail- in Figure 22.2. These are common names and do not able and can be readily purified prior to use. Interaction follow the Commission on the Nomenclature of Organic of alkoxides with water yields precipitates of hydroxides, Chemistry of the International Union of Pure and Applied hydrates, and oxides. The precipitate particles usually Chemistry (IUPAC). In the case of higher alkoxides, range in size from 0.01 to 1 μm, depending on the hydro- i.e., those with five or more C atoms, the nomenclature lysis conditions. So we can easily produce nanoparticles. is derived strictly from IUPAC conventions. For example, the alkoxide group (CH3)3CCH2CH2O– would be referred to as 2,2-dimethylbutoxide. The old name is 22.2 STRUCTURE AND SYNTHESIS neohexoxide. OF ALKOXIDES Most metal alkoxides contain lower aliphatic alkyl groups and are coordinated com- Alkoxides have the general plexes and not single mole- formula M(OR) z where M METAL ALKOXIDE M(OR) cules. Figure 22.3 shows an is usually a metal, but can For convenience we will say “metal alkoxide” even example of a coordination also be a nonmetal such as when referring to alkoxides of nonmetals such as silicon complex of aluminum isop- Si, and R is an alkyl chain. and boron. ropoxide consisting of three Table 22.1 lists some molecules. common alkoxides used in the preparation of ceramics. Even when using the IUPAC convention there is still The nomenclature adopted for the simple alkoxides the distinct possibility of encountering confusion when follows the basic rules of organic chemistry: reading the literature. For example, silicon tetraethoxide 2 2 . 2 S t ru c t u r e a n d S y n t h e s i s o f A l k ox i d e s ....................................................................................................... 401  n-butoxide CH3CH2CH2CH2O TABLE 22.2 Alkoxides of Metals with Different Electronegativities H H H H Electronegativity H C C C C O Alkoxide of metal State H H H H Na(OC2H5) 0.9 Solid (decomposes above ∼530 K) s-butoxide CH3CH2CHOCH3 Ba(Oi C3H7) 2 0.9 Solid (decomposes above H H H H ∼400 K) H C C C C H Y(Oi C3H7) 3 1.2 Solid (sublimes at ∼475 K) Zr(Oi C3H7) 4 1.4 Liquid (boiling point 476 K H H O H at 0.65 kPa) Al(Oi C3H7) 3 1.5 Liquid (boiling point 408 K isobutoxide (CH3)2CHCH2O at 1.3 kPa) Ti(Oi C3H7) 4 1.5 Liquid (boiling point 364.3 K H3C H at 0.65 kPa) H C C O Si(OC2H5) 4 1.8 Liquid (boiling point 442 K at atmospheric pressure) H3C H Fe(OC2H5) 3 1.8 Liquid (boiling point 428 K at 13 Pa) t-butoxide (CH3)3CO Sb(OC2H5) 3 1.9 Liquid (boiling point 367 K at 1.3 kPa) H3C B(On C4H9) 3 2.0 Liquid (boiling point 401 K H3C C O at atmospheric pressure) H3C Te(OC2H5) 4 2.1 Liquid (boiling point 363 K at 0.26 kPa) FIGURE 22.2 Illustration of nomenclature for metal alkoxides. may be referred to as tetraethylsilicate, tetraethylorthosili- expensive materials, for example, TEOS, a colorless liquid, cate (TEOS), and tetraethoxysilane! costs about $40/kg. However, nonstandard alkoxides, for The first alkoxide to be synthesized was silicon tetrai- example, Ba(OC2H5) 2, are more expensive. Barium isop- sopentoxide (formerly called silicon tetraisoamyloxide), ropoxide is an off-white powder and costs about 250 times made by a reaction between silicon tetrachloride and iso- as much as TEOS ($10/g). A 10% w/v solution of pentanol (formerly isoamyl alcohol): Ba(OC2H5) 2 in ethanol will cost about $2/ml. SiCl4 + 4(CH3) 2CHCH2CH2OH → Si(O(CH3) 2CHCH2CH2) 4 + 4HCl (22.1) 22.3 PROPERTIES OF ALKOXIDES Many alkoxides are available commercially, particu- The properties of metal alkoxides depend on the electro- larly those of Si, Al, Ti, B, and Zr. These are not generally negativity of the metal. Pauling’s electronegativity scale was given in Chapter 3. Alkoxides of alkali metals, e.g., sodium alkoxides, and alkaline earth metals are ionic solids. Alkoxides of Ge, Pr iO Al, Si, Ti, and Zr are often covalent liquids. Since most OPr i alkoxides are either liquids or volatile solids (examples are given in Table 22.2), they can be purified by distillation Pr i Al Pr i to form exceptionally pure oxide sources as shown in Table 22.3. O O Pr iO Al Al OPr i TABLE 22.3 Effect of Distillation on the Purity of Silicon Tetraethoxide O Form/impurity Mn Cr Fe Co Ni Cu Pr Oi OPr i As supplied 10 15 86 0.7 <200 <200 Pr i (ppb) Once distilled 0.8 2 31 0.3 11 <20 FIGURE 22.3 Three-molecule coordination complex of aluminum (ppb) isopropoxide. 402 ......................................................................................................................... S o l s , G e l s , a n d O r g a n i c C h e m i s t ry  Hydrolysis Drying  Three-necked flask (contains the mixed solutions) & &  Mechanical stirrer (the mixture is stirred constantly) Condensation Firing  Reflux condenser (needed to prevent the solution from Oxide evaporating) Sol Gel product  Constant temperature bath (the rate of hydrolysis depends on temperature) FIGURE 22.4 The basic steps in the sol-gel process using metal alkoxides. Multicomponent sols can be prepared by mixing dif- ferent precursors, which are selected to give eventually an oxide of the desired composition. Table 22.4 gives exam- ples of typical formulations for both single-component and multicomponent alkoxide solutions. There may be 22.4 THE SOL-GEL PROCESS USING problems if the hydrolysis rates of the precursors are dif- METAL ALKOXIDES ferent, and this can create inhomogeneities in the subse- quent gel. We can allow for this possibility by partially The three basic steps in the sol-gel process are sum- hydrolyzing the less reactive component [e.g., Si(OC2H5) 4] marized in Figure 22.4. The conversion of the sol to a before adding the more reactive one [e.g., Ti(OiC3H7) 4]. gel occurs by hydrolysis For some metals, such and condensation reac- as the alkali metals and tions. The gel is converted SAMPLE RECIPE alkaline earth metals, it is into the oxide by drying PZT thin films can be prepared using a solution of zir- not possible or it is incon- and firing. We will now conium butoxide [Zr(OnC4H9) 4] and titanium propoxide venient to use alkoxides look at each of these steps [Ti(OnC3H7) 4] in 2-methoxyethanol (CH3OCH2CH2OH) because they are either in a little more detail. mixed with lead acetate trihydrate [(CH3CO2) 2Pb·3H2O] unavailable or difficult to that is also dissolved in 2-methoxyethanol. prepare. You can see from Table 22.2 that alkoxides Preparing the Sol of these metals are solids The sol-gel process can be used to make single or multi- with low volatility. In many cases they also have low solu- component oxides. First we will consider the case of a bility. In these situations alternative reactants must be one-component system—silica. Of the many available found. Metal salts such as acetates and citrates, which are silicon alkoxides, TEOS is commonly used. It is insoluble soluble in organic solvents, are a viable alternative. Many in water, but water is necessary for the hydrolysis reaction; of these can be obtained in a high-purity analytical grade. hence we need to select a solvent for both the alkoxide and In cases in which we use both alkoxides and metal salts water. Ethanol is a suitable solvent, and a typical formula- it is usual to first form a solution of all the components tion contains three main components: 43 vol% Si(OC2H5) 4, that are to be added as alkoxides. Then add the salts as 43 vol% C2H5OH, and 14 vol% H2O. solutions in alcohol or, if this is not possible, in the water For small-scale sol-gel processing in the laboratory the that is to be used for the hydrolysis reaction. The final equipment is relatively simple and inexpensive: solution is homogenized by stirring. TABLE 22.4 Formulations for Single-Component and Multicomponent Alkoxide Solutions Three components: One component: Two components: 15 mol% Li2O + 3 mol% 100 mol% SiO2 94 mol% SiO2 + 6 mol% TiO2 Al2O3 + 82 mol% SiO2 Oxide Oxide Oxide Solution content Solution content Solution content concentration (vol%/ concentration (vol%/ concentration (vol%/ Precursor (wt%/100 g) 100 ml) mol g/mol (wt%/100 g) 100 ml) mol g/mol (wt%/100 g) 100 ml) mol g/mol Si(OC2H5) 4 45 43 11 11 35 34 Ti(OC3H7) 4 1 1 Al(OC4H9) 3 1 1 LiNO3 3 1 C2H5OH 40 43 4 36 41 14 29 34 4 H 2O 16 14 4 52 47 50 33 30 8 Oxide (Si + Ti + 1 11.3 1 3.15 1 10.6 Al + Li) 2 2 . 4 Th e S o l - G e l P r o c e s s U s i n g M e ta l A l k ox i d e s ............................................................................................. 403  RO Silicon RO H+ RO H+ tetraethoxide H OR H OR OR HO- + Si OR OH Si OR O + Si O Si RO RO H RO OR OR OR H RO Base OR Acid Acid-catalyzed Insoluble RO Condensation Same as hydrolysis in water (eliminate HOR) before so dissolve R in EtOH OH Si + -OR O H+ OR H + RO OR O Si (A) H RO OR (B) FIGURE 22.5 Schematic showing reaction mechanisms for (a) acid- and (b) base-catalyzed hydrolysis of silicon alkoxides. Hydrolysis and CONDENSATION REACTIONS The silicic acid monomer Condensation The class of organic reactions in which two molecules is not stable and conden- combine eliminating water or another simple molecule. sation of silanol groups Metal alkoxides undergo This produces thermosetting polymers and phenolform- (Si–OH) leads to polymer hydrolysis very easily aldehyde, nylon, and polycarbonates. formation before silanol (meaning they react with groups substitute for all water). In many cases they the alkoxy groups. This are so sensitive to moisture process is illustrated for a general case in Figure 22.6a. that special precautions must be taken in handling and storage (e.g., the use of an N2 glove box and dehydrated solvents). The product vendor will provide information on the sensitivity of the compound. Self-condensation RO RO During the initial stage of hydrolysis an alcohol mole- cule, ROH, is expelled. RO M OR + H2O ROH + RO M OH M(OR) z + H2O → M(OH)(OR) z−1 + ROH (22.2) RO RO This is an example of a condensation reaction involving RO RO RO RO the elimination of an alcohol (e.g., ethanol). RO M OH + RO M OR ROH + RO M O M OR The hydroxy metal alkoxide product can react by a further RO RO RO RO condensation reaction to form polymerizable species. (A) M(OH)(OR) z−1 + M(OR) z → Polymerization (RO) z−1MOM(OR) z−1 + ROH (22.3) Cross-condensation 2M(OH)(OR) z−1 → (RO) z−1MOM(OR) z−1 + H2O (22.4) RO RO Hydrolysis can be carried out either under basic or RO M OR + H2O ROH + RO M OH acidic conditions as shown in Figures 22.5 for TEOS. In RO RO the context of sol-gel processing, acid-catalyzed condi- RO RO RO RO tions are defined as pH <2.5; base-catalyzed conditions are defined as pH >2.5. Of course, this is not our usual RO M OH + RO M* OR ROH + RO M O M* OR definition of acid and base, where a neutral pH is 7, but RO RO RO RO corresponds to the point of zero charge (PZC) at which the surface is electrically neutral. (B) Polymerization Hydrolysis may go to completion leading to the forma- FIGURE 22.6 Schematic showing condensation reactions in tion of the silicic acid monomer. But this generally does (a) single metal alkoxide solutions and (b) mixed metal alkoxide not occur except at low pH and high water concentrations. solutions. 404 ......................................................................................................................... S o l s , G e l s , a n d O r g a n i c C h e m i s t ry For different metal alkoxides the situation is shown in transition. The solution is introduced into the viscometer Figure 22.6b. such that it reaches levels B and C. Liquid is then drawn The experimental variables used in the first stage of up into the left-hand limb until the liquid levels are above the sol-gel process determine the kinetics of the hydrolysis A and at the bottom of the right-hand bulb. When the of the sol to form a gel and have a major influence on gel liquid is released the time for the left-hand meniscus to structure. The relevant variables are pass between marks A and B is measured. Since the pres- sure at any instant driving the liquid through the capillary  Alkoxide concentration is proportional to its density we write  Reaction medium  Concentration of catalyst [The rates of hydrolysis and condensation can be affected by the addition of small η = kρt (22.5) amounts of acid (e.g., HCl) or base (e.g., NH4OH), respectively.] where k is a constant  Temperature known as the viscometer VISCOMETERS coefficient, ρ is the density Used for glass, sol-gels, blood, polymers, etc. The “cup- of the liquid, and t is the The Sol-Gel and-bob” types define the volume of sample to be flow time. The capillary Transition sheared in a test cell. The torque needed to achieve a measurement is simple to Viscosity is a key parame- particular rotational speed is measured. The two geom- operate and quite precise ter that is used to deter- etries are known as the “Couette” or “Searle” systems; (0.01–0.1%). mine when the sol-gel the difference depends on whether the cup or bob rotates. Rotational methods are transition occurs. At the The cup can be a cylinder. particularly suitable for transition there is an abrupt studying the flow of non- increase in viscosity. The Newtonian liquids. An structural changes that occur during gelation for acid- example is the concentric cylinder (or Couette) viscome- catalyzed and base-catalyzed reactions are illustrated in ter. The liquid is sheared between concentric cylinders, Figure 22.7. which are moving relative to one another. The outer cyl- Viscosity can be measured by two simple methods: inder can be rotated (or oscillated) at a constant rate and the shear measured in terms of the deflection of the inner  Capillary flow—most common cylinder, which is suspended by a torsion wire. Alterna-  Rotation—using “Couette flow” The Ostwald viscometer, illustrated in Figure 22.8, is an example of a capillary method used to study the sol-gel A B 10 nm Far From Gel Point Near Gel Point Gel Point Entangled primarily Additional crosslinks linear molecules at junctions (A) C 10 nm Far From Gel Point Near Gel Point Gel Point Branched clusters Growth and Linked clusters additional branching (B) FIGURE 22.7 Illustration of (a) acid- and (b) base-catalyzed FIGURE 22.8 An Ostwald viscometer. The liquid is initially at B polymerization and gelation. and C, then is drawn up to A. 2 2 . 4 Th e S o l - G e l P r o c e s s U s i n g M e ta l A l k ox i d e s ............................................................................................. 405 tively, the inner cylinder can be rotated with the outer used sol-gel liquids are water: 647 K and 22 MPa, and cylinder stationary and the resistance offered by the motor ethanol: 516 K and 6.4 MPa. measured. The coefficient of viscosity is given by During firing, further changes occur as the gel η = Kθ/ωh (22.6) densifies. The driving forces for these changes are as follows: where K is an instrument constant (usually obtained by calibration with a liquid of known η), ω is the angular  The large surface area of the dried gel. A xerogel has velocity of the rotating cylinder, and h is the effective a solid/vapor interfacial area of 100–1000 m 2 /g. Reduc- height of the liquid in contact with the cylinders. This tion of the surface area provides a driving force for method is essentially the same as the Mergules densification. viscometer (Section 21.3) that is used to measure the vis-  The low cross-linked density of the dried gel. The cosity of glass melts; the temperature is very different. free energy, ΔG f (298 K), of the polymerization reaction (Eq. 22.7) is −14.9 kJ/mol, and this acts as a driving force for increasing the amount of Drying and Firing cross-linking. After gelation, the gel usually consists of a weak skeleton of amorphous material containing an interconnected ⬅ Si–OH + HO–Si ⬅ → ⬅ Si–O–Si ⬅ +H2O (22.7) network of small liquid-filled pores. The liquid is usually a mixture of alcohol and water, which must be removed.  Structural relaxation of the solid skeletal phase of the Shrinkage during this step is usually large. gel as the structure approaches that of a supercooled There are several different methods used to dry gels. liquid (if the gel forms a glass) or a crystal line solid Each method produces a (if the gel forms a crystal- dried gel with a specific SHRINKAGE line ceramic). microstructure. In most During drying: Linear shrinkage 50%, volume shrink- cases we obtain either an age 90% aerogel or a xerogel, but During firing: Linear shrinkage 20%, volume shrinkage other microstructures are 50% possible as shown in Table 22.5. The drying process is complicated, particularly when 22.5 CHARACTERIZATION OF THE we want to form monolithic ceramics. One problem is SOL-GEL PROCESS cracking, which is more likely with high drying rates and thick (>1 cm) gels. A number of procedures have Many techniques, in addition to measuring viscosity been developed to increase drying rates while avoiding changes, have been used to follow the transitions that cracking: occur during sol-gel processing. There are the two parts of the process in which we are interested:  Increase the pore size of the gel. 1. The transition from sol to gel  Decrease the liquid/vapor interfacial energy; e.g., use 2. The transition from gel to oxide a solvent with a low γlv.  Strengthen the gel. Examples of techniques used to characterize sol-gel pro-  Use supercritical (hypercritical) drying: the liquid is cesses and the type of information they can provide are removed above its critical temperature, Tc, and critical listed in Table 22.6. We described most of these tech- pressure, pc. The values of Tc and pc for the commonly niques in Chapter 10. TABLE 22.5 The Various Types of Dried Gels Type Drying conditions Microstructure Aerogels In an autoclave, the fluid is removed by hypercritical evacuation A network consisting of ∼95% porosity Xerogels Natural evaporation Dried gel has about 40–60% of the fired density and contains small pores (as small as 2 nm) Sonogels Gel exposed to ultrasound in the 20-kHz range prior to Assists in the formation of multicomponent gels autoclave treatment Cryogels Freeze dried Finely divided powder, not suitable for producing monolithic ceramics Vapogels A fluid stream of SiCl4 is injected into acidified water; this Allows incorporation of additives into the gel, allows rapid gel formation; the gel is then dried to a xerogel e.g., GeO2 if the fluid stream also contains GeCl4 406 ......................................................................................................................... S o l s , G e l s , a n d O r g a n i c C h e m i s t ry  TABLE 22.6 Methods Used to Characterize Sol-Gel Processes Technique What is measured How it is used Ellipsometry Thickness, optical constants of films To measure film thickness changes, for example, during drying Fourier transform IR spectroscopy Vibrational frequencies of chemical bonds, Chemical changes during gelation, drying, and qualitative and quantitative identification firing of functional groups Raman spectroscopy Vibrational frequencies of chemical bonds, Chemical and structural changes during compound identification, structural order gelation, drying, and firing and phase transitions Solid-state nuclear magnetic resonance Interaction between nuclear magnetic Polymerization kinetics, time evolution of (NMR) spectroscopy moments in atoms in the sample with rf condensed species electromagnetic waves, sensitive indicator The chemical shifts in 29Si NMR are functions of of structural and chemical bonding the state of silicon polymerization properties; phase identification and characterization of local bonding environment Transmission electron microscopy Crystallinity and phase identification by Transformation from amorphous to crystalline diffraction, microstructure at high spatial during firing; experiments can be performed resolution in situ X-ray diffraction Crystallinity and phase identification, Transformation from amorphous to crystalline averaged microstructural information during firing; experiments can be performed in situ 22.6 POWDERS, COATINGS, FIBERS, density at temperatures lower than are normally required CRYSTALLINE, OR GLASS? when the particles have been made by other techniques. For example, gel-derived mullite powders can be sintered Sol-gel processing is versatile because it can be used to to full density at <1300°C, whereas the sintering tempera- produce ceramics in a number of different forms: ture is ∼1600°C for crystalline mullite powders. However, the cost of the raw materials limits the use of the sol-gel Powders—because we can make very small particles and method in producing many ceramic powders except for control the composition those used for specialty applications. Example application: bioactive glass powders, with a composition of SiO2–CaO–P2O5 Coatings and Films Coatings—because the sol is a viscous liquid and can be applied to a substrate by spinning Ceramic coatings can be prepared using a sol-gel process Example application: TiO2-based antiglare coatings on involving metal alkoxides. The coatings may be formed glass by Example application: coat steel with alumina to improve wear resistance  Dipping Fibers—because we can pull a thread out that is liquid  Spinning and dry it, coat it, etc.  Spraying Example application: SiO2 fibers used for space shuttle  Lowering (similar to dipping except the substrate tiles remains stationary and the liquid is lowered) Crystalline or Glass? We have the choice. Example application: high-purity porous silica glass for Spinning is widely used for applying sol-gel coatings, filtration and one particular application is to produce thin coatings of PZT for microelectromechanical systems (MEMS). Alkoxide-derived coatings are used for both antireflective Powders layers on glass substrates and solar reflecting coatings on Powders can be obtained via a sol-gel process using metal flat glass. Table 22.7 lists a number of applications for alkoxides or a combination of metal alkoxides and metal sol-gel films and coatings. salts. Because the mixing of the constituents is achieved The advantages of forming coatings via sol-gel reac- at a molecular level, the powders are chemically homoge- tions are neous. Powders produced by the sol-gel method are usually amorphous. This characteristic, together with their high  Large areas surface area, allows them to be sintered to nearly full  Uniform composition 2 2 . 6 P o w d e r s , C oat i n g s , F i b e r s , C ry s ta l l i n e , o r G l a s s ? ................................................................................. 407  TABLE 22.7 Applications of Sol-Gel Films and Coatings Pressure Field Property Examples Electronic Ferroelectric BaTiO3, PZT Piezoelectric PZT High-Tc superconductor Ferrimagnetic YBa 2Cu3O7 Doped Fe2O3 Spinnerette Transparent conductors Indium tin oxide Optical Antireflective TiO2 /SiO2 Solar reflecting TiO2 /Pd Electrooptic PLZT Protective Corrosion resistant SiO2 Abrasion resistant Organic modified silicates Barrier films YSZ Biomaterials Bone cell regeneration Calcium apatites Fibers extrude FIGURE 22.9 Illustration of a spinnerette used to produce fibers  Conformal coating of irregularly shaped substrates, and yarn. e.g., fibers  High purity  Microstructural control, i.e., pore volume (0–65%),  SiO2 pore size (<0.4 nm to >5.0 nm), and surface area  SiO2–TiO2 (10–50 mol% TiO2) (<1–250 m2 /g)  SiO2–Al2O3 (10–30 mol% Al2O3)  Less expensive than vapor-phase processes such as  SiO2–ZrO2 (10–33 mol% ZrO2) chemical vapor deposition (CVD) and sputtering  SiO2–Na2O–ZrO2 (25 mol% ZrO2)  Fibers The properties of some commercial sol-gel fibers are given In Chapter 20 we described various methods of making in Table 22.8. ceramic fibers including the sol-gel process. Fibers can be drawn directly from viscous sols, which are usually made Glasses by acid-catalyzed hydrolysis using low H2O : M ratios. At viscosities greater than about 1 Pa·s (glycerine has a vis- Glasses can be synthesized using the sol-gel process. This cosity of ∼1 Pa·s at room temperature) the sol is sticky and process makes it possible to form a disordered glass we can produce fibers by forcing the sol through a spin- network, not directly at high temperatures from the melt, nerette, illustrated in Figure 22.9. The spinnerette can be but at low temperatures by chemical polymerization in a rotated to produce a yarn. This process is used commer- liquid. cially to produce polymer fibers. The Owens-Illinois Company started an investigation Applications for sol-gel-derived fibers include of bulk glass systems formed by the sol-gel process in 1967. The dried gels were melted and fabricated by  Reinforcement in composites conventional techniques. They found the following  Refractory textiles advantages:  High-temperature superconductors  Lower melting temperatures could be used (the gel is Examples of fibers produced by sol-gel are already amorphous). TABLE 22.8 Properties of Commercial Gel-Derived Ceramic Fibers Tensile Tensile strength modulus Density Producer Name Composition (MPa) (GPa) (g/cm3) 3M Nextel 312 Al2O3, SiO2, B2O3 1750 154 2.70 3M Nextel 440 Al2O3, SiO2, B2O3 2100 189 3.05 3M Nextel 480 Al2O3, SiO2, B2O3 2275 224 3.05 Du Pont PRD-166 Al2O3, ZrO2 2100 385 4.20 Du Pont FP α-Al2O3 1400 3853 3.90 Sumitomo Al2O3, SiO2 Average 2200 Average 230 3.20 408 ......................................................................................................................... S o l s , G e l s , a n d O r g a n i c C h e m i s t ry  FIGURE 22.10 Use of sol-gel processing to produce Si nanoparticles in a glass matrix. (a–c) The time indicates the length of the heat treatment.  It was not necessary to stir the melt (the gel is to conventional ceramic methods is that we are work- homogeneous). ing in uncontaminated conditions and using lower temperatures. It was also found that glasses fabricated from gels and The compaction-and-firing process is similar to tradi- those of the same composition made from oxide powders tional methods for producing ceramics from powders had essentially the same physical properties. But the work except that the powders are derived from the sol-gel was discontinued because of the high cost of the gels process. The pros and cons are the same as those men- compared to the cost of the traditional powders. And, in tioned in forming powders using this method. terms of processing considerations, the gel must be heated very slowly to the melting temperature to ensure that any residual organics and water are removed, otherwise a very Particles in Sol-Gel Films seedy and foamy melt can be obtained. Sol-gel processing can really be justified only for Since the sol-gel films are essentially amorphous in their glasses of certain compositions such as those with high as-prepared state, we can heat treat them to grow nanopar- melting temperatures and high viscosity glasses that are ticles that are then embedded inside an amorphous matrix. difficult to melt conventionally. But glass coatings made The amorphous SiO(C) film in Figure 22.10 was produced by the sol-gel process are still important commercially. by pyrolysis of a sol-gel precursor. The cohydrolysis of triethoxysilane and methyldiethoxysilane (in a molar ratio of 9 : 1) used addition of acidic water (pH 2.25) Monolithic Ceramics to produce the xerogel. The xerogel was pyrolyzed There are basically two MONOLITHIC CERAMICS at 1000°C for 1 hour to routes that can be used to The instruction to build a wall in “monolithic” concrete produce an Si-rich glass. produce monolithic ceram- indicates that it should be a wall of concrete built in The films were heated for ics via a sol-gel process: place and then hardened into a solid unbroken mass. a further 10 hours and Hence a monolithic ceramic is “built” in situ. then 100 hours to produce  Firing: use xerogels or the images shown here. aerogels The dark regions in the images are O depleted and Si rich.  Compaction and firing: use gel-derived powders High-resolution transmission electron microscopy (HRTEM) showed that these were crystalline Si nanopar- Making monolithic ceramics directly by a sol-gel ticles (which have potentially interesting luminescent process is still a challenge. The main issue is how the properties). So not only does this type of study produce gel can be dried without introducing cracks in the dried an interesting material, but it also sheds light on Ostwald body. The advantages of using a sol-gel route compared ripening and devitrification of a glass. CHAPTER SUMMARY You should know that sols and gels are different concepts and that sol-gel uses both. You cannot avoid learning the basic organic chemistry: it is messy and has confusing terminology but is amazingly versatile and can produce nanomaterials routinely. Sol-gel processing is a method that can be used to form ceramic powders, thin films and coatings, fibers, and monolithic ceramics. The advantages of sol-gel processing are that we have excellent control of the C h a p t e r S u m m a ry .......................................................................................................................................................... 409  composition, purity, and homogeneity of our product; how much control depends on the purity of the chemicals with which we start. It also allows us to process materials at lower tempera- tures than any other method because we have small reactive particles. The disadvantages are that the reactants are often expensive and there are problems in producing bulk ceramic com- ponents because of shrinkage. Sol-gel processes are used commercially to produce fibers, coatings, and coated fibers, particularly of ceramics with a high SiO2 content (because process- ing temperatures are much lower). It is also particularly suited to producing thin films of mul- ticomponent oxides such as PZT, which have application in MEMS; and how can you put a more uniform coating on a nanoparticle? PEOPLE IN HISTORY Couette, Maurice Frédéric Alfred (1858–1943) was professor of physics at the University of Angers in France. During his lifetime he published only seven papers. The idea for a viscometer based on shearing a liquid between two surfaces came from his Ph.D. thesis. Ostwald, Wilhelm (1853–1932) won the Nobel Prize in Chemistry in 1909. He held academic positions at several institutions and from 1887 until his retirement in 1906 was Professor of Physical Chemistry at Leipzig University. His famous students included Arrhenius (Nobel Prize 1903), Van’t Hoff (Nobel Prize 1901), and Nernst (Nobel Prize 1920). GENERAL REFERENCES Bradley, D.C., Mehrotra, R.C., and Gaur, D.P. (1978) Metal Alkoxides, Academic Press, London. This is essential reading if you want to find out more. It gives a detailed account of the history and synthesis of metal alkoxides, together with a full list of references. Brinker, C.J. and Scherer, G.W. (1990) Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing, Academic Press, Boston. This is the comprehensive treatment of sol-gel processing. It is the essential resource for those working (or planning to work) in this field. Brinker and Scherer and their co-workers have done extensive work on the densification of gels that form glasses. For more information and specif- ics on this topic, find these papers in your library: Brinker, C.J., Roth, E.P., Scherer, G.W., and Tallant, D.R. (1985) “Structural evolution during the gel to glass conversion,” J. Non-Cryst. Sol. 71, 171; Brinker, C.J., Scherer, G.W., and Roth, E.P. (1985) “Sol → gel → glass: II. Physical and structural evolution during constant heating rate experiments,” J. Non-Cryst. Solids 72, 345; Scherer, G.W., Brinker, C.J., and Roth, E.P. (1985) “Sol → gel → glass: III. Viscous sintering,” J Non-Cryst. Solids 72, 369. Hübert, T., Schwarz, J., and Oertel, B. (2006) “Sol-gel alumina coatings on stainless steel for wear protec- tion,” J Sol-Gel Sci. Techn. 38, 179. Iler, R.K. (1979) The Chemistry of Silica, Wiley, New York. Every aspect of the chemistry of silica in aqueous systems, including polymerization, gelation, gel structure, and applications, is discussed in this classic text. Johnson, J.F., Martin, J.R., and Porter, R.S. (1977) “Determination of viscosity,” in Physical Methods of Chemistry, edited by A. Weissberger and B.W. Rossiter, Vol. 1 Part 6 of Techniques of Chemistry, Wiley, New York, p. 63. Detailed descriptions of measuring viscosity. Rahaman, M.N. (1995) Ceramic Processing and Sintering, Marcel Dekker, New York. Chapter 5 covers sol-gel processing, especially for drying procedures. Segal, D. (1989) Chemical Synthesis of Advanced Ceramic Materials, Cambridge University Press, Cam- bridge. Concise description of the various chemical routes to fabricate ceramics. Contains a large number of references. JOURNALS AND CONFERENCES For coverage of current sol-gel research, the most widely used journals are J. Non-Cryst. Solids, J. Mater. Res., J. Am. Ceram. Soc., J Sol-Gel Sci. Techn., and J. Mater. Sci. The Materials Research Society has sponsored meetings since 1984 under the title Better Ceramics Through Chemistry and has published proceedings. SPECIFIC REFERENCES Ebelman, J.J. and Bouquet, M. (1846) Ann. Chem. Phys. 17, 54. Ebelman was the first person to describe alkoxide synthesis. This paper reported the synthesis of boron methoxide, ethoxide, and pentoxide by the reaction of boron trichloride with the appropriate alcohol. These alkoxides can be used in the synthesis of borosilicate glasses. Piau, J.M., Bremond, M., Couette, J.M., and Piau, M. (1994) “Maurice Couette, one of the founders of rheology,” Rheol. Acta 33(5), 357. 410 ......................................................................................................................... S o l s , G e l s , a n d O r g a n i c C h e m i s t ry  Roy, D.M. and Roy, R. (1955) “Synthesis and stability of minerals in the system MgO-Al2O3-SiO2-H2O,” Am. Min. 40, 147. For studying phase equilibria in minerals homogeneous samples are essential. Hydrolysis of alkoxides was used to synthesize the powders. Rustum Roy of Pennsylvania State University was one of the pioneers in using sol-gel techniques for preparing ceramics. Scherer, G.W. (1990) “Stress and fracture during drying of gels,” J. Non-Cryst. Solids 121, 104. Model for drying gels. EXERCISES 22.1 Sol-gel coatings are usually prepared using either dipping or spinning. What are the advantages and disad- vantages of the two methods? 22.2 Why would spinning rather than dipping be used to produce PZT films for applications such as MEMS? 22.3 The ceramic fibers listed in Table 22.8 are made by sol-gel processing. (a) Why do you think this processing method was chosen? (b) What starting chemicals would be suitable for making these fibers? (c) Are there any alternative approaches that could be used to produce these ceramic fibers? If so, what are they and how do they compare to sol-gel? 22.4 Discuss the economic issues involved in using the sol-gel process to form ceramic powders. 22.5 Explain why 29Si NMR can be used to study the amorphous-to-crystalline transition in a silica gel. [Note: You may find the following references of use: Brown, I.D. and Shannon, R.D. (1973) “Empirical bond-strength bond-length curves for oxides,” Acta Crystallogr. A 29, 266; Smith, K.A., Kirkpatrick, R.J., Oldfield, E., and Henderson, D.M. (1983) “High-resolution 29Si nuclear magnetic-resonance spectroscopic study of rock- forming silicates,” Am. Mineral. 68, 1206.] 22.6 What is the difference between a particulate gel and a polymeric gel? 22.7 What would be appropriate starting chemicals for producing YBa2Cu3O7 films by sol-gel? 22.8 Explain briefly the problems with shrinkage as they apply to sol-gel processing. 22.9 Compare the raw materials costs of preparing PZT powders by conventional solid-state reactions and sol-gel processing. What are the pros and cons of each approach? 22.10 Nylon is prepared by a condensation reaction. Compare this process to that occurring during sol-gel process- ing of ceramics using metal alkoxides. C h a p t e r S u m m a ry .......................................................................................................................................................... 411  23 Shaping and Forming CHAPTER PREVIEW This is the pottery chapter! Many of the techniques that are now being used to shape high-tech ceramics have been used by potters for millennia, but have been refined for today’s high-tech applications and for new ceramic materials. We will try to relate shaping to the potter’s craft throughout the chapter. We can just process dry powder and sinter it, but it is much more common to add some amount of liquid, just as the potter adds water to clay; we then shape the object and fire it. Shaping transforms an unconsolidated powder mixture into a coherent, consolidated body having a chosen geometry. The selection of a shaping operation for a particular product is very dependent on the size and dimensional tolerances of the product, the requisite microstructural characteristics, the levels of reproducibility required, economic considerations, and of course the required shape. We cover shaping of glass in Chapters 21 and 26 so here we will consider the similarities in processing glass and crystalline ceramics. Similarly, we discuss thick films in Chapter 27; here we concentrate on three-dimensional (3D) objects varying from fish-hooks to turbine blades. However, we will cover slip casting, which we used only in a limited way for thin films. 23.1 THE WORDS is quite unlike the casting of metals. The slurry is then poured into a porous mold that removes the liquid (it dif- There is a special vocabulary for shaping ceramics because fuses out through the mold) and leaves a particulate it is an ancient art. Once the constituent powders have compact in the mold. This process is known as slip casting. been prepared in the desired purity and particle size most The process has been used to form many traditional ceramic products must be fabricated into useful shapes. ceramic products (e.g., sanitary ware) and more recently Many shaping methods are used for ceramic products and has been used in forming advanced ceramic products (e.g., these can be grouped into three basic categories, which rotor blades for gas turbines). The other main casting are not necessarily independent. process for ceramics is tape casting, which, as you would guess, is used to make thick films or sheets and is described 1. Powder compaction: dry pressing, hot pressing, cold in Chapter 27. isostatic pressing, etc. Plastic forming consists of mixing the ceramic powder 2. Casting: using a mold with the ceramic as, or contain- with a large volume fraction of a liquid to produce a mass ing, a liquid or slurry that is deformable (plastic) under pressure. Such processes 3. Plastic forming: extrusion, injection molding, etc.— were developed and used originally for clay and have since using pressure to shape the green ceramic been adapted to polymeric materials. For traditional clay- based ceramics the liquid is mainly water. For ceramic Powder compaction is simply the pressing of a free- systems that are not based on clay, an organic may be used flowing powder. The powder may be dry pressed (i.e., in place of, or in addition to, water. The binders are often without the addition of a binder) or pressed with the addi- complex and contain multiple components to achieve the tion of a small amount of a suitable binder. The pressure required viscosity and burn-out characteristics. is applied either uniaxially or isostatically. The choice of Table 23.1 lists the major methods that are included in pressing method depends on the shape of the final product. each of the above categories and the types of shape that We make simple shapes by applying the pressure uniaxi- can be produced. First some of the words: ally; more complex shapes require isostatic pressing. Casting ceramics is carried out at room temperature Binder is a component that is added to hold the powder and generally requires the ceramic powder particles to be together while we shape the body. suspended in a liquid to form a slurry; note this process Slurry is a suspension of ceramic particles in a liquid. 412 .................................................................................................................................................... Shaping and For ming  TABLE 23.1 Various Shaping Methods for Ceramic Components Shaping method Type of feed material Type of shape Dry pressing Free-flowing granules Small and simple Isostatic pressing Fragile granules Larger and more intricate Extrusion Plastic mass using a viscous polymer solution Elongated with constant cross section Injection molding Organic binder giving fluidity when hot Complex Slip casting Free-flowing cream Mainly hollow Plasticizer is the component of a binder that keeps it soft Binders can also be used when metal powders are or pliable; it improves the rheological properties. processed; PMC is precious-metal clay. Green is a ceramic before it is fired. Brown, white, or gray potter’s clays are well known green ceramics. Slip is the liquid-like coating used to form the glaze when 23.3 SLIP AND SLURRY fired. The word slip appears to come (according to Webster’s) Some of the shaping methods we will describe in this from the Old English words meaning cream: the suspen- chapter produce a ceramic compact that is strong enough sion of curds in the liquid when making cheese; the cheese to be handled and machined; however, it is not fully dense was actually sieved through a “slippe clothe.” and the bonds between the grains are not strong. This is In general, slip consists of fine (<10 μm) ceramic- called the “green” state and represents a transition state powder particles that are suspended in a fluid. In the between the loose powder and the high-density sintered pottery industry, the liquid is usually water. The suspen- product. Other shaping methods, those that involve the use sion can have a solid content up to ∼60 vol%. Defloccu- of high temperatures and pressures, can directly produce lents are added to the slip to modify the electrical a very dense sintered product. Much of what we talk about environment of each particle so that the particles repel here has a parallel in the field of powder metallurgy; each other. the theme is often processing powders, which are not necessarily ceramic powders (e.g., they could be pharmaceuticals). Deflocculants: Since deflocculation is defined as the process by which floccules present in a liquid break up into fine particles producing a dispersion, a defloccu- 23.2 BINDERS AND PLASTICIZERS lant is an additive that causes this process. In other words, deflocculation is the opposite of coagulation. It is often necessary to add a binder to the ceramic powder. (A floccule is a small piece of matter or a flock.) The binder has two functions. In some shaping methods, Colloids: Colloids are defined very generally as any such as extrusion, the binder provides the plasticity neces- substance that consists of particles substantially sary for forming. The binder also provides the dry (green) larger than ordinary molecules but much too small shape with strength sufficient to survive the handling to be visible without optical magnification (∼1 nm process between shaping and sintering. One of the most to 10 μm). They can be linked or bonded together important requirements for the binder is that we must be in various ways. Colloidal systems can take several able to eliminate it from the compact during the firing forms; the one relevant to us is the dispersion of one process without any disruptive effect: polymers are thus substance in another. Brownian motion has interested often ideal binders. scientists for generations. Slip is a colloid. We can In pottery, the binder is often water that is present in change the properties of the slip by adding flocculants sufficient quantity to make the clay easily shaped with the or deflocculants. shape being retained during firing. The idea is that we then Slurry: Clay particles are suspended in a liquid (water add a plasticizer to opti- in the case of pottery). As mize the rheology of the the amount of water is material. Note that these BINDERS decreased it becomes more processes are not exclusive Poly (vinyl alcohol) (PVA) and poly (ethylene glycol) solid. Glazes used in to ceramics but are general (PEG) are the two of the most popular binders for dry- pottery have the same base to powder processing. The pressing ceramics: as the clay but with more distinction between binder water content. Potter’s clay and plasticizer is some- PVA provides a high green strength. is made by first producing times not too clear. PEG provide a high green density. a slip from naturally occur- 2 3 . 3 S l i p a n d S l u r ry ................................................................................................................................................... 413  shapes such as seal rings and nozzles can be produced at rates up to several hundred per minute. Small flat parts such as insulators, chip carriers, or cutting tools can be produced at rates up to several thousand per minute. FIGURE 23.1 The stages in dry pressing. 23.5 HOT PRESSING Pressing can also be performed at high temperatures; this process is known as hot pressing. The die assembly used ring clays. The slip is repeatedly filtered to produce a for hot pressing is very similar to that described in Section consistency that is constant over long periods of manu- 23.4 for dry pressing. The main difference is that in hot facture. Slabs of clay are then formed from this colloid pressing the die assembly is contained within a high- by allowing most of the water to evaporate. The final temperature furnace as shown in Figure 23.2. During hot product may be shaped by extrusion and packaged to pressing the ceramic powders may sinter together to form prevent further loss of water. a high-density component. We can summarize the advantages of this process. 23.4 DRY PRESSING  The powder does not have to be of the highest quality. Dry pressing is ideally suited to the formation of simple  Large pores that are caused by nonuniform mixing are solid shapes and consists of three basic steps: filling the easily removed. die, compacting the contents, and ejecting the pressed  We can densify at temperatures lower (typically half solid. the melting temperature of the material) than those Figure 23.1 shows a schematic diagram of the double- needed for conventional pressureless sintering. action dry-pressing process. In a double-action press both  Extensive grain growth or secondary recrystallization the top and bottom punches are movable. When the bottom does not occur when we keep the temperature low punch is in the low position a cavity is formed in the die during densification. and this cavity is filled with free flowing powder. In dry  We can densify covalently bonded materials such as pressing the powder mixture will contain between 0 and B4C, SiC, and Si3N4 without additives. 5 wt% of a binder. (So, dry does not imply that there is no binder.) Once the cavity has been filled, the powder is The principal disadvantage is also important. struck off level with the top of the die. The top punch descends and compresses the powder either to a predeter-  Dies for use at high temperatures are expensive and do mined volume or to a set pressure. During pressing the not generally last long. powder particles must flow between the closing punches so that the space between them is uniformly filled. A particle size distribution of between 20 and 200 μm is often preferred for dry pressing: a high volume fraction of small particles causes problems with particle flow and also Hydraulic Cooled platen results in sticking of the punches. The pressures used in press dry pressing may be as high as 300 MPa, depending upon High-strength refractory block material and press type, to maximize the density of the Furnace insulative refractory lining Refractory punch compact. After pressing, both punches move upward until the bottom punch is level with the top of the die and the Mold top punch is clear of the powder-feeding mechanism. The compact is then ejected, the bottom punch is lowered, and Powder the cycle is repeated. Replaceable Hot mold liner Because the dry-pressing process is so simple and zone Plug involves low capital equipment costs it is the most widely used high-volume forming process for ceramics. Produc- Mold tion rates depend on the size and shape of the part and on support block the type of press used. For large components such as refractories or complex parts such as grinding wheels the Refractory production rates are 1–15 parts per minute. During a tour block of the Wedgwood factory, you will see dinner plates being FIGURE 23.2 Schematic showing the essential elements of a hot dry pressed in a continuous process. Simpler or smaller press. 414 .................................................................................................................................................... Shaping and For ming  TABLE 23.2 Hot Pressed Products small grain size, a high density (low porosity), or low impurity levels. Examples of such products are given in Product Types of material Table 23.2. Optical windows IR: MgF2, ZnS, ZnSe; visible: Y2O3, Isostatic pressing involves the application of hydro- MgAl2O4 static pressure to a powder in a flexible container. The Ceramic armor B4C, TiB2, SiC, Al2O3 advantage of applying pressure in all directions is that Cutting tools Al2O3 particle-reinforced TiC, Si3N4, Si3N4 –AlN–Al2O3 there is more uniform compaction of the powder and more Tooling (molds and dies) Al2O3 –SiCw composites, SiC, Al2O3 complex shapes can be produced than with uniaxial press- Sputtering targets Cr–SiO, TiN, Si3N4, B4C, Al2O3 ing. Isostatic pressing can be performed either with or Heat engine components Si3N4, SiC without applied heat. Ceramic bearings Si3N4 Microwave absorbers MgO–SiC particulate composites, BeO–SiC, Al2O3 –SiC Varistors ZnO 23.6 COLD ISOSTATIC PRESSING Electrooptic materials PLZT Titanates BaTiO3, CaTiO3 There are many variations on using the cold isostatic press Microelectronic packages Cofired W-metallized AlN (CIP); here we just emphasize some basic themes. Figure Resistors Si3N4 matrix with particulates of TiB2, TiC, TiN, or SiC as the dispersed 23.3 illustrates the so-called wet-bag CIP process. Powder conducting phase is weighed into a rubber bag and a metal mandrel is inserted that makes a seal with the mouth of the rubber bag. The sealed bag is placed inside a high-pressure chamber that is filled with a fluid (normally a soluble oil/ Most metals are of little use as die materials above water mixture) and is hydrostatically pressed. The pres- 1000°C because they become ductile, and the die bulges. sures used can vary from about 20 MPa up to 1 GPa Special alloys, mostly based on Mo, can be used up to depending upon the press and the application. For produc- 1000°C at pressures of about 80 MPa. Ceramics such as tion units the pressure is usually ≤400 MPa. Once pressing Al2O3, SiC, and Si3N4 can be used up to about 1400°C at is complete, the pressure is released slowly, the mold is similar pressures. Graphite is the most widely used die removed from the pressure chamber, and the pressed com- material and can be used at temperatures up to 2200°C ponent is removed from the mold. and pressures between 10 and 30 MPa. The difficulty is The advantages of the wet-bag process are that a graphite die will tend to produce a very reducing environment. (You can make an Al2O3 sample vanish  Wide range of shapes and sizes can be produced using a graphite die!)  Uniform density of the pressed product However, graphite does have many properties that  Low tooling costs make it suitable for a die. The disadvantages are  It is easy to machine (but the dust is toxic if inhaled— like coal dust).  Poor shape and dimensional control (particularly for  It is inexpensive. complex shapes)  Its strength increases with increasing temperature.  It has good creep resistance.  It has excellent thermal conductivity. Breach-lock or  It has a relatively low coefficient of thermal pressure cover expansion. Hot pressing, like dry pressing, is limited to simple Pressure Fluid solid shapes, such as flat plates, blocks, and cylinders. vessel More complex or large shapes are difficult and often Mold impossible to produce by hot pressing. Hot pressing is seal plate widely used in the research laboratory for processing very Wire mesh dense, high-purity ceramic components. Although it is basket Rubber extensively used in university and government laborato- mold ries, the technique is limited as a production tool because of its high cost and low productivity. For any mass- Pressurization Powder produced ceramic product there would be considerable source Metal commercial pressure for a company to find a less expen- mandrel sive alternative. However, some commercial hot-pressed ceramic products are available. These products require a FIGURE 23.3 Schematic of a wet-bag isostatic pressing system. 2 3 . 6 C o l d I s o s tat i c P r e s s i n g ..................................................................................................................................... 415  First elastomer Cap Upper Rigid die case Channel to cover distribute liquid Cooling jacket Components Heater Thermo- Pressure couple vessel Power connection Second elastomer To pump Entry port for Spindle pressurized liquid Over-pressure release FIGURE 23.4 Schematic of a die for dry-bag isostatic pressing of Gas in a spark plug insulator. FIGURE 23.6 Schematic of a hot isostatic pressing apparatus.  Products often require green machining (described in Section 23.14) after pressing Production rates of up to 1 part per second are being  Long cycle times (typically between 5 and 60 minutes) achieved industrially. give low production rates The dry-bag CIP has been used for many years to press spark plug insulators. The steps in this process are shown A small wet-bag isostatic press, used to produce labo- in Figure 23.5. Notice the insertion of the inner pin in the ratory samples and low-volume production parts, might mold. The world’s largest producers of spark plugs pro- have an internal diameter of 150 mm and a depth of duced by this method are Champion and AC Spark Plug. 460 mm. Large wet-bag presses may have cavity diameters >1.8 m and lengths up to 3.7 m. The wet-bag CIP process can be automated. 23.7 HOT ISOSTATIC PRESSING A schematic diagram of a mold for the dry-bag CIP is shown in Figure 23.4. The main distinction of the dry-bag The hot isostatic press (HIP) uses the simultaneous appli- process is that the rubber mold is now an integral part of cation of heat and pressure. We refer to this process as the press. The high-pressure fluid is applied through chan- HIPing and the product as being HIPed (but you will see nels in the mold. After pressing, the pressed part is variations on these abbreviations). A furnace is con- removed without disturbing the mold. Hence, the dry-bag structed within a high-pressure vessel and the objects to press can be readily automated. Fully automated units are be pressed are placed inside. Figure 23.6 shows a typical widely available and have been operating in the high- HIP arrangement. Temperatures can be up to 2000°C and volume production of ceramic parts for over 20 years. pressures are typically in the range of 30–100 MPa. A gas Rubber Inner container Powder pin Oil in At air Oil out FIGURE 23.5 Making spark plugs. Hydrostatic pressure is applied by pumping oil around the rubber container, which is part of the press and thus easily removed. 416 .................................................................................................................................................... Shaping and For ming is used as the pressure HIP AND HIPING special mechanical prop- medium, unlike the CIP Used initially for fabricating the cladding for nuclear erties. HIPing has also in which a liquid is often fuel elements. It was called “gas-pressure bonding.” been applied to the for- used. Argon is the most We use the acronym HIP to identify the press and mation of piezoelectric common gas that is used HIPing to identify the action. You will also see HIP used ceramics such as BaTiO3, for HIPing, but oxidizing to mean HIPing and you will see HIPing spelled SrTiO3, and lead zirconate and reactive gases can HIPping! We then say a sample has been HIPed rather titanate (PZT) for use in also be used. Note that the than HIPped. Only nano is HYPed. acoustic wave filters and high-pressure vessel is not oscillators. inside the furnace. There are two variants of HIPing: Uses: produces dense materials without growing the grains  Encapsulated: using a deformable container Disadvantage: cost  Not encapsulated: it is shaped and sintered first, then HIPed 23.8 SLIP CASTING In the original HIPing method the ceramic powder was The slip is poured into a mold (usually plaster of Paris: filled into a deformable metal can and then subjected to 2CaSO4 ·H2O) that has been made by casting round a heat and pressure. This method was subsequently modi- model of the required shape, which was itself suitably fied for small particle sized powders. The powder compact enlarged to allow for the shrinkage of the cast ceramic on was preformed to the desired shape by a process such as drying and sintering. The fineness of the powder (in the dry pressing or injection molding. The green compact was slip) and the consequent high surface area ensure that then encapsulated in a glass envelope that could be removed electrostatic forces dominate gravity so that settling does from the product after HIPing as shown in Figure 23.7. not occur. The electrochemistry of the slip is quite The second variant does not involve encapsulation. complex: Na silicate (or soda ash) is added to the slip to The ceramic powder is first compacted using another deflocculate the particles. The water passes, via capillary shaping method such as dry pressing or injection molding. action, into the porous plaster leaving a layer of the solid It is then sintered at relatively high temperatures in a on the wall of the mold. (We consider this model in Section furnace to close all the surface pores, which prevents the 25.7.) Once a sufficient thickness has been cast, the surplus entry of the gas during subsequent HIPing. The steps in slip is poured out and the mold and cast are allowed to this process, which is sometimes referred to as sinter-plus- dry. These steps are shown in Figure 23.9. This variant of HIP, are shown in Figure 23.8. slip casting, which is the most widely used, is also called Now HIPing is used for a wide variety of ceramic (and drain casting. A very effective technique used by some metallic) components, such as alumina-based tool bits and potters is to produce a multilayer slip, parts of which are the silicon nitride nozzles used in flue-gas desulfurization removed before firing. plants by the utility industry. The advantages of the HIPing Slip casting is a low cost way to produce complex process are becoming more important as interest in struc- shapes and in the traditional pottery industry it is the tural ceramics such as Si3N4 grows. accepted method for the production of teapots, jugs, and Nonoxide ceramics can be HIPed to full density while figurines, although handmade items will likely be hand- keeping the grain size small and not using additives. Very thrown. Large articles, such as wash-hand basins and high densities combined with small grain sizes (because other whitewares, are also mass produced by slip casting. of the relatively low temperatures) lead to products with (Whitewares are not necessarily white.) One of the telltale Strip can Glass envelope Canning Sinter HIP HIP (shrinkage) Preform Preform FIGURE 23.7 Individual steps of cold preforming, canning, HIPing, FIGURE 23.8 Individual steps of cold forming, sintering, and and stripping in the standard HIPing process. HIPing in the sinter plus HIPing process. 2 3 . 8 S l i p C a s t i n g .......................................................................................................................................................... 417  Force Force Slip (A) Green ceramic Spider Needle Extruded rod Extruded tube (A) (B) (B) Mold FIGURE 23.10 Extrusion of (a) a rod and (b) a tube. FIGURE 23.9 Schematic illustrating the drain-casting process. (a) Fill the mold with slip; the mold extracts liquid, forming a compact along the mold walls; (b) after excess slip is drained uniform cross section and a large length-to-diameter ratio and after partially dryed, green ceramic is removed. such as ceramic tubes and rods as illustrated in Figure 23.10. Clay with a suitable rheology for the extrusion process (essentially a paste) can be made by controlling signs of a ceramic product made by slip casting is that it the amount of water. Clay-free starting materials, such as is hollow. Another variant of the slip casting process is Al2O3, are mixed with a viscous liquid such as polyvinyl solid casting. In solid casting, slip is continually added alcohol or methylcellulose and water to produce a plasti- until a solid cast is made. These items will not be hollow— cally deformable mass. Table 23.3 lists the compositions relatively, they will be heavier. of some extrusion bodies. Extrusion of polymers has been Slip casting is also used in the fabrication of some used since the 1860s; it was originally used to process technical and structural ceramics. It is the standard method natural rubber. An extrusion press like those shown in used to make alumina crucibles and has been successfully Figure 23.11 is standard equipment in the potter’s barn. used to make complex structural ceramic components Extrusion is also used to produce the alumina shells such as gas-turbine rotors. The technique of doctor- for sodium vapor lamps and the honeycomb-shaped cata- blading, which we discuss in Chapter 27, is just another lyst supports for automotive emission-control devices (see method of shaping the slip—ensuring that the slip is Chapter 37). The catalyst supports are designed to give a spread as a uniform layer. high surface area and can consist of hundreds of open cells per square centimeter with wall thicknesses <100 μm. To 23.9 EXTRUSION produce these shapes, cordierite ceramic powder is mixed with a hydraulic-setting polyurethane resin. The mix is Extrusion involves forcing a deformable mass through a extruded into a water bath at a rate that matches the rate die orifice (like toothpaste from a tube). The process is of cure of the polyurethane (about 2 mm/s). It is then fired widely used to produce ceramic components having a to produce the final ceramic. TABLE 23.3 Examples of Compositions of Extruded Bodies (Composition in vol%) Refractory alumina High alumina Electrical porcelain Alumina (<20 μm) 50 Alumina (<20 μm) 46 Quartz (<44 μm) 16 Hydroxyethyl cellulose 6 Ball clay 4 Feldspar (<44 μm) 16 Water 44 Methylcellulose 2 Kaolin 16 AlCl3 (pH > 8.5) <1 Water 48 Ball clay 16 MgCl2 <1 Water 36 CaCl2 <1 418 .................................................................................................................................................... Shaping and For ming  Hopper Mold Material Heaters Screw Green body FIGURE 23.12 Cross-sectional side view of a screw-type machine. repeated. Injection molding can be applied to shaping and forming ceramic components if the ceramic powder is added to a thermoplastic polymer. When forming ceramics by injection molding, the polymer is usually referred to as the binder (but we could instead have called the material a ceramic-loaded polymer). The ceramic powder is added to the binder and is usually mixed with several other organic materials to provide a mass that has the desired rheological properties. Table 23.4 shows the additives that have been used to form SiC shapes by injection molding. The organic part of the mix accounts for about 40 vol%. The plastic mass is first heated, at which point the thermoplastic polymer becomes soft and is then forced into a mold cavity as shown in Figure 23.12. The heated mixture is very fluid and is not self-supporting (this is different from the situation encountered in extrusion). The FIGURE 23.11 Extruding clay. Manual and electric extruders. mixture is allowed to cool in the mold during which time the thermoplastic polymer hardens. Because of the large volume fraction of organic material used in the mixture, 23.10 INJECTION MOLDING there is a high degree of shrinkage of injection-molded components during sintering. Shrinkage of 15–20% is Injection molding is another technique that is widely typical, so precise control of component dimensions is used in shaping thermoplastic polymers. A thermoplastic difficult. However, complex shapes are retained with very polymer is one that softens when heated and hardens when little distortion during sintering since the densities, cooled. Such processes are totally reversible and may be although low, are uniform. TABLE 23.4 Additives for Injection Molding of SiC Function Example Quantity (wt%) Volatilization temperature Thermoplastic resin Ethyl cellulose 9–17 200–400°C Polyethylene Polyethylene glycol Wax or high-temperature volatilizing oil Paraffin 2–3.5 150–190°C Mineral oils Vegetable oils Low-temperature volatilizing hydrocarbon or oil Animal oils 4.5–8.5 50–150°C Vegetable oils Mineral oils Lubricant or mold release Fatty acids 1–3 Fatty alcohols Fatty esters Thermosetting resin Epoxy Gives carbon Polyphenylene 450–1000°C Phenol formaldehyde 2 3 .10 I n j e c t i o n M o l d i n g ............................................................................................................................................. 419  Injection molding is used to fabricate ceramic compo- Heated Ceramic powder in nents with complex shapes; because cycle times can be extrusion thermoplastic rapid, injection molding can be a high-volume process. nozzle polymer filament The major limitation is that the initial tooling costs of the mold can be quite high. The mold to fabricate an individ- Green ual turbine blade can be >$10,000 and a mold for a turbine ceramic rotor may be >$100,000, but such molds are reusable since they are never subjected to high temperatures. 23.11 RAPID PROTOTYPING Rapid prototyping (RP) or solid freeform fabrication Platform (SFF) is a relatively recent approach to forming ceramic components. There are various forms of RP techniques, but they are based on a common principle: a computer FIGURE 23.14 Schematic representation of the fused deposition directly controls the shaping process by accessing com- (FD) SFF process. puter-aided design (CAD) files. We can thus use RP to form a 3D component without the use of a die or a mold. loaded with ceramic powders. Si3N4, SiO2, and Al2O3 RP techniques are used commercially for fabrication of powders have all been used for SLA. parts from polymers for design verification and form-and- In FDM the source material is a thermoplastic polymer fit applications; these techniques have more recently been filament that is heated and extruded to form the product applied to forming parts out of ceramics. as shown in Figure 23.14. The product is formed in a layer- In this section we will look at just two of the several by-layer manner similar to building up layers of icing on RP methods a cake. The computer controls the x–y position of the fila- Stereolithography (SLA) ment and the deposition rate. The filament can be loaded Fused deposition modeling (FDM) with up to 60 vol% ceramic powders; once the part is completed the binder is removed and the part is sintered. Both these methods have been successfully used to Most of the work in the RP of ceramic parts by FDM has form ceramic components. The SLA process is illustrated involved Si3N4. The feasibility of making components out in Figure 23.13. In SLA the component is formed from an of Al2O3, SiO2, and PZT has also been demonstrated. The epoxy resin. As the z-stage elevator is lowered, an ultra- abbreviation FDC (fused deposition of ceramics) is used violet (UV) laser beam whose position is controlled by a to identify this special application of FDM. computer cures successive layers of the uncured resin. In this way a 3D component is made one layer at a time. It can take many hours to build a large complex object. But 23.12 GREEN MACHINING this is still rapid compared to the time taken to form a component by, e.g., injection molding, where fabrication To obtain the desired shape of a ceramic product it is often of the tools can take a considerable amount of time. To necessary to machine it. Machining can be performed form ceramic components by SLA the polymer must be either before or after the product has been sintered. If the machining is done before sintering, while the component is still in the green state, the process is called green machining. The advantages of green machining compared to machining the sintered product are that there is a con- Scanner Movable siderable reduction (10×) in machining time and a 20× System Table reduction in cost because of less tool wear and the possi- Green ceramic bility of using cheaper tools. Table 23.5 compares the use TABLE 23.5 Comparison of Cutting Speed versus Tool Life Tool Cutting speed Work-piece material Relative Ceramic material (m/min) removed (cm3) cost factor powder in photo Cubic BN 30 8.2 × polymer Ti-coated 30 13.1 × carbide Support Co-coated 30 19.7 × structures WC Diamond 90 8500 10× FIGURE 23.13 Schematic representation of the SLA SFF process. 420 .................................................................................................................................................... Shaping and For ming of different tool materials in the green machining of an Si T °C 1.33 x 105 compact before nitriding it to form Si3N4. 1200 In the processing of spark plug insulators the final 1.33 x 104 processing step prior to firing involves green machining P Sweep gas T P (Pa) 1000 as shown earlier in Figure 23.5. 1.33 x 103 Cool 800 133 23.13 BINDER BURNOUT 600 13.3 Sinter In pottery, the binder burnout is the removal of water from 400 1.33 Polymer the shaped clay. The rest of the firing process causes removal structure changes and transformations in the silicate itself. 200 Wax removal T 0.133 P Forming methods for engineering ceramics, like injection molding, produce green bodies that can contain 30–50 0 0 4 8 12 16 t (h) vol% of organic binder. We generally want to remove this FIGURE 23.15 Pressure-induced binder removal cycle. binder without cracking or distorting the ceramic compact. Binder burnout is one of the most likely stages to form defects in the processing of a ceramic: macroscopic defects, such as cracks and blisters, can be introduced at Binder burnout continues to be an active area of ceram- this stage, and these will affect the mechanical strength ics research with one of the main thrusts being in develop- and other properties. An additional complication is that ing models of binder decomposition and diffusion. the binder system used in fabricating many commercial ceramic parts often consists of several components. These components have different boiling points and decomposi- 23.14 FINAL MACHINING tion temperatures. Ideally the shaping and forming processes that are employed would produce the ceramic component in the The components with low boiling points (e.g., waxes) desired shape with the specified dimensional tolerances may be removed by evaporation at fairly low and with an acceptable surface finish. However, in many temperatures. cases this is not the situation and some final machining Oxidation or decomposition at higher temperatures re- (after firing/sintering) of the ceramic is necessary. Gener- moves high-molecular-weight components. ally final machining is required to For oxide ceramics, the binder can be oxidized to form  Meet dimensional tolerances H2O, CO, and CO2 when the green compact is heated in  Improve the surface finish air. Binder burnout in air generally presents no problem.  Remove surface flaws However, there are some situations in which binder burnout in air can be a problem. An example is the use of poly(vinyl Machining fired ceramics can be expensive and can butyral) with Al2O3 where carbon residues can be as high represent a significant fraction of the total fabrication as thousands of parts per minute even after burnout in air costs. Ceramic materials are difficult to machine because at 700°C for 24 hours. Nonoxide ceramics generally they are hard and brittle. The tooling costs are high cannot be heated in oxidizing environments and binder because diamond tools are likely to be required or if con- burnout in inert or reducing atmospheres is more difficult. ventional tools are used the tool life is very short. Also Pyrolysis of many binders in these environments is not the time required to machine ceramics is long because if well understood and most binders leave some carbona- high tensile loads are applied to the ceramic part it might ceous residue that could be detrimental to the subsequent fracture. sintering stage. Mechanical approaches to machining ceramics include The process of binder removal is kept slow to reduce the following: the possibility of macrodefects being produced. Figure 23.15 shows a plot of a binder removal cycle. In this plot  Grinding uses tools in which abrasive particles are a pressurized gas, called a sweep gas, has been passed embedded in a softer matrix such as glass, rubber, or over the part to help sweep away the vapor. The cycle time polymer resin, or even a metal (as for WC in Co). also depends on the size of the part. Thin sections take  Lapping uses loose abrasive particles placed on a soft much shorter times than thick sections. The debinding cloth. time is proportional to the square of the section thickness  Sandblasting uses abrasive particles accelerated by of the compact—the familiar parabolic kinetics seen in compressed air and directed through a nozzle at high our discussion of reactions in Chapter 25. velocity. 2 3 .14 F i n a l M ac h i n i n g ................................................................................................................................................ 421   Use large particles with a very small size distribution to avoid dense packing.  Underfire a green compact to leave a large amount of fine pores. Water  Add organic particles (diameter >20 μm) to the powder inlet mixture; when these burn out they will leave behind porosity. We use a controlled version of this technique elsewhere to produce mesoporous photonic materials.  Use a binder system that contains a foaming agent and Abrasive Jewel produces a large amount of gas bubbles in the mixture.  Impregnate a foam that has a continuous porosity and then burn it out.  Use a glass composition that phase separates and then Mixing leaches out (e.g., using an acid) one of the phases to tube produce porous glasses. Guard Mesoporous materials, which have quite a uniform distribution and a very high density of pores, were dis- cussed in Chapter 15. FIGURE 23.16 Schematic of the abrasive waterjet cutting process. 23.16 SHAPING POTTERY We stated at the beginning that this chapter is the pottery chapter. We will now summarize areas in which many of  Water-jet machining uses a high-pressure (∼400 MPa the techniques described above have been used, in some pumping pressure) water jet to transport the abrasive cases for millennia, in pottery; then we can do the same particles to the ceramic surface. for glass. Classical porcelain can be as thin as a sheet of paper (<0.2 mm). Bone china, so called because even The water-jet method is gaining popularity as a high- today it is made by adding ∼50% bone ash to a conven- speed method for machining hard ceramics. Figure 23.16 tional hard-porcelain clay mixture, can be so thin that it shows the basic components of an abrasive water-jet cutter. is translucent. This ingredient is so critical that the UK Cutting rates depend on the material being cut and can imports bone ash from Argentina. vary from 130 mm/min for glass to 5 mm/min for a dense Paper clay is a relatively new material for the potter hard ceramic such as TiB2. In a water-jet, the water is being a mixture of clay and paper in approximately equal pressurized to ∼380 MPa and is forced through a sapphire amounts by volume. The paper (cellulose fiber) gives orifice at a velocity of up to about 750 m/s; in the abrasive added strength to the green body so it can even be made jet, the speeds may be a little lower, but garnet powder is into a sheet that can then be cut and shaped before firing. pulled into the water stream and acts as the abrasive to cut The firing burns out the organics and leaves a ceramic through, e.g., 25 mm of Ti or steel. It can also cut through body that is lighter than usual. Figure 23.17 shows a sheet ceramics and glass. Of course, dentists use the same tech- of paper clay being lifted off the plaster “substrate” (see nique when working on our teeth. The Grand Canyon was also Section 25.7). As you might guess, there are many formed on a larger scale by essentially the same process. variations on this process, which of course are related to Masons use sandblasting to clean the surfaces of old stone the ancient use of straw in making house bricks. buildings. Throwing a pot, as shown in Figure 23.18, is the process of producing hollow clay objects on a revolving pottery wheel. Potters may use their hands as shown here, 23.15 MAKING POROUS CERAMICS or other tools—the step to industry is then a small one. Coiling, pinching, and slabbing are used to form large In many traditional applications for ceramics, particularly pottery objects. Their common feature is that the total in structural and electrical applications, the sintered thickness of the ceramic piece is kept constant so that the ceramic component is required to have minimum porosity. drying and firing process will be even. Wedging is not a However, in a growing number of applications, for shaping process, although the end result is a slab of clay. example, in ceramic humidity and gas sensors, porosity is Rather, it is the process used to remove porosity from clay not just desirable, it is required. Several different methods before it is used to make a pot. This is now carried out can be used to produce porous structures. mechanically in a pug mill. If you pinch the clay or carve 422 .................................................................................................................................................... Shaping and For ming  FIGURE 23.17 Removing paper clay from the substrate. FIGURE 23.18 Throwing a pot. it, you can combine different colored clays and shape and meter-thick molded-glass aspheric lenses that are used in fire them to produce the neriage (marbled) style of the everything from laser printers to optical disc storage potters version of millefiore. devices and optical communications systems. Pressing needs a mold that will be gray cast iron (to 1000°C), stainless steel (can be used for borosilicates at 23.17 SHAPING GLASS 1185°C and glass ceramics at 1480°C), or even bronze. Usually, though, the mold is cooled. The process uses a Glass can be shaped by many different processes. viscosity of ∼4 kP and has been applied to objects weigh- Casting or molding has produced, for example, the ing from 5 g to 15 kg. The finished object can be fire- 20-inch-thick Palomar telescope mirror and the submilli- polished. This process, shown in Figure 23.19, is quite Springs Ring Plunger Gob Mold Gob into mold Gob in mold Lower ring Pressing Plunger retracted, Plate removed complete plate cooling from mold FIGURE 23.19 Automated pressing glass. 2 3 .17 S h a p i n g G l a s s ..................................................................................................................................................... 423 similar to the HIPing technique shown in Figure 23.2 and Spinning is used for fibers and is very reminiscent of predates it, of course. the beginnings of industry (the spinning jenny). Sagging or slumping is a simple method whereby the Rolling is an old technique that is still in use. It is glass is heated so that it “slumps” into the mold. The similar to slabbing in pottery. technique can also be used for clay; effectively it is press- The lost wax process of forming glass shapes has been ing, with gravity providing half the press. used since the fifth century ce. Originally, the molten Glass blowing was clearly in use in the first century glass was poured into an outer mold made of beeswax, bce. The temperature is critical since it determines the which could easily be removed. working range. There will be other factors such as the air Inlays in glass, such as sandwiched-gold glass, was pressure, the role of gravity, and the centrifugal force made perhaps as early as ∼250 bce. Gold leaf is pressed produced by the blower. The craftsman will produce free- between two layers of glass. blown objects or can blow the glass inside a mold. When Final machining using Vycor (the “cor” is from a ribbon or hub machine is used, the glass is invariably Corning), Macor, or similar specially treated glasses. blown into a mold. (Vycor contains “built-in” pores; Macor contains small Drawing is used for glass tubes and sheets. For tubes grains of mica.) the variations include Danner (e.g., tubes for fluorescent Core forming was one of the earliest methods used to lights), Vello (large diameter tubes), downdrawn tubes shape glass (see Figure 21.3). A shape was fashioned in (used for vacuum tubes or uses a vacuum), and updrawn clay and the glass was then trailed around the core until tubes (for glass thermometers). Sheets are drawn in the it completely covered it. It could be heated further so that same way: using a slot orifice, with an overflow pipe, using the coils fused together. When cool, the clay core would updraw or floating. be removed leaving a stand-alone glass vessel. CHAPTER SUMMARY In this chapter we described the methods used to shape and form ceramic components. There are a number of possible choices and the best one depends on the types of shapes being pro- duced, the cost of the component, and the number of units being made. For predominantly covalently bonded ceramics it is necessary to use shaping techniques that involve the applica- tion of pressure and heat if the objective is to obtain a high-purity material. Because ceramics cannot be softened in the same way as polymers and metals it is often necessary to form a plastic mixture of the ceramic prior to shaping. These methods may leave a large amount of organic residue that must be removed during sintering. Binder removal is tricky because it can lead to the formation of voids and cracks in the ceramic component. Machining of ceramics is often performed when they are in the green state—before sintering. This is because the presintered component is much softer and tooling costs are significantly reduced. A relatively recent approach to forming ceramic components is rapid prototyping. The advantage of this technique is that 3D parts can be made without using a die or a mold. The technique has been well established for producing parts made of polymeric materials and is now being extensively investigated for forming ceramic components. PEOPLE IN HISOTRY Brown, Robert, the Scottish botanist (1773–1858), among other activities studied the movement of particles (pollen and inorganic) in water and thus recognized Brownian motion. Champion, Albert founded two companies—Champion and AC Spark Plug. In the 1990s, between them they produced over one-half of the world’s spark plugs. McDougal (1949) gives a review of these two companies. Hamada, Shoji (1892–1978) was born in Tokyo. His home and his pottery are in Mashiko, which is a ceramics town just a short drive north of Tsukuba. Kawai, Kanjiro (1890–1966) lived in Kyoto in a house that is now another wonderful museum. Leach, Bernard Howell (1887–1979) is probably the best-known British potter. He was born in Hong Kong and worked in Japan (with Shoji Hamada) and at St. Ives in England. Spode, Josiah (1733–1797) founded his pottery in 1770 at Stoke. He developed the formula for bone china that is still used. Tomimoto, Kenkichi (1795–1835) was born and raised in Japan and helped make style part of everyday Japanese pottery. Wedgwood, Josiah (1730–1792) was born in Burslem, Staffordshire. He joined the firm of Thomas Wheildon at Fenton, who gave him the freedom to experiment, and founded a factory in Etruria with his business 424 .................................................................................................................................................... Shaping and For ming  partner Thomas Bentley. He was elected a Fellow of the Royal Society for inventing the pyrometer: he used the fact that porcelain shrinks in the furnace to measure the temperature of the furnace. His daughter, Susannah, had a son, Charles Darwin. Yanagi, Soetsu (1889–1961) created the mingei (folk art) movement in Japan in the 1920s; this movement has influenced much of Japan’s stunning pottery. GENERAL REFERENCES For information on modeling binder removal see the papers by Barone and Ulicny (1990), Stangle and Aksay (1990), Evans et al. (1991), and Matar et al. (1993). Birks, T. (1998), The Complete Potter’s Companion, Bulfinch Press, Boston. Photos of techniques are espe- cially clear and instructive. Engineered Materials Handbook, Volume 4, Ceramics and Glasses, ASM International. Section 3 covers, in considerable detail, many aspects of shaping and forming as practiced in industry. Leach, B. (1944) A Potter’s Book, Faber & Faber Ltd., London. Onoda, G.Y. and Hench, L.L. (1978) Ceramic Processing Before Firing, Wiley-Interscience, New York. Peterson, S. (2003) The Craft and Art of Clay, 4th edition, The Overlook Press, Woodstock, NY. Much more than shaping; glazes, kilns, design, history. Rahaman, M.N. (1995) Ceramic Processing and Sintering, Marcel Dekker, New York. Less well known than Reed but very useful. Reed, J.S. (1988) Introduction to the Principles of Ceramic Processing, John Wiley, New York. A classic text on processing. Richerson, D.W. (2006) Modern Ceramic Engineering, 3rd. edition, CRC Press, Boca Raton, FL. Chapter 13 describes the important shape-forming processes. Solid Freeform Fabrication Symposium Proceedings (held annually, University of Texas, Austin). The forma- tion of ceramic components by RP or SFF is a developing field. These proceedings give current information. SPECIFIC REFERENCES Barone, M.R. and Ulicny, J.C. (1990) “Liquid-phase transport during removal of organic vehicle in injection moulded ceramics,” J. Am. Ceram. Soc. 73, 3323. Evans, J.R.G., Edirisinghe, M.J., Wright, J.K., and Crank, J. (1991) “On the removal of organic vehicle from moulded ceramic bodies,” Proc. R. Soc. (London) A432, 321. German, R.M. (1987) “Theory of thermal debinding,” Int. J. Powder Met. 23, 237. Classic article on this topic. Gault, R. (2005) Paper Clay (Ceramics Handbook), 2nd edition, A&C Black, London. Mater, S.A., Edirisinghe, M.J., Evans, J.R.G., and Twizell, E.H. (1993) “The effect of porosity development on the removal of organic vehicle from ceramic or metal mouldings,” J. Mater. Res. 8, 617. McDougal, T.G. (1949) “History of AC spark plug division, General Motors Corporation,” Am. Ceram. Soc. Bull. 28, 445. Stangle, G.C. and Aksay, I.A. (1990) “Simultaneous momentum, heat and mass transfer with chemical reac- tion in a disordered porous medium: Application to binder removal from a ceramic green body,” Chem. Eng. Sci. 45, 1719. WWW www.stratasys.com/NA/index.html A commercial supplier of FDM equipment and software. www.optima-prec.com For molded glass lenses www.raku-yaki.or.jp The Raku Museum www.ceramicsmuseum.alfred.edu The site for Alfred’s museum. www.omax.com For information on abrasive waterjets. www.potterymaking.org Pottery Making Illustrated. EXERCISES 23.1 Explain briefly why melting and solidification can be used for shaping glasses (as well as many metals and polymers) but in general not for forming crystalline ceramics. 23.2 Briefly describe the differences between hot pressing and cold pressing. C h a p t e r S u m m a ry .......................................................................................................................................................... 425  23.3 Explain why hot pressing is often used when ceramics with a small grain size are required. For what applica- tions must grain growth be minimized? 23.4 Why are graphite dies widely used for hot pressing? Under what conditions would the use of graphite not be appropriate? 23.5 Which method would you choose to form each of the following shapes; briefly justify your choice. (a) A cyl- inder; (b) a tube; (c) a cube; (d) a teapot; (e) a rotor blade; (f) a spark plug insulator; (g) an insulator for a power cable. 23.6 Why is it necessary to use an organic binder when forming a ceramic component by extrusion? What are the main requirements for the binder? 23.7 Why is it difficult to use injection molding for near net shape manufacturing? 23.8 Briefly explain why it is better to machine in a ceramic component when it is in its green state rather than when it has been fired. 23.9 Keramica is a new company that wants to manufacture alumina furnace tubes and they hire you as a consul- tant. You are asked to propose a process for the fabrication of such tubes. Give a general description of the process you would propose. Explain the roles of the different steps involved. 23.10 Porcelain figurines are manufactured worldwide in large quantities. In most cases, many figures are made with an identical shape. As you know, such figures are often hollow. Explain the process used to form such figures economically. 426 .................................................................................................................................................... Shaping and For ming  24 Sintering and Grain Growth CHAPTER PREVIEW Sintering is the process of transforming a powder into a solid body using heat. Why is there a whole chapter on sintering? Partly for historical reasons—it has traditionally been the principal method of processing ceramic bodies. Sintering is still the most important process in making bulk ceramics, but the process is not unique to ceramics. There is a large field known as “powder metallurgy” that considers many of the concepts and problems that we address for ceramics. One of the reasons for processing metals by sintering is to control the grain size, which is precisely what we usually need to do in ceramics. We can discuss the topic at different levels of complexity. The phenomenon is quite straight- forward and involves deciding how best to pack particles (that are usually modeled as spheres), understanding the movement of grain boundaries (GBs), and knowing how the packing geom- etry and GB migration is affected by the need to balance surface tensions (interface energies). The quantitative analysis of the process is much more difficult since it involves transport of several different species with different chemical driving forces. In multiphase systems, quan- titative analysis is not yet possible. The other point to emphasize is that for many years the aim of sintering has been to make dense ceramics. The terms sintering and densification were almost used interchangeably. Today, there are many uses for porous ceramics and these materials must also be sintered. The aim is then different and the process must change accordingly. Most of the time we assume that the material we are sintering is single phase, so we make some assumptions that will not nec- essarily be valid for multiphase materials that also need to be sintered. 24.1 THE SINTERING PROCESS 24.2 will tend to be strongly faceted parallel to the close- packed planes, {111} if cubic or (0001) if hexagonal. The idea of sintering is to join particles together without Consider the logic of the sintering process: melting them. We may, however, use an additive that does melt. The particles can be crystalline or amorphous—we  When crystalline powder particles join together, the can sinter glass marbles as long as we do not melt them: junction is a GB. of course, the particles need not be spheres. At too high a  It is likely that the solid body thus formed will not be temperature, the marbles also deform. 100% dense, so it will contain pores. The problems involved in sintering can be appreciated  Pores are a structural component of the solid body (see by examining Figure 24.1. We often model sintering by Chapter 15). They often behave like grains of a differ- packing spheres of various sizes together. If we use spheres ent material. of only one radius, then the maximum initial density  Although sintering explicitly involves solid powder would be 74%. Note, that the schematic in Figure 24.1 is grains, a liquid may form if a component that has a only an idealized two-dimensional picture of the packing low melting temperature is present. This is then known of circles! Figure 24.1b shows a disordered structure of as liquid-phase sintering (LPS) (Section 24.7). We the same size “spheres” so there is even more open space. must thus consider films, tubes, and droplets (or parti- If we fill this space with smaller spheres we can achieve cles) of noncrystalline material. There may be no trace a much higher “density,” as you see in the adjacent region. of the liquid when the sample is examined at room Also keep in mind that the object is to produce a product temperature after sintering; such a liquid is referred to like that shown in Figure 24.2, which is a sintered SiC as a transient phase. radiant-heat U tube. The actual structure of the sintered  After and during sintering, some grains will grow, body will look something like that shown in Figure 24.3. consuming others. This process is known as grain The SiC particles involved in forming the tube in Figure growth and is essentially an Ostwald ripening process. 2 4 .1 Th e S i n t e r i n g P r o c e s s ....................................................................................................................................... 427  (A) (B) FIGURE 24.1 Model grain/shape distributions in 2D; packing FIGURE 24.3 SiC processed with addition of Al2O3 at 2050°C; identical spheres can never achieve less than 26% porosity: etched polished surface. (a) ideal planar packing, (b) less-dense packing of larger spheres, part with inserted smaller spheres giving a higher local density.  How do we maintain a porous structure? (Why do we want some materials to be porous?) Note: this topic is often referred to as solid-state sinter-  How do we achieve full density? ing. We have to be careful about making assumptions. It  How do we maintain the shape of the green body? is often implicitly assumed in our analysis that all grains  What changes in the analysis/process if the grains do have the same composition. This chapter will include a not all have the same composition? real example of the packing of spheres, namely the forma- tion of opal. (We also include the inverse opal.) We are often preoccupied with grain boundaries, but triple junctions may be even more important in the sinter- ing process since these may be open pipes for transporting material. Part of the reason for this bias is that triple junc- tions are very difficult to study and to model (see Section 14.9). The topic of capillary forces was introduced in Section 13.6. This topic is extremely important in sintering when there is a liquid phase present. The overall “plan” of our discussion is shown in Figure 24.4. individual interfacial isolated energy particles why? join sinter capillary curved? forces faceted? GBs structures TJs pores energies liquid impurities move GBs mechanisms clean GB grains grow diffusion surface pores shrink how? lattice FIGURE 24.4 Thinking about sintering: some of the concepts and FIGURE 24.2 A radiant U tube produced by sintering SiC. processes. 428 .................................................................................................................................... Si nt er i ng a n d Gr a i n Grow t h 24.2 THE TERMINOLOGY OF SINTERING 24.4 SINTERING SPHERES AND WIRES Since sintering is an ancient process, it has its own Models in Sintering language, much of which preceded the scientific We first summarize the steps that must occur during sin- analysis. tering and then consider simplified models that allow us to examine aspects of these different processes. We need Green bodies. All types of unfired ceramic are included. to examine the following processes: Volatiles. During processing we may remove volatile materials; even though we think of sintering as a  How do two grains join together? solid-state phenomenon, the gas phase is important.  How do we remove pores once they are formed? This The gaseous component may form as water or is the essential step in densification. other solvents are removed or as organics undergo  Why do we want to densify the material? burnout.  Why do some grains absorb others and how does this Hot pressing is the addition of pressure (uniaxial or hydro- occur? static) while sintering. This is a large topic, so we address it again in a separate section. After the ceramic has been shaped as a green body, it Desintering is the reverse of sintering and may be associ- must be fired, often at very high temperatures, to develop ated with the reverse of densification. useful properties. The sintering process has several dis- A monolithic ceramic is a uniform ceramic piece. tinct stages. The importance of the shape of the particles before  We consolidate the product during firing. and during sintering is an extra complication. Corners and  We remove the pores between the starting particles. sharp junctions are difficult to treat in any continuum  The components shrink. model of sintering.  Some grains grow while others shrink. The simplest model is that of two spheres in two 24.3 CAPILLARY FORCES AND dimensions shown in Figure 24.5. Notice that the two SURFACE FORCES A curved surface will always want to become flat as we discussed in Chapter 13. The result is that there is a pres- sure difference, ΔP, between the inside and the outside of ρ a curved surface. R x ΔP = 2γ/r (24.1) E-C Here γ is the surface free energy and r is the radius of the SD sphere. The radius of curvature r is positive or negative VD depending on whether the center of radius is inside or GB outside the material, respectively. Consequently, negative PF VD pressure is exerted on the concave surface. (A) GB We should remember that the principle that leads to Eq. 24.1 assumes that there is only one value of the surface energy; the surface energy is assumed to be isotropic. When the particle size of the powder is small, the powder R has a large surface area in comparison with a similar ++ 2x ++ volume of bulk solid. We can say that a small particle, which is assumed to be a sphere, has surface properties that are different from those of a bulk solid because it has a large surface-to-volume ratio and because its surface has a small radius of curvature. In sintering, we see the effect of this curvature first Lo-ΔL when grains (viewed as spheres) join together. This is the (B) Lo=D curvature of the initial particle surfaces. Then the GBs FIGURE 24.5 (a, b) Sintering and curvature. The two-sphere will move: this is the same effect but for internal surfaces model showing the transport paths, the two curvatures (ρ and x), and leads to grain growth during sintering. and the process leading to densification. 2 4 . 4 S i n t e r i n g S p h e r e s a n d W i r e s .......................................................................................................................... 429  R (A) Neck GB (B) (C) FIGURE 24.7 Two Si spheres partly sintered (TEM image). 1.26R Changes that occur during the firing process are related (D) to (1) changes in grain size and shape and (2) changes in pore size and shape. Before firing, a powder compact is FIGURE 24.6 Coalescence of two spheres (a–d). composed of individual grains and may contain as much as 60 vol% porosity. The amount of porosity will depend on the size and size distribution of the powder particles and the shaping method (see Chapter 23). To maximize properties such as compressive strength, translucency, and thermal conductivity, we want to eliminate as much of this spheres can no longer be spherical if we have started to porosity as possible (i.e., we want a dense ceramic). This form the neck as shown in Figure 24.5a. Notice also that objective can be achieved during firing by the transfer of in Figure 24.5b the centers of the two spheres must have material from one part of the structure to another. There moved toward one another. We know the situation at the are several mechanisms for material transfer and some of start and at the end; the question is, what happens in the the processes are listed in Table 24.1. Note that sink and middle? We can even do the experiment of joining two source refer to matter, not defects. such spheres as shown schemetically in Figure 24.6. Figure 24.7 shows experimental results for the nearly nanoscale As sintering progresses, the two spheres move together. case. This schematic of the two spheres emphasizes some This movement is the essential step in densification. important points and omits others. We can extend this analysis to three or more spheres There are two radii to consider (x and ρ). as shown in Figure 24.8 and then to three dimensions. There will be a GB between the two spheres if they are With three spheres we introduce another degree of single crystals; if they are glass spheres, then there is freedom: the outer spheres can also move together until no GB; if the spheres are polycrystalline there will be they form a pore. A model experiment that avoids this many GBs. movement uses a wire that is wound on a reel and sintered; There is always a GB groove where the GB meets a free the experiment can, in principle, be adapted for ceramics, surface. but it may be using straight fibers. TABLE 24.1 Mechanisms and Transport in Sintering (Diffusion to the Neck) Mechanism Transport path Source SD Surface diffusion Surface VD Volume diffusion Surface E-C Evaporation–condensation Surface GB GB diffusion GB VD Volume diffusion GB PF Plastic flow Dislocations 430 .................................................................................................................................... Si nt er i ng a n d Gr a i n Grow t h  Δy + x VD VD SD GB ρ + E-C PF x r FIGURE 24.9 Angles and grains. In 2D the grains shrink if there + are fewer than six sides and expand if there are more than six sides. The effect of the pressure difference caused by a curved GB is to create a difference in free energy (ΔG) on FIGURE 24.8 Sintering three spheres; showing the diffusion paths two sides of the boundary; this is the driving force that from the GB to the neck surface and the development of a pore makes the boundary move toward its center of (2D projection). curvature. ΔG = 2γ V/r (24.2) where V is the molar volume. We might expect that the 24.5 GRAIN GROWTH rate at which the boundary moves is proportional to its curvature and to the rate at which the atoms can jump For a grain structure to be in metastable equilibrium the across the boundary. surface tensions must balance at every junction between the GBs. It is theoretically possible to construct a three- dimensional polycrystal in which the boundary tension 24.6 SINTERING AND DIFFUSION forces balance at all faces and junctions, but in a real random polycrystalline aggregate there are always going There is a significant difference between the paths for to be boundaries with a net curvature in one direction and matter transport shown in Figure 24.8. Transfer of mate- thus curved triple junctions. Consequently, a random grain rial into the “pore” must occur if the porosity of the structure is inherently unstable and, on heating at high compact is to shrink. You can imagine that in three dimen- temperatures, the unbalanced forces will cause the bound- sions (3D), this requires that matter transfer from the bulk aries to migrate toward their center of curvature. of the grain, from the GB between particles, or from the The effect of grain-boundary curvatures in two dimen- outer surface by diffusion through the grain or through sions is shown in Figure 24.9. It has been assumed that the GB. (Alternatively, you can think of vacancies moving equilibrium at each two-dimensional (2D) GB junction out from the pores.) results in angles of 120°. Therefore, if a grain has six For the case of matter transport from the grain bound- boundaries they can be planar (i.e., flat) and the structure ary to the neck by lattice diffusion, we can derive an metastable. However, if the total number of boundaries equation for the rate of growth of the neck area between around a grain is less than six, each boundary must particles. concave inward. These grains will therefore shrink and 1/ 5 eventually disappear during sintering. Large grains, on the x ⎛ 40 γ a 3 D* ⎞ other hand, will have more than six boundaries and will =⎜ ⎟⎠ r −3 / 5 t 1 / 5 (24.3) r ⎝ kT grow. The free-energy change that gives rise to grain growth is the decrease in the surface area between the Here, the volume of the diffusing vacancy is a3 and D * is fine-grained material and the larger-grain-sized product the self-diffusion coefficient. In view of the approxima- and the corresponding lowering of the grain-boundary tions in the model, it is not worth learning this equation, energy. but notice the terms involved. 2 4 . 6 S i n t e r i n g a n d D i f f u s i o n ................................................................................................................................... 431  With diffusion, in addition to the increase in contact area between particles, particle centers move toward one another. We can derive an equation for the rate of this approach. 2/5 ΔV 3ΔL ⎛ 20 γ a D* ⎞ 3 = = 3⎜ ⎟ r −6 / 5 t 2 / 5 (24.4) V0 L0 ⎝ 2 kT ⎠ The decrease in densification rate gives rise to an apparent end-point density if experiments are carried out for similar time periods as shown in Figure 24.10. The same comments hold for the details (beware) and the suggested trends (good). It is seen that the sintering rate steadily decreases with time, so that merely sintering for longer periods of time to obtain improved properties is impractical. Once again, control of particle size is very important. Consider how the curved GB in Figure 24.11 moves; the classical picture for the change in energy as an atom changes its position is shown in Figure 24.12, but reality is clearly much more complex. This diagram is drawn to FIGURE 24.11 Atomistic model for GB migration. show the (100) surface of MgO. If the curved interface is actually normal to the plane of the figure, the GB is pure tilt in character. It is clear from Figure 24.12 that not all to the right while others may move at 90° to this direction. the ions move in the same direction. If you select different (This should remind you of atom motion during the glide ions in Figure 24.11 you can appreciate that some move of dislocations.) Some ions cannot move until others have moved, as a result of Coulomb interactions. The frequency of atomic jumps in the forward direction is given by 1.00 C Relative fAB = ν exp(−ΔG*/RT) (24.5) A B density 0.98 The frequency of reverse jumps is given by 0.96 f BA = ν exp(−ΔG* + ΔG/RT) (24.6) 0.94 The frequency factor, ν, has, for solids, a value of about 1013 Hz. For the net growth process 0.92 U = λ( f BA − fAB) (24.7) 0.90 0 600 1200 t (s) (A) Free 1.00 Energy Relative B density A 0.98 C 0.96 ΔG† 0.94 0.92 A 0.90 ΔG 0 2400 4800 t (s) 7200 (B) FIGURE 24.10 Calculated densification curves at final stage of B sintering at 1727°C for alumina powder compacts for grain size of (a) 0.8 μm and (b) 4.0 μm at 90% density. The curves are Position calculated using different equations but show the same trends. FIGURE 24.12 Activation barrier model for GB migration. 432 .................................................................................................................................... Si nt er i ng a n d Gr a i n Grow t h Here λ is the distance of each jump, and U is given by TABLE 24.2 Applications of LPS γV ⎛ 1 + 1 ⎞ ⎤ exp Δ S * exp ⎛ − Δ H* ⎞ Material Application U = νλ ⎡⎢ ⎜⎝ ⎟ (24.8) ⎣ RT r1 r2 ⎠ ⎥⎦ R ⎝ RT ⎠ BaTiO3 /LiF/MgO Capacitors BaTiO3 /SiO2 Capacitors The important result is that the rate of growth increases Co/WC; TiC/Mo/Ni Cutting tools exponentially with temperature. Fe/Al2O3 /C Friction materials When considering ceramic sintering processes, you Al2O3 /glass Grinding materials Si3N4 /Y2O3 Metal-working tools should always remember that the oxidation state of the Clay/feldspar/flint Porcelain cations may vary depending on the environment. For Si3N4 /MgO; SiC/B Refractories example, when CeO2 is sintered at high temperatures the Al2O3 /MgO/SiO2 Refractories Ce4+ may be partially reduced to Ce3+ , which can cause AlN/Y2O3 Substrate cracking in the compact. Such cracking will, of course, ZnO/Bi2O3 Varistor change the available diffusion paths.  The solid particles quickly rearrange when the liquid 24.7 LIQUID-PHASE SINTERING forms.  Solute reprecipitation takes place if this is thermody- Liquid-phase sintering is the sintering of a powder in the namically possible (if some solid can dissolve in the presence of a liquid; the liquid generally solidifies below liquid). the sintering temperature. The details depend on the inter-  Microstructural coarsening occurs with slow solid- facial energies: is the liquid wetting or not? Either way state sintering of the solid. liquid may be present in triple junctions (TJs), quadruple junctions (QJs), and GBs because it simply cannot get to In the first stage, capillary forces play a major role as voids the external surface. If it can reach the outer surface then are removed from the body. we have another capillary geometry as shown in Figure There are several points we should keep in mind. 24.13. As the sample cools after processing, the still- molten liquid can be drawn back into the grains because  Glass may dissolve the matrix, which may reprecipi- of differences in the thermal expansion coefficients. We tate elsewhere on the grains. then see liquid at the GBs in the image. We may also  Diffusion through the glass is almost always faster precipitate out crystalline material as the glass cools. than through a structured GB. The densification of LPS materials takes place in three  Crystal/glass interface energies do depend on the stages: orientation of the interface. Some of the difficulties include the following: Surface  The composition of the glass may not be uniform.  When the layer is thin it may be more appropriate to call it an absorption layer.  The viscosity of glass changes with T.  The composition of the glass in equilibrium with crystal changes with T.  The viscosity of glass changes with changes in composition.  The expansion coefficient of glass will generally not be the same as the crystal grains. Examples of processing using LPS are given in Table 24.2; it is a useful exercise to identify the liquid in each case. 24.8 HOT PRESSING Glass We noted in Section 24.1 that we are able to sinter glass Grain spheres as long as we do not melt them. This process is a FIGURE 24.13 Liquid at surfaces. special sintering situation because we do not form GBs. 2 4 . 8 H o t P r e s s i n g ......................................................................................................................................................... 433 You can imagine that if we heat the spheres to a tempera- meters that will allow the sintering behavior of materials ture below Tg we can decrease the viscosity significantly to be predicted even if the shape of the body is complex and then apply a pressure so that the spheres will plasti- or if materials are being cosintered. These parameters cally deform (change shape) so as to fill the empty space, include viscosity, a viscous Poisson’s ratio, and the sinter- especially if we did this in a vacuum. The deformation of ing stress. This stress is the driving force for sintering and the glass spheres occurs by viscous flow. (We will see this results from the interfacial energies associated with pores again when discussing paté de verre in Section 26.14.) and GBs. In this situation, the concept of viscosity is not Exactly the same process happens if the particles are crys- taken to imply that the material is liquid, but rather that talline, except that the deformation of the particles occurs the strain rate is linearly related to the strain rate of the by other mechanisms (movement of crystal-lattice defects); free sample and, through a uniaxial viscosity, Ep, to the the precise deformation mechanism will depend on the stresses in the material. temperature of the treatment and the applied pressure. In this case GBs are formed. Hot pressing allows us to produce material with very little porosity; since the temperature is 24.9 PINNING GRAIN BOUNDARIES not taken too high, grain growth is minimized. Hot forging is the application of a uniaxial stress while When grains grow to be so large that they are nearly the the samples are held at temperature. Discontinuous hot same size as the specimen in one or more dimensions, forging has been used to extract the temperature depend- grain growth stops or becomes very slow. Similarly, inclu- ence of the so-called constitutive sintering parameters for sions increase the energy necessary for the movement of alumina. This analysis showed for alumina that creep and a grain boundary and inhibit grain growth. If we consider densification during sintering are kinetic processes that a moving GB, the total interface energy is decreased are both controlled by GB diffusion. Such studies of sin- when it reaches an inclusion as shown in Figure 24.14a–d: tering are aimed at producing a set of constitutive para- the energy decrease is proportional to the cross-sectional y γs Vp ja φ pore x ja ψ ja ja θ (A) γb (E) GB m (B) (F) (C) pore pore (D) FIGURE 24.14 (a–e) GB/pore interaction: the break-away process. 434 .................................................................................................................................... Si nt er i ng a n d Gr a i n Grow t h area of the inclusion because we remove that much GB. 50 (This assumes that the surface energies are the same, which you know is not necessarily true.) The total energy 3 must be increased again to pull the GB away from the 4 inclusion. Consequently, when a number of inclusions are present on a grain boundary, its normal curvature becomes insuf- 6 ficient for continued growth after some limiting size is 10 6 reached. We can estimate this limiting grain size using a simple equation. 6 dl ≈ di /fdi (24.9) FIGURE 24.16 Growth of the largest grain. Here di is the particle size of the inclusion and fdi is the volume fraction of inclusions. For the process shown in Figure 24.14a–d, the bound- 24.10 MORE GRAIN GROWTH ary approaches, becomes attached to, and subsequently breaks away from a pore; the diagrams have been drawn The classic idea is suggested in Figure 24.16: large grains so as to encourage you to think about how the shape of grow while small grains shrink. The direction of GB the pore will change. Actually, the process is similar movement is always toward the center of curvature (which whether the obstacle is a pore or a particle; just the details reduces the area of the interface). The idea behind this of the interface differ. The image in Figure 24.14F reminds schematic is to apply the principle of balancing interfacial us that the pore will probably be faceted in a material like tensions, which we illustrated in Figure 24.9, to a poly- alumina, although the details of the faceting may vary crystal. The problem is that the diagram is 2D so it can with temperature. Another possibility is that the grain be misleading. Figure 24.17 makes the problem clear. The boundary drags the obstacle, which remains attached to same area is shown before and after annealing; the dashed the boundary as it moves. If the obstacle is a particle, the lines in Figure 24.17b show the original position of the second phase gradually becomes concentrated at bound- GBs (from Figure 24.17a). The grain that is smallest in the ary intersections and agglomerates into larger particles as grain growth proceeds. Now if we take TJs into account the picture becomes more complicated as shown in Figure 24.15: the TJ becomes the pinning defect. In the next section, we consider what is really happen- ing at the atomistic scale, namely dissolution and precipi- tation. Inhibition of grain growth by solid-phase inclusions has been observed for MgO additions to Al2O3 and for CaO additions to ThO2. (A) (B) FIGURE 24.15 Coalescence of three TJs due to grain shrinkage and associated increase of material in the pocket. FIGURE 24.17 (a, b) AFM of grooves at migrating GBs. 2 4 .10 M o r e G r a i n G r o w t h ......................................................................................................................................... 435  A B C D A B C D FIGURE 24.18 Side view schematic of “small grain” growing. FIGURE 24.19 GB movement in bicrystals showing the large- and small-scale faceting. original atomic force microscopy (AFM) image has grown. (Aside: look back at Figure 14.34 and then look again at are shown in Figure 24.20. One DP is from the large grain the upper part of these two figures.) The schematic in on the right and the other is from the point marked X. You Figure 24.18 provides the explanation for the growth of can see that the two DPs are related by a mirror running the smallest grain. This small grain is actually a large down the middle of the page so that grain X and the large grain but only part of it is seen at the polished surface. grain are basal-twin related. EBSD is able to determine Thus grains that appear to be large and many sided can the orientations of very large numbers of grains and thus shrink while others that appear to be small and have fewer to produce an orientation map. The value in grain growth than six sides can grow. studies is clear from Figure 24.20. The basal-twin bound- You can appreciate how GBs move from Figure 24.11. ary has not moved. Even more importantly, most of the Matter is transported across the grain boundary from one GB above it has not moved, although one facet has started grain to the other. The example shown here is a curved to move and this will eventually move the whole GB: the <100> tilt boundary in MgO. On the atomic scale, the mobility of the GB depends on its orientation. motion takes place by ions moving from one facet to the other as would occur for the GB shown in Figure 24.19. We know the direction of migration in this case because 24.11 GRAIN BOUNDARIES, SURFACES, it is a bicrystal and we can see the remnant groove. In AND SINTERING Figure 24.11, these facets are only atomic in size, but are clearly recognizable. Crystallography is important in determining the geometry Some final points: moving MgO GBs have been of surfaces, glass/crystal interfaces, and grain boundaries. observed in real time using a transmission election micro- For example, at temperatures at least as high as 1450°C, graph (TEM) with a heating holder going to ∼2000°C. Al2O3 shows a strong tendency to facet parallel to the basal Diffusion-induced GB plane when heated in air, migration (DIGM) has although the {112̄0} and been reported in ceramics. ELECTRON BACKSCATTERED DIFFRACTION {101̄2} planes are also The difficulty is that all (EBSD) favored. The presence of observations are made Although we have always known that diffraction occurs glass enhances this facet- after cooling the specimen in scanning electron microscopy (SEM), EBSD is a rela- ing, since it increases the to room temperature. Dif- tively new technique, partly because of the experimental kinetics of the process. fusion along GBs (as challenge of recording electron diffraction patterns that The crystallography of opposed to across them) is are noisy; however, image processing solves this problem. surfaces during sintering an important process in The power of the technique is that you can collect X-ray is clearly important in sintering. energy-dispersive spectrometry (XEDS) data at the understanding the behav- An image and two same time, so you have an image, the chemistry, and the ior of pores during this EBSD patterns from Al2O3 crystallography from the same area. process. 436 .................................................................................................................................... Si nt er i ng a n d Gr a i n Grow t h  tainly occur both before and during sintering. At higher temperatures, roughening transitions may become impor- tant, but we have no observations on this process for ceramics. 24.12 EXAGGERATED GRAIN GROWTH A primary requirement in many sintering processes is the need to control the grain size. In ceramics, we usually refer to secondary recrystallization as discontinuous or exaggerated grain growth. The process occurs when some small fraction of the grains grows to a large size, consum- ing the surrounding smaller grains. Once a grain grows in size to a point at which it has many more sides than the neighboring grains, the curvature of each side increases, and it grows more rapidly than the smaller grains with fewer sides. An example of exaggerated grain growth is shown in Figure 24.21. Aside: Classical primary recrystallization is the nuclea- tion and growth of new strain-free grains in a matrix of heavily deformed material. The driving force arises from the decrease in strain energy. There is an induction period as the system forms stable nuclei. FIGURE 24.20 SEM image and two EBSD patterns from a series of engineered GBs in Al2O3. The upper DP is from point X and the Secondary recrystallization is particularly likely to lower is from the large grain on the left showing the basal-twin occur when continuous grain growth is inhibited by the relationship. presence of impurities or pores. Under these conditions the only boundaries able to move are those with a curvature Particles that are initially spherical will facet when a much larger than the average. Secondary recrystallization powder is heated to the sintering temperature. Thus, again is common for titanate and ferrite ceramics in which grain using alumina as the example, particles may join with growth is frequently inhibited by minor amounts of second their basal facets parallel to one another so that either a phases or by porosity during the sintering process. The single crystal or a twinned bicrystal may form (Σ = 7, 13, result is that both the sintering of the ceramic and the 21, and 39 may also be favored). The twin interface is a resultant properties change. Excessive grain growth is fre- low-energy grain boundary, and the bicrystal “grain” will quently detrimental to mechanical properties. effectively have twice the volume of the initial particles; if the grains are slightly rotated away from the exact twin misorientation, secondary dislocations will form in the resulting interface. Such an unusually large particle may initiate exaggerated grain growth. Twin boundaries are found in many large grains in sintered materials. This process can occur even for a high-angle grain boundary such as the Σ = 13 boundary (rotate nearly 30° about the [0001] axis); a high-resolution image of a Σ = 13 bound- ary, which was formed by hot-pressing together two crys- tals of Al2O3, showed that the interface appears to very abrupt. Several parameters are involved in determining whether special GBs will form during sintering. The kinetics of faceting The crystallography and size of the surface steps The crystallography of the facet planes Since sintering of Al2O3 usually takes place at tempera- tures in excess of 1600°C, such faceting will almost cer- FIGURE 24.21 Elongated exaggerated grain in Al2O3. 2 4 .1 2 E x ag g e r at e d G r a i n G r o w t h ........................................................................................................................... 437  increased to 93% alignment, corresponding to the struc- tural change brought about by secondary recrystallization. It seems apparent that the few large grains in the starting material are more uniformly aligned than the fine sur- rounding material. These grains serve as nuclei for the secondary recrystallization process and give rise to a highly oriented final product. 24.13 FABRICATING COMPLEX SHAPES We consider shaping in Chapter 23, but mention some additional features here. The method used depends on the material. Either brute force or a plasticizer should be used. The classic example is pottery—we mold the clay. Then we have the alumina thermal conduction module (TCM), cordierite honeycombs, Si3N4 fishhooks, and carbide FIGURE 24.22 Using a single-crystal sphere to model exagger- blades for kitchen knives. ated grain growth in Al2O3 doped with 1 wt% MgO; at 1800°C for The TCM process involves sintering as many as 40 60 minutes. layers of ceramic. Vias are drilled through the layers before firing (which is much easier and cheaper to do than after firing) but must still line up after sintering when each Modeling grain growth experimentally is illustrated in layer will have shrunk considerably. Figure 24.22. Such studies are an extension of the The mechanism can be changed with liquids. A sig- measurement of GB migration. nificant proportion of ceramic products used in low- In Ostwald ripening the driving force is the reduction of temperature applications are predominantly crystalline total energy. The mechanism may require diffusion of materials containing a minor amount of a glass phase (as one component through the other, as shown in Figure noted in Section 24.7), for example, alumina substrates 24.23, which thus imposes an activation barrier. used in the electronic packaging industry usually contain 96% Al2O3 and 4% of a silicate glass. The liquid phase An application in which secondary recrystallization may be a glass added to the crystalline ceramic compact has been useful is in the development of textured ceramics or a mixture of oxides that becomes liquid at the sintering in which the preferred orientation is produced by seeding. temperature. (More about this is given later.) The magnetically hard Liquid-phase sintering occurs most readily when the ferrite, BaFe12O19, may thus be produced with large grain liquid completely wets the surfaces of the solid particles sizes. For this ferrimagnet it is desirable to obtain a high at the sintering temperature. The liquid in the narrow density as well as a high degree of preferred orientation channels results in the development of a substantial capil- in the sintered product. Particles of the powdered material lary pressure, as illustrated in Figure 24.13. For submi- can be oriented to a considerable extent by subjecting crometer sizes, capillaries with diameters in the range of them to a high magnetic field while forming. On sintering 0.1–1 μm develop pressures on the order of 7 MPa for sili- there was a 57% alignment after heating to 1250°C. cate liquids. On further heating at 1340°C the preferred orientation The capillary pressure developed between the particles results in dissolution of material into the liquid and its Pore Pore subsequent precipitation elsewhere. The degree of wetting depends on the relationship between the interfacial and grain-boundary energies according to the relationship cos φ/2 = (1/2)(γss /γsl) (24.10) Here γss is the grain-boundary energy, γsl is the interfacial energy, and φ is the dihedral angle, as illustrated earlier. Solid  When φ > 120° the second phase forms as isolated pockets at the GBs. Liquid  When φ is 60°–120° the second phase partially pene- FIGURE 24.23 Schematic of Ostwald ripening. trates along the GBs. 438 .................................................................................................................................... Si nt er i ng a n d Gr a i n Grow t h   When φ < 60° the second phase is stable along the entire GB length forming triangular prisms at the TJs.  When φ = 0 the grains are completely separated by the second phase. The resulting microstructure for each of these cases is shown in Figure 14.33. The process of LPS is also impor- tant in forming dense powder compacts of nonoxide ceramics such as the nitrides. In these ceramics, where the bonding is predominantly covalent, atomic mobility is limited and sintering to high density is difficult in the absence of a liquid phase or without the application of high pressure. An example of such a system is AlN, which is impor- tant as a substrate material for electronic packaging appli- cations because of its high thermal conductivity. Its ability to remove heat from a mounted device is decreased if oxide is present in the GBs. It is made commercially by sintering AlN powder and Y2O3 at temperatures above FIGURE 24.24 Pores trapped in grains. 1800°C. The Y2O3 reacts at high temperature with the oxide coating on the AlN grains to form a liquid phase. On cooling, the liquid phase crystallizes to form Y–Al Many of these pores have become isolated within the oxides (particularly YAG). These phases are located grains so that further reduction in their size will require mainly at triple points. lattice diffusion unless another GB migrates and inter- sects them during further processing. Pillared interlayered clays (PILCs) are a special group 24.14 POTTERY of porous ceramics. We saw in Chapter 7 that clays are layered materials. The idea behind PILCs is to intercalate Since ceramic studies began with pottery, we should con- a large polyoxocation between the silicate sheets, forcing sider how sintering relates to pottery. In pottery, the green the sheets to separate, and then to convert these large body is the clay pot before it is fired; in this state it can particles into large metal-oxide clusters by heating to easily be shaped. The binder is generally water. A slurry cause dehydration and dehydroxylation. Although some or slip is prepared by adding just enough water to the clay processes involve heating to only 400°C—not too high, to ensure that the viscosity of the green body is low. Some some of the PILCs are stable to above 700°C. The metal- pots are given a low temperature (biscuit or bisque) firing oxide clusters are then called pillars and permanently hold to remove the water and binder and to give the pot some the clay layers apart. The interlayer spacing is still small, mechanical strength so that it can then be glazed and fired the size of the molecules, and the new material has a to a higher temperature to give the final ceramic body. The microporous structure. The intercalation process is also processes occurring during the firing of a pot are much known as a cation-exchange reaction, but we do not need more complex than sintering alumina, for example, to exchange anything; we can intercalate Na between the because phase transformations occur simultaneously with layers of graphite or MoSi2, for example. The process the sintering. One important process that occurs is the studied most uses montmorillonite, but mica, vermiculite, formation of glass in the silicate body, which allows suf- and other layered materials have also been examined. The ficient mobility for the surface tension to consolidate the polycation Al13O4 (OH) 24 (H2O)12 (known as Al13) is widely article and thus reduce porosity. Shrinkage at this stage used, and the resulting materials are then refered to as can be 40%. The same liquid-forming process occurs Al-pillared clays. Today, a wide range of cations can be externally in the formation of salt glazes as we saw else- incorporated into the pillars. These PILCs are used as where; in this case, the NaCl reacts with the silicate to catalyst supports; the active metal is intercalated between produce a low-viscosity glass—the glaze. the widely spaced sheets giving an extremely high surface area. By changing the active cation, many different reac- tions involving organic-compound conversion can be cata- 24.15 PORES AND POROUS CERAMICS lyzed. The idea of pillaring has been extended to layered titanates, for example; in principle, any layered material The challenge in sintering porous ceramics is the need to can be used. While these materials are primarily used in avoid rather than attain densification. Figure 24.24 shows catalysis at present, they are also potential hosts for storing a rather uniform distribution of pores in a sintered body. waste materials. 2 4 .1 5 P o r e s a n d P o r o u s C e r a m i c s ............................................................................................................................ 439  of a two-phase structure, you must see both GBs and phase boundaries (PBs). In Figure 24.26a we have two phases. If the GBs in phase B move, we can generate a microstruc- ture of isolation grains of phase A inside a single-crystal matrix of phase B. (Phase A could, for example, be poros- ity.) A three-phase system could, in principle, contain only PBs with no GBs (or the GBs could disappear by “local” grain growth inside that particular phase). The grains of the three phases shown here cannot grow unless we have diffusion of material A along the interface between phases B and C, for example. As was the case for Figure 24.16, the situation in 3D will be more complex with more con- nections and the likelihood of percolation phenomena. Two images of a two-phase material are shown in FIGURE 24.25 Porous ceramic. Figure 24.27: the material is ZTA 30% (zirconia-tough- ened alumina with 30 vol% YSZ, which itself contains 10 molar% yttria). The smaller grains are in the as-sintered The IUPAC definition of porous describes three ranges material; the larger grains are after heat treating at 1600°C of pore sizes: microporous (<2 nm), mesoporous (2– for 30 hours. In both cases, the microstructure closely 50 nm), and macroporous (>50 nm). In 1992 a new porous resembles Figure 24.26a, showing that the phases remain material similar in many ways to the natural zeolites and dispersed after a long anneal. You can imagine the three- known as MCM-41 was patented; the name stands for phase situation if we add a nonreaction metal (e.g., Nb) to Mobil Composition of Matter No. 41. Actually this is just the two oxide phases. The result would be a cermet one of a family of mesoporous molecular sieves known as (ceramic/metal composite), a type of composite material M41S. It has a hexagonal array of mesopores giving chan- nels 1.5–10 nm in diameter amd a surface area of up to 700 m2 /g. The mechanism proposed for their formation is referred to as liquid-crystal templating (LCT), which is similar to one model proposed for the formation of natural zeolites. The idea is that we start with two phases and burn out one leaving a porous medium. MCM-41 is essentially a honeycomb structure (it has hexagonal symmetry), but it could have been an ordered foam. Honeycombs and foams are two forms of cellular ceramics. We can also make porous (cellular) ceramics by simply adding air to the green body before firing; this is exactly how nature produces pumice of course, except the green body is molten glass. By analogy with pumice, a simple route is to add pores to a slurry. This is essentially the route taken to make MCM-41; such materials may be (A) referred to as reticulated ceramics—the result of a replica- tion process. A completely different approach is to foam a liquid that contains the ceramic precursor (the approach used by nature to form pumice). We can use mechanical agitation, bubbling gas through the liquid, or generating the gas in the liquid. An example of a structure produced by this method is shown in Figure 24.25. (Compare this to the pores in Chapter 15.) 24.16 SINTERING WITH TWO AND THREE PHASES What is new? There are two situations: (1) reactions occur between the components and (2) no reaction occurs. You (B) can see from the schematic in Figure 24.26 that this is FIGURE 24.26 Schematics of multiphase ceramics; (a) two related to the tiling problem. In a 2D cross-sectional view phases and (b) three phases. 440 .................................................................................................................................... Si nt er i ng a n d Gr a i n Grow t h  much lower than for conventional powders. However, they are also reactive even when you do not want them to be. In this case we can coat the nanoparticles to induce a repulsion or simply to physically prevent them from joining. Materials are bonded together during packaging in IC fabrication using several different technologies, such as anodic bonding, Si-fusion bonding, surface-activated bonding, and intermediate thin-film bonding. In each scheme, heat is applied to sinter two surfaces together. (A) Diffusion bonding of Si wafers may require very little diffusion if the wafers are nearly atomically flat. We can improve the bonding by applying a voltage; this is the anodic bonding process and is used to join Si to SiO2. Millefiore paperweights are essentially formed using sintering. The individual canes of glass are bonded together in a glass matrix: the essential point is that the canes do not melt. 24.18 COMPUTER MODELING (B) Sintering can be modeled in many different ways. One FIGURE 24.27 Two-phase ceramics. (a) As sintered and (b) heat particularly interesting approach is to use Surface Evolver treated at 1600°C for 30 hours. ZTA 30% (zirconia-toughened to model how the shape of spheres will change when they alumina with 30 vol% YSZ containing 10 molar% yttria). are placed in contact. In the calculation, which can in principle be extended to many more contacting spheres, the surface is allowed to move with a velocity that depends widely used in different compositions. You can see how on the local curvature of the surface. At this time, the the materials can quickly become complicated. The only model assumes isotropic surface energies and sintering requirement is that the different phases are not reacting. occurs by an evaporation/condensation mechanism. The One phase could be a glass (or even a polymer), in which approach is illustrated in Figure 24.28a, which shows two case we need not worry about GBs in that phase. spheres that have started to sinter together. The surface of the sphere on the right is represented as a triangular mesh; the triangles are essentially small facets of a particular 24.17 EXAMPLES OF SINTERING surface orientation. The total surface area determines the IN ACTION surface energy, since it is isotropic. Surface Evolver lets the surface change toward a minimum value under some Some of these examples are discussed in detail elsewhere constrained conditions and a grain boundary, with energy in the text. Here we are concerned with why the sintering proportional to its area, is included in the calculation. The process is used. gradient of the energy is a force that is then converted to Why do we use translucent polycrystalline alumina give the velocity of the interface. The motion of the surface rather than single-crystal alumina, which is transparent, in is some multiple of the velocity; this scale factor can then alumina lamp envelops? Why use alumina and not yttria be regarded as the time step, which is used in determining for this application: the yttria would allow the lamp to the dynamics of motion. The GB energy and the surface operate at higher temperatures producing a whiter light? energy are related in the usual way through Young’s equa- The answer in both cases is the cost; both would be tech- tion so that the calculation can be run for different GB- nologically possible. The alumina envelope is particularly to-surface energy ratios, which influences the development interesting because of the use of MgO to limit grain of the neck geometry as shown in Figure 24.28b. growth. Many other aspects of sintering are now becoming Templated growth of materials like BaTiO3 presents an amenable to computer modeling and a new understanding attractive route to producing a textured ceramic. Tem- of the relative importance of the different stages of sinter- plated grain growth of alumina was discussed above. The ing and the different diffusion parameters will become principle involved here is the use of a seed to initiate exag- more widely available in the near future. Indeed, most gerated grain growth. sintering models come from what has been termed the Nanomaterials are very reactive, which means that we pre- “computer-simulation age.” New models are already can usually sinter nanoparticles at temperatures that are relating these different processes at the different stages. 2 4 .18 C o m p u t e r M o d e l i n g .......................................................................................................................................... 441  (A) (B) FIGURE 24.28 (a, b) Modeling sintering using Surface Evolver. CHAPTER SUMMARY The fundamental feature of the sintering process is the joining together of two particles without either of them melting. This process can take place fully in the solid state, although there may be a liquid involved as in the case of LPS. In fact, liquids in the form of a binder are common in commercial processes. In practice, the process may be even more complex because phase transformations may occur at the same time as sintering, and there may be more than one phase present. A full understanding of sintering makes use of everything we learned about GBs, grain growth, diffusion, and second phases in the form of pores. Computer modeling is beginning to be applied to sintering and should become more commonplace in the future. PEOPLE IN HISTORY Coble, Robert (Bob) L. (1928–1992) was best known for showing that small additions of MgO made it possible to form polycrystalline translucent alumina (Lucalox). This occurred while he was at the General Electric Research Laboratory in Schenectady, New York. He joined MIT in 1960. [More about this appears in the special alumina issue of J. Am. Ceram. Soc. 77(2), 1994.] He is also known for Coble creep. Kingery, W. David (1926–2000) was awarded the Kyoto Prize in 1999. David Kingery put the science into ceramic science for two generations of ceramicists. His books, including those exploring the link between the (really) old ceramics and the new, are always worth studying. GENERAL READING Exner, H.E. (1979) Principles of Single-Phase Sintering, in Reviews on Powder Metallurgy and Physical Ceramics 1, 1–251. Freund Pub. House, Tel-Aviv, Israel. Not just ceramics; a very useful review. German, R.M. (1996) Sintering Theory and Practice, Wiley, New York. The standard reference. Not only concerned with ceramics. Kang, S.-L.L. (2005) Sintering: Densifi cation, Grain Growth and Microstructure, Elsevier, Oxford. Very readable. Kuczynski, G.C. et al. (Eds.) Sintering Processes, Materials Science Research; Plenum Press (now Springer), New York. Another series of Proceedings from the 1960s and 1970s. More classic discussions. Microporous and Mesoporous Materials. This journal is a source for current research. Sintering and Related Phenomena. Proceedings from the 1960s and 1970s. Many classic discussions. SPECIFIC REFERENCES Ashby, M.F. (1974) “A first report on sintering diagrams,” Acta Met. 22, 275. Casellas, D., Nagl, M.M., Llanes, L., and Anglada, M. (2005) “Microstructural coarsening of zirconia- toughened alumina composites,” J. Am. Ceram. Soc. 88(7), 1958. Clay and Clay Minerals. The journal of The Clay Minerals Society. 442 .................................................................................................................................... Si nt er i ng a n d Gr a i n Grow t h  Gil, A., Gandía, L., and Vicente, M. (2000) “Recent advances in the synthesis and catalitic applications of pillared clays,” Catal. Rev-Sci. Eng. 42(1&2), 145. A comprehensive review. Green, D.J. and Colombo, P. (2003) “Cellular ceramics: intriguing structures, novel properties, and innovative applications,” MRS Bull. (April), 296. Kingery, W.D. (1959). “Densification during sintering in the presence of a liquid phase 1. theory,” J. Appl. Phys. 30, 301. The LPS paper. Maximemko, A.L. and Olevsky, E.A. (2004) “Effective diffusion coefficients in solid-state sintering,” Acta Mater. 52, 2953. An example of the use of computer modeling to analyze the role of different diffusion processes in the various stages of sintering. Mortensen, A., (1997) “Kinetics of densification by solution-reprecipitation,” Acta Mater. 45, 749. Quite recent update to the classic studies of LPS by Kingery. Swinkels, F.B. and Ashby, M.F. (1981) “A second report on sintering diagrams,” Acta Met. 29, 259. Tikare, V. and Cawley, J.D. (1998) “Numerical simulation of grain growth in liquid phase sintered materials-I. model,” Acta Mater. 46, 1333. Wakai, F. and Aldinger, F. (2003) “Sintering through surface motion by the difference in mean curvature,” Acta Mater. 51, 4013. Uses Surface Evolver to examine sintering. Zhou, Y. and Rahaman, M.N. (1997) “Effect of redox reaction on the sintering behavior of cerium oxide,” Acta Mater. 45, 3635. Sintering CeO2 as Ce 4+ is reduced to Ce3+ . Zuo, R. and Rödel, J. (2004) “Temperature dependence of constitutive behavior for solid-state sintering of alumina,” Acta Mater. 52, 3059. Includes a discussion of hot-forging of alumina. EXERCISES 24.1 You have sintered your ceramic at 1800°C for 12 hours and attained 95% theoretical density. You then con- tinue to heat treat it for another 12 hours at the same temperature but detect no change in density. Could the grain size of the material have changed? 24.2 You have two 1 μm-diameter spheres of amorphous Si and two similar spheres of crystalline Si. You bring the two pairs of spheres into contact without any applied pressure and heat for 1 hour at 1000°C. Discuss all the differences you will find when comparing the two pairs of dumbbells. 24.3 You place two spheres of crystalline MgO in contact without applying pressure. You find that each sphere experiences a stress due to contact with the other. Why is this so? 24.4 A sample consists of two slabs of TiO2 separated by a 100 nm film of silica. The sample is heated to 1500°C. What do you expect to occur? How would you make use of information on the Hamacker constant in discuss- ing this material? 24.5 A translucent alumina is prepared commercially by adding up to 200 ppm of MgO before sintering at 1800°C. This addition allows the alumina to be sintered to full density. Summarize the possible reasons for this effect and suggest an alternative additive. 24.6 What would be the advantages and disadvantages of making Na-vapor lamp envelopes using yttria instead of alumina? 24.7 You are given batches of powder of LiF, NaCl, and KCl; each has a grain size (grain diameter) of 100 nm. You cold isostatic press (CIP) each sample to 95% density and then sinter each at 1100°C. After 5 hours you remeasure the percent density. What results do you expect to see? 24.8 A glass contains pores that are 1 μm in diameter and are filled with N2 at 0.8 atm pressure. If the surface tension of the glass is 28 Pa and the relative density is 0.85, what will the pore size be when the gas pressure just balances the pressure due to the surface tension? Repeat this calculation for pores that are 0.1 μm and 10 μm in diameter and discuss the changes. 24.9 In a sample of MgO held at 1500°C grains of MgO grew from 1 μm diameter to 10 μm diameter in 1 hour. If the grain boundary diffusion energy is 250 kJ/mol, what will the grain size be after 2 hours and 4 hours? If the experiment were repeated at 1600°C, how would these results change? 24.10 Imagine making a close-packed material by filling a container with 20-μm-diameter glass spheres. You then heat this “material” for 12 × 103 seconds at 650°C and the “material” shrinks by 5 vol%. You take an identical sample and find that the same shrinkage is achieved in 360 seconds at 700°C. Assuming that the surface energy of the glass is 0.3 J/m 2, calculate the viscosity of the glass at each temperature and deduce an activa- tion energy. C h a p t e r S u m m a ry .......................................................................................................................................................... 443  25 Solid-State Phase Transformations and Reactions CHAPTER PREVIEW A phase transformation occurs when one material changes its composition or structure. The transformation can be caused by a change in temperature so that no other material is involved or it may involve the reaction with another material, which may or may not be a ceramic, and may be in the liquid or gaseous phase. In this chapter, we will restrict the discussion to phase transformations in which the ceramic is in the solid state. Whenever a phase transformation occurs, a phase boundary must move. Phase transformations occur at interfaces and require the interface to move. A solid-state phase transformation occurs when the interface between two grains that are chemically or structurally different moves. If the grains are chemically the same but have different structures, the process is referred to as a (structural) phase transformation and local atomic movements can induce the change; if the grains have a different chemistry, then long-range diffusion must occur and the process is most likely part of a solid-state reaction. Clearly there are many fea- tures in common with grain growth where the grains are chemically and structurally the same. In particular, the ideas of curvature and capillarity carry over. This chapter thus builds on our discussion of all types of interfaces. 25.1 TRANSFORMATIONS AND The reason phase transformations are so important for REACTIONS: THE LINK ceramics is that ceramics are usually processed in the solid state. A major difficulty in studying these processes In Chapters 14 and 15 we discussed grain boundaries is that they usually occur at high temperatures. (GBs) and phase boundaries (PBs), respectively. These We will consider three types of phase transformation: two chapters described the interfaces and crystal defects. (1) crystal → crystal, (2) glass → crystal, and (3) crystal In Chapter 24 we examined how the movement of GBs → amorphous. Transformations (1) and (2) are closely can lead to sintering, grain growth, and densification. In related to solidification from the melt and dissolution into this chapter we examine how the movement of PBs leads a liquid. Solidification is a major theme in Chapter 29. to transformations and reactions. Some examples of reac- There are two topics to address: tions involving the movement of a PB are given in Table 25.1: not all of these are solid-state reactions. Do atoms move further than atomic distances? How special is this topic for ceramics? These pro- Is charge transferred during the process? cesses do occur in metal/semiconductor systems. In ceramics, solid-state reactions usually involve the move- We can put these questions another way: is the driving ment of two species because the species are likely to be force due to a gradient in the chemical potential or in the charged and we must maintain electrical neutrality. The electrochemical potential? It is important to remember special feature in ceramics is therefore the movement of that phase diagrams describe the equilibrium state. Phase charge and the requirement for overall electrical neutral- transformations occur because the system is not in its ity. We can thus apply a voltage to the system and cause equilibrium state. We can change P, T, or c and then an electric or ionic current to flow. As in other systems, examine how long it takes to reach equilibrium and how the slower moving species will control the rate of the we can get there. Our main tool will be our understanding reaction. of point defect mobility and diffusion. In general, we will 444 ........................................................................................... S o l i d - S tat e P h a s e Tr a n s f o r m at i o n s a n d R e ac t i o n s  TABLE 25.1 Reactions by PB Movement  Displacive transformations: atoms remain attached to the same neighbors. Examples of special features and System challenges  Reconstruction transformations: bonds are broken and atoms are rearranged. Calcination Removing CO2 and other gases during firing Dehydration Removing water before and during firing The driving force for reactions is either a chemical Gas/solid reactions Vapor phase at high T: oxidation or corrosion potential or an electrochemical potential. The electro- Hydration reactions Cement; changes over long time periods chemical potential takes account of the fact that in ceram- NiO/Al2O3 Large structure change at one interface, ics we have charged defects and these charged defects may less at the other move at different rates. NiO/CoO Need diffusion data; Darken equation required Precipitation With control: glass-ceramics Lacking control: devitrification of glass 25.3 TECHNOLOGY Transport through Important for glass crystallization; e.g., after a fluid nucleation From a general technological viewpoint, not only are poly- Phase separation in glass crystalline ceramics almost always very impure by metal- Vitrification Pottery; salt glazes lurgical standards (3N, i.e., 99.9%, being typical high purity), but also it is common practice to add other oxides to enhance densification during processing. If the concen- tration of the additives exceeds the solubility, a second consider model systems, but even then, the data available phase may form. Remembering our discussion in Section are often not very good. 24.1, imagine sintering blue and yellow colored marbles. If the temperature stays low, the marbles remain distinct but deform and rearrange to form a dense material. If 25.2 THE TERMINOLOGY the temperature increases the glasses may mix to give a uniform green glass, which in our analogy is the reacted As described in Chapter 5 the polymorphic form of a material. Whether a reaction takes place therefore de- material that has the lowest free energy is the most stable. pends on factors such as the temperature; changes in the The free energy, G, of each phase is given by the usual morphology of reactants can be affected by other relation G = E − TS. At absolute zero, the entropy term considerations. (TS) is zero and the phase with the lowest internal energy will be most stable. However, at higher temperatures other New Materials polymorphic forms can exist despite their higher internal energy because of the dominance of TS (see Figure Solid-state reactions are also used to produce new materi- 5.10). als. For example, although equimolar Mg–Al spinel (i.e., MgAl2O4 or MgO · Al2O3) powder is available commer-  Polymorphic transformation: The chemistry is cially, nonequimolar Mg–Al spinel powders may be less unchanged. easy to obtain. (A similar processing method is used to produce many of the spinel-structured ferrites.) These Polymorphic transformations can be classified into spinel powders may have useful properties since they can two general types, depending on the kind of changes be used to produce polycrystalline compacts that deform occurring in the crystal. Displacive transformations, as the more readily than the equimolar material. Such materials name suggests, involve displacements of the atoms only; can be prepared by firing an intimate mixture of the equi- there is no structural rearrangement. The displacive trans- molar spinel with high-purity alumina powder. A closely formation that has been extensively studied in metals is related process (structurally the opposite) occurs when γ- the martensite transformation. Martensitic transforma- alumina is transformed to α-alumina, for example, when tions are actually quite common in ceramics, but they are alumina is prepared from boehmite. generally not as rapid as in metals even though they are YBCO, (Sr,Ba)TiO3, BSSCO, and PZT are all essen- transformations. tially prepared by combining oxides or their precursors. Reconstructive phase transformations are associated with high activation energies. The structural change Multiphase Materials involves breaking of bonds. The energy required is at least partly recovered when the new structure is formed. Recon- There is a growing interest in the development of multi- structive transformations are frequently sluggish and, con- phase ceramics. Both the processing and the use of each sequently, the high-temperature forms can often be cooled of the materials described above may involve a solid-state to room temperature without reverting to the thermody- reaction and the movement of a phase boundary. There namic stable form. are, of course, many other situations in which solid-state 2 5 . 3 Te c h n o l o g y ........................................................................................................................................................... 445  ferroelectric materials almost always involves manufac- turing multilayers. It is essential that the layers should not react with one another. Changing Properties We can add a second phase to modify the mechanical properties of a ceramic. An example we discussed in Chapter 18 is the toughening of alumina using zirconia. In this application again, the materials should not react (which is why zirconia is used). FIGURE 25.1 Technical application 1. Monazite on alumina fibers as a barrier layer in a ceramic–matrix composite. Degrading Thermal Barrier Coatings A model thermal barrier coating (TBC) is shown in Figure reactions are important. In electronic packaging, chro- 25.3. The white band separates the Al-rich bond coat from mium is first bonded to alumina and the copper conduc- the underlying Ni-rich superalloy. Capping the structure tion lines are then, in turn, bonded to the chromium. It is is the columnar YSZ TBC. The role of the bond coat, as likely that thin spinel layers are formed in the process. Ore its name implies, is to ensure that the coating continues to reduction is another important example, as illustrated by adhere to the metal during oxidation. Between the bond the reduction of hematite to Fe via magnetite and wüstite. coat and the YSZ is an oxide layer that forms during oxi- A special case is the reaction that can take place when dation (the overlayer or thermally grown oxide—TGO). fibers are encapsulated in a matrix to enhance mechanical Between the bond coat and the superalloy is a thin reac- properties of the matrix as illustrated in Figure 25.1. If the tion layer. fiber reacts with the matrix, the two are no longer able to deform independently and the mechanical properties of Impurity Phases the composite are degraded. For this reason barrier layers may be used to coat the fibers before enclosing them in A well-known example of this process is the addition of the matrix. MgO to alumina to permit sintering to theoretical density as required for the production of translucent alumina tubing (see Section 24.17). If, in this example, MgO is Growth of Thin Films added in excess of the solubility limit (∼210 ppm is used; The first example shown in Figure 25.2 occurred when the actual solubility varies with temperature), then spinel YBCO was grown on a substrate of ZrO2. The intermedi- is formed, which may in turn react with Na during use to ate layer grew by a solid-state reaction during the deposi- produce a precipitate of β-alumina. This reaction can tion. This can be a problem since complicated multilayer cause the failure of sodium-vapor lamps. Since oxides are devices are needed for many new applications. The use of frequently processed at high temperatures, it is also likely that the vapor pressure can become appreciable for certain additive oxides. YBCO YBCO TBC Reaction layer Bonding layer YSZ YSZ FIGURE 25.3 Technical application 3. TBC on a metal with a FIGURE 25.2 Technical application 2. YBCO on YSZ. reaction layer and a bonding layer. 446 ........................................................................................... S o l i d - S tat e P h a s e Tr a n s f o r m at i o n s a n d R e ac t i o n s  mation of twinned “particles” as shown in Figure 25.5a. YVO4 An idea of how this might occur can be obtained by con- sidering Figure 25.5b. The particle effectively contracts along its length by the (001) c planes rotating to the (001) m planes of twin-variant 1 and back to the (001) m planes of twin-variant 2 so there is no long-range shear. Where (001) m1 planes change to (001) m2 planes we form a twin boundary. Depending on the details of the crystallography (which planes match best), the twin boundaries may lie along the short (as here) or long axis. A displacive transformation is diffusionless and requires only a shear of the parent structure to produce the new phase; consequently the rate of transformation at any temperature occurs nearly instantly. An important example of the displacive transformation is the change from tetragonal to monoclinic ZrO2. In this example there is a 5 vol% increase during cooling, which can result in internal stresses in the ceramic and lead to weakening or YSZ even fracture. However, the controlled transformation of ZrO2 particles in a ceramic matrix (e.g., Al2O3) can be FIGURE 25.4 Corrosion of YSZ by V2O5 vapor. used to strengthen the matrix. (We discussed fracture of ceramic materials in Chapter 18.) The addition of MgO, CaO, or Y2O3, to ZrO2 can stabilize the cubic (fluorite) Corrosion of Oxides structure. When ZrO2 transforms from the cubic to the Even sapphire and YSZ can be corroded at relatively low temperatures. Figure 25.4 shows polycrystalline YSZ being corroded by V2O5 vapor to form a reaction layer of YVO4. This process may actually be important when a burning fuel contains V and the TBC contains YSZ. The Y that is stabilizing the YSZ diffuses out to react with the V2O5 to form YVO4. The result is that the Y is no longer available to stabilize the ZrO2, which therefore undergoes a phase change and can fracture. 25.4 PHASE TRANSFORMATIONS WITHOUT CHANGING CHEMISTRY Phase transformations are, of course, closely linked to phase diagrams, but remember that if a phase transforma- tion is occurring, then the system is not in equilibrium and the equilibrium phase diagram can be used only as a guide. Metastable phases may form during a reaction. The (A) stability of a phase is determined by the relative value of (001)c G. Although the chemistry does not change, the redistribu- tion of charge can be very significant, leading, for example, (001)m to the piezoelectric effect. Polymorphic transformations do not change the chemistry of the material. Since dis- placive transformations do not require a change in the first (100)m coordination of the atoms, there is no bond breaking, only bond bending. The distorted form is a derivative structure of the starting material usually losing one or more sym- metry elements. Displacive transformations to lower tem- perature forms commonly result in twins. As we saw in Chapter 14, a crystal is twinned when one portion of the (B) lattice is a mirror image of the neighboring portion, the FIGURE 25.5 Twins in transformed particles: (a) experimental mirror being the twinning plane. This can lead to the for- observation and (b) a possible mechanism. 2 5 . 4 P h a s e Tr a n s f o r m at i o n s W i t h o u t C h a n g i n g C h e m i s t ry ........................................................................... 447 tetragonal phase or from the tetragonal to the monoclinic In the formation of NiAl2O4 by solid-state reaction, we phase the volume changes. This volume change is the key have diffusion of Al3+ ions and Ni2+ ions. If the Al3+ to using such mechanisms in toughening ceramics since ion moves faster than the Ni2+ ion, then we would build it relaxes local stresses at a crack tip. up charge; this would create an electric field that would Barium titanate is cubic with a perovskite structure. then act to reverse the flow of ions rather than allow a However, at room temperature (actually below the Curie build-up of charge. (More details are provided in temperature of 120°C) it is tetragonal with a spontaneous Section 25.9.) electric polarization in the direction of the c-axis (only the higher temperatures form is shown in Figure 7.2). In this Precipitation ferroelectric condition a crystal of BaTiO3 has a domain structure. Precipitation usually involves a change in local chemistry. The classic example of a reconstructive phase trans- Since we are creating a new particle, we form a new PB formation in ceramics is the transformation between the (see Chapter 15). As the particle grows, this PB moves. low and high forms of SiO2: the distorted form of quartz The balance between kinetics (of interface motion and structure is stable at the lower temperature. Twins are diffusion) and energy (of the new bulk and the new PB) again often formed during reconstructive phase transfor- may determine the shape of the particle during growth. mations when these lead to a decrease in symmetry since Three factors in particular must be considered. the change can often occur in symmetry-related ways; the twins are then related by the “lost” symmetry element. 1. Number of particles per unit volume 2. Shape of the particles 3. Size of the particles (and hence volume fraction of the 25.5 PHASE TRANSFORMATIONS precipitate) CHANGING CHEMISTRY As for metals, we can change T or the chemical poten- For short-range or long-range chemistry changes it is nec- tial. Particles in ceramics have not been as widely used as essary for ions to move. Atoms diffuse and charge is in metals because we do not need to pin dislocations. transferred. If charge is moved an electric field may However, particles can still inhibit GB motion, act as sinks develop in the material or we can influence the transfor- for impurities, or modify mechanical properties. The mation by applying an electric field. The structure may widespread occurrence and usefulness of precipitation in also change, so the beginning of the process (the nucle- ceramics are becoming more fully recognized. Things ation stage) may be controlled by the difficulty in chang- happen slowly in ceramics. If there is a good alignment ing the structure. At a later stage diffusion almost between the matrix and the precipitate, the transformation invariably controls such reactions. can occur by the movement of dislocations as in Figure The reaction can be considered as involving three 25.6, which shows a plate of hematite growing in an Ni–Fe steps. spinel matrix. Notice that the interfacial dislocations bow out in the direction of movement and that the plate thick- 1. Transport to the interface ens as they move. 2. Reaction at the interface 3. Transport away from interface of the product and heat As usual, the slowest step controls the rate. The rate of such reactions is controlled by gradients in the chemical potential or, if there is a local variation in charge, by the electrochemical potential. This concept is very important because the chemical potential and the electrical potential can act in opposite directions. There are many model and technological appli- cations of this concept. Silver sulfides provide a model system for studying this effect partly because the processes occur at relatively low temperatures. In oxides such as ZrO2, flow of oxygen ions can be mea- sured and related to the difference in oxygen partial FIGURE 25.6 Movement of interfacial dislocations between pressure across the ZrO2 layer since an electrochemi- hematite and NiFe2O4 spinel during oxidation leading to thickening cal potential is generated. of the precipitate. 448 ........................................................................................... S o l i d - S tat e P h a s e Tr a n s f o r m at i o n s a n d R e ac t i o n s  0.3 1 – 2μ f2 0.2 4 – 6μ 10μ 0. 1 0 0 300 600 t (min.) 900 FIGURE 25.8 Reaction by weight. f 2 is the square of fraction reacted. FIGURE 25.7 Growing particle of spinel in a matrix of Fe-doped Al2O3 during internal reduction. sensitive. A modern microbalance can weigh samples up to 3.5 g with an accuracy of 0.1 μg. A quartz-crystal micro- balance (QCM) can actually measure mass changes in the Internal Oxidation and Reduction nanogram range. So we use a piezoelectric ceramic, a thin The thought experiment: imagine a 1-mm cube of Fe- plate of quartz, to make the device, which then allows us doped Al2O3 in which all the Fe is in the 3+ state. Now to study reactions in ceramics (and other materials). heat the cube in a reducing atmosphere at ∼1500°C. The matrix is unchanged (it is Al2O3), but the Fe3+ is reduced Using Visible Light Microscopy, to Fe2+ . Initially, this phase change can happen only at the the Microprobe, and Scanning surface where the oxygen activity has been lowered, but Electron Microscopy then the “reduction” front moves into the cube like a PB (but there is no change in phase). The Fe2+ is no longer The reacted microstructure is often best analyzed using soluble in the matrix and precipitates out as FeAl2O4 low-voltage scanning electron microscopy (LVSEM) in spinel. The result is that we can see where the front has the backscattered-electron (BSE) imaging mode. The low passed through by where the precipitates, such as that in voltage means that we need only a thin conductive coating Figure 25.7, have formed. (Notice the curvature of the (if any) to prevent an insulator from charging. The BSE dislocations implying their direction of movement.) The mode allows the phases present to be readily recognized converse process, namely internal oxidation, can be dem- because the backscatter coefficients are likely to be dif- onstrated using a similar cube of Fe(II)-doped NiO. ferent for the reactants and the reaction product. Using Transmission Electron Microscopy 25.6 METHODS FOR STUDYING KINETICS The movement of a particular PB is illustrated in Figure 25.9. A spinel particle has been grown on the edge of a We need to understand what controls the rate of a phase transformation. We can monitor both chemical and struc- tural changes to address the sometimes subtle question— which change (chemistry or structure) occurs first? The answer depends on why the phase change itself occurs. The experimental techniques we use are those given in Chapter 10, so we just give some specific illustrations here. The classical approach used to study the kinetics of solid-state reactions between two ceramic oxides is to react a bulk diffusion couple in much the same way as, for example, when studying the Kirkendall effect in metals. Using Weight Change We can weigh the sample and plot the fraction that has reacted as a function of time as illustrated in Figure 25.8. FIGURE 25.9 Particle of Ni–Al spinel growing on an Al2O3 thin Microbalances now allow us to make this technique very film. 2 5 . 6 M e t h o d s f o r S t u dy i n g K i n e t i c s ..................................................................................................................... 449  Slip: suspended Cast layer Plaster of paris clay particles mold JH2O Ps Pm FIGURE 25.10 Rutherford backscattering spectrometry (RBS) of a x reaction between NiO and Al2O3 substrates for different surface orientations. FIGURE 25.11 Schematic of slip drying to form a slip-cast layer. thin film of Al2O3 by reacting the film with NiO vapor, dation, and MgO/Al2O3 reactions. In slip casting, a mold looked at in the transmission electron micrograph (TEM), is made from gypsum (Plaster of Paris: CaSO4 · 2H2O). replaced in the reaction chamber, and looked at again. You Gypsum contains fine capillaries that remove water from can see that the spinel has grown into the Al2O3. In this a slip at a predictable rate. The clay particles in the slip case, the PB moves in the solid state, but the NiO is pro- are platelets as shown in Figure 25.11, so a more compact vided from the vapor phase. The spinel particle changes layer forms as the water is removed. In the compacted cast only where it grows into the sapphire. layer there are fewer capillaries, so it becomes more dif- ficult to remove more water. Hence as the thickness increases, the rate of material transported decreases. Using Rutherford We can write an expression for the flow (current) of Backscattering Spectrometry atoms (the transport equation) as This technique is very direct and measures the thickness of a reaction layer. The lateral resolution is the width of KdP the ion beam (∼0.1 μm). An example from a thin layer of J= (25.1) dx NiO reacting with differently oriented surfaces of Al2O3 is illustrated in Figure 25.10. The thickness of the spinel is obtained by fitting the data to a simulated profile (using The water pressure gradient is dP/dx; K, the permutation RUMP) and shows in this example that the rate of growth coefficient, depends on the particle size, the viscosity, and of the spinel layer does indeed depend on the orientation T. The pressure at the surface of the slip, Ps is 1 atm. The of the surface. pressure at the slip/mold interface, Pm is determined by the surface tension in the capillaries (which are assumed to have a fixed radius rc). 25.7 DIFFUSION THROUGH A LAYER: SLIP CASTING 2g ΔP = Ps − Pm = (25.2) rc We consider the kinetics of HOW THIS PARABOLIC slip coating or slip casting RELATIONSHIP ARISES The flux can also be for two reasons: (1) as a expressed as a volume  J is proportional to dx/dt: J depends on velocity. model for the transport of (proportional to ρ−1) multi- a reactant through a planar  J is also proportional to 1/x: ΔP is the driving plied by the velocity of the boundary layer, and (2) force. slip/layer interface because it is a very impor- tant aspect of ceramic pro- So, dx/dt is proportional to 1/x: hence it is parabolic. When x is very small, dx/dt is very large. 1 dx cessing. The model actually J= (25.3) applies to reduction, oxi- When x is very large dx/dt is very small. (κρ) dt 450 ........................................................................................... S o l i d - S tat e P h a s e Tr a n s f o r m at i o n s a n d R e ac t i o n s Combining Eqs. 25.1 through 25.3 gives used that allow the actual movement of individual inter- faces to be studied and the kinetics of the earliest stages dx dp Δp 2g of the reactions to be determined. J = 1 / (κρ) =K = −K = −K (25.4) dt dx x rc x When alumina and NiO react to form a layer, the equa- tion is Then by rearranging we get an expression for the interface velocity NiO + Al2O3 ⇒ NiAl2O4 (25.6) dx 2g There are many possible reaction paths. The chosen path = − K κρ (25.5) dt rc x may depend on whether the reaction occurs in air. In all three cases, electrical neutrality is maintained. If we integrate, we find that x2 is proportional to t, so the There are three main possibilities: kinetics are parabolic. κ is a volume factor relating to the difference between water and the clay particles. 1. 2B3+ ions move in one direction; electrons or O2− ions A pot can be slip cast to a thickness of several milli- move in the opposite direction. meters in a few hours. The potter would then pour off the 2. 3A2+ ions move in one direction; electrons or O2− ions remaining slip, let the pot dry and shrink, and remove it move in the opposite direction. from the mold, which can then be reused. 3. 2B3+ move in one direction and 3A2+ move in the oppo- site direction. 25.8 DIFFUSION THROUGH A LAYER: These processes are summarized in Figure 25.12. SOLID-STATE REACTIONS Mechanisms 1 and 2 require that O2− diffuse, which may not be likely, or that electrons can move, which may be In solid-state reactions, the reactants are initially in contact the case in semiconducting oxides unless it is prevented. and combine chemically to form the reaction product. The The third mechanism is the counterdiffusion of cations, kinetics of the initial stage of such a reaction depend on the parameters of the interface (the crystallography of the contacting surfaces, etc.). The fundamental point is 1 that we start with one interface and immediately create 2 O2 two new interfaces. We will consider the example of NiO/Al2O3. Similar systems include MgO/Al2O3 and AO AB2O4 B2O3 FeO/Fe2O3. The mechanism for such reactions, as proposed by A2+ Wagner, is the counterdiffusion of cations. It has been found that this mechanism does occur for purely ionic 2e– materials. Counterdiffusion of cations in ionic systems is 3 dictated by charge-balance considerations rather than 2 O2 cation mobilities. Thus significant deviations from the pre- dicted balance may occur when electronic carriers (i.e., AO AB2O4 B2O3 electrons and holes) are present. The initial position of the interface between the reac- 2B3+ tant oxides can be labeled by “inert” Pt markers or recog- nized by the presence of voids. Some early measurements 6e– were not in agreement with this model but may have suf- fered from the fact that inert markers can move even AO AB2O4 B2O3 though they remain inert. 2B3+ (1) 3A2+ 25.9 THE SPINEL-FORMING REACTION A2+ The phase transformation at the Al2O3/spinel phase bound- (2) 02– ary involves both a change in the distribution of cations and a change in the structure of the oxygen sublattice. At 2B3+ (3) the spinel/NiO interface the oxygen sublattice remains 302– cubic, although misfit dislocations may be introduced. It is not possible to observe directly the movement of par- FIGURE 25.12 Mechanisms for the reaction between AO and ticular interfaces using bulk samples. Techniques can be B2O3. 2 5 . 9 Th e S p i n e l - F o r m i n g R e a c t i o n .......................................................................................................................... 451  RTBi Di = − (25.10) N 1500°C 20 140 (Δ) 2 The parabolic rate law holds when the reaction layer x 105 (cm2) Δ μm is thick. When trying to be quantitative, there is the obvious question how to “mark” the location of the origi- nal interface. An additional complication arises if AO and 122 AB2O4 are both cubic but not lattice matched; then misfit dislocations must be present at the interface and these can move only if point defects on the O sublattice move. 10 100 25.10 INERT MARKERS AND REACTION BARRIERS We saw examples of structures in which reactions would 1400°C destroy the device in Section 25.1—this is where we need 71 barriers. When we study the kinetics of reactions we would like to mark the initial location of the interface(s)— this is where we need markers. In both cases, the barrier/ marker must be inert; it should not participate in any reac- 0 tion. This topic can be illustrated by two examples: 0 100 t (h) 200  Behavior of rows of Pt particles forming a marker FIGURE 25.13 Kinetics of the reaction between bulk NiO and bulk Al2O3 to form spinel. layer  Failure of a coating on a fiber during formation of a fiber-reinforced composite which avoids the build-up of electric charge but does not We will consider the example of diffusion couples require O2− ions or electrons to move: it is a purely ionic prepared by depositing an In2O3 thin film on a cleaved process. When thickness is plotted against time for the bulk single-crystal substrate of MgO and identify the loca- bulk reaction (Figure 25.13), the gradient of the straight tion of the initial interface by an array of Pt particles as line depends on T and we can directly determine a value illustrated in Figure 25.14. The Pt particles are prepared for the diffusion coefficients. We know that if there is a charge build-up then we will have an electrochemical potential, ηi, rather than the simple chemical potential, μi. These two potentials are related by taking account of φ, the electrical potential acting on this charge. ηi = μi + ZiFϕ (25.7) The subscript i refers to the ith species, which has an effective charge of Zi, and F is the Faraday constant. The current is the product of charge and velocity. (A) ji = civi (25.8) Remember that velocity is mobility times force. 1 d ηi vi = − Bi ⋅ Force = − Bi (25.9) N dx and ci Bi ∂hi ji = (25.8) N ∂x (B) FIGURE 25.14 SEM backscattered electron images of an as- We can then define a diffusion coefficient, Di. deposited In2O3 film on MgO with Pt markers. 452 ........................................................................................... S o l i d - S tat e P h a s e Tr a n s f o r m at i o n s a n d R e ac t i o n s by first sputter coating the MgO substrate with a 2-nm- 10-7 thick continuous film of Pt. The Pt-film/MgO-substrate couple is then heated to 1175°C for 5 minutes. This heat D 60 Co treatment causes the Pt film to dewet the MgO surface and (cm2/sec) thus form small islands. This array of small Pt particles then serves as the marker layer. After dewetting, thin films 1445 °C of MgIn2O4 and In2O3 can be deposited onto the decorated substrate using pulsed-laser deposition (PLD). This inter- mediate MgIn2O4 layer acts as the nucleation layer for the 10-8 1300 °C reaction product so that the markers do not affect the initial nucleation of the spinel. (It can also be grown on the MgO before depositing the Pt.) Markers of various compositions and sizes have been used in numerous studies to track the movement of inter- faces in a wide variety of material systems. In many of these studies, the markers were intended to serve as a fixed 60 reference point and typically are used to aid in determin- Co -9 ing which species were diffusing during a reaction process. 10 57 When a material is used as a marker it is usually assumed Ni to be inert, i.e., the marker should neither affect nor be affected by the reaction process. Direct analysis of these thin-film diffusion couples can show directly whether the 60 Co markers are inert and how they behave during such reac- tions. The markers may affect the reaction process or the 57 reaction process may cause the markers to move. The Ni interface between the marker and the surrounding matrix 10 -10 1.0 0.8 0.6 0.4 0.2 0 plays a critical role in determining the inertness of the c in (CocNi1– c) O marker. This is especially significant when diffusion (A) couples are reacted in an applied electric field. The idea of a barrier layer is to prevent two materials ~ D (cm2/sec) coming into contact that would react. Applications include protecting reinforcing fibers and separating layers in mul- 10-10 tilayer thin films. Such barrier layers could also be used to exclude water from hydrophobic layers. 25.11 SIMPLIFIED DARKEN EQUATION 1200 °C The diffusion coefficient actually will depend on the com- position. Consider NiO/CoO, which is a nearly ideal solid 1300 °C solution. The activity coefficient is ∼1. 10-11 1370 °C μi = μ0i + RTInc (25.11) We can write an “average” diffusion coefficient as 1400 °C T T D = D xCo + D (1 − xCo ) (25.12) Co Ni 10 20 30 40 at. % Ni (B) In this equation, which is known as the Darken equation, FIGURE 25.15 D as composition varies: (a) using tracer diffusion x indicates the mole fraction of Co or of Ni. The equation at two values of T in CoO–NiO mixed oxide and (b) diffusivities for assumes local equilibrium everywhere and that D̃ is MgO–NiO mixed oxides. a chemical or interdiffusion coefficient in a chemical potential gradient. The matrix is CoxNi1−xO. D is plotted as a function of concentration for both Ni and Co diffusing in the mixed oxide at 1300°C and 1445°C in Figure 25.15a. 2 5 .11 S i m p l i f i e d Da r k e n E q uat i o n .......................................................................................................................... 453  °C matic plane so reactions at basal planes tend to nucleate 1700 1600 1500 1400 1300 1200 10-7 more slowly than on prismatic planes. (More is given in ~ D Section 25.14.) (cm2/sec) 25.13 PARTICLE GROWTH AND THE 10-8 EFFECT OF MISFIT Al2O3-MgO (1 m/o Al2O3) Al2O3-NiO The lattice misfit at moving phase boundaries is accom- (2 m/o Al2O3) modated by misfit dislocations, lattice rotations, etc. An important consideration will be the role of size in deter- Cr2O3-NiO mining these effects; neither misfit dislocations nor lattice 10-9 (1 m/o Cr2O3) rotations may be necessary when the new phase is very CoNiO2 small. The chemical abruptness of the interface is particu- MnO-MgO larly interesting when the oxygen sublattice is almost common to the two materials as we saw in Section 15.6 for the NiO/NiFe2O4 interface. This interface can then Fe2O3-MgO 10-10 move by only the cations moving. However, if misfit dis- Cr2O3-MgO locations are present, as in Figure 15.3, then the anions (1 m/o Cr2O3) FexO-MgO (10 m/o FeO) must also move. The growth of β-alumina into spinel shown in Figure 25.17a is an example of a special situation in which the 10-11 misfit between the precipitates and the matrix is very NiO-MgO (10%m/o NiO) 10-12 4.6 5.0 5.4 5.8 6.2 6.6 7.0 1/T (x 104) (K) FIGURE 25.16 Dependence of diffusion coefficients on T for different oxides. The mean value from Eq. 25.12 is plotted in Figure 25.15b. (A) D̃ can also be plotted as a function of temperature as shown for many more oxide systems in Figure 25.16. This analysis is useful but be cautious. The oppositely charged point defects Ni3+ and V″ form an associated defect, which diffuses at a different rate. You can measure D but modeling D̃ is difficult; essentially predictions are tricky. 25.12 THE INCUBATION PERIOD (B) The initial stage of a solid-state reaction was historically referred to as the “incubation period.” Early studies of such reactions in oxides lacked the required spatial resolu- tion so that measurements were not made until the reac- tion layer was ∼1 μm thick (the resolution limit for chemical analysis in a microprobe operating at ∼30 kV). Often, the reactants were not initially in ideal contact. The nucleation of spinel or other reaction products can now be detected at a very early stage using TEM. The kinetics of such early stages of reactions are often controlled by the difficulty of (C) nucleating the reaction product, which may indicate a FIGURE 25.17 Chemical reactions by movement of steps on in crystallographic factor. Thus, for example, the basal plane interface. a) β-Al2O3 growing in spinel; (b,c) amphibote growing in in Al2O3 tends to dissolve less readily than, say, a pris- orthodyroxene. 454 ........................................................................................... S o l i d - S tat e P h a s e Tr a n s f o r m at i o n s a n d R e ac t i o n s small along one plane, thus creating a low-energy inter- face. This situation is not unique as shown in Figure 25.17b. The result of such a reaction is the formation of particles that appear to be very large in one direction: the particle may be large in two directions—hence a platelet. (A) Isolated steps move across the larger surface. Incidentally, always remember that most observations of such phenom- ena are made at room temperature. 25.14 THIN-FILM REACTIONS (B) Understanding how phase boundaries in oxides move is essential for a comprehensive understanding of solid-state reactions between ceramic oxides. The factors that deter- mine the mobility of a phase boundary may involve the usual aspects of structure, bonding, and chemistry. (C) Because thin-film reactions can be carried out at low tem- peratures, the morphology of the interface can easily be “frozen in.” Grain boundaries and other defects can affect the rate of a reaction in several ways. They can act as short-circuit paths to allow more rapid diffusion of reac- tants, or simply act as nucleation sites for the growth of a (D) new structure. Evidence for both of these mechanisms was FIGURE 25.18 SEM images of reactions at GBs in thin films of found in the study of the reduction of Fe-doped Al2O3. It NiO deposited on (0001) Al2O3. has also been shown that grain boundaries are a necessary product of the growth of spinel into alumina. By combining TEM and field emission gun (FEG)- SEM we find that the formation of spinel occurs more  We can grow material M1 on a single crystal of mate- quickly along GBs in thin-film reaction couples as illus- rial M2, or vice versa, and thus predetermine the loca- trated in Figure 25.18. At the earliest stages of these reac- tion of grain boundaries. tions, the kinetics are controlled by the interface mobility  We can control the oxidation state of the reactants. rather than by diffusion through the reactant. Thin-film reaction couples can be prepared by growing This approach overcomes the difficulty encountered thin films on a specially prepared substrate; PLD works using classical bulk diffusion: we know that there is inti- well for the deposition but molecular beam epitaxy (MBE) mate contact between the substrate and the thin film. If and chemical vapor deposition (CVD) could be used the materials are not in direct contact, the earliest stages equally well. of the reaction will likely involve a vapor-phase This geometry offers many advantages over bulk component. samples. The key feature is  The reaction tempera- always that phase bound- tures can be much MISFIT AND SPINEL FORMATION aries move during solid- lower than with bulk When NiO and Al2O3 react, the lattice misfit at the state reactions. Defects reaction couples. initial NiO/Al2O3 interface (when perfectly aligned) is and grain boundaries influ-  The cooling rate can be shared almost equally between the NiO/NiAl2O4 and the ence both the mechanisms very rapid. NiAl2O4 /Al2O3 interfaces. However, when NiO and and the rates of solid-state  We control the micro- Fe 2O3 react, the misfit at the NiO/NiFe2O4 interface is reactions, but with bulk structure, crystallogra- close to zero so that nearly all the misfit is accommo- reactants you do not know phy, and morphology dated at the NiFe2O4 /Fe2O3 interface. where to start. The volume of the substrate. probably changes during  We can study the same interface before and after the the reaction. reaction. When the epilayer contains grain boundaries, the thin-  We can thus directly study the role played by steps on film approach allows us to examine how the nucleation the surface of the substrates and grain boundaries in rate depends on the type of grain boundary (misorienta- the thin films. tion, grain-boundary plane, etc.) intersecting the phase  We can use a combination of materials or a graded boundary. The growth of the product will depend on the reactant. nucleation site. 2 5 .14 Th i n - F i l m R e a c t i o n s ......................................................................................................................................... 455  Δ (nm) 300 1100°C 200 (A) 100 0 0 2x105 4x105 t (s) 6x105 FIGURE 25.20 Kinetics of reactions between thin films of NiO (B) deposited on (0001) Al2O3 when an initial buffer layer of spinel is present. substrate geometry to examine the role of grain boundaries in the two materials separately. (C) In the second type of sample a buffer layer of the FIGURE 25.19 SEM images of growth of spinel between thin films reaction product or a reaction-barrier layer is grown of NiO and (0001) Al2O3 when an initial buffer layer of spinel is before growing the reactant layer. This geometry allows present. us to quantify the kinetics of the reaction separately from the nucleation. We can then examine the morphological development of the two moving interfaces and the effect If, as is often drawn schematically, a continuous reac- of lattice misfit on this morphology. The expansion that tion layer forms, then the volume change may be accom- occurs when the spinel forms can be readily accommo- modated by an expansion normal to this layer (analogous dated if a buffer layer is present forming a uniform layer to the tetragonal distortion as you can see in Figure in semiconductor multilay- DIFFUSION COUPLES 25.19. In this case, the ers). If the reaction occurs The diffusion couple (approximately 1 mm thick) is kinetics can be deduced initially along the triple placed between two Pt electrodes with the thin film in directly as shown in Figure junction where a grain contact with the cathode and the bulk MgO substrate in 25.20. Notice that t and Δ boundary meets the sub- contact with the anode as illustrated in Figure 25.23a. are much smaller than in strate, the constraints are The reaction takes place in air with a voltage of −10 V Figure 25.13 and that the very different. The thin applied across the sample. T depends on the material, kinetics are linear. At the film can become exten- ∼1350°C for In2O3/MgO but as low as 700°C for Fe2O3/ early stages of the reac- sively deformed in accom- MgO. A second diffusion couple, without the applied tion, the rate is determined modating this volume field, is placed with the thin film down on a piece of Pt by the interface. change. There is, for foil to ensure similar reaction conditions. The two This reaction geometry example, an ∼7% volume samples are kept close together to ensure they are reacted can be extended to a situa- expansion when NiO reacts at the same temperature. tion in which there are with Al2O3 to form the several reaction products spinel. as illustrated for the Al2O3/ Two types of reaction GROWING AIN IN AN ELECTRIC FIELD Y2O3 system in Figure sample are illustrated in Place a single-crystal of α-Al2O3 between two Pt elec- 25.21. Finally we should Figures 25.18 and 25.19. In trodes in an N2-rich environment. The Pt electrodes act note that reactions often the first, the reactant mate- as chemically inert conductors with a high melting tem- take place more easily at rial is grown directly on perature. We have to scratch the Pt electrodes with an surfaces since there is no the substrate so as to abrasive to roughen the surface and thus allow the nitro- volume constraint. examine the nucleation of gen to reach the entire surface of the Al2O3. If N2 trans- A special thin-film the reaction product and to port across the surface is inadequate, the Al3+ cations reaction (though it becomes quantify the role of grain arriving at this surface would either evaporate or form more general as it pro- boundaries in the poly- an alloy with the Pt electrodes. After the furnace is ceeds) is the corrosion of crystalline material. We evacuated to 10−6 torr and heated to remove excess water, a ceramic by a metal or can easily reverse the layer/ backfill with a 5% H2 /95% N2 gas mixture and react. another ceramic. Phase 456 ........................................................................................... S o l i d - S tat e P h a s e Tr a n s f o r m at i o n s a n d R e ac t i o n s  2440° L 2400 h–Y + L. T (°C) (5%) 2310° c-Y + L. 2050° 2000 1967° 1977° A + L. 1942° (29%) 1917° (A) (43%) (57.5%) 1910° 1905° 1820° (79%) YA + Y3A5 1600 Y2A + c-Y + Y2A YA A + Y3A5 1200 (B) 0 20 40 60 80 100 Y2O3 Y4Al2O9 YAlO3 Y3Al5O12 Mol % Al2O3 (Y2A) (YA) (Y3A5) (C) FIGURE 25.21 Forming YAG by a thin-film reaction: (a) intermediate state; (b) final state for the same film; (c) the equilibrium phase diagram. boundaries form during the corrosion process just as they 25.15 REACTIONS IN AN do when a metal oxidizes or when an oxide is reduced; ELECTRIC FIELD the only special feature is that the action takes place close to the surface, so there are fewer constraints. Figure 25.22 Diffusion in ionic materials occurs primarily by the move- illustrates the PB formed when K 2O vapor corrodes (reacts ment of charged species. Therefore, the application of an with) alumina. The DP shows that the two phases are electric field can provide a very powerful driving force for topotactically aligned. mass transport. There have been numerous studies on the effects of electric fields on transport phenomena. Several studies have been performed on the evaporation of alkali halides in the presence of an external field. These investi- gations showed that the application of an electric field enhanced the evaporation of the crystal species. Similar studies have been performed on oxide ionic conductors, including ZrO2 and β-aluminas. However, only a few experiments have been performed on classical insulating oxides such as α-Al2O3 and MgO (perhaps because they are insulators). Polycrystalline diffusion couples can be studied in a similar way. Results show an increased transport and con- sequently an increase in the growth of the reaction product. However, the polycrystalline nature of the compacts makes A A it difficult to separate the influence of grain boundary dif- fusion and bulk diffusion. This thin-film geometry can also help us understand FIGURE 25.22 Corrosion of Al2O3 by reaction with K 2O vapor how an electric field affects heterogeneous solid-state showing a TEM image, the DP, and a schematic of the DP. reactions and transport phenomena. The spinel-forming 2 5 .1 5 R e a c t i o n s i n a n E L E C T R I C F I E L D ............................................................................................................... 457  sure. By applying an electric field with an appropriate electrode material, at elevated temperatures, across Al2O3, a flux of Al3+ cations toward the cathode is induced. The cations arriving at the surface of the Al2O3 then react with a nitrogen gas atmosphere to form a thin epitactic film of AlN on the Al2O3. The hydrogen portion of the mixture serves to help reduce the oxygen activity in the gas atmo- sphere so that Al2O3 does not reform. Under the reaction conditions used for the formation of these films, it is esti- (A) mated that the partial pressure of oxygen in the chamber is between 10−21 and 10−26! For a more accurate determina- tion, we would need to know the amount of water vapor in the chamber. The gas mixture used for this study is critical: e.g., using 99.999% N2 gas results in the formation of only Al2O3 (the oxygen activity is too high). The Al2O3 is reacted at, e.g., 1250°C for 2 hours. The properties of AlN make it an interesting material for applications in the microelectronics industry: it has a large bandgap, good thermal conductivity, high-temperature stability, and chemical inertness. Thin AlN films on basal Al2O3 sub- strates are used as buffer layers for the growth of GaN on alumina. 25.16 PHASE TRANSFORMATIONS INVOLVING GLASS The crystallization of glass is so well established that it is (B) (C) responsible for the development of a whole class of materi- FIGURE 25.23 Reaction between a thin film of Fe2O3 and a layer als known as glass-ceramics. There is therefore a large of MgO in an electric field at 1150°C for 2 hours: (a) schematic of body of literature on this subject. When glass is present the set up; (b) no applied field; (c) 2 kV/cm applied field. The MgO has grown on top of the spinel. The reaction is fastest at GBs in in a GB, there is an additional constraint on the crystalli- the thin film. zation since a second “nucleating” interface is present. For example, it is possible that a glass that will crystallize on a free surface may not do reaction between MgO and NUCLEATING AGENTS so in a GB due to the com- Fe2O3 deposited on thin Different types are used to promote the process of petition between the two single-crystal films of crystallization. “seed” grains. There is a iron oxide on {001} MgO The Pt group and noble metals: concentration growing number of studies using PLD is shown in ∼0.05% of the crystallization of Figure 25.23a. The diffu- Fluorides (e.g., Na2AlF6 or Na2SiF6): concentration glass in different systems, sion couples are then 2–4% but few relationships reacted at elevated tem- TiO2: concentration 2–21 wt% between the new crystals peratures under an applied and the crystalline grains electric field. The electric have been reported. Much field can increase mass transport in the bulk and can of the work on this topic has been carried out on com- change the resulting microstructure and the interface mercially available material where other elements may be topology as shown in Figure 25.23b and c. The controlled present in the glass. nature of the experiment and the simple reaction geometry Glass can dissolve crystal. The kinetics of dissolv- allow the transport phenomena and reactions to be exam- ing crystalline sapphire in a CaO–Al2O3 –SiO2 melt are ined directly. We can study the reaction with NiO instead shown in Figure 25.24. We see parabolic kinetics—it is a of MgO with the electronic contribution to the process diffusion-controlled reaction. Glass can penetrate poly- removed by including layers of ZrO2 next to the Pt crystalline compacts and dissolve or redistribute the crys- electrode. talline phase. In the case of polycrystalline MgO, further We can grow thin films of AlN on sapphire by apply- heat treatment caused the glass to crystallize as monticel- ing an electric field to a sample heated in a nitrogen-rich lite. A particularly interesting observation in this study atmosphere with an extremely low oxygen partial pres- was that the impurities, which were present in the sintered 458 ........................................................................................... S o l i d - S tat e P h a s e Tr a n s f o r m at i o n s a n d R e ac t i o n s  lites, which limit the propagation of flaws. (See also the 60 discussion in Section 21.11, including the mention of Corrosion 1550 °C ΔR (μm) devitrite.) 40 25.17 POTTERY 1480 °C 1410 °C The phase transformations that take place in pottery and glazes on pottery have not been studied as extensively as 20 the model NiO/Al2O3 reaction in part because the pro- cesses are complex and perhaps because they are not the basis of high-tech applications. The glazes are usually 1350 °C silica based with high concentrations of dopants to lower Tg or produce other special properties. The best example 0 0 20 40 60 t1/2 (sec)1/2 80 of a phase transformation in a glaze is the crystallization FIGURE 25.24 Dissolution of sapphire in a CaO–Al2O3 –SiO2 glaze discussed in Section 21.12. What happens when we silicate melt. heat clay therefore depends on the clay, which depends on where you are since most clay firing is local. The topic is enormous and varied. When we glaze the pot, the forma- MgO (primarily ZrO2: a grain-growth inhibitor), were tion and behavior of the different glazes depend not only swept into the residual glass regions between the crystal- on the composition of the glaze but also on the firing line monticellite grains (known as the snow-ploughing temperature and environment. process). Glass can crystallize. Glass-ceramic materials are pro- duced by the controlled crystallization of appropriate 25.18 CEMENT glasses. The glass-ceramic typically consists of 95– 98 vol% of very small crystals, generally <1 μm in size, Cement is not only an extremely important ceramic but is with the residual glass phase making up the rest of the also a very complex one. One factor in this complexity pore-free material. When these materials are fabricated, results from the importance of hydration reactions. the required shape is produced using conventional glass- Cements are, by definition, powder ceramics that react forming techniques. To obtain small crystals of uniform with a liquid (usually, though not necessarily, water) to size in the glassy matrix, a uniform density of nuclei of undergo a chemical reaction to form a solid structure. A the order of 1012–1015 cm−3 is required. Selected nucleating cement paste is the suspension of this powder in a liquid agents are added to the batch during the melting operation phase. Some cement pastes require the presence of air or and a controlled heat treatment is performed. CO2 to harden, while others can harden under water. The role of the different nucleating agents and the Pozzolanic cements are Si- or Al-based powders that can mechanism that leads to a subsequent volume crystalliza- react with water providing Ca(OH) 2 is also present. The tion are not yet entirely clear. For the metals, the solubility situation can be further confused by the presence of non- decreases as T in the glass melt decreases and small metal- reactive constituents that are added to change the rheology lic particles precipitate out. In the case of oxide nucleating of the mixture. The rheological properties change as the agents, the crystallization process appears to take place fresh cement hardens. This setting process is thus quite by an induced phase separation (demixing) followed by like the solidification of glass, but it takes place at ambient crystallization. (We considered phase separation of glasses temperature and involves a change in structure. (So, it is in Section 21.11). For a TiO2-nucleated Li2O–Al2O3 –SiO2 completely different.) The two fundamental (do not say glass-ceramic, the nucleation involves a phase separation basic, since the basicity of CaO is an important factor on a scale of ∼5 nm followed by the formation of a crystal- here) reactions with CO2 and H2O are illustrated by these line TiO2-rich nucleating phase. simple equations. As a result of carefully controlled thermal treatment, the initial glass is converted into a polycrystalline material Ca(OH) 2 + CO2 → CaCO3 + H2O (25.13) in which the final properties depend on the nature of the precipitated phases, the final degree of crystallinity, the CaO · Al2O3 + 10H2O → CaO · Al2O3 · 10H2O (25.14) size of the crystallites, etc. The material is generally opaque, although translucent and even transparent glass- The water content can vary producing different hydrate ceramics have been produced. The small size of the grains phases. If sulfur is present (in gypsum) the reaction and the absence of porosity are characteristics of glass- becomes more complex and leads to the formation of the ceramics. These result in excellent mechanical properties. mineral ettringite, Ca6Al2 (SO4)3 (OH)12 · 26H2O, during This is explained in part by the action of the microcrystal- the hydration of Portland cement. 2 5 .18 C e m e n t .................................................................................................................................................................. 459  In an alkali silica cement, we see a new setting/hard- salts rather than from the oxides themselves. As the CaCO3 ening reaction with quartz becoming a factor. decomposes to form the oxide, emitting CO2, heat moves into the core of the particle and CO2 move outward. The 2(Na2O · nSiO2) + Na2SiF6 → (2n + 1)SiO2 + 6NaF (25.15) result is the formation of another reaction layer, which further slows down decom- We have mentioned position. Of course, in this PORTLAND CEMENT cement terminology in case we can expect the Hydraulic cement is produced by pulverizing Portland Chapter 2: C is CaO, S is CaO to be porous so that cement clinker and usually contains CaSO4 (<5%). SiO2, and A is Al2O3. the CO2 can evolve quite Portland clinker is produced by heating a mixture of CA is the main constituent easily. CaO, SiO2, Al2O3, and Fe2O3 until partly molten. in calcium aluminate When SiO2 dissociates, C3S is the essential constituent of Portland clinker; C2S, cement (referred to as the situation is not so C3A, and C2 (A,F) will also be present. CAC). In high-alumina simple. This reaction is cement (HAC), the Al2O3 important not just because content ranges from 40% to 80%; it contains some C2S SiO2 itself is important, but also because SiO2 is present but no C3S. Its value is that it sets much more quickly than in glass, furnace bricks, and alumina furnace tubes. Portland cement. For reasons that are obvious, pores are an important 2SiO2 (s) ⇒ 2SiO (g) + O2 (g) (25.16) component in concrete and are the main flaw in the mate- rial. This is unfortunate in a material primarily needed for its strength. At 1320°C we can write the reaction coefficient in terms Not all cement is based on CSx or CA x. A group of of the partial pressures. cements known as glass ionomer cements (GICs) is used as cements in dentistry. The reaction involves an ion- ( P )2 p O2 leachable alumina-silicate glass and an aqueous solution K eq = SiO = 10 −25 (25.17) of polyalkenoic acid. The resulting cement consists of ( aSiO2 ) 2 glass particles in a polysalt matrix. This is a specialty topic with far-reaching applications. Assuming the concentration of SiO2 is unity (it is the principal component), we can express PSiO in terms or the oxygen partial pressure. [We are using pO2 (as is conven- 25.19 REACTIONS INVOLVING tional) to represent the partial pressure of O2 but Px to A GAS PHASE represent the partial pressure of X—to keep the notation clear!] The gas phase becomes important when a vapor is either intentionally used in a reaction or is created during a reac- K eq1/ 2 tion, as is the case in the decomposition of a product. The PSiO = (25.18) problem is illustrated by the carbonate reaction shown in p O12/ 2 Figure 25.25; many ceramics are processed from their This equation indicates that the oxygen partial pressure controls the vaporization of the silica. For example, if the pO2 is 10−18 atm (a reasonable value in a reducing atmo- Pf < Ps < Pr Tf > Ts > Tr sphere of H2 or CO), then the PSiO will be ∼3 × 10−4, which Gas flow Heat flow is quite high, so the SiO2 evaporates. Hence SiO2 would not be a good refractory in a dry reducing atmosphere. r rs The effect can be minimized by adding a small amount Porous of H2O if H2 is present. CaO A similar situation arises when an oxide is reacted in a chloride gas. This reaction is actually used in growth of Tr thin films by vapor transport. CaCO3 Ts q2 FeO (s) + 2HCl (g) ⇒ FeCl2 (g) + H2O at high T (25.19) Ps J2 Pr q1 FeO (s) + 2HCl (g) ⇐ FeCl2 (g) + H2O at low T (25.20) J1 Pf Tf The reaction of the active gas with the ceramic increases FIGURE 25.25 Schematic of the processes involved in decompos- the vapor transport. What we are actually doing is control- ing a carbonate. ling the chemical potential (concentration) of the reaction 460 ........................................................................................... S o l i d - S tat e P h a s e Tr a n s f o r m at i o n s a n d R e ac t i o n s gases and hence controlling the rate of deposition. We can and apply Fick’s law: ⎡ 2 P FeCl ⎤ ΔG 0h,c = − RT ln ⎢ 2 2 ⎥ (25.24) dn ∂c Δc c − cc ⎣ ( B − 2 P FeCl2 ) ⎦ = − AD = − AD = − AD h (25.21) dt ∂x L L 25.20 CURVED INTERFACES With some manipulation we can express the concentration difference as a pressure difference and see that the diffu- The equation given by Thompson and Freundich (the sion from hot (h) to cold (c) is driven by the concentration Thompson–Freundich equation) relates the concentration gradient and the direction of the reaction is just due to the in equilibrium with a curved surface to that in equilibrium enthalpy of the reaction. At equilibrium we can write an with an infinite flat surface. expression for ΔG. ⎛ c ⎞ 2E M RF ln ⎜ a ⎟ = (25.25) ⎛ PFeCl2 PH2 O ⎞ ⎝ cpi ⎠ a r ΔGh = − RT ln ⎜ ⎝ PHCl ⎟⎠ (25.22) Here ca is the concentration at the curved interface, cpi is the concentration at the planar interface, M is the molecu- In a closed system, the initial amount of HCl is B atm. lar weight, E is the interfacial energy, and ρ is the density. Then two molecules of HCl gives one molecule of FeCl2 Thus the concentration in equilibrium for a curved surface and one molecule of H2O. differs from that for a flat surface. This result is not due just to the reduction of surface area. This phenomenon is PHCl = B − 2PFeCl2 + PH2O = PFeCl2 (25.23) known as the Gibbs–Thompson effect. CHAPTER SUMMARY The key idea for solid-state reactions and phase transformations is that they occur by the move- ment of interfaces no matter what phase is involved. A phase transformation can occur by one interface moving, but even if a reaction starts at one interface, we will have two interfaces as soon as a reaction product forms. When either a solid-state reaction or a phase transformation occurs, the system is not in equilibrium and the equilibrium phase diagrams can serve only as a guide to what the final product will be. Diffusion of point defects is an essential feature in solid-state reactions, but understanding the kinetics of these processes is not necessarily straightforward because the diffusion coefficients change as the composition of the phase changes (the Darken equation). The situation can be even more complex if the structure of the reaction product is also new and if misfit dislocations form at the phase boundary. The use of slip casting to explain the physical basis of parabolic reaction kinetics is extremely instructive and builds on a real ceramic process. Like slip casting; many phase transformations in ceramics involve the transfer of water or a gas phase; the setting of cement and the corrosion of TBCs are two such examples. PEOPLE IN HISTORY Schmalzried, Hermann (1932–) is an exception to the rule. Formerly a postdoc with Carl Wagner, Hermann has been a mentor and inspiration to many of the current generation of researchers in the field of solid- state reactions in ceramic systems and is profusely thanked by the authors. Wagner, Carl was born May 25, 1901 in Leipzig and died December 10, 1977 in Göttingen. He wrote the seminal text with Schottky and laid the foundations for understanding corrosion and reactions between oxides. GENERAL REFERENCES Christian, J.W. (2002) The Theory of Transformations in Metals and Alloys (Part I + II), 3rd edition (Hard- cover), Elsevier, UK. 1216 pages written by the expert: not easy reading. Porter, D.A. and Easterling, K.E. (1992) Phase Transformations in Metals and Alloys, 2nd edition, CRC Press, New York. Although written for metallic systems, this text is at just the right level and is still the standard. Schmalzried, H. (1981) Solid State Reactions, 2nd edition, Verlag Chemie, Weinheim, Germany and (1995) Kinetics of Reactions, VCH (now Wiley-VCH), Weinheim, Germany. Two texts by the master. Very condensed! C h a p t e r S u m m a ry .......................................................................................................................................................... 461  Journals: Clay Minerals; Cement Concrete Res.; J. Mater. Sci.; Appl. Clay Sci. Clays Clay Minerals (the Clay Minerals Society). SPECIFIC REFERENCES Butman, M.F., Smirnov, A.A., Kudin, L.S., and Munir, Z.A. (2000) “Determination of the sign of the intrinsic surface charge in alkali halides from ionic sublimation measurements,” Surf. Sci. 458, 106. Using an electric field to study ion vaporization. Clarke, D.R. and Levi, C.G. (2003) “Materials design for the next generation of thermal barrier coatings,” Annu. Rev. Mater. Res. 33, 383. Discusses the background to Figure 25.3. He, T. and Becker, K.D. (1997) “Optical in-situ study of a reacting spinel crystal,” Solid State Ionics 101–103, 337. Studying solid-state reactions by weighing the products. Johnson, M.T., Schmalzried, H., and Carter, C.B. (1997) “The effect of an applied electric field on a hetero- geneous solid-state reaction,” Solid State Ionics 101–103, 1327. Odler, I. (2000) Special Inorganic Cements, E&FN Spon, London. A very helpful resource. Smith, D.C. (1998) “Development of glass-ionomer cement systems.” Biomaterials 19, 467. EXERCISES 25.1 Two cubes (400 μm long on each side) of NiO and Al2O3 are reacted at 1600°C. Assuming that the reaction takes place without significant movement of electrons or oxygen and that a reaction layer is produced that is 100 μm thick, what are the respective thicknesses of the remaining NiO and Al2O3? 25.2 Given the densities of some of the polymorphs of SiO2, should it be possible to convert β-cristobalite to some of the other forms by applying pressure? Briefly explain the reasoning behind your answer and indicate to which of the four forms, if any, the transformation might occur. 25.3 Calcium carbonate (CaCO3) exists in two polymorphic forms, calcite and aragonite. The standard state enthalpy of calcite is −1207.37 kJ/mol, while that of aragonite is −1207.74 kJ/mol. The entropies of aragonite and calcite under the same conditions are 88 J mol−1 K−1 and 91.7 J mol−1 K−1, respectively. What is the stable polymorph at 25°C and 1 atm? Is there a temperature above which the other polymorph would be the equi- librium phase? If so, what is that T? If not, why not? 25.4 You want to prepare a sample of mullite by reacting alumina and silica powders. If the activation energy is 210 kJ/mol and the reaction is 10% complete at 1400°C, how long will it take to convert 50% to mullite at 1400°C and at 1500%C? How will you determine that 50% has indeed been converted? 25.5 You place two perfect crystals of alumina and magnesia in contact with flat (0001) and (111) surfaces in contact. What orientation will you choose to produce the fast reaction when you heat these to 1400°C for 1 hour? You make the assumption that oxygen does not move during this heat treatment, but this cannot be strictly true. Explain. 25.6 You react two samples of alumina and magnesia at 1400°C for 1 hour. This time the MgO is a perfect single crystal but the alumina is 100-nm grain size polycrystalline material. Will the reaction proceed more quickly or more slowly on average? 25.7 Explain the geometry of the precipitates in Figure 25.5 and the defects they contain. 25.8 Consider Figure 25.13. What can you determine about the activation energies involved and the diffusion processes. 25.9 Consider Figure 25.21. How do you explain the experimental observations in the images in view of the phase diagram and other factors you know about these materials? 25.10 Consider Figure 25.24. What can you determine about the energies involved in this reaction? 462 ........................................................................................... S o l i d - S tat e P h a s e Tr a n s f o r m at i o n s a n d R e ac t i o n s  26 Processing Glass and Glass-Ceramics CHAPTER PREVIEW Glass has changed the world more than any other material. In Chapter 21 we described some of the different types of glass and their properties. In this chapter we will look at the main methods used to fabricate glass products. In terms of the volume of glass that is produced each year, glass processing could be said to be the most important processing method for ceramics. The largest segments of the market are  Flat glass for windows  Containers (including bottles, jars, and tableware) These products are formed using essentially two methods [one is recent (in glass terms) the other has its roots in antiquity]:  The float glass process  Blowing We will also look at some processes that are used to modify glass for specific uses such as the application of thin-film coatings for solar radiation control and tempering and laminating for safety glass. In the last section of this chapter we will examine how glass-ceramics are produced. This chapter does not cover the processing of some special glass products. For example, the processing of optical fibers is described in Chapter 32, but we introduce the important ideas here. Optical fibers must meet stringent quality requirements. We must understand these requirements to understand why the elaborate processing methods are necessary. This chapter covers three closely related topics:  Processing as dictated by applications  Shaping  Treating 26.1 THE MARKET FOR GLASS AND Hollow glass includes most of the container glass and table- GLASS PRODUCTS ware we use (i.e., consumer glassware). Table 26.1 lists examples of the applications for these product categories. More than half of the total worldwide ceramics market is glass products, accounting for over $50 billion/year. Figure 26.1 shows the distribution of glass sales. The 26.2 PROCESSING BULK GLASSES market for manufactured glass products emphasizes three main types of glass: Glass production starts with a mixture of raw materials, which for glass manufacture often contain a high propor-  Hollow glass (bottles, drinking glasses, lamp bulbs, tion of naturally occurring minerals (for example, sand glass containers) 35% and limestone). However, some industrial chemicals such  Flat glass (mirrors, windows) 30% as sodium carbonate (Na2CO3) and alumina (Al2O3) are  Fiberglass (includes glass fiber) 17% also used. The mixture containing the raw materials in the 2 6 . 2 P r o c e s s i n g B u l k G l a s s e s ................................................................................................................................... 463  processes occurring during melting, and fining (see Lighting 18% Section 26.3). Containers 12% We must also consider the possibility of oxidation and/or reduction of the glass, homogenization processes, and defect in the glass. Fiberglass 17% By far the greatest amount of flat glass is soda-lime Flat glass 32% silicate glass. You must be familiar with the terminology used in the glassmaking industry: soda is sodium oxide TV tubes, (Na2O) and lime is calcium oxide (CaO), so soda-lime sili- CRTs 9% cate glass consists mainly of Na2O, CaO, and SiO2. Glass manufacturers often use the common names for these oxides, which are not always the generally recognized sci- Consumer Other 1% entific name. If you are unsure of the composition of a glassware 5% Technical/laboratory 1% particular mineral then you need to look at its formula. FIGURE 26.1 Percent distribution of glass sales; total: $48,260 All manufacturers of flat glass use basically the same million. formula, but they never actually use the compounds Na2O or CaO. Values of the components are usually given in TABLE 26.1 Glass Product Types and Applications weight percent (wt%). Typical values are 72 wt% SiO2, 14 wt% Na2O, wt% CaO, 4 wt% MgO, and 1 wt% Al2O3. Glass product type Applications The molecular formula for a glass of this composition can Flat glass Automotive: cars and trucks be calculated as follows. Architectural: commercial buildings, storefronts Step 1: Divide the wt% of each component in the batch by Residential: windows, doors, sunrooms, its molecular weight. skylights Patterned glass: shower doors, privacy Molecular weight wt%/molecular glass Oxide wt (g) (g/mol) weight (mol) Ratio Blanks for microscopes and telescopes Containers/tableware Beverage SiO2 72 60.1 1.20 120 Liquor, beer, wine Na 2O 14 62.0 0.23 23 Food CaO 9 56.1 0.16 16 Pharmaceutical, drugs MgO 4 40.3 0.10 10 Glasses, plates, cups, bowls, serving dishes Al2O3 1 102.1 0.01 1 Fiberglass and glass Wool: insulation, filters fiber Textile: plastic or rubber tire reinforcements, Step 2: Divide each ratio by the smallest ratio in column fabrics, roof shingle and roll goods reinforcement 4. This gives the number in column 5. Optical communications Step 3: Write out the molecular formula for the glass. Specialty glass Artware, stained glass, lead and lead The molecular formula of our flat glass is then crystal, lighting Al2O3 ·10MgO·16CaO·23Na2O·120SiO2. TV picture tubes and flat-panel displays, ovenware and stovetop Ophthalmics, aviation, tubing, foamed To make the batch it would not be economical to use glass, marbles only synthesized or pure ingredients. For most glasses a large proportion of the batch is made up of naturally occurring minerals that appropriate amounts is FLAT GLASS RAW MATERIALS have been through a bene- known as the batch. The ficiation process. Table  Limestone, CaCO batch contains a mixture 3 26.3 (top) shows the typical  Silica sand, SiO of glass formers, modifi- 2 batch constituents used to  Soda ash, Na CO ers, and intermediates; the 2 3 make the Al2O3 ·10MgO·16  Alumina hydrate, Al O ·3H O amount of each component 2 3 2 C a O · 2 3N a 2 O ·12 0 Si O 2  Burnt dolomite, CaO·MgO depends on the application glass. To determine how of the final glass product. much of the raw material In Table 26.2 we link the we need to add to the batch to obtain the desired amount different ways of giving a batch composition and the of oxide in the final glass, we need to know the fraction sources of some of the raw materials. of that oxide in the raw material. For the principal raw materials used in glass making this fraction is given in Batch melting depends on the source of energy, the refrac- column 5 in Table 26.2. For example, during melting lime- tory used to contain the glass, details of the batch, stone will decompose as follows: 464 .................................................................................................................... P rocessing Glass and Glass- Ceramics  TABLE 26.2 Principal Raw Materials Used in Glassmaking Material Alternative name Theoretical formula Oxides Fraction Batch Purpose Alumina Calcined alumina Al2O3 Al2O3 1.000 1.000 Aluminum hyd. Hydrated alumina Al2O3 · 3H2O Al2O3 0.654 1.531 Aplite (typical — — Al2O3 0.240 4.167 Source of Al2O3 composition) — — Na 2 (K 2)O 0.100 — — — SiO2 0.600 — — — CaO 0.060 — Feldspar Microcline (composition K 2O · Al2O3 · 6SiO2 Al2O3 0.180 5.556 Source of Al2O3 of commercial spar) — K 2 (Na 2)O 0.130 — SiO2 0.680 — Nepheline syenite — — Al2O3 0.250 4.000 Source of Al2O3 (typical composition) — — Na 2 (K 2)O 0.150 — — — SiO2 0.600 — Calumite Calcium-aluminum 2CaO · MgO · 2SiO2 SiO2 0.380 silicate 2CaO · Al2O3 · SiO2 Al2O3 0.117 2(CaO · SiO2) CaO 0.400 MgO 0.080 Kyanite (90% — Al2O3 · SiO2 Al2O3 0.567 1.763 concentrate) — — SiO2 0.433 — Kaolin China clay Al2O3 · 2SiO2 · 2H2O Al2O3 0.395 2.57 — SiO2 0.465 — Cryolite Kryolith Na3AlF6 — — — Flux and opacifier in opal glasses Antimony oxide — Sb2O3 Sb2O3 1.000 1.000 Arsenious oxide White arsenic As2O5 As2O5 1.160 0.860 Fining and decolorizing Barium carbonate — BaCO3 BaO 0.777 1.288 Source of BaO Barium oxide Baryta BaO BaO 1.000 1.000 Barium sulfate Barytes BaSO4 BaO 0.657 1.523 Flux and fining Boric acid Boracic acid B2O3 · 3H2O B2O3 0.563 1.776 Source of B2O3 Borax — Na 2O · 2B2O3 · 10H2O B2O3 0.365 2.738 Source of B2O3 — Na 2O 0.163 6.135 Anhydrous borax (“Pyrobor”) Na2O · 2B2O3 B2O3 0.692 1.445 Source of B2O3 — — Na 2O 0.308 3.245 Lime, burnt Quick lime CaO CaO 1.000 1.000 Lime, hydrated Calcium hydrate CaO · H2O CaO 0.757 1.322 Limestone Calcium carbonate CaCO3 CaO 0.560 1.786 Source of CaO Calcium carbonate Whiting CaCO3 CaO 0.560 1.786 Source of CaO Lime, dolomitic Burnt dolomite CaO · MgO CaO 0.582 1.720 Source of CaO — — MgO 0.418 2.390 and MgO Dolomite Raw limestone CaO · MgO · 2CO2 CaO 0.304 3.290 Source of CaO (dolomitic) MgO 0.218 4.580 and MgO Lime, hydrated, dolomitic Finishing lime CaO · MgO · 2H2O CaO 0.423 2.363 Source of CaO — MgO 0.304 3.290 and MgO Litharge Lead oxide, yellow PbO PbO 1.000 1.000 Red lead Minium Pb3O4 PbO 0.977 1.024 Source of PbO Bone ash Calcium 3CaO · 2P2O5 + xCaCO2 CaO 0.372 2.700 phosphate P2O 5 0.628 1.592 Iron oxide, red Rouge Fe2O3 Fe2O3 1.000 1.000 Color Potassium hydroxide Caustic potash KOH K 2O 0.838 1.194 Source of K 2O Potassium nitrate Saltpeter KNO3 K 2O 0.465 2.151 Source of K 2O Potassium carbonate. Calcined potash K 2CO3 K 2O 0.681 1.469 Source of K 2O Glassmaker’s potash Potassium carbonate, K 2CO3 · −32 H2O K 2O 0.570 1.754 Source of K 2O hydrated Sand Glass sand, quartz SiO2 SiO2 1.000 1.000 Soda ash Sodium carbonate coml. Na 2CO3 Na 2O 0.585 1.709 Source of Na 2O Sodium nitrate Saltpeter chili NaNO2 Na 2O 0.365 2.741 Oxidizing and fining Salt cake Sodium sulfate Na 2SO4 Na 2O 0.437 2.290 Oxidizing and fining Zinc oxide — ZnO ZnO 1.000 1.000 2 6 . 2 P r o c e s s i n g B u l k G l a s s e s ................................................................................................................................... 465  TABLE 26.3 Batch Composition and Sources in the United States Oxides Fraction Weight of oxide Weight of raw material Raw material supplied of oxide required (g) in batch (g) Limestone CaO 0.560 90 61 Silica sand SiO2 1.000 720 720 Soda ash Na 2O 0.585 140 239 Alumina hydrate Al2O3 0.654 10 15 Burnt dolomite CaO 0.582 90 96 MgO 0.418 40 Source U.S.A. location Silica sand Bank sand Jersey shore Sandstone Allegheny mountains Soda ash Trona deposits Wyoming Limestone Dolomite All over, e.g., Alabama Feldspars In pegmatites North Carolina B2O3 Borax California CaCO3 (s) → CaO (s) + CO2 (g) (26.1) are 100 m long and 13 m wide.) The furnace is constructed of alumina/zirconia refractories that can withstand the The fraction of CaO (molecular weight: 56.1 g/mol) in high temperature and corrosive environment of the melt CaCO3 (molecular weight: 100.1 g/mol) is 0.560, or 56%. (see Chapter 9). The life of a tank furnace is about 8 Hence, for each kilogram of limestone added to the batch years. the melt will contain only 0.56 kg of CaO. So using the raw With reference to Figure 26.3: The batch is loaded into materials listed above, and by bearing in mind the fraction the hopper (1). In industry, the batch-loading compartment of each oxide provided by each mineral, we can determine is referred to as the “doghouse.” In region (3) the batch the batch composition for a 1 kg melt of flat glass. These begins to melt. The surface temperature of the melt peaks are the numbers given in Table 26.3 (top). Note that the in region (4). During the melting process it is important lime comes from both burnt dolomite and limestone. A to control the homogeneity of the mixture and the oxida- batch weighing 2 t can be measured to an accuracy of tion state of the components. Region (5), the throat, divides 0.1%. the furnace into two parts—the melting end and the con- Table 26.3 (bottom) shows where we might actually ditioning, or working, region to the right. In the working have to go to obtain these raw materials. [If we are making region the melt is cooled down to about 1300°C and the bottles and jars the batch will likely contain cullet, recy- glass viscosity increases. The glass travels through narrow cled glass; see Section 37.7.] tunnels called the forehearth (7), where the temperature After the batch has been thoroughly mixed, it is melted is further lowered to 1000–1100°C, and on to the forming at high temperature to form a homogeneous liquid melt. For small-scale melting of glass the batch will be placed in a crucible. For glass-melting experiments in the labora- tory it is common to use Pt, or a Pt alloy such as Pt-5% Au or Pt-20% Rh crucibles. These crucibles are very expensive, but they can with- stand high temperatures, they do not contaminate the glass melt, and they can be easily cleaned and reused. Other crucible materials, usually used for larger batch sizes, include silica, alumina, and mullite. Large-scale industrial production of glass is carried out in continuous furnaces called tanks. Glass-melting tanks are the second largest industrial furnaces, the largest being the blast furnaces used in making iron and steel. Figure 26.2 shows the inside of a glass-melting tank and Figure 26.3 shows a schematic of a glass-melting tank for producing glass containers. The tanks are typically 10– 40 m long, 3–6 m wide, and 1–1.5 m deep and contain over 2 kt of molten glass. (The largest glass-melting furnaces FIGURE 26.2 Inside a typical glass melting tank. 466 .................................................................................................................... P rocessing Glass and Glass- Ceramics  1700°C Side View 1600°C Temperature distribution 1500°C 1 8 2 9 9 9 9 7 3 4 Tank 5 6 Feeder for automated processing Top View Regenerative chambers 7 Manual processing 9 9 9 9 7 Tank furnace 3 4 5 6 7 7 9 9 9 9 Regenerative 7 chambers FIGURE 26.3 Schematics of a glass melting tank for producing containers. machines. Depending upon the requirements of the working point is 104 dPa-s (see Chapter 21). The regenera- forming machines, the glass may be delivered in the form tive chambers, region (9), are used to preheat the fuel of a continuous stream (as shown in Figure 26.4) or in gases and air to increase the combustion efficiency of the discrete amounts, called gobs. The viscosity of glass at the furnace. 26.3 BUBBLES The temperature required to form a glass melt varies with the composition of the batch. Typically melting tempera- tures are in the range 1300–1600°C. At this stage of the process the melt may contain many gas bubbles, mainly CO2 and SO2, from the dissociation of carbonates and sulfates. Bubbles also come from reactions between the glass melt and the refractories. Gas bubbles (which are known as seeds or blisters if the size is >0.5 mm) are usually undesirable in the final product because they affect its appearance. Bubbles are eliminated during melting by a process known as fining. Fining can be achieved by increasing the temperature of the molten glass by about 150°C to reduce its viscosity. From Stokes’ law (or by comparing the rise of bubbles in FIGURE 26.4 Pouring molten glass into a mold. Cola versus liquid soap) we know that the drift velocity 2 6 . 3 B u b b l e s ................................................................................................................................................................... 467   Rolling  Drawing  The float process The float process is so important to the glass industry that we will discuss it separately in the next section. In this section we will discuss the formation of flat glass by rolling and drawing. Figure 26.6 shows an example of a method for producing flat glass by rolling. The molten glass flows from the tank furnace over a refractory lip and between a set of water-cooled rollers where it solidifies into a continuous ribbon. The glass ribbon is transported over rollers into a tunnel-like annealing furnace (called a lehr in the glassmaking industry). Inside the lehr, the glass is first reheated to between 600 and 800°C. On the way through the lehr the temperature decreases slowly in a carefully controlled manner to minimize the develop- ment of internal stresses within the glass. The glass thickness is controlled by a combination of factors: FIGURE 26.5 Example of a bubble deliberately blown in glass.  The rotational speed of the rollers  Their spacing  The glass pull rate of the bubbles toward the DEFECTS IN GLASS MELTS Typical pull rates are surface of the melt is Stones: opaque particles of rock or batch material 0.5–5 m/min producing increased as the viscosity embedded in the glass sheets 3–15 mm thick and of the melt is decreased. Cords: thin string of inhomogeneity up to 3.6 m wide. Fining is also tradition- Seed or blister: elongated bubble (∼0.5 mm) A drawing process can ally achieved by adding also be used to produce flat fining agents, such as glass. A solid metal plate Na2SO4 or NaCl, to the melt at the end of the melting is dipped into a bath of molten glass and then slowly process. The fining agent decomposes as shown in Eq. withdrawn from the melt. This process would present no 26.2 to produce a large quantity of gas bubbles, which problems if we were interested in producing a glass rod coalesce with existing bubbles, increasing their volume (Figure 26.7). Producing a planar sheet is problematic and hence taking them to the surface faster. because the sheet would neck down to a narrow ribbon. This difficulty is overcome by cooling the sheet as it is Na2SO4 (s) → Na2O (l) + SO2 (g) + 1/2O2 (g) (26.2) drawn; it is passed between two coolers as shown in Figure Arsenic oxide, As2O3, is another fining agent (giving a mixed-valence effect), but it is not so widely used today because it is toxic. The reaction involving arsenic oxide is a little more complicated than that shown for Na2SO4, but α the effect is the same. Fining will occur toward the end of region (4) in Figure 26.3. Modern systems will also use Furnace mechanical bubblers. Inclined rollers In some studio glass and tableware, bubbles are intro- duced intentionally as illustrated in Figure 26.5. Glass 26.4 FLAT GLASS Flat glass is not necessarily flat but is generally flatish! Casting Inclined table Historically, glass windows were not made in the way they Furnace rollers are now. There are three basic methods for producing flat glass: FIGURE 26.6 Continuous casting of flat glass. 468 .................................................................................................................... P rocessing Glass and Glass- Ceramics  Cooled glass Cooled Cooled Cooler glass Cooler glass Pulling meniscus Bath Bath of molten glass Débiteuse (A) (B) (C) FIGURE 26.7 Principle of drawing from molten glass: (a) a circular rod; (b) problem of pulling a planar sheet; (c) use of a débiteuse and cooling to allow the formation of a sheet of constant width. 26.7c. These coolers solidify the glass and produce a sheet In the Libbey–Owens or Colburn–Libbey–Owens of fixed width. (We will see a similar process used in process the drawn glass sheet is bent through 90°, ∼1 m crystal growth in Section 29.6.) above the surface of the bath, on a polished chrome-nickel There are several variations on the drawing process alloy roll; there is no debiteuse. The glass then travels into and these are illustrated schematically in Figure 26.8, a horizontal lehr for annealing. which gives a different view of Figure 26.7. By the mid 1900s these three processes were In the Fourcault process the glass is drawn through a responsible for the world’s entire production of flat glass, slot in a clay block (called the debiteuse or draw bar). The with 72% being made by the Fourcault process, 20% glass sheet is pulled upward through a system of steel by the Colburn–Libbey–Owens process, and 8% by the rollers about 7 m high. The sheet at the mouth of the deb- Pittsburgh process. These processes have now been iteuse is cooled at its edges in order to retain the width. replaced almost entirely by the float process. As the glass travels upward it is annealed in a vertical lehr. Plate glass is flat glass that has been ground and pol- After annealing and cooling the glass can then be cut into ished to produce two perfectly plane and parallel faces sections. with a high quality optical finish. The surface of a flat In the Pittsburgh process, the draw bar is completely glass sheet is flattened by grinding it between two cast- submerged where it lowers the temperature of the glass iron wheels with sand abrasive and water lubricant. As the below the meniscus. This modification allows increased grinding progresses, the particle size of the abrasive is drawing rates. decreased producing a very fine satin surface. The opera- tion is completed by polishing the sheet with a suspension (A) (B) of iron oxide on felt pads; this abrasive is known as rouge because of its color (see Chapter 36). The processing of Fourcoult Pittsburgh plate glass can be entirely mechanized with continuous simultaneous grinding and polishing on both faces. However, the float-glass process has almost entirely ended this older method of manufacturing plate glass. The quality of float-glass may not be quite as high as that of plate glass, but the cost is considerably lower because of the elimination of the mechanical grinding and polishing operations. 26.5 FLOAT-GLASS The float process was developed in 1959 by Pilkington in (C) the UK and revolutionized the flat-glass industry. It has D been hailed as one of the major inventions on the twentieth century. Worldwide, there are only ∼170 float-glass plants, Libbey-Owens but these have a combined output of 3000 miles of flat glass, 4–8 feet wide, each day. Annually these plants produce the equivalent of a ribbon of glass over one FIGURE 26.8 Drawing processes for window glass. (a) Fourcault, million miles long. Over 90% of the world’s window glass (b) Pittsburgh, and (c) Libbey-Ownes. is produced using the float process. 2 6 . 5 F l oat - G l a s s ........................................................................................................................................................... 469  Heating zone Flame polish zone Cooling zone Molten glass Burners Annealing lehr Cutting Melting tank Rollers Metal bath FIGURE 26.9 Schematic diagram of the float glass process. A schematic of the float process is shown in Figure and the maintenance of constant surface tension, which 26.9. Molten glass is fed from the furnace between two controls the thickness of the sheet. The atmosphere is rollers onto a bath containing molten tin at about 1000°C approximately 90% N and 10% H. The hydrogen ensures (the melting temperature of tin is 232°C). The tin bath is that there is an oxygen-free environment: molten tin is 4–8 m wide and up to 60 m long. Equilibrium between easily oxidized. The glass can, itself, be affected adversely gravitational forces and surface tension produces a sheet by the presence of oxygen, which can make the surface of uniform thickness. The equilibrium thickness, he, can appear hazy. Purity and reliability are therefore critical be calculated using an equation derived by Langmuir: factors in float-glass manufacture. Approximately 5 m3 of hydrogen is required for each ton of glass produced. ⎧ ( γ + γ G t + γ tv ) 2ρt ⎫ 1/ 2 he = ⎨ Gv ⎬ (26.3) ⎩ gρG (ρt − ρG ) ⎭ 26.6 GLASSBLOWING There are three interfacial energy (γ) terms between the different phases glass (G), air (v), and tin (t); g is The classic glassblowing pipes are made from iron tubes the acceleration due to gravity, which has a value of about 100–150 cm in length with an opening about 1 cm in 9.806 m/s2, ρG and ρt are the density of the glass and tin, diameter. At one end the tube had a mouthpiece and at the respectively. other end it has a button- In practice, it is possi- like extension. The glass- ble to produce glass thick- GLASS THICKNESS maker gathers a gob of nesses between about 2 mm It is instructive to estimate the value of he. A reasonable molten glass on one end and 20 mm using the float value for the glass/Sn interfacial energy is ∼1 J/m2, the then blows through the process, depending upon surface free energy of molten tin is 0.68 J/m2, the density mouthpiece to form a the glass viscosity and the of Sn is 7.5 g/cm3, the surface free energy of a molten hollow shape as demon- drawing speed. At the soda-lime-silicate glass is 0.35 J/m2, and the density for strated in Figure 26.10. exit, the temperature of a silicate glass is 2.5 g/cm3, hence he is ∼9 mm. This This process was important the glass is decreased to calculated value is actually slightly higher than the historically because by ∼600°C, at which point actual equilibrium thickness, ∼7 mm. Remember that we blowing glass with a pipe it the tin is still fluid, but are using only an estimate for the energy of the glass/Sn was possible not only to the glass can be removed interface. produce simple round in a “rigid” condition. The shapes but also other thin- glass ribbon leaves the bath and enters the lehr for anneal- walled objects. By blowing the glass into a wooden mold it ing. The glass leaves the lehr at ∼200°C, is cooled to room became possible to produce items with a standard reproduc- temperature, and is cut to size. The main advantage of the ible shape. The glassblowing pipe was also the first step in float process is the production of planar glass sheets with making flat glass. The glass was blown into a large cylindri- a high optical quality—the planarity approaches that of cal body, cut along its length, and “ironed” flat while it was plate glass without the need for polishing. Moreover, the still hot and soft. This is known as muffle glass and is still output rate is 5–10 times higher than the drawing rate for used today to make traditional stained glass. window glass. About 25 t of finished glass can be pro- Today the glassworker’s blowpipe is very similar to the duced per hour by the float process. original design and works in the same way. The original On the negative side, the equipment requires careful blowing technique is used now mainly for specialty glass control of the atmosphere above the bath, which must be applications such as glass ornaments and studio-art neutral or slightly reducing to avoid oxidation of the bath glass. 470 .................................................................................................................... P rocessing Glass and Glass- Ceramics  To produce hollow glassware for bottles and jars the original blowing technique has been mechanized. The process starts by forming a blank or preform (called a parison) by blowing into or pressing a gob of glass as illustrated in Figure 26.11. (The hole into the furnace is called the parison hole; traditionally, the glassblower would gather a glob, or gob, of glass on the blowpipe and roll it to make the parison.) After the initial shaping process, the parison is blown by compressed air to the final shape. With today’s automated techniques, from parison to final product can take less than 10 seconds.  The blow-and-blow process is used to make narrow- neck containers (Figure 26.11a).  The press-and-blow process is used to make wide- mouth jars (Figure 26.11b). Figure 26.12 shows the ribbon machine developed in 1926 by Corning for high-speed production of light bulbs. In this process a stream of molten glass is made into a ribbon by passing it through a pair of rollers. The ribbon FIGURE 26.10 Demonstration of blowing glass into a mold. Note the worker’s bench, the annealing burners, and the box of frit. (A) (B) FIGURE 26.11 Automatic fabrication of hollow ware: (a) formation of the blank by blowing followed by blowing in a mold (blow and blow); (b) formation of the blank by pressing followed by blowing (press and blow). Blow heads Glass ribbon Blow box Blow box Stripper Water-cooled Crack-off rollers bar Blow heads Rotating Glass paste molds bulbs Ware Rotating conveyor Mold-closing cam Mold-opening cam paste molds FIGURE 26.12 The Corning ribbon machine for glass lamp bulbs. 2 6 . 6 G l a s s b l o w i n g ........................................................................................................................................................ 471 passes under a series of blowheads that are attached to a Absorption glass Normal glass rotating turret (the blowhead turret). Air is puffed into the Incide nt glass and the glass begins to take the form of a blown light Direc shell. The glass shell is then enveloped by a mold mounted transmt Long wave is sion on a rotating turret below the blowhead turret. The shells radiation & are blown to their final form while in the mold. The fin- convection Absorption ished shells are cracked away from the ribbon, collected, and carried through the annealer. More than 50 light bulb shells (in single molds) can be made per second in one Secondary emission machine! Gold coating Incide 26.7 COATING GLASS nt light Direc ion transmt sion lect is Coated glass also has a long history. Stained glass used in Ref church windows has long used flashed glass, which is clear Absorption glass with a coating of a colored glass. Today we use many other types of coatings, but flashed glass is still used in Secondary the glass studio (see Section 26.14). emission Normal window glass transmits between 75% and Long wave radiation & 90% of the incident radiation. We can apply thin coatings convection to the surface to alter the radiation and heat-transmission Interference coatings characteristics. In architectural applications, coatings on Incide nt glass are used to reduce the amount of energy needed to light Direc heat buildings in the winter and cool them in the summer. tion transmt lec ission One way to do this is by allowing the transmission Ref of visible light while reducing the transmission of infrared (IR) radiation (heat). Such glass would reduce the amount of energy required to air condition a room in the summer. One conventional way to reduce the transmission of heat is to add a component to the glass batch that strongly absorbs radiation in the IR region. When FeO is added to FIGURE 26.13 Illustration of approaches for solar protective double glazing with absorbing and reflecting panes. the glass formulation, the product strongly absorbs radia- tion in the 0.7–2.5 μm range. Since the absorption sharply increases above 0.6 μm, the transmitted visible light does have a noticeably green tint. But this can be corrected to tivity. The metal layer is deposited using physical vapor a certain extent by adding other components (commonly deposition (PVD) techniques such as evaporation and Se and Co). A 6-mm-thick glass window that contains sputtering (see Chapter 28). Metal coatings can also be FeO may absorb ∼50% of the total incident radiation but applied using dipping and spraying techniques, followed only ∼25% of the radiation in the visible part of the elec- by firing to densify the coating (see Chapter 27). tromagnetic spectrum. Single-layer and multilayer coatings of oxides are also Thin films are also used to control the light- used to enhance reflectivity in the near IR. These coatings transmission characteristics of window glass by reflecting work because of optical interference effects and usually a large amount of IR radiation. have a thickness about one-quarter of the wavelength of Such films allow a higher retention of heat in a room the radiation such that the primary wave reflected off the during the winter, thus reducing the energy costs associ- first interface is 180° out of phase with the secondary wave ated with heating. Normal flat glass can be coated with reflected from the second interface. The result is destruc- metallic or nonmetallic layers to maintain a high degree tive interference of the two waves. Thin films of TiO2, of visible light transmis- Ti3N4, CrNx, and Zn2SnO4 sion combined with a con- are all used commercially siderable amount of heat MULTILAYER COATING for this application. reflection (40–60%). Thin An example of the effectiveness of a multilayer coating, Figure 26.13 shows a (10–20 nm) metal films of which works on the interference principle, is the Sb2S3/ schematic diagram sum- Cu, Ag, and Au are all CaF2 superlattice. For 11 alternating layers of Sb2S3 marizing the principles used commercially; each (n = 2.70) and CaF2 (n = 1.28), the reflectance is 0.9999 behind solar radiation gives a very high reflec- at λ = 1 μm. control panels. For solar- 472 .................................................................................................................... P rocessing Glass and Glass- Ceramics protective double glazing, a coated glass pane is combined that used to make crackle glass: the internal stress at the with an uncoated pane. surface is different from that in the bulk. Radiation can also be modified using electrochromism. The other form of safety glass is laminated glass, Electrochromism is the production of color by applying which consists of two or more glass sheets (usually float an electrical field. Electrochromic compounds such as glass) joined with a layer of an elastomeric polymer such WO3 are coated on the glass using a variety of thin film as poly (vinyl butyral) (PVB). The glass layers are bonded techniques. The point defect reaction is reversible. to the polymer by a combination of pressure and heating. When laminated glass is broken, the broken pieces of glass are stuck to the polymer and the broken sheet remains WO3 + xM + + xe− = M xWO3 (26.4) transparent. Car windshields are laminated glass in which the two bonded sheets are both tempered glass. If a stone When a direct current (dc) voltage is applied, the optical breaks the windshield when the car is moving, the polymer absorption characteristics of the compound change. The sheet holds the fragments of glass together so that they do gain/loss of color occurs by the inclusion/elimination of not cause injury to the occupants of the car. The side and the M + ion. In this case, the M + ion can be H + , Li + , Na + , rear windows of an automobile are routinely made from or Ag + . The absorption characteristics of electrochromic tempered glass. materials can thus be tailored for specific applications The front and rear windows of an automobile are often simply by adjusting the applied voltage. curved. The flat glass is shaped before the tempering process because the tempered condition would disappear at the bending temperature. One of the advantages of laminated glass over tempered glass is that laminated 26.8 SAFETY GLASS glass can be processed further; for example, it can be cut and drilled. Bulletproof glass is thick laminated glass Flat glass often breaks due to impact or to the application (25–60 mm thick) consisting of at least four layers of glass of a relatively low applied pressure. At most temperatures, laminated with an elastomeric polymer. the failure occurs in a brittle manner and results in the production of a number of sharp fragments, which, of course, can cause serious injury. Special treatment of the glass can make it less susceptible to breaking and can thus 26.9 FOAM GLASS reduce the chance of injury. Hence the United States and many other countries require the use of safety glass in Because we do not usually want glass to contain large buildings and vehicles. There are two forms of safety numbers of bubbles, we reduce the number of bubbles glass: in the glass melt using the fining process. The opposite approach is used to make foam glass: additional gases or  Tempered gas-bearing materials are added to the melt producing a  Laminated large quantity of bubbles. One of the major applications of foam glass is in the manufacture of insulating panels for buildings. Insulating Tempered glass (or toughened glass as it is also often panels made from foam glass can be light, rigid, and good called) is made by quickly heating flat glass thermal insulators. As usual for porous materials, the to about 150°C above Tg. (Remember: the viscosity at the thermal property is due to Tg is ∼10 dPa·s.) For a 13 the low heat conductivity of soda-lime silicate glass CRACKLE GLASS the bubbles (i.e., pores). 150 + Tg is 525–545°C. The Crackle glass has been produced for its artistic appear- glass is then blasted with ance for over 150 years (perhaps since the sixteenth cold air. The outside of the  Foam glass is the porous century in Venice). The glass is heated to ∼1000°C and glass cools much more ceramic of the glass then plunged into water causing cracks to form across quickly than the inside. world. the surface; if reheated and blown further the cracks Hence the inside is still  Bubbles may be inten- heal on the interior; a similar effect is produced in contracting after the tionally included in art glazes. surface has already solidi- glass. fied. The result is that the outer surface layer is subject to compression and the inside layer is subject to tension. This tempering process changes 26.10 SEALING GLASS the behavior of the glass when it breaks. For example, when a sheet of tempered glass breaks, the fragments are Special glasses have been developed that are used as the small and almost regularly shaped with no sharp edges. “glue” usually between another glass and a metal. The The principle used in the tempering process is the same as main challenge is engineering α while controlling 2 6 .10 S e a l i n g G l a s s ..................................................................................................................................................... 473 the chemistry and keeping the sealing temperature 26.12 PHOTOCHROMIC GLASS reasonable. PHOTOSENSITIVE AND PHOTOCHROMIC Photosensitive glass is the Borosilicate (alkaline glass analog of photo- Photosensitive: the glass is sensitive to light. earth/alumina) glass is graphic film where Au or Photochromic: the color is changed by exposure to used to seal glass to W Ag atoms (as halide parti- light. (lighting applications). cles) are affected by the Borosilicate (Na) glass is action of light. Such glass used to seal glass to Mo. is used in printing and image reproduction. Heat treating Borosilicate (K) glass, with a high concentration of B after exposure to light can cause a permanent change in the (20% B2O3), is used to bond to Kovar (Westinghouse’s glass. Photochromic glass (discovered at Corning in the trade name for the Fe–Ni–Co magnetic alloy that has 1960s), darkens when exposed to light but then returns to α close to that of the glass). its original clear state when the light is removed; hence it Pb glass is used if electrical insulation of a joint is is used in sunglasses or other ophthalmic lenses. The light critical. affects small (∼5 nm or a little larger) AgCl xBr1−x crystals in the glass. To manufacture photochromic glass the glass must be heated to over 1400°C, shaped, and then annealed 26.11 ENAMEL again at 550–700°C to allow the small halide crystals to form in the initially homogeneous glass. Large flat glasses Ceramic enamel compositions are used for a wide variety are not generally affordable, but the new approach is to use of applications, including decorative coatings for glass- sol-gel processing (Chapter 22) to form a photochromic ware and china. In industry they are used in coating baths, layer on conventional preformed glass sheets. stovetops, etc. They are used whenever a metal requires a The principle is that the near-UV radiation generates coating that is more durable than paint. It is also used to electron-hole pairs in the halide particles. The electrons form colored borders around glass sheets used as automo- are trapped by the interstitial Ag ions producing Ag col- tive windshields. The reason for the colored borders is to loids on the surface of the halide particle. The activation enhance the appearance and to decrease the degradation energy for this process is only 0.06 eV so the Ag ion moves of the underlying adhesives by ultraviolet (UV) radiation. easily in the halide; in addition, a small amount of Cu The enamel compositions consist of a glass frit (a pow- increases the effect by at least an order of magnitude. This dered glass), a colorant, and an organic vehicle. The is the same process used in photography and is explained mixture is applied to the required part and then fired to by the same Gurney–Mott theory. The metal particles burn off the organic vehicle and to fuse the enamel to the formed in the process are 1–5 nm in size, but because the surface of the substrate. halide must be >5 nm to show the effect the second anneal- In the art world, enameling is carried out using small ing T is critical. furnaces and grams of powdered glass; in industry, square meters of surface can be enameled uniformly. The prin- ciple is the same, only the scale differs. A large piece like 26.13 CERAMMING: CHANGING GLASS a cast-iron bath would be shot-blasted to clean it, coated TO GLASS-CERAMICS with a ground coat that will bond to the Fe, dried, and heated to nearly 1000°C. It is then sprinkled with dry Worldwide sales of glass-ceramic products exceed $500 enamel frit while still hot and brought back to tempera- million a year. The highest volume is in cookware and ture. Five such coatings of enamel would be routine. tableware consumer items (such as plates and bowls) and The composition of the enamel must be chosen so that domestic ovens (stovetops and stove windows). In this it is in compression after cooling. The composition section we will look at how these commercially important would be modified on curved regions to maintain this ceramics are processed. compression. Glass-ceramics are formed by controlled crystalliza- Color is produced in ways similar to other glass. (We tion of a glass. They consist of a high density (maybe discussed color in glass in Section 21.8.) As recently as >95 vol%) of small crystals in a glass matrix. The impor- 1999, the French Consumer Safety Committee considered tant feature of the processing of glass-ceramics is that the the safety of the use of UO2 dye to make enamels for the crystallization must be controlled. As usual, crystalliza- preparation of jewelry and enameled tiles. Old yellow tion occurs in two stages: enamels contained up to 9% UO2 and frits using nonde- pleted U are certainly more “radioactive” than those of  First the crystals are nucleated. today. The committee noted that having 50% Pb in the frit  Then the crystals grow. might help absorb the radiation, but this increased the tox- icity of the frit powder! Safety in enameling is therefore The rate at which these two processes occur is a function always a concern because the technique uses powders. of temperature. We can control the nucleation process by 474 .................................................................................................................... P rocessing Glass and Glass- Ceramics adding a nucleating agent ION EXCHANGE β-quartz. The β-quartz (typically either TiO2 or Glass can be strengthened by ion exchange in which crystals are <0.1 μm in ZrO2) to the glass batch. small ions in the surface layer are replaced by larger diameter. Crystal sizes Initially the glass batch ions, which put the surface into compression. below the wavelength of is heated to form a homoge- + + Step 1: Rapid exchange of Na or K with H or H3O+ + visible light (λ = 0.7– neous melt. The shape from solution: 0.4 μm), a good match in of the desired object is refractive index between formed from the glass at Si–O–Na + + H + + OH− → Si–OH + + Na + (solution) + OH− the glass and the crystal the working point by the phase, coupled with a low usual processes such as This step is usually controlled by diffusion and exhibits birefringence result in high pressing, blowing, rolling, −1/2 t dependence. transparency. Table 26.4 or casting. Remember, the Step 2: Loss of soluble silica in the form of Si(OH) 4, lists the compositions and viscosity of the glass is resulting from breaking of Si–O–Si bonds and the applications of some com- ∼104 dPa-s at the working formation of Si–OH (silanols) at the glass solution mercial transparent LAS point (like honey). After interface: glass-ceramics based on annealing to eliminate β-quartz. internal stresses, the glass Si–O–Si + H2O → Si–OH + OH–Si object then undergoes a Application 1: Machin- thermal treatment that con- This stage is usually reaction controlled and exhibits a able glass-ceramics verts it into a glass-ceramic. 1.0 t dependence. are derived from the The first part of the heat Step 3: Condensation and repolymerization of an K 2 O – M g O – A l 2O 3– treatment is nucleation. The SiO2-rich layer on the surface depleted of alkalis and SiO 2 system contain- optimum nucleation tem- alkaline-earth cations. ing some fluorine. In ® perature generally corre- 2+ 3− Step 4: Migration of Ca and PO4 groups to the Macor the crystalline sponds to a glass viscosity surface through the SiO2-rich layer forming a CaO– phase is potassium flu- 11 12 of 10 –10 dPa·s. During P2O5-rich film on top of the SiO2-rich layer, followed orophlogopite [KMg3 this step, which may last for by growth of the amorphous CaO–P2O5-rich film by (AlSi3O10F2)]. Phlogo- several hours, an extremely incorporation of soluble calcium and phosphates from pite is a mica mineral high density (1012–1015/cm3) solution. and the plate-like of nuclei forms. Following Step 5: Crystallization of the amorphous CaO–P2O5 mica crystals are ran- nucleation, T is increased − 2− − film by incorporation of OH , CO3 , or F anions from domly oriented in the to allow growth to occur. solution to form a mixed hydroxyl, carbonate, fluorapa- glass phase as shown in The crystal-growth step, tite layer. Figure 18.23. Macor® like nucleation, may take can be machined to several hours. The optimum precise tolerances temperature for crystal growth is selected to allow for the (±0.01 mm) and into intricate shapes using conventional maximum development of the crystalline phase without steel tools: they can be drilled, cut, or turned on a lathe. viscous deformation of the object. Figure 26.14 shows the complete processing cycle for a glass-ceramic. The glass-ceramic process uses the same rapid form- ing techniques employed in glassworking, permitting the economical production of objects with complex shapes or thin walls that are difficult or impossible to produce with other, more traditional, ceramic-forming T(°C) Melting η techniques. 1600 Working (dPa.s) The most important and useful glass-ceramic system Shaping point is the Li2O–Al2O3 –SiO2 (LAS) family that was first devel- 1250 ~104 oped at the Corning Company by Stookey. One commer- Growth cial LAS glass-ceramic is Pyroceram®, which has 900 β-spodumene (LiAl[Si2O6]; α = ∼10−6 /°C) as the major Nucleation ~107.6 crystalline phase. The low α, together with excellent high temperature stability and insensitivity to thermal 800 Softening shock, means that these materials find applications as point cookware, benchtops, hot-plate tops, ball bearings, and 650 Tg ~1013.4 matrices for fiber-reinforced composites. If the crystallization temperature is kept ≤900°C the t crystalline phase that is formed in LAS glass-ceramics is FIGURE 26.14 Processing cycle for a glass-ceramic. 2 6 .13 C e r a m m i n g : C h a n g i n g G l a s s t o G l a s s - C e r a m i c s ..................................................................................... 475  TABLE 26.4 Base Compositions and Applications of Transparent Glass-Ceramics Based on Quartz Solid Solutions Composition, wt% Commercial Material SiO2 Al2O3 MgO Na2O K2O ZnO Fe2O3 Li2O BaO P2 O 5 F TiO2 ZrO2 As2O3 application Vision 68.8 19.2 1.8 0.2 0.1 1.0 0.1 2.7 0.8 — — 2.7 1.8 0.8 Transparent cookware Zerodur 55.5 25.3 1.0 0.5 — 1.4 0.03 3.7 — 7.9 — 2.3 1.9 0.5 Telescope mirrors Ceran 63.4 22.7 u 0.7 u 1.3 u 3.3 2.2 u u 2.7 1.5 u Black infrared transmission cooktop Narumi 65.1 22.6 0.5 0.6 0.3 — 0.03 4.2 — 1.2 0.1 2.0 2.3 1.1 Rangetops; stove windows u = unknown Application 2: Another commercial fluoromica glass- 4. Reexpose the glass to UV (no mask) and anneal; all ceramic called Dicor® has been developed for dental is then polycrystalline, e.g., with 0.001% Au, 0.001– restorations. Dicor has better chemical durability and 0.03% AgCl, or 0.001–1.00% Cu2O. translucency than Macor. It is based on the tetrasilicic Before leaving the topic we should mention that this is mica, KMg2.5Si4O10F2, which forms fine-grained not the only way to prepare glass-ceramics. Another group (∼1 μm) anisotropic flakes. Dicor dental restorations of these materials used for dentistry go by the label In- are very similar to natural teeth both in hardness and Ceram®. The material is prepared as a porous crystalline appearance. They are easy to cast using conventional ceramic (alumina, spinel, and zirconia have all been used) dental laboratory methods and offer significant advan- and then infiltrated with an La-rich glass. The resulting tages over traditional metal–ceramic systems. glass-infiltrated ceramic can be quite translucent, can be Application 3: Calcium phosphate, Ca3 (PO4) 2, glasses can colored to match other teeth, and is mechanically tough be made into glass-ceramics to form a material resem- (for a ceramic). It can be coated with porcelains for bling the mineral part of bone. Since bone is porous, improved appearance. the first step is to produce a foam glass. This is achieved by decomposing carbonate in the glass melt. The foam glass simultaneously undergoes a controlled crystalli- 26.14 GLASS FOR ART AND SCULPTURE zation, transforming it into a porous glass-ceramic. The dimensions of the interconnections between the Today, the glass art world is very active with more abstract pores must be sufficient to allow the ingrowth of living pieces by Chihuly and others being hung in many public bone tissue, which ensures a permanent joint with the buildings (e.g., the Victoria and Albert Museum in London; surface of the prosthesis. Figure 26.16). Exhibitions travel round the United States and the world. The field is actually much wider than you In principle, any glass can be converted to a glass- might imagine. ceramic by finding a suitable nucleation agent and the The glass harp produces the “sound of the universe” appropriate heat treatment. In practice, a number of tech- according to Goethe. The musician Gluck gave an entire nical factors (among which is the production of the base concert using the glass harp in London in 1746. Sound is glass) limit the choice. We can use the phenomenon of photosensitivity to Mask make a machinable glass! For example, we could use CorningWare (Li2O·Al2O3 ·SiO2) as the starting material Au+ and then add <1 wt% Cu, Ag, or Au. The idea behind the technique is similar to the photochromic glass, but we UV Au° then leach out the Li2SiO3 crystals to leave a high density of small voids in the glass. Au+ 1. Irradiate the glass with UV (Figure 26.15). 2. Anneal Au0 agglomerates (small particles); nuclei for crystalline ceramic Li2SiO3 (2SiO2·Li2O). Au° 3. Place the glass in dilute HF to dissolve the Li2SiO3 (dissolution is 10× faster than for the glass). This Au+ method can produce densities of 3.6 × 104 holes/square inch. FIGURE 26.15 Process for making porous glass. 476 .................................................................................................................... P rocessing Glass and Glass- Ceramics  FIGURE 26.17 Millefioré paperweight showing the different glass canes used. FIGURE 26.16 Chihuly installation at the Victoria and Albert Museum in London. Art glass, usually in the form of figures and vases, became popular in the 1800s with Lalique, Gallé, Daum Frères, Tiffany, and others made when a wine glass MARBLES as illustrated in Figure “sings”: run your finger 6 Marble King in Virginia makes 10 marbles every day. 26.18. around the rim. The sound Between 1886 and is thus produced by making 1936, the father and son the glass vibrate rather than by making the air in the team of Leopold and Rudolph Blaschka produced the container vibrate (like blowing over a bottle). Benjamin Harvard glass flowers (shown in Figure 26.19) for use in Franklin made a glass armonica (Mozart wrote music for teaching botany (there are other collections, but this is the the armonica): he placed glasses inside one another (not best known). Tiffany produced similar specimens for the touching) and rotated them on a spindle to make playing easy! Galileo actually explained the resonance phenome- non in 1638. The tone will depend on the mechanical (elastic) properties of the glass. Murano, a small island near the city of Venice, was the center of glass making for many years. The location was chosen to stop glassworkers from moving away from the vicinity of Venice. It is still famous for its art glass and the glass companies provide free boat taxis from the mainland to encourage customers. The millefiore insets seen in paperweights and glass sculptures, and illustrated in Figure 26.17, are usually associated with Murano. Actually, the technique had already been used in the first century ce. Paté de verre is an art glass made by sintering pieces of glass, including powder, to make objects with distributions of color that would not be possible if the glass were melted. Essentially, the millefiore glass of Murano is made by this technique but now with larger “particles.” It is now being used by industry for the same purpose. The classical sinter- ing technique for processing ceramic powders is thus being used to produce unique glass objects. FIGURE 26.18 Small vase by Daum Frères. 2 6 .14 G l a s s f o r A r t a n d S c u l p t u r e ........................................................................................................................ 477  developed in the early twelfth century stained glass has been made using several different techniques. Pot-metal glass is bulk glass that has been colored by adding metal oxides in the usual way (Cu for red, Fe for green, Co for blue, etc.). Since the glass must be thick enough for the window, light transmission was often reduced (making the church dark). Flash glass is produced by dipping a gob of clear glass into a pot of colored glass. When the glass is then blown, the two layers are thin. The colored layer remains only a fraction of the total thickness. If the glass were uniformly colored but not flashed, it would transmit too little light (old church windows make for dark interiors); if the glass were uniformly colored but thin so as not to decrease the light it would have insufficient mechanical strength. The layer can be abraded to produce variations in color on the one piece of glass. Details in the window images can be drawn on the glass using an iron oxide pigment. The drawing is then fired to incorporate it into the glass. FIGURE 26.19 Example of a Harvard flower. 26.15 GLASS FOR SCIENCE AND ENGINEERING art market. The idea is that the color of glass does not Lenses have been made using glass since microscopes and change with time and the flowers are three-dimensional. telescopes were first invented. When visible light is used, Actually, the Blaschkas used wire, paint (especially in the this is still generally the case. For transmitted light, the early years), varnish, and glue to enhance the models challenge is usually to minimize absorption; some tele- at the time. Thus they will not be quite as inert to the scopes, such as that on Mount Palomar, use a very wide atmosphere as hoped, but they are superb examples of coated glass reflector. The critical factor is now not trans- lampworking (heating a soda-rich glass and shaping it by mission but thermal expansion. pulling and pinching with various tools including Stepper lenses are used in producing very large-scale tweezers). integration (VLSI) chips using photolithography. The In some countries, the best-known form of art glass is stepper lens is the opposite of an enlarging lens—it shrinks the stained-glass window (Figure 26.20). Since it was first the circuit pattern and prints it onto the semiconductor surface. (The term stepper is used to denote the step-and- repeat exposure system.) In 1997 the line width was 0.25 μm; it is now around 60 nm. The challenge then is to focus light, which has a wavelength much larger than the required resolution. The Hale Telescope is a 200-inch telescope that was built in ∼1949 using a Pyrex blank manufactured by Corning Glass works. Schott Glass has since produced a telescope with a dish that is 8.2 m wide; it is made from Zerodur®, Schott’s glass ceramic, using a centrifugal casting process. An interesting link between art and science is the proposal by David Hockney that some of the masters used mirrors and lenses to help compose their paintings. Glass lenses range in size from the end of a fiber used in near-field scanning optical microscopy (NSOM) (see Chapter 10) to the Fresnel plate that was used in lighthouses. Glass is one of our most important building materials. In 1851, the windows in the Crystal Palace used 300,000 panes, which accounted for 33% of England’s annual pro- duction of glass. Biosphere 2 (built in the late 1980s) relies FIGURE 26.20 Example of drawing in stained glass. entirely on glass to separate the interior from Biosphere 1. 478 .................................................................................................................... P rocessing Glass and Glass- Ceramics  Glass fibers are used FORMING MICROSPHERES Traffic signs and road in textiles for clothing. 1. Glass melting marking tape contain The spacesuits used on a. Select chemically pure raw materials (oxides) that do spheres that are ∼200 μm the Apollo lunar missions not contain any impurities that would form undesirable in diameter and act as were made from glass fiber radioisotopes during neutron irradiation. microlenses. industrial fabrics. b. Mix the raw materials. In the Ballotini flame Glass microspheres are c. Melt the raw materials to form homogeneous glass. drawing process, glass used, for example, in traffic 2. Spheroidization (microsphere formation): powder is injected into a signs and drug delivery. We a. Crush the glass to particles of the desired size. flame that draws it up a will describe radiotherapy b. Inject particles into a gas-oxygen flame to melt each tower until it melts and glasses used in the treat- particle and form a solid glass sphere (flame spray forms spheres (1–60 μm ment of unoperable cancers powder). diameter) dropping out- in more detail in Chapter c. Collect microspheres in a suitable container. side the flame and cooling 35. The key process is 3. Sizing: screen or separate microspheres into desired size under gravity. Filaments forming uniform glass range. used to make the biprism spheres. We willalso discuss for electron holography Bioglass in Chapter 35 but are made in the laboratory not ceramic cremation tiles for after-life applications. using a variation on the same principle. CHAPTER SUMMARY The production of glass is a multibillion dollar industry. The widespread use of glass products has gone hand-in-hand with developments in glass processing. Arguably the most significant recent development was the float glass process, which allowed high-volume production of very high-quality glass sheets for architectural and transportation applications. Our city skylines certainly are influenced by the use of glass. More recent developments have led to improve- ments in the energy efficiency of buildings by controlling the transmission and absorption properties of glass. This is part of the “green” revolution in architecture. Glass processing, which is an industry and art, has its own language. It is necessary to learn that language: in particular, frit, cullet, lehr, fining, gob, and ribbon. The processing terms are from engineering: floating, rolling, drawing, tempering, laminating, and ceramming. PEOPLE IN HISTORY Abbe, Ernst (1840–1905) was a professor of optics who worked with Schott, the glassmaker, and Zeiss, the lensmaker, in Jena. Burne-Jones, Sir Edward Coley (1833–1898) designed stained glass working with William Morris. Gallé, Émile (1846–1904) was a pioneer in the Art Nouveau movement; he used wheel cutting, acid etching, casing (i.e., layers of various glass), including metallic foils and air bubbles. He called his experiments “marquetry of glass.” When you see heavy pieces of deeply colored, nearly opaque glasses, which use several layers of glass and are then carved or etched to form plant motifs, you think of Gallé. Lalique, René (1860–1945) was one of the creators of Art Nouveau glass. Etched clear glass is a particular trademark. Littleton, Harvey K. (born 1922 in Corning, New York) was the University of Wisconsin professor who introduced Chihuly, Lipofsky, and others to glass and began the American Glass Movement. Owens, Michael (1859–1923) invented the automatic bottling machine. Schott, Otto (1851–1935) see Abbe. Stookey, S. Donald (another exception to the rule) is one of the greatest scientific creators from Corning Glass. Trancrede de Dolomieu, Guy S. (1750–1801) was a French professor of mineralogy. The mineral dolomite is named after him. Zeiss, Carl Friedrich (1816–1888) gave his name to the optics company that was, for many years, based in Jena. GENERAL REFERENCES Bach, H. and Krause, D. (Eds.) (1999) Analysis of the Composition and Structure of Glass and Glass Ceram- ics, Schott Series on Glass and Glass Ceramics, Springer, Berlin. Bach, H. and Krause, D. (Eds.) (1997) Thin Films on Glass, Schott Series on Glass and Glass Ceramics, Springer, Berlin. C h a p t e r S u m m a ry .......................................................................................................................................................... 479  Bach, H. and Neuroth, N. (1995) The Properties of Optical Glass, Schott Series on Glass and Glass Ceramics, Springer, Berlin. Bach, H., Baudke, F.G.K., and Krause, D. (2000) Electrochemistry of Glass and Glass Melts, Schott Series on Glass and Glass Ceramics, Springer, Berlin. Beall, G.H. (1992) “Design and properties of glass-ceramics,” Annu. Rev. Mater. Sci. 22, 91. For more infor- mation about the different types of glass-ceramic written by the expert. Ellis, W.S. (1998). “The story of the substance that changed the world,” Glass. Avon, New York. Includes more on the glass harp and marbles. McMillan, P.W. (1979) Glass-Ceramics, 2nd edition, Academic Press, London. The standard glass-ceramics text. Pfaender, H.G. (1983) Schott Guide to Glass, Van Nostrand Reinhold, New York. A concise overview of glass-forming processes. Schultes, E.S. and Davis, W.A. (1982) The Glass Flowers at Harvard, Botanical Museum of Harvard University, Cambridge, MA. Tooley, F.V. (1983) The Handbook of Glass Manufacture, 3rd edition, Volumes I and II, Ashlee Publishing Co., New York. A comprehensive manual for industrial glass formation. Designed primarily for the person in industry. Waseda, Y. and Toguri, J.M. (1998) The Structure and Properties of Oxide Melts, World Scientific Pub. Co., Singapore. A compact book concerned primarily with silicate melts. Varshneya, A.K. (1994) Fundamentals of Inorganic Glasses, Academic Press, Boston. One of the most com- prehensive books on glasses. Chapter 20 is on the fundamental aspects of glassmaking. Zarzycki, J. (1991) Glasses and the Vitreous State, Cambridge University Press, Cambridge. This book was originally published in French as Les Verres et l’Etat Vitreux in 1982. The English edition does include an updated bibliography and some additional information not in the original version. SPECIFIC REFERENCES Langmuir, I. (1933) “Oil lenses on water and the nature of monomolecular expanded films,” J. Chem. Phys. 1, 756. McNally, R.S. and Buschini, N. (1993) “The Harvard glass flowers: Materials and techniques,” JAIC 32, 231. Miller, J. (2004) 20 th-Century Glass, Dorling Kindersley Ltd, London. Among the best. EXERCISES 26.1 Describe how cords and stones could be removed. 26.2 How much glass in your area is recycled as cullet? 26.3 Why did ancient glass batches contain so much alkali content? 26.4 Why is tin used in the float glass process? 26.5 We process the glass to remove bubbles and thus avoid stresses in the glass. Is this statement true or false? Explain your answer. 26.6 On ceramming a glass, we produce a density of 1015/cm3 nuclei. How far apart are the nuclei and how does this affect the resulting grain size? 26.7 Why has the art of glass produced so much new interest? Is it new? Discuss. 26.8 Figure 26.1 shows the distribution of glass sales. Using the internet or otherwise, compare these with the figures for Al, steel, and Cu. Discuss your results. 26.9 Estimate the cost of an automobile’s windows assuming they are made from tempered glass. 26.10 What are the compositions of some of the common sealing glasses? 480 .................................................................................................................... P rocessing Glass and Glass- Ceramics  27 Coatings and Thick Films CHAPTER PREVIEW The term “thick film” does not just refer to film thickness but rather to layers or a coating made by certain processing techniques. Most of the methods that we describe in this chapter involve suspending ceramic particles either in a solution or in a mixture of organic solvents (known as the vehicle). It will be necessary to remove all the volatile material from the coating to produce a dense adherent ceramic layer. Many of the processes described in this chapter are relatively inexpensive (at least compared to those used to produce thin films that we describe in Chapter 28) and simple. Tape casting is used to produce flat sheets of many different ceramics for applications as substrates, capacitor dielectrics, and fuel cell electrolytes. Some of the techniques described in this chapter, for example, spin coating, are useful only for producing films on flat substrates. However, dip coating and electrophoretic deposition can be used to coat complex shapes. We finish by describing how thick-film circuits are made. In this application the ceramic is used as the substrate onto which the films are deposited and as important ingredients of the pastes that are used to form the circuits. The principle of the technology is not difficult, but control- ling the processes may be. All of these techniques are important in industry and you should know the language of thick films, e.g., slurry, slip, and paste. 27.1 DEFINING THICK FILM In addition to describing some of the methods used to apply thick ceramic films to a substrate, we also describe A thick film will typically have a thickness in the range the tape casting process. Films produced by tape casting 10–25 μm; thin films are usually <500 nm. However, what are not used as coatings but as self-supporting ceramic really distinguishes thick films and thin films, more than sheets (down to 25 μm thick) that are widely used in the just their relative thickness, is the way in which they are production of thick-film circuits. produced. Thin films are often deposited using vacuum techniques such as sputtering and molecular beam epitaxy (MBE). We describe these techniques and consider 27.2 TAPE CASTING acronyms and hyphens in Chapter 28. Thick films Tape casting is used to are deposited from a solu- TAPE CASTING make flat ceramic sheets tion or paste, which must Band casting and the doctor-blade process are other having a thickness up to be dried and then often names. about 1 mm. The process sintered to produce the was developed during the final coating. 1940s for capacitor dielectrics. The production of ceramic There are several advantages of thick-film capacitors is still one of the most important applications processing: of tape casting. In tape casting, a slurry (also called a slip) containing  Simple a powdered ceramic together with a complex mixture of  Easy to automate solvents and binders is spread onto a moving polymer  Rapid (such as MylarTM) sheet as shown in Figure 27.1. In the  Inexpensive early form of tape casting the slurry was actually spread  Versatile onto moving plaster-of-Paris plates. The use of a polymer  Coating of complex substrates sheet was patented in 1961 and since then the process has 2 7. 2 Ta p e C a s t i n g ......................................................................................................................................................... 481  Green tape Slurry container Exhaust Doctor blade Drying zone Carrier tape FIGURE 27.3 Typical doctor blade assembly. h high percentage of organics in the form of the polymer FIGURE 27.1 Schematic diagram of the tape casting process. binder and is referred to as being “green.” This term is used to describe any unfired but shaped ceramic. The preparation of the slurry is very important. A slurry formulation used in processing alumina sheets for use as substrates for electronic devices is shown in Table 27.1.  The solvent controls the viscosity of the slurry allow- ing it to be spread on the polymer sheet. FIGURE 27.2 Illustration of a triple doctor blade for producing  The binder holds the ceramic particles together until multilayer tapes. the tape is sintered and must be removed during the sintering process.  Plasticizers increase the flexibility of the green tape. not significantly changed. The principle of the process is  Dispersants (deflocculants) avoid settling of the powder essentially identical to spreading plaster on a wall, icing particles. on a cake, or painting. The thickness of the deposited layer is determined by Dispersants work by a process known as steric hin- the height of the doctor blade above the polymer sheet. drance. The long-chain organic molecules such as those Multilayer films are possible using the approach illus- in Menhaden fish oil (a long-chain fatty acid) attach them- trated in Figure 27.2. The special feature of the doctor selves to the ceramic particles with their long molecular blade is that it produces a very uniform thickness. A tails pointing outward. This orientation prevents the par- typical doctor blade assembly is shown in Figure 27.3. The ticles from getting too close together and hence reduces cast tape is dried, peeled from the polymer sheet, and the extent of agglomeration or settling. Menhaden fish reeled up to wait for further processing. At this stage of oil is a natural product and is widely used in the ceramics the process the tape is flexible because it still contains a industry because it is cheap. TABLE 27.1 Materials for the Preparation of Alumina Slurries for Tape Casting Milling step Material Function wt% Stage 1: Mill for 24 hours Alumina powder Substrate material 59.6 Magnesium oxide Grain growth inhibitor 0.15 Menhaden fish oil Dispersant 1.0 Trichloroethylene Solvent 23.2 Ethyl alcohol Solvent 8.9 Stage 2: Add to above Poly(vinyl butyral) Binder 2.4 and mill for 24 hours Poly(ethylene glycol) Plasticizer 2.6 Octyl phthalate Plasticizer 2.1 482 ........................................................................................................................................... C oat i n g s a n d Th i c k F i l m s  Figure 27.4 shows a commercial tape-casting machine for the continuous production of ceramic tape. These machines range in size from 2 m to more than 35 m in length and from about 100 mm to more than 1.25 m in width. The size determines the rate at which tapes can be produced. Typical casting speeds are on the order of 0.15 m/min. For quick drying compositions the casting speed can be as high as 2 m/min. In industrial production it is often important to have continuous measurement of the tape thickness. These measurements can be made through a hole in the support plate downstream of the FIGURE 27.4 Example of an industrial tape casting machine. doctor blade. Several different approaches are used com- mercially: (1) X-ray backscattering from below, (2) X-ray transmission involving instrument heads below and above Extensive shrinkage occurs during drying and firing (a technique commonly used in the aluminum industry to of the tape because of the large volume fraction of organ- measure the thickness of Al plates), or (3) reflecting visible ics in the slurry. For example, when the alumina slurry light at an angle from the top surface of the cast tape. The shown in Table 27.1 is cast to a thickness of 1.50 mm it X-ray transmission method is generally preferred because will dry to produce a 0.75-mm green tape (about a 50% of its greater accuracy. reduction). When sintered, the tape will shrink further to Figure 27.5 illustrates the production of an integrated a final thickness of about 0.60 mm. circuit (IC) package that uses tape cast alumina sheets. 1 Holes pierced 2 Metallizing 3 Laminating in the blanks printing Green tape Hot pressing at 80-150°C and 50-150 kg/cm2 4 Punching 5 Metallizing printing on the reverse side 6 Sintering Wet hydrogen atmosphere, 1500-1650°C 7 Nickel plating 8 Components Kovar ring 9 Brazing 10 Gold plating, inspection Silver solder ring 800-850°C in dry hydrogen Ceramic assembly Silver solder Nickel plated layer Kovar lead FIGURE 27.5 The steps in the production of an integrated-circuit package. 2 7. 2 Ta p e C a s t i n g ......................................................................................................................................................... 483  low. The final film is obtained after firing the coated Pulley Motor object. Dip coating has the following advantages:  It is simple.  It is inexpensive. Coated object  Complex shapes can be coated.  Planar substrates can be coated on both sides at once. The thickness, t, of the liquid film depends on the viscosity, η, of the solution and the speed, v, with which the object is withdrawn from the solution and is Coating solution given by 1/6 1/2 FIGURE 27.6 Schematic of a simple dip coating process. ⎛ ηV ⎞ ⎛ ηV ⎞ t = 0.944 ⎜ ⎝ γ lv ⎟⎠ ⎜⎝ ⎟ (27.1) ρg ⎠ The green tape can easily DIP COATING where γlv is the liquid– be punched to produce The high-tech version of the dipping process used to vapor interfacial energy, ρ holes or vias, which are an glaze pottery. is the density of the solu- important part of the pro- tion, and g is the accelera- cessing of IC packages. In tion due to gravity. The addition an ink or paste made of a mixture of metallic thickness will, of course, be less in the final fired film due powder (tungsten or molybdenum), organic binders, and to shrinkage. There are several applications for dip-coated solvents is screen printed onto the green tape. The tape is ceramic films as shown in Table 27.2. then fired in a wet hydrogen atmosphere to produce a strongly adherent metal layer on the sintered alumina. We describe the screen printing process in more detail in 27.4 SPIN COATING Section 27.7. Spin coating, like dip coating, starts with a solution that is often a mixture of metal alkoxides. The basic idea is 27.3 DIP COATING illustrated in Figure 27.7 and there are two variants: A ceramic film can be formed very easily on a substrate  Static by dip coating as illustrated in Figure 27.6. The starting  Dynamic material usually consists of metal alkoxides, but solutions of metal salts, such as nitrates, may be used instead. The In the static spin process, a few volumes of solution is substrate, or object to be coated, is lowered into the solu- dropped onto the substrate and allowed to spread until it tion and withdrawn at rates between 10 and 30 cm/min. covers most of the surface. Once the liquid has reached a It is necessary that the solution wets and spreads over the specified diameter the chuck is accelerated to a predeter- surface of the substrate and so the contact angle must be mined speed, on the order of 20,000 rpm. TABLE 27.2 Applications of Dip Coated Sol-Gel Preparations Film use Composition Conditions Mechanical protection SiO2 Multistep process; alternating dips and firings at >400°C; increase thickness by 100 nm each cycle Chemical protection SiO2 Great care in drying; minimize cracking and crazing Transparent electrode In2O3 –SnO2 Single dip process Antireflecting Na 2O–B2O3 –SiO2 Specific absorption TiO2–SiO2 Cr 2O3 –SiO2 Fe2O3 –SiO2 Catalytic Low temperature gelling below 400°C ensures a porous Photo mode TiO2 film that has a high surface area Ionic mode β-Al2O3 Ta 2O5 484 ........................................................................................................................................... C oat i n g s a n d Th i c k F i l m s  Pressurized sol Nozzle Powder Spray Film Fuel gases Air Substrate Flame Turntable Air Powder C2H2 Spin coating After drying flow O2 FIGURE 27.7 Schematic of the spin coating process. trigger FIGURE 27.8 Thermal spraying with a gas combustion/powder gun. In the dynamic spin process the solution is dispensed onto the substrate surface, which is spinning at a low found some application in forming films of piezoelectric speed of about 500 rpm. After the liquid has spread the materials for microelectromechanical systems (MEMS). rotation speed is increased to produce the final film. The dynamic spin process is better for producing uniform coatings on larger diameter substrates. 27.5 SPRAYING Spin coating can be used only for single-side coatings and generally is applicable only to fairly simple planar Forming ceramic coatings by spraying is an impor- shapes. Also spinning of very large objects is impractical. tant industrial process, in particular for applying wear- The thickness of the coating varies inversely with the resistant and thermal-barrier coatings. There are several angular velocity (ω −2/3) of the spin coater and is propor- different types of the spraying process. In thermal spraying, tional to the viscosity of the solution (η1/3). Spin coating illustrated in Figure 27.8, the powder is melted or softened is used widely in industry for forming polymer coatings, by passing it through an oxyacetylene flame. A variant of in particular for the deposition of photoresist layers prior the basic thermal spray process called plasma spraying, to the patterning of semiconductor devices. Although not which utilizes a plasma heat source, is illustrated in Figure widely used for producing ceramic films, spin coating has 27.9. The plasma temperature is typically >28,000°C, well Powder feeder Powder + Gas Tungsten — + Gas cathode Plasma Tungsten Arc anode Carrier gas Cooling Carrier Powder water gases feed Arc trigger power Power supply/control unit Gun manipulator FIGURE 27.9 Thermal spraying using a plasma arc. 2 7. 5 S p r ay i n g ................................................................................................................................................................. 485 above that attained in Yttria-stabilized zirco- SPRAY PAINTING CARS gas combustion processes. nia (ZrO2 with between 6 The paint contains TiO2 powder. The velocity of the plasma/ and 8 wt% Y2O3) is one of droplet stream that exits the the materials investigated nozzle is usually subsonic, although high-velocity plasma for thermal barrier coatings. Figure 27.10 shows a schematic torches with constricted nozzle designs are available. representation of the cross section of such a coating. An Thermal spray processes are generally suitable for applying Ni–Cr–Al–Y alloy (called the bond coat in Figure 27.10) any material that melts or becomes plastic in the heating provides an adherent interlayer between the metal compo- cycle and does not degrade at high temperature. nent and the ceramic coating. Joining metals and ceramics Plasma spraying is widely used in forming wear- is not a trivial issue and the approach mentioned here is just resistant coatings on diesel engine components and for one of the methods that we mention in this book. producing thermal barrier coatings on metals for gas The source material for spraying can be a solution that turbine engines. The efficiency of gas turbine engines is forced through a spray gun onto a heated substrate. In depends on the maximum temperature that can be sus- this case the spraying is not “thermal” and is more akin tained by the rotor blades during continuous operation. to paint spraying. The glass industry uses this approach Applying a ceramic coating (called a thermal barrier for depositing conductive layers of SnO2 on glass. coating) to the metal can allow the engine temperature to be increased by between 50 and 200°C without the tem- perature of the metal increasing significantly. There is a 27.6 ELECTROPHORETIC DEPOSITION corresponding improvement (up to about 12%) in engine efficiency with considerable financial savings. Thermal Electrophoresis is the movement of charged particles barrier coatings must have the following properties: through a liquid under the influence of an external electric field. Electrophoretic deposition, which is very similar to the electrodeposition  High coefficient of process used to form metal thermal expansion EXAMPLE OF ELECTROPHORETIC coatings, can be used to  Low thermal conduc- DEPOSITION form a ceramic coating up tivity For β-Al2O3 coatings the ceramic powder is suspended to 0.6 mm thick on a metal-  Chemically stable in in an organic liquid mixture composed of nitromethane lic substrate. The substrate the gas turbine envi- (CH3NO2) and benzoic acid (C6H5CO2H). The benzoic forms one of the electrodes ronment acid produces a positive charge on the surface of the β- in an electrochemical cell  Thermal shock resis- Al2O3 particles by adsorption of protons. The particles as illustrated in Figure tant can be used to coat a negatively charged electrode. 27.11. The main advantage V Sample cell + — I Coolant v T Combustion gases Metal wall Bond coat YSZ coating FIGURE 27.10 Schematic representation of a thermal barrier coating. The relative temperatures in the different parts of the coating are indicated. FIGURE 27.11 Schematic diagram of a particle electrophoresis cell. 486 ........................................................................................................................................... C oat i n g s a n d Th i c k F i l m s of electrophoretic deposition is that coatings can be formed Zeta potential (ζ) on nonplanar objects. ζ ∼ φd The particles that will form the coating are suspended in a liquid, which produces a surface charge on the parti- cles, for example, by the adsorption of protons. When a particle with charge q is placed in an electric field, E, it experiences a force, F F = qE (27.2) Particle This force accelerates the particle toward the oppositely charged electrode. The particle also experiences a retard- ing force due to friction as it moves through the fluid. You will recall from Chapter 20 that Stokes’ law gives the retarding force due to viscous flow: φ0 Shear plane Surface potential F = 3πηdv (27.3) FIGURE 27.12 Illustration of the ζ potential and the effective size of a charged particle. where v is the terminal velocity. We can write this as qE ν= (27.4) 2κε 0ζ 3πηd μ= (27.7) 3η In terms of mobility, μ For concentrated electrolytes we use the Helmholtz– ν q Smuluchowski equation to give us the mobility: μ= = (27.5) E 3πηd From Eq. 27.5 we would expect that particle mobility κε 0ζ μ= (27.8) would be increased for small particles in a solution of a η low viscosity. This assumption is not entirely true. For example, the mobility of Li + ions in aqueous solution is The important point from both Eqs. 27.7 and 27.8 is that lower than that of K+ ions even though r K+ = 133 pm com- mobility is proportional to κ. For rapid coating we want pared to r Li + = 60 pm. The discrepancy can be accounted to use a liquid with a high dielectric constant. The advan- for by considering solvation effects. Solvent molecules can tage of using aqueous solutions is clear—water has a cluster around an ion increasing its effective size. Small high dielectric constant. Dielectric constants of some ions are the source of stronger electric fields than large other liquids are given in Table 27.3. ions, hence solvation is more extensive in the case of small Figure 27.13 shows the electrophoretic mobility of ions giving them a larger effective size and lower drift TiO2 particles in aqueous solutions of potassium nitrate velocities. A similar effect can occur for charged ceramic (KNO3); in this plot, σ0 is the surface charge density, particles moving through a liquid during electrophoretic deposition. The zeta potential, ζ, which is illustrated in Figure 27.12, is the potential on the surface of the charged parti- cle moving through the liquid. TABLE 27.3 Dielectric Constants of Certain Liquids at 25°C For a particle in a dilute electrolyte solution ζ is given and Zero Frequency by Nonpolar molecules Polar molecules q Methane 1.70 (at 173°C) Water 78.54 ζ= (27.6) 2πκε 0 d 80.37 (20°C) Carbon 2.274 Ammonia 16.9 where κ is the dielectric constant of the liquid and ε0 tetrachloride 22.4 (−33°C) is the permittivity of a vacuum (a universal constant = Cyclohexane 2.105 Hydrogen sulfide 9.26 (−85°C) 8.85 × 10−12 F/m). Benzene 2.274 Methanol 32.63 Ethanol 24.30 We can now obtain an expression for μ in terms Nitrobenzene 34.82 of ζ: 2 7. 6 E l e c t r o p h o r e t i c D e p o s i t i o n ............................................................................................................................. 487  4 -20 27.7 THICK-FILM CIRCUITS Rutile σ0 KNO3, 21°C (μC.cm-2) Thick-film circuits are single or multilayer structures pro- 3 10-3 M -15 μm.s-1 3 x 10-3 duced by depositing a layer, or layers, of a specially for- V.cm-1 10-2 mulated paste or ink onto a suitable substrate. Thick-film 2 10-1 -10 technology began in the early 1960s when DuPont intro- duced a thick-film resistor system for application in min- iaturized circuits. IBM used thick-film materials in their 1 -5 family of IBM/360 computers. Currently the worldwide market for thick-film circuits and devices is around $14 0 0 billion. Most thick-film circuits are still used in electronic applications such as in computers (Figure 27.14). There are three basic classes of thick-film material -1 5 (conductors, resistors, and dielectrics) and all have at least one component that is a ceramic. They are supplied in the -2 10 form of a paste or ink, which contains the following:  The functional inorganic component or components; -3 15 4 5 6 7 8 pH 9 this is in the form of a fine powder.  An organic binder; this is used to provide the green FIGURE 27.13 The surface charge density and electrophoretic mobility as functions of pH for rutile in aqueous solutions of strength. potassium nitrate.  A low boiling point organic solvent; this provides the required viscosity to allow the paste to be depos- ited onto the substrate. which was measured using the Brunauer, Emmett, and Screen Printing and Processing Teller (BET) method. The mobility is a function of the solution pH. Thick-film materials are deposited onto flat substrates by screen printing. The origins of screen printing date back  In acidic solutions the surface of the TiO2 particles has more than 3000 years when the Chinese used “silk screen” a positive charge due to cation adsorption. printing to deposit multilayered colored patterns onto  In basic solutions the powder particles have a negative fabrics. A similar process is still used today to print charge due to the adsorption of anions. designs and logos onto T-shirts. Figure 27.15 shows a schematic diagram of the screen- At a pH of 5.9 the mobility is zero: this point is referred printing process. The paste is forced through holes in a to as the isoelectric point (IEP). At the IEP the ζ potential screen using a rubber squeegee. The viscosity of the ink is zero. Table 27.4 shows IEPs for several different oxides. is determined by the type and amount of organic solvent Acidic oxides such as SiO2 have low IEPs and basic oxides added to the formulation. Common solvents include pine such as MgO have high IEPs. oil, terpineol, and butyl carbitol acetate. The ideal thick- TABLE 27.4 Isoelectric Points of Some Oxides Material Nominal composition IEP 96% Al2O3 Thick-film substrate resistor Quartz SiO2 2 Soda-lime silica glass Na 2O–0.58 CaO · 3.70 SiO2 2–3 Potassium feldspar K 2O · Al2O3 · 6SiO2 3–5 Zirconia ZrO2 4–6 Ceramic-chip Apatite 10CaO · 6PO2 · 2H2O 4–6 capacitor Tin oxide SnO2 4–5 IC package Titania TiO2 4–6 Kaolin (edges) Al2O3 · SiO2 · 2H2O 5–7 Mullite 3Al2O3 · 2SiO2 6–8 Thick-film Chromium oxide Cr 2O3 6–7 conductor Hematite Fe2O3 8–9 Zinc oxide ZnO 9 Sealing Alumina (Bayer process) Al2O3 8–9 glass Calcium carbonate CaCO2 9–10 Magnesia MgO 12 FIGURE 27.14 A typical thick film circuit used in a personal computer showing the different components. 488 ........................................................................................................................................... C oat i n g s a n d Th i c k F i l m s  Substrates for Thick-Film Circuits Substrates for thick-film circuits generally have to satisfy Squeegee the following requirements: Screen  A uniform surface (surface roughness between 20 and 40 μm is typical)  Minimum distortion or bowing (0.010–0.22 cm/cm) Substrate  The ability to withstand processing temperatures of up to 1000°C  Tight dimensional tolerances (±0.07–0.10 mm size; ±0.02–0.10 mm thickness) Ink  Strength  High thermal conductivity  High electrical resistivity  Chemically compatible with paste constituents  Low dielectric constant  Inexpensive FIGURE 27.15 The screen printing process for depositing thick film Alumina (96% Al2O3 with 4% of a glass containing circuits. The ink is forced through the screen, which then snaps MgO, CaO, and SiO2) is the most common substrate mate- away leaving a film on the substrate. rial because it meets all of the above requirements to an acceptable degree. The substrates themselves are fre- quently made by tape casting, which we described in Section 27.2. film paste should have a low viscosity at a high shear rate When a circuit will be used in conditions in which a produced when the squeegee traverses the screen so that significant amount of heat will be transferred through material transfer onto the substrate occurs. The viscosity the substrate but the thermal conductivity of alumina is should remain low for a short time after the squeegee not high enough, then alternative materials may be used. passes and the screen snaps off of the substrate so that the For many years the only alternative to Al2O3 was beryllia printed film can level to fill in the unevenness from the (BeO). The disadvantages of BeO are its cost and high screen wires. The viscosity should then increase rapidly toxicity in both vapor and powder form as encountered in to a very high value to prevent spreading of the deposited processing. Aluminum nitride (AlN) is another option; it film. not only has a high thermal conductivity but is closely The equipment used to deposit thick-film pastes is matched in coefficient of thermal expansion to silicon similar to that used in printing T-shirts, but for electronic in the temperature range 25–400°C (αSi = 4.0 ppm/°C; applications much higher precision in the placement of αAlN = 4.3 ppm/°C). The three substrates are compared in material and thickness control is required. It is possible to Table 27.5. produce circuit lines having a width of 5 μm and a thick- Although the properties of AlN make it very well ness of 5 μm. After printing, the substrates (coated with suited for electronic packaging, there have been several the wet paste) are moved to a drying oven where the low problems in commercializing: boiling organic solvents are removed. The circuit lines still contain the organic binder, which gives the green  Most commercial AlN substrates have thermal conduc- strength to the deposited film. tivities ∼170 W m−1 K−1, which is considerably lower than The choice of binder is as important as the choice of the theoretical thermal conductivity of 320 W m−1 K−1. solvent. The binder contributes to the overall rheological properties of the paste, but it must be removed completely during firing. Ethyl cellulose is a common binder for air- fired materials. Binders for firing in inert or reducing atmospheres must be chosen carefully to avoid leaving a T 600-900 °C carbon residue in the fired film; suitable choices include nitrocellulose and copolymers of ethylene and vinyl acetate. Burn out The furnace is a belt furnace with a well defined tem- perature profile as shown in Figure 27.16. The time at peak temperature is between 6 and 10 minutes during which time the inorganic components sinter together and bond t to the substrate. FIGURE 27.16 Typical thick film circuit firing profile. 2 7.7 Th i c k- F i l m C i r c u i t s ............................................................................................................................................. 489  TABLE 27.5 Properties of Different Substrate Materials (AlN sublimes) Property Units 96% Al2O3 BeO AIN Thermal conductivity W m−1 K−1 15–20 230–260 120–210 Coefficient of thermal expansion 10 −6 °C−1 7.2 8.3 4.3 (RT −400°C) Electrical resistivity Ω · cm >1014 >1014 >1014 Dielectric constant (RT at 1 MHz) Unitless 9.4 6.7 8.6 Dielectric loss (RT at 1 MHz) Unitless 0.0001 0.0003 0.0002 Dielectric strength kV/mm 15 10 15 Density g/cm3 3.75 2.85 3.3 Melting temperature °C 2030 2530 2300 Modulus of rupture MPa 358 280 280–350 Knoop hardness GPa 19.6 9.8 11.8 Modulus of elasticity GPa 303 345 331  AlN powder costs more than four times that of alumina Frit bonding is the most common method, but there powder. are several advantages to reactive bonding. First, very  The adhesion of pastes designed for alumina is low small amounts of additive are needed, which means that on AlN unless the surface is preoxidized prior to the electrical resistivity of the conductor is kept as low as deposition. possible. Second, the surface of the conductor is nearly pure metal, which enhances the attachment of thin Au or Al wires during wire bonding. Some thick-film conductor Thick-Film Conductors compositions are termed “mixed bonded” and these con- The general requirements for thick-film conductors are tain a glass frit together with a mixture of oxides.  Low electrical resistivity Thick-Film Resistors  Good adhesion to the substrate  Good line definition The functional phase in thick-film resistors is a mixture of electrically conducting (or semiconducting) ceramic In addition there may be the following considerations: powders such as ruthenium dioxide (RuO2), bismuth ruthenate (Bi2Ru2O7), lead ruthenate (Pb2Ru2O6), and  Ability to be wire bonded or soldered for external Ag–Pd–PdO mixtures for use in air-fired pastes and tan- connections talum nitride (TaN) for nitrogen-fired pastes. The resis-  Resistant to electromigration tance of thick-film resistors is specified in terms of sheet  Compatible with other thick film components such as resistance, which has units of ohms/square (Ω/). resistors and dielectrics  Acceptable cost TABLE 27.6 Metals and Alloys Used in Thick Film Conductors The functional material in a thick-film conductor is a metal. The important metals and alloys used in thick-film Metal or alloy Principal features conductors, together with some of their characteristics, are listed in Table 27.6. There are two mechanisms for achiev- Ag $ Highest conductivity; Ag ion migrates; tarnishes; ing adhesion of the metal film to the substrate: seldom in microcircuits; migrates through glass and between conductors Pd–Ag $$ Pd inhibits migration but lowers conductivity  Frit bonding. A small amount (2–10%) of glass powder Pt–Ag $$ Smaller quantity of Pt replaces palladium in the is added to the paste formulation. During firing the binary alloy glass softens, wets the substrate, and penetrates into Au $$$$ Highly conductive and chemically inert; reliable the metal network to develop an interlocking structure. bonds to Au wire; high solubility in common The most common glasses used in frit-bonded conduc- solders makes soldering difficult Pd–Au $$$$ Compared with Au the solubility in solder is tors are lead borosilicates, e.g., 63 wt% PbO–25 wt% reduced but conductivity is impaired B2O3 –12 wt% SiO2. Pt–Au $$$$ Reliable solderable alternative to Au; not so  Reactive bonding. A small amount (0.1–1%) of CuO conductive or CdO is added to the paste formulation. During firing Cu $ High conductivity; fire in reducing atmospheres to the oxides react with the alumina substrate to form achieve excellent solderability Ni $ Can fire in air but not solderable from the furnace a copper or cadmium spinel, CuAl2O4 or CdAl2O4, respectively. $ lowest cost; $$$$ highest cost. 490 ........................................................................................................................................... C oat i n g s a n d Th i c k F i l m s  0.010 m RT - R25 pp δ 00 R25 +1 S3 = 0.005 R TC L #1 S2 #2 0 L #3 S1 TC R= -50 w L ppm (A) (B) -0.005 -0.010 -50 0 50 100 T (°C) FIGURE 27.18 Typical resistance versus temperature profiles for thick-film resistors. (C) FIGURE 27.17 (a–c) Illustration of sheet resistance. The concept of sheet resistance is illustrated in Figure tance (ΔR/R) versus temperature as illustrated in 27.17a, which shows a sheet resistor of length l, width w, Figure 27.18. The TCR limits specified for a particular and thickness d, having a resistance, R given by formulation are the slopes of the two lines passing through the reference points on the curve that bound the ρl resistance deviation. Typically the reference temperature R= (27.9) is 25°C and the temperature range is −55°C to +125°C. dw TCR values for thick-film resistors are typically less than where ρ is the resistivity. If the resistor is square in ±100 ppm/°C. shape, as in Figure 27.17b, then l = w and Eq. 27.9 Resistor patterns are designed so that the average value becomes of the fired resistor is lower than the required value. The final resistor is then trimmed using a laser, or an abrasive ρ jet, to remove material and increase the resistance to R= (27.10) d within ±1% of the desired value. For a given material and thickness, all square sheets SHEET RESISTANCE Thick-Film have the same resistance It depends only on the thickness of the resistor and its Dielectrics independent of the size of resistivity. the square. The resistance Dielectrics are used in of such squares is known several difficult applica- as the sheet resistance. Figure 27.17c shows a complex tions in thick-film circuits: thick-film resistor configuration, but the resistance can easily be determined by dividing it into squares, counting  To isolate circuit lines in multilayer structures the number of squares per strip, and multiplying by the  As a dielectric layer in thick-film capacitors sheet resistance.  To encapsulate circuit components Thick-film resistors are available with sheet resistance values in the range from 0.1 to 10 M Ω/. By blending For multilayer applications the functional material is different quantities of conductive material and an electri- commonly a glass or a glass-ceramic. It must have a low cally insulating glass the resistivity is controlled. For a dielectric constant and be thermal expansion matched to high sheet resistance formulation the ratio of conductor to the substrate to prevent stresses that can cause the sub- glass would be about 70/30. strate to bow. The film must also be stable as it may be An important parameter for thick-film resistors is their subjected to many firing cycles in the fabrication of a temperature coefficient of resistivity (TCR), which is a multilayer structure. measure of how much the resistance changes with tem- For thick-film capacitor applications the dielectric perature. It is defined as the slope of the change in resis- composition will contain a material with a high dielectric 2 7.7 Th i c k- F i l m C i r c u i t s ............................................................................................................................................. 491 constant such as barium titanate. Encapsulants are used to resistors (which would change their resistance values). protect resistors from harmful environmental conditions Typical firing temperatures for encapsulant glasses are such as high humidity and reactive organic solvents, and ∼500°C. Most glass formulations used in the thick-film to protect silver-containing conductors from silver migra- industry are proprietary. But to achieve low softening tem- tion. The glass is chosen so that it can be fired at low peratures the glass used for encapsulation will probably temperatures to avoid significant refiring of the thick-film contain a significant amount of either PbO or B2O3. CHAPTER SUMMARY The term thick-film refers to layers and coatings made by certain types of processing techniques. Such films are usually not prepared using vacuum conditions. In this chapter we described most of the techniques that are used to produce thick ceramic films. Some of these processes are extremely simple and inexpensive such as dip coating, which can be accom- plished, at a minimum, with simply a beaker and a pair of tweezers. However, processes such as thermal spraying require specialized equipment. In this chapter we described tape casting. This process is used to make flat sheets. Although this is a means of shaping and could have been described in the “shaping” chapter we described it here because it shares a common feature with the other thick film coating methods: it uses a slurry. It also is the process most often used to make ceramic substrates for thick-film circuits. Ceramics are a major component of thick-film circuits. Even in thick-film conductors, ceramics are important in ensuring adhesion between the metal layer and the substrate (which is invari- ably also a ceramic). GENERAL REFERENCES Budinski, K.G. (1988) Surface Engineering for Wear Resistance, Prentice Hall, Englewood Cliffs, NJ. Describes various thermal spray techniques. Kuo, C.C.Y. (1991) in Engineered Materials Handbook Volume 4: Ceramics and Glasses, ASM International, pp. 1140–1144. A brief review of thick film circuits. Mistler, R.E. (1995) in Ceramic Processing, edited by R.A. Terpstra, P.P.A.C. Pex, and A.H. De Vries, Chapman & Hall, London. A detailed discussion of tape casting. Rahaman, M.N. (1995) Ceramic Processing and Sintering, Marcel Dekker, New York. Covers many of the processing techniques for ceramic films and coatings at a level similar to this book. SPECIFIC REFERENCES Howatt, G.N., Breckenridge, R.G., and Brownlow, J.M. (1947) “Fabrication of thin ceramic sheets for capaci- tors,” J. Am. Ceram. Soc. 30, 237. The original description of tape casting. Howatt obtained a U.S. patent (2,582,993) for the process in 1952. Parks, J.L., Jr. (1961) Manufacture of Ceramics, U.S. Patent 2,966,719. Patent for the use of polymer film in tape casting process. EXERCISES 27.1 The slurry formulation for tape casting barium titanate sheets consists of the following ingredients: barium titanate powder, phosphate ester, methyl ethyl ketone, ethanol, acrylic resin, benzyl butyl phthalate, and poly(ethylene glycol). (a) Explain the function that each of the ingredients has in the formulation. (b) What would be the usual amounts (in wt%) of each of the ingredients in a typical tape cast formulation? 27.2 Explain why shrinkage of a cast tape occurs during drying and firing. Which of the ingredients in the above formulation would you expect to be lost at each stage of the process? Justify your answer. 27.3 Of the methods described in this chapter which one would you choose to produce a uniform 10 μm coating of BaTiO3 on a 5-cm-diameter silicon wafer? Justify your choice. 27.4 Of the methods described in this chapter which one would you choose to produce a uniform 100 μm coating of Al2O3 on a 5-mm-diameter steel rod? Justify your choice. 27.5 Would thermal spraying be a suitable technique for forming thick films of aluminum nitride (AlN)? Explain the reasoning for your answer. 27.6 Alumina substrates for electronic packaging usually contain 96% Al2O3 and the remaining 4% is a mixture of CaO–MgO–SiO2. Why do you think these constituents are added to the alumina and what effect, if any, do you think they will have on the properties of a 96% alumina substrate compared to a 99.5% alumina substrate? 492 ........................................................................................................................................... C oat i n g s a n d Th i c k F i l m s  27.7 In glass formulations used in thick-film inks alkali metal constituents are avoided. Why? 27.8 Who are the major vendors for thick-film materials? 27.9 Rank the thick-film conductors in Table 27.6 in terms of electrical conductivity starting with the most conduc- tive. Is the trend consistent with their cost? 27.10 Figure 27.14 shows a thick-film circuit. (a) What is the role of the sealing glass? (b) Why is it green? (c) What properties are important for the sealing glass? C h a p t e r S u m m a ry .......................................................................................................................................................... 493  28 Thin Films and Vapor Deposition CHAPTER SUMMARY Thin films are often deposited relatively slowly so that the growth can be strongly influenced by the substrate, which plays a key role in determining film microstructure and properties. The substrate is much more important in growing thin films than it is for thick films and is a crucial factor if we want to grow oriented (epitactic) films. At the end of this chapter we describe some of the requirements for the substrate. The growth techniques described in this chapter involve vacuum chambers and are generally expensive so that thick films are grown by other methods, particularly when epitaxy is not required. Much of this topic is carried over from the semicon- ductor industry and is often not thought of as ceramic processing. However, without thin films of Si oxide and Si nitride, “Silicon Valley” might still be green fields. 28.1 THE DIFFERENCE BETWEEN THIN Chemical vapor deposition techniques use either gas FILMS AND THICK FILMS phase reactions or gaseous decomposition as the source of material. Physical vapor deposition techniques rely on In Chapter 27 we described how thick films of ceramics excitation of a source (sometimes called the target) that is are produced. The difference between thick films and thin usually solid to produce the necessary material for film films is not really the thickness of the layer; it is how the formation. In addition to the basic difference in the way layer is formed. In general, thin films are ≤500 nm in that material transfer from the vapor phase to the solid thickness whereas thick films may be several tens of phase is accomplished, there are other differences between micrometers in thickness or even thicker depending upon CVD and PVD. For example, CVD is often used to produce the particular application. Thin films are generally pre- thicker films (i.e., films >1 μm in thickness). The reason pared from the vapor phase whereas for thick films we use is that the growth rate by CVD is on the order of microm- a solution or slurry. Furthermore, thin films are often eters per minute (e.g., 2 μm/min), whereas for PVD tech- crystallographically oriented in a particular way with niques the growth rate is often orders of magnitude lower respect to the underlying substrate. This orientation rela- (e.g., growth rates in the range 0.01–0.03 μm/min are tionship, known as epitaxy, is determined by the crystal typical). There are other differences that will become structures and lattice parameters of the film and the sub- evident as we describe the different techniques in the fol- strate. In general, thick films and coatings have no specific lowing sections. orientation and contain a large number of randomly ori- Thin-film technology is replete with acronyms and ented crystalline grains. several of the main ones you will encounter are listed in Table 28.1. Molecular beam epitaxy (MBE) is the only acronym that assumes a crystalline structure and align- ment of the thin film. Molecular-beam evaporation would 28.2 ACRONYMS, ADJECTIVES, be much better, especially when used to grow amorphous AND HYPHENS films! We defined epitaxy in Chapter 15. Incidentally, the The thinnest thin films are almost exclusively formed grammatically correct adjective from epitaxy is epitactic from the vapor or gaseous phase and although there are or better still epitaxic, but epitaxial has come to be accepted many different deposition techniques they can be divided even by the Oxford English Dictionary because it is now into two basic classes: so widely used. In many of the deposition techniques, it is not clear where the hyphen(s) should be (if there should  Physical vapor deposition (PVD) be one) but thin-film growth is always the way to grow thin  Chemical vapor deposition (CVD) films and adverbs are never hyphenated to parts of verbs. 494 ............................................................................................................................. Th i n F i l m s a n d Va p o r D e p o s i t i o n  TABLE 28.1 Some Common Acronyms in Thin-Film example is BaTiO3. The ferroelectric form of BaTiO3 is Technology tetragonal. CVD Chemical vapor PVD Physical vapor The final characteristic is the film surface. In general technique deposition technique deposition we want to have smooth films, but this requirement is not universal and is really based on what we want to do with APCVD Atmospheric- MBE Molecular-beam the film. If the film is part of a multilayer structure, i.e., pressure CVD epitaxy LECVD Laser-enhanced PLD Pulsed-laser there are going to be other layers deposited on top, then it CVD deposition is clearly important for the underlying surface to be smooth. LPCVD Low-pressure IBAD Ion-beam-assisted If the film is to be patterned using photolithographic tech- CVD deposition niques (the same techniques used to pattern semiconductor MOCVD Metal-organic RE Reactive devices) then smooth surfaces are essential. Some proper- CVD evaporation PECVD Plasma- ties are dependent upon surface roughness. For example, enhanced rough surfaces can contribute strongly to propagation CVD losses in films used for guiding microwave radiation. From the above discussion you can see that there are several stringent requirements for ceramic thin films. For this reason, there are numerous techniques that have been 28.3 REQUIREMENTS FOR THIN used to form such films. Some techniques work better for CERAMIC FILMS some materials whereas other techniques work better for other materials. We describe some of the techniques used There are four general characteristics that we usually want to form ceramic thin films in the following sections, but to control when growing ceramic thin films: this is not a comprehensive list.  Crystal structure  Stoichiometry 28.4 CHEMICAL VAPOR DEPOSITION  Phase  Surface morphology/topography Chemical vapor deposition involves either We will now look at each of these characteristics and  Chemically reacting a volatile compound of a material explain the rationale behind why they are important. The to be deposited, with other gases, to produce a non- thin film may be crystalline, often epitactic, or sometimes volatile solid or polycrystalline or amorphous. The reason for requiring  Pyrolysis (decomposition) of a compound at high tem- crystallinity is that for thin films we are often making use perature to produce a solid. of a particular electronic, optical, or magnetic property of the material. These properties are frequently anisotropic. In either case the solid forms as a film on a suitably placed Hence we want to ensure that the film is crystalline and substrate. It is important that the reaction takes place only oriented in the correct way to optimize the desired prop- on the substrate surface. If the reaction takes place in the erty. This alignment is best achieved by judicious choice gas stream above the substrate then particulates will form. of substrate and, therefore, we make use of epitaxy. Many Under these conditions the film will have a low density properties of ceramic thin films are affected by the pres- and a large number of voids. There are several different ence of grain boundaries. In epitactic films it is often geometries for a CVD reactor and some of these are illus- possible to control the types of grain boundary that are trated in Figure 28.1. The substrates are usually placed on produced. Generally these boundaries are low-angle grain a graphite slab, which acts as a susceptor for radiofre- boundaries, but they can be high-angle grain boundaries quency induction heating. The gases are introduced into that may be associated with large distortions. the reactor chamber, sometimes in the presence of an inert The correct stoichiometry, or composition, is neces- carrier gas such as argon. As an example of a CVD reac- sary because for some materials they exhibit the required tion consider the formation of SiC from silicon tetrachlo- property only within a certain composition range. An ride (SiCl4) and methane (CH4): example is the high-temperature superconductors whose structures we described in Chapter 7. For YBa2Cu3O6+x SiCl4 (g) + CH4 (g) → SiC (s) + 4HCl (g) (28.1) (YBCO), the value of the superconducting transition tem- perature depends on the value of x. When x is close to one Silicon tetrachloride is a liquid at room temperature the transition temperature is ∼90 K. When x = 0.3 the and can easily be vaporized (it boils at 57.6°C) and trans- transition temperature is reduced to 30 K. The change in ported to the reactor chamber. Methane can be supplied oxygen stoichiometry is associated with a change in the as a high-purity gas directly from a bottle. The reaction structure of the material. Many technologically important between SiCl4 and CH4 to produce SiC films occurs at ceramics exist in different crystalline forms. Another 1400°C. Two aspects of the temperature are important: 2 8 . 4 C h e m i c a l Va p o r D e p o s i t i o n .............................................................................................................................. 495  Quartz Inlet Gas inlet bell jar nozzle Si wafers Induction coil or heaters Exhaust Exhaust Gas inlet (A) Radiant heaters Quartz bell jar Gas Induction coil or Si wafers inlet radiant heaters Quartz tube Exhaust (B) Gas Three-zone control temperature Exhaust control Tilt Pressure angle sensor Mechanical (C) pump Exhaust 3-zone resistance heater Vent (D) FIGURE 28.1 Examples of CVD reactor configurations: (a) pancake, (b) barrel, (c) horizontal, (d) LPCVD.  It must be sufficiently high so that the reaction Chemical vapor deposition is one of the most impor- occurs. tant deposition techniques for forming ceramic films and  If an epitactic deposit is required, it must be high coatings. We described two examples in Chapter 20 in enough to allow the condensing species to diffuse which CVD is used in composites. It is used to form SiC across the crystal surface to find their required lattice fibers by the reaction between CH3SiCl3 and H2 on a tung- crystal positions. sten wire. It is also used to form the matrix phase in a ceramic matrix composite (CMC) by a process known as A variety of oxide, carbide, nitride, and boride films chemical-vapor infiltration. In later chapters we describe and coatings can be readily prepared by CVD techniques the CVD technique again, e.g., it is used in the formation as shown in Table 28.2. The reacting compounds must of optical fibers. exist in a volatile form and Before we leave this must be sufficiently reac- ELECTRONIC GRADE SILICON (EGS) section there is one addi- tive in the gas phase. The annual worldwide production capacity is >107 kg. It tional example of the Examples of other reac- is all made by CVD. importance of CVD. All of tions that can be used to the electronic grade silicon produce ceramic films by (EGS) used in the fabrica- CVD are given below: tion of silicon wafers is made by CVD. The highest purity EGS is made by decomposition of silane (SiH4), which itself can be prepared in extremely high purity. The TiCl4 (g) + CH4 (g) → TiC (s) + 4HCl (g) (1000°C) substrate is an electrically heated U-shaped rod made of BF3 (g) + NH3 (g) → BN (s) + 3HF (g) (1100°C) single crystal silicon. The silane decomposes to form AlCl3 (g) + NH3 (g) → AlN (s) + 3HCl (g) (1000°C) silicon, which deposits on the U-shaped rod in the form of 496 ............................................................................................................................. Th i n F i l m s a n d Va p o r D e p o s i t i o n  TABLE 28.2 Examples of Ceramic Films and Coatings Produced by CVD Film Substrate Reactants Deposition T (°C) Crystallinity a Si Si Either SiCl2H2, SiCl3H, 1050–1200 E or SiCl4 + H2 600–700 P SiH4 + H2 Ge Ge GeCl4 or GeH4 + H2 600–900 E SiC Si SiCl4, toluene, H2 1100 P AlN Sapphire AlCl3, NH3, H2 1000 E In2O3 : Sn Glass In-chelate, 500 A (C4H9) 2Sn(OOCH3) 2, H 2O ZnS GaAs, GaP Zn, H2S, H2 825 E CdS GaAs, sapphire Cd, H2S, H2 690 A Al2O3 Si Al(CH3) 3 + O2 275–475 A Cemented carbide AlCl3, CO2, H2 850–1100 A SiO2 Si SiH4 + O2 450 A SiCl2H2 + 2N2O 900 Si3N4 SiO2 SiCl2H2 + NH3 ∼750 A SiNH SiO2 SiH4 + NH3 (plasma) 300 A TiO2 Quartz Ti(OC2H5) 4 + O2 450 A TiC Steel TiCl4, CH4, H2 1000 P TiN Steel TiCl4, N2, H2 1000 P BN Steel BCl3, NH3, H2 1000 P TiB2 Steel TiCl4, BCl3, H2 >800 P a E, epitactic; P, polycrystalline; A, amorphous. a columnar “feather-like” polycrystalline layer as shown in it proceeds at very low rates then it will not be commer- Figure 28.2. The overall thickness of this layer can exceed cially useful. 5 cm, so CVD can be used to produce very “thick” films! We can calculate the standard free energy, ΔG 0, of many reactions using tabulations of thermodynamic data. Consider the reaction between TiCl4 and CH4: 28.5 THERMODYNAMICS OF CHEMICAL VAPOR DEPOSITION TiCl4 (g) + CH4 (g) → TiC (s) + 4HCl (g) (28.2) Thermodynamics indicates whether a particular chemical To find the standard free energy, ΔG 0r, for this reaction reaction is feasible. However, it will not provide any infor- we need to consider the standard free energies for forming mation about the speed of the reaction and film growth the reactants and the products from their elements in the rates. Even if a reaction is thermodynamically possible, if standard state at the temperature of interest. If we assume a reaction temperature of 1200 K we can look up ΔG 0 for the individual reactions below: Ti + 2Cl2 → TiCl4 ΔG 10 = −610 kJ C + 2H2 → CH4 ΔG 20 = 42 kJ 1/2H2 + 1/2Cl2 → HCl ΔG 03 = −102 kJ Ti + C → TiC ΔG 40 = −171 kJ From basic thermodynamics we know ΔGr0 = ∑ ΔG 0 products − ∑ ΔG 0 reactants (28.3) Hence, for the reaction in Eq. 28.2 ΔG 0r = (ΔG 04 + ΔG 03) − (ΔG 02 + ΔG 10) (28.4) The numbers are FIGURE 28.2 TEM image showing a polysilicon layer grown on a single crystal Si rod by CVD. ΔG 0r = [−171 + 4(−102)] − (42 − 610) = −11 kJ (28.5) 2 8 . 5 Th e r m o dy n a m i c s o f C h e m i c a l Va p o r D e p o s i t i o n ........................................................................................ 497 The negative value of ΔG 0r indicates that the reaction will Metal layer 2 proceed spontaneously at 1200 K to produce TiC. Con- sider a similar calculation at 298 K instead of 1200 K. The W SiO2 via calculated values for ΔG 0 are now Metal layer 1 Ti + 2Cl2 → TiCl4 ΔG 10 = 718 kJ W SiO2 Gate via C + 2H2 → CH4 ΔG = 51 kJ 0 2 P-Si Source Drain 1 1 H 2 + Cl 2 → HCl ΔG 03 = 95 kJ 2 2 Si Ti + C → TiC ΔG = 180 kJ 0 4 FIGURE 28.3 Schematic cross section of a multilayer metallization to a polysilicon gate field effect transistor. The contacts to the Therefore, at a temperature of 298 K the value of ΔG 0r is source and drain are silicides. Tungsten is used to provide vertical interconnects through vias in the oxide layer. +109 kJ. The positive value of ΔG 0r indicates that the reac- tion between TiCl4 and CH4 to form TiC will not proceed spontaneously at room temperature. single-crystal epitactic films. The use of thermodynamics We now consider a generalized chemical reaction implies that chemical equilibrium has been attained. between two gases A and B to produce a solid C and Although this may occur in a closed system, it is generally another gas D. not the case in an open system such as a flow reactor, where gaseous reactants and products are continuously aA (g) + bB (g) = cC (s) + dD (g) (28.6) introduced and removed. The equilibrium constant for this reaction is 28.6 CHEMICAL VAPOR DEPOSITION K = [C] c [D] d /[A] a [B] b (28.7) OF CERAMIC FILMS FOR SEMICONDUCTOR DEVICES where [ ] indicates the equilibrium activity of each com- ponent of the reaction. As usual, we can take the activity Ceramic films are widely used in the fabrication of semi- of a pure stable component as unity. Pressures may be conductor devices. The two materials that are presently of used to approximate the activities of the gaseous species, major interest are silicon dioxide (SiO2) and silicon nitride hence (Si3N4). These are deposited as thin films using CVD. SiO2 films can be deposited with, or without, dopants. K ≈ (pD) d /(pA) a (pB) b (28.8) Undoped it has multiple uses: where (p) are the equilibrium pressures of the reactants  Insulating layer between multilevel metallizations and products. The driving force for growth may be (Figure 28.3) expressed as  Implantation or diffusion mask  Capping layer over doped regions to prevent outdiffu- ΔG 0r = −RT ln K (28.9) sion during thermal cycling R, the gas constant, is 8.314 J K−1 mol−1. A suitable reaction to produce SiO2 is the oxidation of It is usually desired that the concentration of the vola- silane (SiH4) at 450°C: tile reactant species be fairly high so that the transport of reactants to the substrate is very rapid. If the concentration SiH4 (g) + O2 (g) → SiO2 (s) + 2H2 (g) (28.10) of reactants is too low, it will be difficult to produce a reasonable flow of material to the substrate surface. Thus, Above 600°C water vapor is produced: we want the value of K to be small. Assuming that the reaction to produce TiC was carried out in a closed system SiH4 (g) + 2O2 (g) → SiO2 (s) + 2H2O (g) (28.11) (so that the HCl was not being removed), the value of ln K would be 1.1. [Sometimes the equilbrium constant term is The SiO2 film produced by either of the above two reac- expressed as a logarithm in base 10 (log) rather than as a tions is amorphous. natural logarithm, ln; the desired value would then be For some applications we need doped SiO2 films. Dopant log K = 0.5.] When ln K species include boron and is very large, the driving phosphorus. Doped oxide force is very large, which CVD films are made by intro- tends to produce a poly- This is an empirical method of film growth guided by ducing dopant compounds crystalline film rather than thermodynamics. such as phosphine (PH3) 498 ............................................................................................................................. Th i n F i l m s a n d Va p o r D e p o s i t i o n or diborane (B2H6) into the gas stream along with the nitride film are pushed up and away from the silicon SiH4 and an oxygen source. The chemical reactions for surface. After oxidation the Si3N4 layer is removed. phosphorus-doped oxides are Si3N4 layers are also used for passivating Si devices because they act as an extremely good barrier to the dif- SiH4 + O2 → SiO2 + 2H2 (28.12) fusion of water and Na. These impurities can cause device metallization to corrode or devices to become unstable. and 4PH3 + 5O2 → 2P2O5 + 6H2 (28.13) 28.7 TYPES OF CHEMICAL VAPOR DEPOSITION Phosphorus-doped silica films are used as There are several forms of CVD and each form has its  Insulators between metal layers own acronym. If the process takes place at atmospheric  Device passivation pressure (AP) it is referred to simply as CVD or APCVD.  Diffusion sources In APCVD systems the gas flow is almost exclusively parallel to the surface. The reactor configurations shown One application that we will describe in a little more in Figure 28.1 are all examples of configurations used for detail is the use of phosphorus-doped glass (called P-glass APCVD. in the semiconductor industry) as an insulator between When lower pressures are used the operation is low- polysilicon gates and the top metallization in a metal pressure CVD (LPCVD). The gas pressure is usually in oxide semiconductor field effect transistor (MOSFET). the range 0.5–1 torr for LPCVD reactors, distinguishing it The P-glass is used because steps formed by the polysili- from APCVD systems operating at 760 torr. In LPCVD con gate make uniform deposition of the metal film impos- reactors the substrates are mounted vertically. sible. The P-glass layer is deposited by CVD and then If a plasma is used to generate ions or radicals that heated until it softens and flows: this process is called recombine to give the desired film, the process is plasma- reflow. The reflow characteristics depend on the concen- enhanced CVD (PECVD). In PECVD it is possible to use tration of P in the glass, which is typically between 6 and much lower substrate temperatures because the plasma 8 wt%. Silica doped with both P and B is also used for the provides energy for the reaction to proceed. A major com- reflow process. Typical concentrations are 1–4 wt% B and mercial application of PECVD is the formation of silicon 4–6 wt% P. The borophosphosilicate glass (BPSG) has the nitride films for passivation and encapsulation of semicon- advantage of lower flow temperatures; however, care must ductor devices. At this stage of the fabrication process the be taken to carefully control the dopant concentrations, device cannot tolerate temperatures much above 300°C. otherwise separation of a B-rich phase can occur. High temperatures would still be required if crystalline or Si3N4 layers deposited by CVD are important in the epitactic films were required. Many nitrides have been fabrication of certain semiconductor devices. One area is prepared in thin-film form by PECVD, including AlN, in the so-called LOCOS (local oxidation of silicon) GaN, TiN, and BN. A more complete list of films depos- process. This method is used in both bipolar and metal ited by PECVD is given in Table 28.3. oxide semiconductor (MOS) devices to isolate active PECVD has also been used to fabricate carbon nano- device regions. The process works as follows: A layer of tubes and other one-dimensional nanostructures such as Si3N4 is deposited on the silicon wafer by CVD either by boron carbide nanowires and nanosprings. A convenient reacting silane and ammonia at temperatures between 700 precursor for boron carbide nanowires is orthocarborane and 900°C (C2B10H12). MOCVD is distinguished from other forms of CVD 3SiH4 + 4NH3 → Si3N4 + 12H2 (28.14) in that the precursors are metalorganic compounds. MOCVD is widely used in the semiconductor industry but or by reacting dichlorosilane and ammonia between 700 not so widely used in forming ceramic films. One example and 800°C of a ceramic film formed by MOCVD is AlN, where the precursors are trimethyl aluminum [TMAl = Al(CH3)3] 3SiCl2H2 + 4NH3 → Si3N4 + 6HCl + 6H2 (28.15) and ammonia (NH3) Like the SiO2 films described earlier the Si3N4 is amor- (CH3)3Al (g) + NH3 (g) → AlN (s) + 3CH4 (g) (28.16) phous. The exposed regions of the silicon wafer are then oxidized whereas the areas covered by Si3N4 are protected. LECVD (laser-enhanced CVD) uses a laser beam to The oxidizing agent cannot diffuse through the Si3N4 layer enhance reactions at the substrate surface. One feature of to reach the silicon surface. However, oxidation does occur this technique is that it is possible to “write” materials on a small distance below the edges of the silicon nitride the substrate: the deposit is formed only where the scanned layer. If the oxide layer is sufficiently thick, the edges of light beam hits the substrate. 2 8 .7 Ty p e s o f C h e m i c a l Va p o r D e p o s i t i o n ............................................................................................................. 499  TABLE 28.3 PECVD Reactants, Deposition Temperatures, and Growth Rates Film T (K) Rate (cm/s) Reactants −8 −7 a-Si 573 10 –10 SiH4; SiF4 –H2 ; Si–H2 c-Si 673 10 −8 –10 −7 SiH4 –H2 ; SiF4 –H2 ; Si–H2 C (graphite) 1073–1273 10 −5 C–H2 ; C–N2 CdS 373–573 10 −6 Cd–H2S SiO2 523 10 −8 –10 −6 Si(OC2H5) 4; SiH4 –O2, N2O GeO2 523 10 −8 –10 −6 Ge(OC2H5) 4; GeH4 –O2, N2O SiO2 /GeO2 1273 3 × 10 −4 SiCl4 –GeCl4 + O2 Al2O3 523–773 10 −8 –10 −7 AlCl3 –O2 TiO2 473–673 10−8 TiCl4 –O2 B2O3 B(OC2H5) 3 –O2 Si3N4 (H) 573–773 10 −8 –10 −7 SiH4 –N2, NH3 AlN 1273 10 −6 SiCl4 –N2 GaN 873 10 −8 –10 −7 GaCl3 –N2 TiN 523–1273 10 −8 –5 × 10 −6 TiCl4 –H2 + N2 BN 673–973 B2H6 –NH3 SiC 473–773 10 −8 SiH4 –Cn H m TiC 673–873 5 × 10 −8 –10 −6 TiCl4 –CH4 + H2 Bx C 673 10 −8 –10 −7 B2H6 -CH4 28.8 CHEMICAL VAPOR of critical injuries and resulted in the plant being closed DEPOSITION SAFETY for several months. Safety issues are particularly important for CVD since many of the source compounds are toxic and disposal of 28.9 EVAPORATION waste products, e.g., HCl, is often problematic. Additional problems can occur if the reactants are pyrophoric (ignite Experimentally, evaporation is a very simple method for in contact with air). Table 28.4 lists some of the source forming thin films. The source is either a liquid or a solid gases used in CVD and their potential hazards. Silane is that is heated to produce a flux of atoms or molecules. In widely used in the semiconductor industry and was the general, it will be necessary to melt the material if the cause of a major explosion and fire at a manufacturing vapor pressure is <10−3 torr at its melting temperature. plant in Moses Lake, WA. The incident caused a number Most metals fall into this category and so liquid sources TABLE 28.4 Hazardous Gases Used in CVD Gas Corrosive Flammable Pyrophoric Toxic Bodily hazard Ammonia (NH3) X X Eye and respiratory irritation Arsine (AsH3) X X Anemia, kidney damage, death Boron trichloride (BCl3) X Boron trifluoride (BF3) X Chlorine (Cl2) X X Eye and respiratory irritation Diborane (B2H6 ) X X X Respiratory irritation Dichlorosilane (SiH2Cl2) X X Germane (GeH4) X X Hydrogen chloride (HCl) X Hydrogen fluoride (HF) X Severe burns Hydrogen (H2) X Phosphine (PH3) X X X Respiratory irritation, death Phosphorus X pentachloride (PCl5) Silane (SiH4) X X X Silicon tetrachloride X (SiCl4) 500 ............................................................................................................................. Th i n F i l m s a n d Va p o r D e p o s i t i o n are used. Some metals reach sufficiently high vapor pres- –2 kV sures below their melting temperature (e.g., Cr) and can Insulator be used as solids. Evaporation of metals is generally straightforward because they evaporate either as atoms or as clusters of Cathode Cathode atoms. However, most compounds dissociate when heated shield and therefore the vapor composition will be different from Ar ions Target that of the source. Consequently, the stoichiometry of the Si wafer e- deposited film will also be different from that of the source. An example of an oxide that dissociates on heating Anode Vacuum is ZrO2 chamber 1 ZrO2 (s) → ZrO(g) + O2 (g) (28.17) Needle 2 valve Vacuum pumps Ar Films formed directly from evaporation of ZrO2 tend to be metal rich. To maintain the desired stochiometry it FIGURE 28.4 Schematic of a sputtering system. is necessary to perform the evaporation in an oxygen-rich environment. This is called reactive evaporation (RE). A similar approach needs to be used with SiO2, GeO2, TiO2, substrate placed facing the cathode will be coated with a and SnO2. film of the material sputtered off the target surface. [If Some ceramics sublime, i.e., they go from a solid to a you have any experience with sputter coating samples for vapor without dissociation, for example electron microscopy you will realize that the inside walls of the vacuum chamber also become coated.] A wide AlN (s) → AlN (g) (28.18) range of ceramics can be deposited by sputtering; some examples are given in Table 28.5. Thus film stoichiometry would be maintained in the There are several characteristics of the sputtering deposit. Several oxides also behave in this way, for process that need to be considered before using this tech- example, B2O3, GeO, and SnO. nique for film growth: For some ceramics the high sublimation temperatures require special heating sources for evaporation. One such  It does not involve melting and therefore materials with source is a focused electron beam. The process is then high melting points can be deposited. called electron beam (or simply e-beam) evaporation.  It is a relatively slow process.  It may be difficult to maintain stoichiometry of a mul- ticomponent target due to the different sputtering rates 28.10 SPUTTERING of the constituents.  When the substrate and target are facing each other An example of a simple sputtering system is shown in (on-axis configuration) the growing film may be Figure 28.4. Atoms are dislodged from a solid target damaged by bombardment by energetic species from through the impact of energetic gaseous ions. The usual the plasma. sputtering gas is argon, which is ionized forming a plasma. An argon plasma has a characteristic purple color, which As with CVD and evaporation, there are various types you see during sputter coating of samples for scanning of sputtering. The process we have described so far is DC electron microscopy (SEM) and transmission electron sputtering, also called diode or cathodic sputtering. It is the microscopy (TEM) analysis. The plasma forms as a result easiest process to visualize, but cannot be used for insulat- of collisions between energetic electrons in the gas and ing targets. There are two approaches for ceramics: the argon atoms. The positive Ar+ ions in the plasma are attracted toward the cathode (the target) and the electrons  Reactive sputtering uses DC sputtering of a metal toward the anode (the substrate). The energy of the Ar+ target in a reactive gas environment. For example, we depends on the value of the applied electric field, but is can make AlN films by sputtering an Al target in either sufficient to cause atoms to be ejected from the target nitrogen or ammonia (mixed in with the working gas, surface. When an ion reaches the target it collects an Ar). electron, supplied via the  RF sputtering uses an external circuit from the alternating RF signal anode, and become a Ar IN PLASMA FORMATION between the electrodes. neutral atom that returns to It is used because of its high mass, which creates a high Typical frequencies are the gas to be reionized. A momentum and more ejected particles from the target. between 5 and 30 MHz. 2 8 .10 S p u t t e r i n g ........................................................................................................................................................... 501  TABLE 28.5 Ceramic Sputtering Targets Material Applications Oxides Al2O3 Insulation, protective films for mirrors BaTiO3, PbTiO3 Thin-film capacitors CeO2 Antireflection coatings In2O3 -SnO2 Transparent conductors LiNbO3 Piezoelectric films SiO2 Insulation SiO Protective films for mirrors, infrared filters Ta 2O5, TiO2, ZrO2, HfO2, MgO Dielectric films for multilayer optical coatings Yttrium aluminum garnet (YAG), Magnetic bubble memory devices yttrium iron garnet (YIG), gadolinium gallium garnet (GGG, Gd3Ga5O12) YVO3 –Eu2O3 Phosphorescent coating on special currency papers YBa 2Cu3O7 High-temperature superconductors Fluorides CaF2, CeF3, MgF2, ThF4, Dielectric films for multilayer optical coatings (antireflection coatings, Na3AlF6 (cryolite) filters, etc.) Borides TiB2, ZrB2 Hard, wear-resistant coatings LaB6 Thermionic emitters Carbides SiC High-temperature semiconduction TiC, TaC, WC Hard, wear-resistant coatings Nitrides Si3N4 Insulation, diffusion barriers TaN Thin-film resistors TiN Hard coatings Silicides MoSi2, TaSi2, TiSi2, WSi2 Contacts, diffusion barriers in integrated circuits Sulfides CdS Photoconductive films MoS2, TaS2 Lubricant films for bearings and moving parts ZnS Multilayer optical coatings Selenides, tellurides CdSe, PbSe, CdTe Photoconductive films ZnSe, PbTe Optical coatings MoTe, MoSe Lubricants 28.11 MOLECULAR-BEAM EPITAXY separate furnaces called Knudsen effusion cells, which are bottle-shaped crucibles with a narrow neck. A resist- Molecular-beam epitaxy is a technique that has mainly ance heater wound around the cell provides the heat neces- been used by the semiconductor industry for producing sary to evaporate the material. As in the case of thin films of compound semiconductors (e.g., GaAs and conventional evaporation the source may be solid or liquid InP) used in the fabrication of LEDs, laser diodes, etc. depending upon its vapor pressure. The rate of deposition Because these inorganic semiconductors are ceramics of each species is determined by the vapor pressure above it should not be surprising that the technique can also the source, which is a strong function of temperature. The be used to grow other ceramic thin films, such as the temperature of each of the Knudsen effusion cells there- high-temperature superconductor YBa2Cu3O7. In fact, fore controls the flux of atoms reaching the substrate. MBE is ideal for ceramics that have layered structures Molecular-beam epitaxy of semiconductors requires the because it allows precise sequential deposition of single use of an ultrahigh vacuum (UHV) chamber (background monolayers. pressure 10−8–10−10 torr). For oxide ceramics background A diagram of an MBE system is shown in Figure 28.5. pressures of ≤10−4 torr are more common. The high vacuum The materials to be deposited are usually evaporated from requirement of MBE presents a problem for the growth of 502 ............................................................................................................................. Th i n F i l m s a n d Va p o r D e p o s i t i o n  Substrate holder and heater ω Mass spectrometer High vacuum Mass-flow RHEED valve Electron gun Target Plume Substrate Ion Process sputtering control gun unit Substrate Auger heater cylindrical analyzer Effusion cells Fused silica window Shutter cont. Focusing lens From Thermocouples laser Variable aperture Liquid UHV Heater control nitrogen pumps FIGURE 28.6 Schematic of a PLD system. FIGURE 28.5 Schematic of an MBE system. many multicomponent PRESSURE Excimer lasers operat- oxides such as the high- Pressure is often quoted in the non-SI units of torr, 1 torr ing in the UV are the laser temperature superconduc- being equivalent to 1 mm Hg. The SI unit for pressure is of choice for most PLD tors because most of these the pascal, Pa. One Pa is equal to one newton per square systems. The operating compounds require oxygen meter (N/m2). To convert between torr and Pa, simply wavelengths used in com- pressures much higher than multiply the pressure in torr by 133.3 to obtain the pres- mercial systems are shown this to form. This limita- sure in Pa (750 torr = 105 Pa). in Table 28.6. Pulse ener- tion has been overcome by gies up to 500 mJ are used the use of highly oxidizing with repetition rates up to gases, such as NO2, atomic several hundred hertz. O, or O3, near the surface of PLD GROWTH OF BaTiO3 THIN FILMS Pulsed-laser deposition the growing film, while the CONDITIONS offers several advantages background pressure is Chamber evacuated to <5 μtorr over other PVD methods: maintained as low as Pressure during deposition 400 mtorr of O2 possible. KrF excimer laser λ = 248 nm The interaction of the  In addition to the Pulse repetition rate 50 Hz laser beam and the target requirement of high Pulse energy 85 mJ produces a plasma con- vacuum or UHV environ- Target to substrate distance 4 cm sisting of species hav- ments, other features of Substrate temperature 750°C ing high kinetic energy, MBE limit its use: which enables epitactic film growth at low sub-  The equipment is expensive (>$1 million) so the value strate temperatures. added must be high.  Growth of films having complex stoichiometry can be  Deposition rates are low: ≤1 μm/h is typical. achieved.  The irradiation source is outside the deposition chamber allowing flexibility. Multiple chambers can 28.12 PULSED-LASER DEPOSITION TABLE 28.6 Excimer Laser Wavelengths In pulsed-laser deposition (PLD) a laser beam is used to ablate material from a solid target. The experimental Excimer molecule Wavelength (nm) arrangement, which is very simple, is shown in Figure F2 157 28.6. However, the laser–target interactions are very ArF 193 complex and result in the formation of a plume of material KrCl 222 (often visible and brightly colored) that contains all the KrF 248 XeCl 308 necessary components (often in the correct proportions) XeF 351 for film growth. 2 8 .1 2 P u l s e d - l a s e r D e p o s i t i o n ................................................................................................................................. 503  use a single laser and the irradiation source can be  Increase film adhesion easily changed.  Modify grain shape  Relatively high deposition rates (>10 nm/s) can be  Induce crystallization achieved.  It is fairly inexpensive. These changes are possible because the incident ion beam may But it also has several drawbacks:  Alter surface chemistry  It is difficult, at present, to cover large substrates uni-  Create extra nucleation sites formly since the plume peaks in the forward  Increase the surface mobility of the adsorbed atoms direction.  Raise film temperature leading to higher reaction and  The technique is line of sight. diffusion rates  It is difficult to coat a large number of substrates at once.  Laser–target interactions can result in the deposition 28.14 SUBSTRATES of large (micrometer-sized) particles on the surface of the film. This presents problems if we want to produce There are many considerations when choosing a substrate multilayer structures. for thin-film growth:  Chemical compatibility. There should be no deleteri- 28.13 ION-BEAM-ASSISTED DEPOSITION ous reactions between the film and the substrate. For the high temperatures (≥700°C) used during the growth There are two forms of ion-beam-assisted deposition of many ceramic thin films this requirement may be (IBAD). The first is a dual-ion-beam system in which quite restrictive. one source is used to sputter a target to provide a source  Matched coefficient of thermal expansion (α). In of atoms for deposition (the same process we described cases in which the film and substrate are different it in Section 28.10). Simultaneously a second ion beam is will be almost impossible to achieve an exact match aimed at the substrate and bombards the depositing film. in α. A significant difference in α should be avoided In the second configuration, shown in Figure 28.7, an because it can cause poor adhesion and cracking ion source is combined with an evaporation source. of the film. The latter problem is particularly relevant The use of ion bombardment during film growth can to ceramics, which are often brittle. Brittle materials modify film properties. For example, IBAD of SiO2 with are particularly weak in tension and therefore it 300 eV O2 + ions during growth can change the refractive is better if αfilm < αsubstrate: this will put the film in index. It is also possible to compression.  Surface quality. The surface of the substrate is impor- tant because it is here that film nucleation and growth Substrate occur. The surface of a single-crystal substrate can holder Ion contain a variety of defects of different sizes, from Shutter probe emergent dislocations, to surface steps, to scratches due to polishing. The defects are important because they can act as preferential sites for nucleation. Figure 28.8 shows the nucleation of islands of Fe2O3 at step edges formed in a Al2O3 substrate by high-temperature Ion annealing. This type of orientation mechanism is beam known as graphoepitaxy, in which the topography of the substrate surface controls the microstructure of the film. Pump  Cleanliness. It is important to ensure that each sub- strate is cleaned before film deposition. For example, Evaporant single-crystal MgO substrates are often packaged in mineral oil prior to shipping to avoid the reaction between the MgO and water vapor that results in the formation of Mg(OH) 2. The oil can be removed by Ion soaking in acetone. Many laboratories develop their Gas source e-beam inlet evaporator own in-house cleaning procedures. The main steps involve degreasing in organic solvents, possibly fol- FIGURE 28.7 Ion-beam-assisted deposition system. lowed by a high-temperature anneal. 504 ............................................................................................................................. Th i n F i l m s a n d Va p o r D e p o s i t i o n   Thermal stability. Phase transformations occurring during heating and cooling can result in the generation of stresses within the film. Perovskite substrates undergo phase transformation. If we want to form epitactic films, then we also need to consider the following:  Lattice mismatch. In semiconductor systems lattice mismatches of only a few percent, or less, are desired to reduce the number of dislocations in the film. In ceramic thin films larger mismatches (generally <15%) are tolerated because higher defect densities in the film FIGURE 28.8 Growth at surface steps. are acceptable. In some situations a certain number of defects are actually beneficial to film properties (they can provide pinning sites in high-temperature super- conductors that can trap magnetic flux lines).  Substrate homogeneity. In many single-crystal sub-  Crystal structure. A close match in the lattice parame- strates this is not a problem. But in materials that ters of the film and substrate is one important require- are heavily twinned, such as LaAlO3 and LaGaO3, ment for epitactic growth. There must also be a twin boundaries that propagate through the substrate reasonable number of coincident lattice sites on either can act as nucleation sites. In bicrystal and poly- side of the interface. Frequently, although not always, crystal substrates the presence and orientation of the this means that the film and substrate should have grain boundaries affect film microstructure and similar crystal structures. The higher the number of properties. coincident sites, the better the chance of good epitaxy. CHAPTER SUMMARY Thin films of ceramic materials are important both scientifically and commercially. For example, the operation of semiconductor devices relies on thin dielectric layers. In this chapter we described some of the main techniques used to produce such films. The common feature of all techniques for growing thin films is that we require a vacuum chamber. Deposition may occur at atmospheric pressure (e.g., some versions of CVD), but prior to deposition the chamber was evacuated. The choice of technique is based on several factors, including the type of mate- rial being deposited, whether we need an epitactic layer, and often the cost. The substrate plays an important role in the growth of thin films and thus we need to know the properties of the substrate and how to prepare it. Some of the techniques we described, such as PECVD, are important not only for growing thin films but also for producing nanostructures such as nanowires and nanosprings. PEOPLE IN HISTORY Pascal, Blaise (1623–1662) was a French mathematician and philosopher who invented the first digital cal- culator to help his father, a tax collector. Among his other notable contributions to mathematics and science was laying the foundation for the theory of probability. The SI unit of pressure, the pascal, Pa, is named after him. Torricelli, Evangelista (1608–1647) was born in Faenza (the home of faience pottery). He invented the barom- eter and worked in geometry. He died in Florence and the unit of pressure, torr, is named after him. GENERAL REFERENCES Chrisey, D.B. and Hubler, G.K. (1994) Pulsed Laser Deposition of Thin Films, Wiley, New York. A com- prehensive survey of PLD and an excellent resource for information about materials grown by this technique. Ohring, M. (1992) The Materials Science of Thin Films, Academic Press, Boston. Covers many aspects of thin-film deposition of all types of material. A very useful resource. Pierson, H.O. (1992) Handbook of Chemical Vapor Deposition (CVD): Principles, Technology, and Applica- tions, Noyes Publications, Park Ridge, NJ. Everything you want to know about CVD. Chapter 7 covers CVD of ceramics. C h a p t e r S u m m a ry .......................................................................................................................................................... 505  Smith, D.L. (1995) Thin-Film Deposition: Principles and Practice, McGraw-Hill, New York. A comprehen- sive handbook on thin-film growth. Thin Solid Films. An international journal devoted to thin films. SPECIFIC REFERENCES Adams, A.C. (1988) “Dielectric and polysilicon film deposition,” Chapter 6 in VLSI Technology 2nd edition, edited by S.M. Sze, McGraw-Hill, New York. Gives an overview of the use of ceramic insulating layers in semiconductor device fabrication. Kubaschewski, O., Evans, E.L., and Alcock, C.B. (1967) Metallurgical Thermochemistry, 4th. edition, Per- gamon Press, Oxford. A good standard thermodynamics text with lots of useful data collected in appendices. Phillips, J.M. (1996) “Substrate selection for high-temperature superconducting thin films,” J. Appl. Phys. 79, 1829. EXERCISES 28.1 What reactive gases would be suitable for forming the following ceramic thin films by reactive sputtering?: (a) Al2O3, (b) TaN, (c) TiC, (d) CdS. 28.2 Name two of the ways that you might use to make sputtering targets. 28.3 Thin films can grow by three distinct mechanisms. Name the three mechanisms and explain how they differ. 28.4 Why is it often desirable to form thin films at the lowest possible substrate temperature? 28.5 What advantages are there, if any, of working at high substrate temperature? 28.6 What reactant gases might you use for making the following films by CVD?: (a) ZrC, (b) TaN, (c) TiB2. 28.7 Consider the data given below: Reaction A B C TiCl4 = Ti + 2Cl2 180,700 1.8 −34.65 2TiN = 2Ti + N2 161,700 — −45.54 SiCl4 = Si + 2Cl2 155,600 3.64 −43.90 SiC = Si + C 14,000 1.3 −5.68 C + 2H2 = CH4 −16,500 12.25 −15.62 −12 H2 + −12 Cl2 = HCl −21,770 0.99 −5.22 SiO2 = Si + O2 215,600 — −41.50 The values of A, B, and C are given for ΔG 0 = A + BT log T + CT (ΔG 0 in cal.). From these data determine whether it would be thermodynamically feasible to form the following ceramic films by CVD at a temperature of 850°C. (a) TiN from the nitridation of TiCl4, (b) SiC from the reaction between SiCl4 and methane, and (c) SiO2 from the oxidation of SiCl4. 28.8 What technique would you use to produce a 100-nm thin film of AlN on silicon? Explain why you chose your technique and its pros and cons. 28.9 What technique would you use to produce a 5-nm thin film of BaBiO3 on MgO? Explain why you chose your technique and its pros and cons. 28.10 Which of the techniques described in this chapter is most suitable for producing thin films on large substrates? What is the largest substrate that can be coated? 506 ............................................................................................................................. Th i n F i l m s a n d Va p o r D e p o s i t i o n  29 Growing Single Crystals CHAPTER PREVIEW We will now describe the important methods used to produce single crystals of ceramic materi- als. Single crystals are important in many applications ranging from synthetic gemstones for jewelry to hosts for solid-state lasers. The method that is selected to grow a particular type of crystal depends on several factors. The selection criteria are determined by the properties of the material—whether a suitable solvent can be found, if the solid melts congruently or incon- gruently, or if it sublimes, and the economic factors—the volume of material to be produced and the capital equipment costs. Remember that without the growth of ceramic single crystals, the Si Age would never have happened. 29.1 WHY SINGLE CRYSTALS? as diamond simulants, are available only as synthetics. In its pure form the cubic polymorph of zirconia is not stable For some applications, ceramic materials must be pre- at room temperature and must be stabilized by the addi- pared as single crystals. When used as substrates for thin- tion of CaO, MgO, or Y2O3. The cubic form of ZrO2 does film growth [e.g., silicon-on-sapphire (SOS) technology or exist in nature; it was discovered in 1937 as tiny crystals the growth of superconductor thin films] it is the crystal- in an amorphized piece of zircon (ZrSiO4), but it is not line perfection of a single crystal that is important. In abundant. optical applications, e.g., the use of ruby and yttrium– aluminum–garnet (YAG) for laser hosts and quartz and sapphire for optical windows, single crystals are used to 29.2 A BRIEF HISTORY OF GROWING minimize scattering or absorption of energy. In piezoelec- CERAMIC SINGLE CRYSTALS tric materials, e.g., quartz, the optimum properties are obtained in single-domain single crystals. Table 29.1 lists Although crystal growth is a relatively new industry, we some of the applications that utilize the desirable optical, can trace its origin back to 2500 bce when salt was puri- electrical, magnetic, or mechanical properties of ceramic fied by crystallization. Systematic work in crystal growth single crystals. started in c. 1600 ce with the growth of crystals from Because preparing single crystals is in most cases a aqueous solution and in c. 1850 from the melt and the more difficult and expensive process than preparing the vapor. same compositions in polycrystalline form they are often Hydrothermal growth. Growth of large single crystals much more expensive than their polycrystalline counter- of a ceramic material using the hydrothermal growth parts. For example, you can buy 99.9% pure MgO powder method was first demonstrated for α-quartz. This method in small quantities for about $2/gram. Single crystal slices uses an aqueous solution that is usually heated and pres- of MgO of the same purity cost about $300/gram! The surized. The growth process closely reproduces the growth increased cost of the single crystal not only involves the of amethyst in nature. The principle is essentially the same extra processing costs but may also include costs associ- as used for growing salt or copper sulfate crystals in high ated with orienting, cutting, and polishing. school. Silica is soluble in water, which is where diatoms When used for jewelry, synthetic single crystals can find their silica. The special feature of the hydrothermal be more costly than naturally occurring ones. For example, growth of quartz is the use of pressure to increase the the cost of a gem-grade faceted synthetic diamond may be solubility of SiO2 in H2O. 10 times that of an equivalent natural diamond. However, Flux growth. First practiced by French and German flux-grown emeralds and rubies are about one-tenth the chemists and mineralogists in the late 1800s, this tech- cost of natural stones of comparable quality. (The syn- nique is also known as molten-salt growth. Flux growth thetic stones are often much more perfect than the natural did not become an important method for forming ones.) Large single crystals of cubic ZrO2, which are used single crystals until the 1950s. A particularly significant 2 9. 2 A B r i e f H i s t o ry o f G r o w i n g C e r a m i c S i n g l e C ry s ta l s ........................................................................... 507  TABLE 29.1 The Uses of Single Crystals produced by the Cz method in 1950. This process is now used in the semiconductor industry for preparing very Semiconductor devices 1. Diodes Si, Ge large single crystals of Si and, with some slight modifica- 2. Photodiodes Si, GaAs, CdxHg1−xTe tions, it can be used to produce single crystals of com- 3. Transistors Si, GaAs, SiC pound semiconductors (e.g., GaAs). The first oxide crystals 4. Thyristors Si to be grown extensively by the Cz process were calcium 5. Photoconductive devices Si, CdxHg1−xTe tungstate (CaWO4), a laser host. Melt growth of single 6. Integrated circuits Si, GaAs 7. Light-emitting diodes GaAs, GaN, SiC crystals in crucibles was first used by Bridgman and the 8. Radiation detectors Si, Ge, CdTe, YAG method was significantly improved by Stockbarger and 9. Strain gauges Si became known as the Bridgman–Stockbarger method. 10. Hall effect magnetometers InSb Two melt-growth techniques that have emerged since Mechanical components 1950 are zone refining and the floating-zone (FZ) method; 1. Abrasives and cutting tools SiC, Al2O3 2. Substrates Diamond, Al2O3 some of the thin-film methods discussed in Chapter 28 Magnetic devices can also be thought of as melt techniques. Zone refining 1. Transformer cores Ferrites is used to purify single crystals (also for polycrystals). 2. Electric motors Ferrites Although zone refining is applicable to all types of single 3. Tape heads Ferrites crystal, its use is widespread only in the semiconductor 4. Microwave circulators Garnets Piezoelectric devices industry where crystal purity is of great concern. The FZ 1. Resonant bulk wave devices SiO2, LiTaO3 method was first applied to the growth of Si crystals. It 2. Surface wave devices SiO2, LiNbO3, AlN has since been used to form single crystals of other ceram- Optical devices ics but is mainly limited to high-purity Si. 1. Windows Al2O3 Although vapor-phase techniques are widely used to 2. Lenses CaF2 3. Polarizers CaCO3 make thin films they are not used extensively in the growth 4. Laser hosts YAG, Al2O3, alexandrite of large single crystals. One of the most interesting vapor- 5. Magnetooptical devices YIG phase methods is the vapor–liquid–solid (VLS) mecha- 6. Electrooptic devices LiNbO3, ADP, KDP nism first identified by Wagner and Ellis. This mechanism 7. Nonlinear devices ADP, KDP, LiNbO3 allows the growth of thin single-crystal whiskers that can Jewelry Diamond, cubic zirconia Pyroelectric devices be used as reinforcements in ceramic-matrix composites X-ray and particle optical devices (see Chapter 20). It is also widely discussed regarding the 1. Collimators and focusing SiO2 growth of nanotubes, nanowires, and nanosprings. elements 29.3 METHODS FOR GROWING SINGLE CRYSTALS OF CERAMICS contribution during this time was the growth of BaTiO3 single crystals using a KF flux at Bell Telephone Labora- The growth of single crystals involves one of the following tories in New Jersey. These crystals were of interest to changes of state: Bell Labs for ferroelectric storage elements for digital computers and telephone switching systems. Single crys-  Liquid (pure or solution) → solid tals were preferred over polycrystalline sintered BaTiO3  Gas → solid ceramics because the single crystals had a more rectangu- lar hysteresis loop and lower coercive fields. (See Chapter The atomic or molecular species in a fluid are, on 31 for more on ferroelectric ceramics.) average, arranged randomly. During crystal growth they Verneuil, Czochralski, and Bridgman. The Verneuil must move to the correct sites in the ordered structure of process, also known as the flame-fusion method, was first the crystalline phase. If crystal growth is too rapid, disor- described in 1902 by Auguste Verneuil. His original appa- dered regions (crystal lattice defects such as dislocations) ratus has been preserved and is in the Museum of Arts are trapped in the crystal or many smaller crystals with and Sciences (Musée des Arts et Métiers) in Paris. This varying orientations are nucleated thereby destroying the process was used in the early 1900s to make synthetic desired single-crystal perfection. The growth process rubies. Although the initial application for these crystals involved in producing a single crystal must therefore be was in jewelry, their hardness made them suitable for slow and so it requires precise control over the growth bearings in clocks and watches, which eventually has conditions (e.g., temperature) for prolonged periods. become their main use. Other methods for growing crys- Several different methods are used commercially to tals from the melt followed. Pulling the crystal from the grow single crystals. These methods, which can be divided melt was first practiced by Czochralski (Cz) in 1917. He into melt, solution, and vapor-phase techniques, are sum- grew crystals of low-melting temperature metals including marized in Table 29.2. Here, the operating cost does not Sn, Pb, and Zn. Single crystals of Ge and Si were first include the cost of labor, the skill refers only to the diffi- 508 ............................................................................................................................................ G r o w i n g S i n g l e C ry s ta l s  TABLE 29.2 Factors Relevant to the Choice of a Growth Technique for Crystal Production Equipment Operating Skill Development Range of Growth Crystal investment costs needed needed materials rate perfection Cz High Medium Medium Medium Many Rapid High Bridgman Low Medium Low Little Many Medium Medium Verneuil Medium Low High Little Some Rapid Low Skull melting High Medium Medium Medium Some Rapid Medium Flux Medium Medium Low Much Few Slow Variable Hydrothermal Very high High Medium Much Few Slow Variable UHP Very high High High Much Few Slow Variable Gas phase Low Low Low Varies Few Very slow Variable culty in using the equipment, not in developing the process, Many other techniques can be used to produce single the crystal perfection assumes the optimum conditions, crystals; solid–solid phase transformations or growth not the fastest, and the rate of flux growth depends on the from gels are modern examples. Although such methods complexity of the reaction—as is the case with growth of may be useful in the laboratory for producing small single emerald. crystals of ceramics they are not currently of commercial The method chosen depends on the type of crystal, the importance. application for that crystal, and the required size. The most widely used growth technique is the Cz process because it can produce very large dislocation-free crystals 29.4 MELT TECHNIQUE: VERNEUIL of silicon. It is also used to form single crystals of many (FLAME-FUSION) oxides. For oxides containing more than one cation the general requirement for forming a crystal by the Cz The Verneuil, or flame-fusion, method is illustrated in process is that the material melts congruently. In such Figure 29.1. It is a well-established technique for growing cases crystal growth of compounds by pulling is similar single crystals of oxides that have high melting tempera- to growing elemental crystals. If the compound melts tures. The largest application of the Verneuil method is incongruently the Cz method can still be used, if special for the growth of sapphire and ruby. precautions are taken, or an alternative method, e.g., For growing sapphire crystals, high-purity aluminum growth from solution or from a flux, may have to be oxide powder of a uniform particle size is fed at a used. controlled rate down a tube Most methods of single- at the end of which the crystal growth seek to SINGLE-CRYSTAL TERMINOLOGY particles are melted by an control the nucleation of A large single crystal in the as-grown form is often oxyhydrogen flame. The the crystalline phase. This referred to as a boule, from the French word for ball, or molten particle then falls is achieved by arranging as an ingot (which may also be used to describe a into a shallow (∼20-μm- for the crystal to grow on polycrystal). deep) pool of liquid on a “seed” (which is the When a boule is cut into flat sections, the single- top of a seed crystal. The nucleus). The seed crystal crystal slices are typically referred to as wafers. pool of liquid is held on is usually a single crystal When the wafers are cut into small units (usually the seed crystal by sur- of the same composition as either square, rectangular, or circular) they are referred face tension. The seed is the crystal to be grown. It to as substrates or windows. lowered into the annealing is often oriented in such a zone of the furnace at the way as to facilitate growth of one specific crystalline ori- same rate as the new material arrives, thus growing the entation. In the Bridgman–Stockbarger method a seed crystal. The growing crystal cools slowly helping to reduce crystal is not used. In this method advantage is taken of strains and minimizing the chance of forming lattice the tendency for crystals to grow more rapidly in one defects. It is always preferable to anneal the crystal from crystallographic direction than in another. the growing temperature without first cooling to room Vapor-phase techniques are not as widely used as temperature. If the crystal is first cooled to room tempera- growth from the melt or solution because the growth rate ture and then annealed it is much more difficult to remove is generally slow or only small crystals can be grown. any defects that have formed. Remember that the crystal However, two vapor-phase techniques have commercial will still contain point defects as these are equilibrium application: the growth of whiskers or small islands (e.g., defects at high T and so cannot easily be annealed out. SiC and GaN) by the VLS process and the growth of SiC Since a gas flame and powder are used in the process, and nanotubes by sublimation processes. trapped pores are common defects. 2 9. 4 M e lt Te c h n i q u e : Ve r n e u i l ( F l a m e - F u s i o n ) ................................................................................................. 509  acteristic deep red color. Artificial blue sapphires are Vibrator obtained when a mixture of 1 at% TiO2 and 2 at% FeO is added to the feed powder. O2 One advantage of the Verneuil method is that it does Hopper (Dispenser) not use a crucible to contain the melt—only a shallow pool of liquid is present throughout the growth process. An important constraint of liquid-to-solid transitions for Gas Alumina controls powder crystal growth is the reaction of the melt with the con- tainer. For crystals with a high melting temperature (the situation we often encounter in ceramics) this constraint becomes especially severe. Even if reactivity is not a H2 problem it is still difficult to find suitable containers that can withstand very high temperatures without melting or degrading. The other advantages of the Verneuil method are that it is relatively inexpensive and quick. Crystals can easily be obtained in a matter of hours (typical growth rates are 10−2 m/h) compared with the months needed for some solution techniques. The main disadvantage of the Verneuil process is that there is relatively poor control over the growth parameters, particularly the temperature, because of the very small Flame melt volume. As a consequence the quality of the crystal Sight is often inferior to that obtained by, for example, the Cz hole method. Typically, Verneuil-grown crystals have high dis- location densities, which makes them most suitable for applications in which such imperfections are not so impor- Boule tant (e.g., jewelry or jewel bearings). Very large single crystals cannot be produced by the Verneuil method. Ver- neuil-grown boules may be up to 9 cm in diameter. Table Pedestal 29.3 lists some of the ceramic crystals that have been grown by the Verneuil method. Verneuil sapphire is used as the starting material (crackle) for Cz sapphire. The FZ method shares many similarities with the Ver- FIGURE 29.1 The Verneuil technique. neuil method. The main difference is that the source is a dense polycrystalline rod To produce artificial of the same composition as rubies and sapphires STALAGMITES the desired single crystal, various transition metal The Verneuil technique is related to the growth of sta- rather than the free-flowing oxides are added to the lagmites in nature. Liquid drips (from the stalactite) powder used in the Ver- alumina feed powder. For onto the stalagmite, but instead of settling there and neuil method, but it still rubies, between 1 and 3 freezing (like a stalagmite icicle would) some of the uses a constrained volume at% Cr2O3 gives the char- mineral content is deposited as the water evaporates. of liquid. The advantage of TABLE 29.3 Crystals Grown by Verneuil and Arc-Image Techniques Material Comments TM (°C) Al2O3 Corundum, sapphire Growth in a variety of directions; best growth 2040 in a cone of directions 60° from c Al2O3 : Cr Ruby Verneuil MgAl2O4 Magnesium-aluminum spinel Verneuil 2130 3Al2O3 · 2SiO2 Mullite Verneuil 1810 CaWO4 Scheelite Verneuil 1530 TiO2 Rutile Verneuil 1830 ZrO2 Zirconia Verneuil 2700 Y2O3 Yttria Verneuil 2400 MgFe2O4 Magnesium (nonstoichiometric) spinel Arc-image >1200 NiFe2O4 Nickel ferrite Arc-image >1200 510 ............................................................................................................................................ G r o w i n g S i n g l e C ry s ta l s  Chuck Crystal RF heating Ceramic feed rod coil Ellipsoidal reflector Melt Crystal Halogen Quartz lamp Lens tube Chuck (A) Screen Seed crystal Quartz tube (B) FIGURE 29.2 (a) Vertical float zone. (b) Arc image furnace. the FZ method is that like the Verneuil method, no cruci- arc-image growth process. The radiation from the light ble is used: the material is its own crucible as shown in source is focused by parabolic reflectors and allows sample Figure 29.2a. A thin region of melt is again held in place temperatures >2500°C to be attained. If a controlled or by surface tension, this time between two parts of the feed inert atmosphere is needed around the sample then it can rod. Not having a container removes one possible source be enclosed in a suitable transparent tube (envelope). of contamination; this is why the FZ method is used to MgFe2O4, and NiFe2O4, have both been grown by this produce high-resistivity silicon. The disadvantages of the technique. The main advantage of using arc-image heating FZ method are that it is not as amenable as the Cz method is that it is easy to provide a clean high-temperature envi- for producing very large high-quality single crystals. For ronment with a controllable atmosphere (which is particu- ceramics the FZ method may use the arc-image heating larly important when Fe cations are involved). method to attain the necessary high temperatures. 29.6 MELT TECHNIQUE: CZOCHRALSKI 29.5 MELT TECHNIQUE: ARC-IMAGE GROWTH A schematic diagram of the Cz technique is given in Figure 29.3a. The melt is kept at a temperature just above Several techniques for growing single crystals combine its freezing point and a seed crystal, rigidly fixed to a aspects of the FZ method and the Verneuil flame fusion rotating tube, is lowered into the surface of the melt. The method, but the heat source is not a flame. One such temperature of the melt is reduced until the molten mate- “modified” FZ growth technique is called arc-image rial begins to freeze onto the seed. Pulling is then started growth. Heat is supplied using a focused light source. and more material solidifies onto the crystal as it is with- Figure 29.2b shows a schematic arrangement of the drawn. The shape of the meniscus is determined by the 2 9. 6 M e lt Te c h n i q u e : C z o c h r a l s k i ......................................................................................................................... 511  Crystal tube Gas out Crystal rod Crystal rod Glass Die Melt bell Die ZrO2 Crystal jar heat Pull rod shield Chuck Iridium Stabilized crucible ZrO2 Melt Melt and lid tube & lid Stabilized (B) ZrO2 powder Crystal Fused silica tube RF heating coil Melt RF lead Gas in RF lead FIGURE 29.3 (a) The Czochralski technique for pulling crystals. (b) Modifica- (A) tions to Czochralski. Compared with the conventional geometry (left). surface tension of the liquid. The seed crystal is normally can be rotated at the same rate and in the same direction! rotated as it is withdrawn to average out any thermal For nonoxide crystals the whole apparatus is maintained asymmetries in the heating elements. This rotation also in an inert environment (e.g., Ar). Table 29.4 summarizes produces a stirring action, which can help homogenize the the relevant growth conditions that have been used to melt. At the same time, it accelerates crucible erosion and produce different crystals. A variation is to use a die to hence can introduce additional impurities into the melt. In produce tubes, fibers, or sheets of sapphire or garnet as cases in which the impurity concentration must be kept to illustrated in Figure 29.3b. Actually single-crystal tubes a minimum the crucible containing the melt and the crystal can be produced inside single-crystal tubes. TABLE 29.4 Materials Grown by the Cz Technique (for Crystals ~2 cm in Diameter) Pulling rate Rotation rate Material TM (°C) Crucible Atmosphere (mm/h) (rpm) Zn 419 Pyrex Vacuum 400–800 10–30 GaSb 712 Graphite Hydrogen 50–100 10–30 FeGe2 866 Alumina Vacuum 5–20 20–50 Bi11GeO20 930 Platinum Oxygen 5–15 10–50 Ge 937 Graphite H2 /N2 60–120 20–50 ZnWO4 1200 Platinum Air 8–16 50–100 GaAs 1237 Silica Arsenic 20–30 10–30 LiNbO3 1250 Platinum Oxygen 3–8 20–30 Srx Ba1−x Nb2O6 1400 Platinum Oxygen 3–6 10–20 Si 1420 Silica Argon 100–200 10–20 MnFe2O4 1500 Iridium 3–6 10–20 CaWO4 1650 Rhodium Air 8–16 50–100 LiTaO3 1650 Iridium Nitrogen 8–15 20–40 Y3Al5O12 1950 Iridium Nitrogen 1–3 40–60 Al2O3 2037 Iridium Argon 1–3 30–50 MgAl2O4 2100 Iridium Argon 4–8 20–40 512 ............................................................................................................................................ G r o w i n g S i n g l e C ry s ta l s  where kL is the thermal conductivity of the liquid and dT/ dx L is the thermal gradient in the liquid. qin is also the heat flow down the crystal, which is given by dT qin = Aks (29.4) dxs where ks is the thermal conductivity of the crystal and dT/dxs is the thermal gradient in the crystal. By substitut- ing Eqs. 29.2, 29.3, and 29.4 into Eq. 29.1 we find dT dx dT Aks = Aρs ΔH fus + AkL (29.5) dxs dt dxL Upon rearranging dx 1 ⎛ dT dT ⎞ = ⎜⎝ ks − kL ⎟ (29.6) dt ρs ΔH fus dxs dxL ⎠ FIGURE 29.4 Lower part of sapphire boule grown by the Cz If the pulling rate exceeds the value of dx/dt given by technique, the boule was 100–150 mm diameter; 300 mm long. Eq. 29.6 the crystal separates from the melt; if it less than that given by Eq. 29.6, then A will increase. Figure 29.5 shows the rings that develop around a single crystal as it grows with dx/dt constantly changing to keep A constant. Figure 29.4 shows part of a sapphire boule produced According to Eq. 29.6 the maximum growth rate by the Cz process. Sapphire boules can be up to 150 mm possible occurs when dT/dx L approaches 0 (if dT/dx L in diameter and 600 mm in length and weigh >40 kg. Most becomes negative the liquid would be supercooled and the sapphire is grown in the r-plane orientation (the growth interface would advance rapidly and dendritic growth axis is normal to the r plane). If an Si crystal is grown would occur). The maximum growth rate, (dx/dt) max, is with a 300 mm (12 inches) diameter to a length of 0.5 m, then given by the crystal weighs ∼82 kg. To determine the factors that affect the growth rate of ⎛ dT ⎞ ⎛ dx ⎞ = 1 the crystal we need to consider the heat flow in the system. ⎝ dt ⎠ max ρs ΔH fus ⎜⎝ ks ⎟ (29.7) dxs ⎠ The heat input, qin, to the crystal across the crystal/melt interface is given by the sum of the heat associated with We can see from Eq. 29.7 that the value of (dx/dt) max crystallization, q L, and the heat flow from the melt, qM: depends on the temperature gradient in the solid. The largest gradients in the solid may be obtained by deliber- qin = q L + qM (29.1) ately introducing large heat leaks from the growing crystal; q L is given by one method is to water-cool the seed holder. However, the high rates obtained under such conditions are generally not dx qL = Aρs ΔH fus (29.2) dt where A can be considered to be the area of the crystal at the liquid–solid interface. Actually, A is the area of the isotherm that goes through a point in the liquid close to the interface; however, very close to the interface this area is approximately the liquid–solid interfacial area. The density of the solid is ρs, ΔHfus is the heat of crystallization (fusion), and dx/dt is the rate of growth. To a good approx- imation the growth rate can be considered equal to the pulling rate, which from Eq. 29.2 we can see is inversely proportional to A. Therefore the faster the crystal grows, the smaller its diameter. The heat flow from the melt, qM, is given by dT qM = AkL (29.3) FIGURE 29.5 Growth rings on crystal surface: top section of Si dxL crystal after removing seed. 2 9. 6 M e lt Te c h n i q u e : C z o c h r a l s k i ......................................................................................................................... 513 useful because the crystal perfection under such growth There are several disadvantages to the Cz process. conditions is usually not very high. Typically, growth rates for good crystal quality are 10−4 –10−2 mm/s, 30–50%  It is applicable only to materials that melt congruently slower than the maximum values given by Eq. 29.7. or nearly congruently (see Sections 8.10 and 29.10). The Cz process has the following principal  The melt must be contained in a crucible; this is a advantages: problem for reactive high-temperature melts.  The capital cost is high. A Cz furnace used to produce  Excellent control over the growth conditions produces 8-inch-diameter sapphire boules costs $400,000. For very high quality crystals. larger boules the furnace can cost $1 million.  It is relatively fast.  Very large crystals can be produced. Despite these disadvantages the Cz technique is the most important crystal-growth technique for producing large A particular feature of the Cz process is that it is pos- high-quality single crystals. sible to produce dislocation-free single crystals. As dis- cussed in Chapter 12, dislocations are not equilibrium defects. Therefore it is, in principle, possible to produce 29.7 MELT TECHNIQUE: SKULL MELTING crystals that are free of dislocations. Although a small number of dislocations in a single crystal of most ceramics One of the problems with growing single crystals of does not normally present any problems, this must be ceramic materials is that they often have very high melting avoided if we are using the ceramic for its electrical/semi- temperatures. When molten, the liquid can be extremely conducting properties. Dislocation-free crystals can be corrosive to any crucible. In skull melting the melt is achieved once growth has started on the seed if the diam- contained within a frozen shell of the material itself—the eter of the crystal is slowly reduced to a minimum size. material acts as its own crucible. In perhaps the first appli- The minimum size is the size that can still support the cation of the skull melting process the technique was weight of the crystal to be grown (without deforming combined with crystal pulling to produce single crystals plastically and multiplying the number of dislocations). of manganese ferrite. Later (1961) the same method was Typically the minimum size is ∼3 mm in diameter and successfully applied to the growth of single crystals of 30 mm long; a 3-mm-diameter sapphire rod will support sapphire and YAG. [The technique is also known as induc- ∼200 kg. During this period, the crystal-melt surface tion skull melting (ISM) and is used for casting Ti and Ti becomes strongly concave as illustrated in Figure 29.6 so alloys—for the same reason.] that dislocations present in the initial seed can glide to the The most important economic application of the skull sidewalls of the crystal. Dislocation glide is facilitated if melting technique for ceramics has been the production of the glide plane makes a large angle to the growth axis. cubic zirconia (TM = 2700°C), which is manufactured at For crystals with a diamond-cubic structure the glide rates in excess of 300 tonnes (1.5 billion carats) per year. plane is {111}; for crystals with a rocksalt (NaCl) structure Cubic zirconia is the best of the diamond simulants and the glide plane is {110} (unless it is not—see Section 17.2). the growth of large (centimeter-sized) crystals became Subsequent growth is slowly modified to give the desired feasible only with the use of the skull melting technique crystal diameter and a dislocation-free crystal is then (Figure 29.7). The zirconia powder containing some small pulled. The dislocation density in Cz sapphire boules is pieces of Zr metal is contained in a water-cooled assembly typically in the range of 103 –104 cm−2. and heated by means of high-frequency induction heating (see Section 9.6). The Zr metal is used to couple with the high-frequency radiation. Once the temperature has reached 1100°C the zirconia becomes electrically con- Seed ducting and itself acts as a susceptor. The material close to the water-cooled walls remains solid, thus forming a dense sintered shell or “skull.” The rest of the zirconia liquefies. To induce crystallization, the melt is lowered slowly (∼1 cm/h) from the heating coil, as shown in Figure Slip trace Neck 29.7b. Crystal growth begins at the base of the melt and large columnar crystals (to ∼7 cm long) can be produced. The cost of cubic ZrO2 crystals varies depending on Boule supply and demand. The selling price for single crystals cap is only ∼$0.80 g−1. This makes them a low-cost commodity material for the gem trade and necessitates large-scale production to make the process economically feasible. However, once the crystals have been oriented, cut, and FIGURE 29.6 Schematic illustration of neck-down and flare-out polished for use as substrates for thin-film growth (e.g., geometries for growing dislocation-free crystals. the high-temperature superconductors) the equivalent cost 514 ............................................................................................................................................ G r o w i n g S i n g l e C ry s ta l s FIGURE 29.7 (a–c) The skull melting process. Porous RF crust heating Water-cooled coil jacket Sintered shell (or skull) Melt Growing crystals Grown crystals Cooling water inlet Lowering Cooling mechanism water outlet (A) (B) (C) is ∼$150 g−1 [∼$50 for a single 1 × 1 × 0.05-cm-thick (100) walls of the cone; only those crystals oriented so that the oriented substrate]. growth is favored in the axial direction persist into the bulk of the charge as the crucible is lowered into the cooler zone. As a result the upper part of the crucible finally 29.8 MELT TECHNIQUE: contains either a single crystal or a few large crystals. One BRIDGMAN–STOCKBARGER of the problems associated with the Bridgman–Stock- barger method occurs if the crystal expands on freezing The Bridgman–Stockbarger technique is illustrated in (this happens in covalently bonded crystals Si and Ge—as Figure 29.8. The powdered charge is melted in a crucible, it does with ice). The crucible acts as a constraint on the which is often a refractory metal Pt, Ir, or Mo. This tech- growing crystal and the expansion usually leads to large nique necessitates that the melt does not significantly react stresses, which can result in the introduction of disloca- with the crucible. The furnace is designed such that there tions and low-angle grain boundaries (GBs) and even is a sharp drop in temperature just below the bottom tip cause the crucible to burst. It is difficult to produce single of the crucible in its initial position. crystals with dislocation densities less than 104 cm−2 by The crucible is lowered (typically at a rate of 1 to this technique. There are other geometries for the Bridg- 30 mm/h) so that the tip enters the colder zone causing the man–Stockbarger technique. One configuration is the nucleation of crystals. The crystals grow fastest in particu- horizontal configuration in which the crystal is grown lar crystallographic directions and crystals growing at horizontally in a boat. angles greater than half the cone angle terminate at the The Bridgman–Stockbarger method has been used pri- marily in the growth of alkali halides and alkaline-earth Upper halides (e.g., LiF and CaF2). Table 29.5 summarizes some furnace Pt crucible TABLE 29.5 Typical Conditions for Bridgman–Stockbarger Growth Growth rate Melt Crystal TM (°C) (mm/h) Crucible Heating Al2O3 2037 2–8 Molybdenum coils ZnS 1850 0.5–2 Silica supported by graphite FeAl2O3 1790 5–10 Iridium GaAs 1238 2–6 Sand-blasted silica Cu 1083 6–60 Graphite powder Ge 937 50–150 Graphite- or carbon-coated Baffle silica As 814 5–12 Thick-walled silica AgBr 434 1–5 Pyrex Lower NaNO2 271 3–6 PTFEa furnace Insulation K 63.7 1–4 Stainless steel coated with paraffin Ar −189.2 0.7–1.5 Mylar FIGURE 29.8 The Bridgman–Stockbarger technique. a PTFE, polytetrafluoroethylene. 2 9. 8 M e lt Te c h n i q u e : B r i d g m a n – S t o c k b a r g e r .................................................................................................... 515 of the other crystals that have been grown by this method.  The boule can be annealed in situ after growth. This table is by no means complete; indeed, several thou-  Nothing moves mechanically. sand different crystals have been reported. In many cases the furnace tube is filled with an inert gas to protect the In the HEM technique, the Mo crucible, the seed, the charge and crucible. If the crystal is volatile, and the cru- melt, and the growing crystal are all located in the heat cible is silica or pyrex, the crucible may also be sealed. zone. Heat is removed using a W He-gas heat exchanger and is thus a temperature gradient technique (TGT). The technique uses directional solidification of the melt from 29.9 MELT TECHNIQUE: a seed that is in contact with the heat exchanger placed at HEAT-EXCHANGE METHOD the base of the crucible. The furnace elements melt the sapphire crackle and control the temperature of the liquid. The heat-exchange method (HEM) (also known as the The temperature of the seed is allowed to increase to melt Schmid–Viechnicki method) is best known for its use in back its surface and then growth begins by lowering the growing large crystals of sapphire. Sapphire crystals of temperature of the seed and the melt. Crystallization is a 34 cm diameter and 65 kg in weight are grown in a produc- three-dimensional process. The whole process takes about tion facility, up from the initial 20 cm diameter, 20 kg 72 hours and is followed by a similar annealing period. weight. (These values should be compared to a maximum Growth of (0001) boules is most difficult because the diameter of 15 cm for Cz growth.) Sapphire is particularly solid/liquid interface is convex toward the liquid in challenging since it is essential to use low thermal gradi- the HEM process, which increases solidification stresses. ents during growth and cool down to prevent cracking of The situation can be remedied by carefully controlling the the boule. The furnace is shown schematically in Figure temperature gradients. The resultant boule has a flat top 29.9. The furnace has several special features: surface making a large fraction suitable for preparing windows, etc.  Heat extraction and input can be controlled Fluorite crystals for use in ultraviolet (UV) independently. (λ = 193 nm) and vacuum ultraviolet (VUV) (vacuum UV; λ = 157 nm) lithography up to 20 cm diameter have been grown using a modified TGT, which is another variation on View point the directional solidification approach to crystal growth. Insulation The inner diameter of the high-purity graphite crucible used is 300 mm. An interesting feature of this method is the use of 2 wt% PbF2 to scavenge oxygen impurities. Blocks of the CaF2 /PbS2 mixture are pressed into the cru- cible with a (111) seed at the bottom. The vacuum is kept at ∼10−3 Pa with a graphite lid on the crucible to minimize Power vaporization and the thermal gradient can be controlled by leads Heating changing the position of the crucible in the furnace or element adjusting the flow of cooling water to the bottom of the crucible support. Crystals of CaF2 up to 250 mm diameter Crucible can also be grown by the Bridgman method. In either case, a temperature of ∼1500°C is used for the growth. Melt To vacuum pump 29.10 APPLYING PHASE DIAGRAMS TO Seed SINGLE-CRYSTAL GROWTH crystal An important consideration in the crystal growth of oxides containing several cations is whether the melting is con- gruent or incongruent. The discussion in this section Pyrometer builds on that in Section 8.10. If the compound melts congruently then crystal growth will proceed easily. For Heat Chamber example, the crystal could be grown by the Cz method in exchanger a way similar to growth of an elemental crystal. Crystals of lithium niobate, LiNbO3, can be readily grown using the Cz process. Its large nonlinear optical Helium gas coefficients have led to an intense interest in this material. FIGURE 29.9 Illustration of the heat-exchange (Schmid– Figure 29.10 shows part of the Li2O–Nb2O5 phase diagram. Viechnicki) method. The congruent melting temperature is not exactly at the 516 ............................................................................................................................................ G r o w i n g S i n g l e C ry s ta l s T (°C) so that the liquid near the crystal does not become depleted 1236 in Ba. Only a fraction of the melt can be obtained as single-crystal BaTiO3 since the whole of it solidifies, 1200 1200 forming a mixture of cubic BaTiO3 and Ba6Ti17O40, when 1197 1190 the BaO content falls to about 32 mol%. If the desired compound melts incongruently it is often 1160 easier just to use a technique like flux growth to obtain LN single crystals. N 1100 29.11 SOLUTION TECHNIQUE: L HYDROTHERMAL In the hydrothermal method single crystals are grown from an aqueous (hydro) solution. Although many crystals have been grown hydrothermally, α-quartz crystals are 1000 the only ones that are produced on a large scale. For this 30 40 50 Mol % L 60 reason we will describe the method used for growing large FIGURE 29.10 Part of the Nb2O5 –Li2O phase diagram. α-quartz crystals, although the system used for other materials (including emerald and ruby) is very similar. An stoichiometric composition but at 51.4 mol% Nb2O5. Solid- important feature is that the low-symmetry form of quartz ifying a melt of the composition 48.6% Li2O and 51.4 mol% is produced directly since T is low. Nb2O5 can produce a high-quality single crystal, but the Pure finely divided particles of mineral quartz are cation stoichiometry will placed at the bottom of a not be 1 : 1. To obtain stoi- tall cylindrical autoclave chiometric Li1.00Nb1.00O3 AUTOCLAVE that is 80% filled with a it is necessary to cool a An autoclave is a thick-walled vessel, usually made of basic solution, for example, melt containing excess steel, which allows us to carry out reactions under pres- 0.5 M NaOH. Suitably ori- sure and at high temperatures. (The original definition Li2O. For example, refer- ented seed crystals of α- ring back to Figure 29.10, implied a self-closing vessel with internal pressure quartz are held in wire a melt of composition sealing its joints; the closure is now made externally.) frames near the top of the 55 mol% Li2O and 45 mol% autoclave. Nb2O5 will solidify below ∼1200°C producing a stoichio- Thermometers allow temperature control within the metric solid. During growth of the crystal the melt will chamber. The seed crystals are usually naturally occur- become depleted in Nb. To counteract this loss it is neces- ring quartz, since this usually has a very low dislocation sary to ensure the melt is homogenized by stirring; if a density. The base of the autoclave is kept at 400°C; in this large melt volume is used, and a moderately sized crystal section the quartz fragments dissolve so it is called the is grown, the composition change will be small. dissolving section. The top of the autoclave, which is As noted in Section 8.10, pure cubic BaTiO3 cannot be called the growth section, is maintained at a temperature grown from a melt of that composition because, as shown some 40°C cooler than the dissolving section. The α–β in Figure 8.23, the hexagonal phase is in equilibrium with transition in quartz occurs at 573°C. For highly perfect the liquid at the solidification temperature (1618°C). The single crystals, growth should be carried out below the hexagonal phase transforms to the cubic phase at 1460°C, transition temperature. The solution at the bottom of but the phase change is very slow and thus the hexagonal the autoclave will saturate and move by convection to the phase can persist at room temperature. The hexagonal growth zone where the seed crystals are located. In the form of BaTiO3 is not ferroelectric. Its structure contains growth zone the solubility is lower, the solution becomes the required TiO6 octahedra, but the linking of the octa- supersaturated, and material is deposited onto the seed hedra is different from that found in cubic BaTiO3. In crystals. Figure 29.11 shows a schematic of an autoclave cubic BaTiO3 the octahedra share corners; in hexagonal used for hydrothermal growth. The baffle shown in the BaTiO3 some of the octahedra share faces. lower half of the autoclave is a perforated metal disk sepa- Cubic BaTiO3 can, however, be grown from a melt rating the dissolving and growth sections and helping to composition containing 35 mol% BaO and 65 mol% TiO2, localize the temperature differential. For piezoelectric which solidifies below 1460°C, the temperature below applications, the principal faces of the seed crystals are which the cubic form is stable. The melt is held just above {0001} and the crystals grow at ∼1 mm/day in both <0001> its solidification temperature, a seed crystal is dipped into directions producing crystals weighing over a kilogram its surface, and the crystal is pulled from the melt at a rate in a few weeks. Figure 29.12 shows a hydrothermally of 0.5–1.0 mm/h. The seed crystal is rotated during growth grown α-quartz crystal. Table 29.6 lists other ceramic 2 9.11 S o l u t i o n Te c h n i q u e : H y d r o t h e r m a l ............................................................................................................ 517  crystal carrier Seeds Baffle Nutrient FIGURE 29.11 A silver-lined laboratory hydrothermal autoclave, about 35 cm long. It can be much longer. FIGURE 29.12 Hydrothermally grown quartz crystal; note the colorless seed and the Pt support wire at the top. TABLE 29.6 Examples of Hydrothermally Grown Crystals Growth zone Dissolution zone Pressure or Crystal Solvent temperature (°C) temperature (°C) degree of fill α-SiO2 1 N Na 2CO3 360 400 80% 1.0 M NaOH + 0.025 M Li2CO3 374 397 88% + 0.1 M Na 2CO3 LiGaO2 3.5 M NaOH 385 420 70% BiTi2O12, Bi12TiO20 KF 550∼600 — >70∼80% K(Ta,Nb)O2 15 M KOH 650 690 1000 atm KNbO3, KTaO3 KOH 400∼600 450∼680 70∼80% PbTiO3, PbZrO3 KF 570 585∼590 50∼55% Pb(TixZr1−x)O3 >10 wt% KF 580 ∼618 83% R9Al3 (BOH) 2Si4O19 H3BO3 + NaCl or NaF 400∼700 — 1000∼3000 atm AlPO4, GaPO4 6.1 M H3PO4, 3.8 M ADP 150 300 80% (Mn,Fe,Zn) 8 [Be6Si6O24]S2 1% NaOH or 8% NH4Cl 450 480∼500 1500∼2000 atm Na 2ZnGeO4 30 wt% NaOH 250∼300 253∼310 50∼90% NiFe2O4 0.5 N NH4Cl 470∼480 — 70∼75% (1100∼1300 atm) Fe3O4 10 M NaOH 500 550 1000 atm ZnFe2O4 NaOH 400 — — Y3Fe5O12 1∼3 M Na 2CO3 or 1∼3 M NaOH 400∼750 — 200∼1350 atm 20 M KOH 350 360 88% Y3Ga5O12 1∼3 M Na 2CO3 or 1∼3 M NaOH 400∼500 — 1000–3000 atm K 2CO3 500 550 ∼1000 atm α-Al2O3 2∼3 M Na 2CO3 or 1 M K 2CO3 390∼490 500∼540 75∼82% (1100∼1600 atm) 10% K 2CO3 or 10% KHCO3 530∼600 540∼640 50∼70% 4 M K 2CO3 370 390 85% HCl — — — Y3Al5O12 2 M K 2CO3 550 600 1000 atm CaWO4 4 wt% NaOH 380 430 60∼70% SrWO4, BaWO4 7∼10 wt% NaOH 410∼485 450∼500 70% 5∼7 wt% NH4Cl or 15∼20 wt% 430∼485 450∼500 65∼70% LiCl or 30∼40 wt% NaCl CdWO4 7 wt% NH4Cl or 16∼25 wt% LiCl 430∼455 450∼470 75% SrMoO4, BaMoO4 5∼7 wt% NH4Cl or 15∼20 wt% 430∼485 450∼500 65∼70% LiCl or 30∼40 wt% NaCl ZnO 5.45 M KOH + 0.7 M LiOH 353 467 83% PbO 1 N LiOH 430 450 60% ZnS 2∼5 M NaOH 350∼380 410∼560 50∼80% single crystals grown by the hydrothermal method and the dilute aqueous solution containing 0.025 M Zn(NO3) 2 and experimental conditions used. 0.025 M HMTA maintained in the range 70–90°C for 1–3 hours. 29.12 SOLUTION TECHNIQUE: 29.13 SOLUTION TECHNIQUE: HYDROTHERMAL GROWTH AT FLUX GROWTH LOW TEMPERATURE Crystals of many ceramics can be obtained by cooling a Low temperatures are suitable for nanowires etc. because solution of the required compound in a suitable flux or they do not have to grow very large! An example is the solvent (serving the role of water in Section 29.11). The growth of ZnO nanorods. The early stage of growth on a common fluxes include KF, PbO, and PbF2. The flux is sapphire substrate is shown in Figure 29.13. The principle selected to give minimum contamination: of the synthesis is the hydroxylation of Zn2+ ions in an  PbO and Bi2O3 are good fluxes for the growth of oxides aqueous solution in the presence of hexamethylenetetra- because Pb and Bi atoms are so large that they do not mine [HMTA: (CH2) 6N4]. fit into many lattices. The hydrolysis reactions are  Alkali metal ions do not fit well into many lattices either because the sizes or the charges are wrong. (CH2) 6N4 + 6H2O ⇒ 6HCHO + 4NH3 (29.8) To illustrate the flux-growth process for growing single NH3 + H2O ⇒ NH4 + + OH− (29.9) crystals we will look at three examples. Yttrium iron garnet This promotes the hydrox- (Y3Fe5O12 or YIG) is ferro- ylation of Zn2+ ions in Pb WARNING magnetic. Approximately solution to form dissolved If the temperature is much above 1350°C PbO is reduced 52.5 mol% PbO, 44 mol% complexes, which are pre- to Pb and this can alloy with the platinum crucible! Fe2O3, and 3.5 mol% Y2O3 cursors to nucleation of the are mixed together in a Pt ZnO precipitate phase. crucible and heated to 1250–1350°C. After the melt has homogenized it is cooled at a rate of 0.5°C/h. The solidified (2 n − m )+ n [ Zn (H 2 O ) p ] ⎯⎯⎯ → [ Znn (H 2 O )np − m (OH )m ] 2+ OH − melt contains crystals of Fe2O3, PbFe12O19, and the required Y3Fe5O12. The mixture is crushed and digested in nitric − ⎯OH ⎯⎯ → nZn (OH )m (29.10) acid to free the crystals from the flux. In any flux-growth process it is important to have a solvent that dissolves the Though this route has been used for the synthesis of ZnO flux but does not affect the desired crystals. The crystals nanorods in solution, crystal growth can occur on sub- are separated magnetically at temperatures above and strates when they are exposed to the vapor phase above a below the appropriate Curie temperatures. The garnet crystals are equiaxed and can also be picked out of the crushed mixture visually. BaTiO3 crystals have been prepared using a KF flux containing 30% BaTiO3. The mixture is homogenized at 1150–1200°C for about 8 hours. The temperature is then lowered to 900°C and the flux is poured off. The BaTiO3 crystals are allowed to cool in the furnace to room tem- perature. A characteristic feature of flux-grown BaTiO3 crystals is that they form pairs of triangular plates (“but- terfly twins”) as shown schematically in Figure 29.14. The cooling rate determines the plate thickness making it pos- sible to form thin sheets directly, without them having to be cut from larger single crystals. In some cases a small amount of iron, about 0.2 wt% Fe2O3, is added to the start- ing mix. Iron assists in the formation of large area plates. However, a small amount of Fe3+ is then incorporated in the BaTiO3 lattice on Ti4+ sites. The charge difference is compensated for by the replacement of an equivalent number of O2− ions by F− ions. Although many details of the process used are kept secret, emeralds [Be3Al2 (SiO3) 6] can be produced by dis- FIGURE 29.13 Hydrothermal ZnO nanorods seen nearly end on. solving BeO, Al2O3, and SiO2 in an Li2O–MoO3 flux using 2 9.13 S o l u t i o n Te c h n i q u e : F l u x G r o w t h .............................................................................................................. 519  Bottom (100) addition Precious tube metal (111) 38°56Õ crucible Flux (100) SiO2 nutrient Seed plates Al2O3 + BeO nutrient (A) [011] FIGURE 29.14 Butterfly twins in BaTiO3. (B) an arrangement shown in Figure 29.15; emeralds can grow FIGURE 29.15 Flux growth of emerald: (a) schematic; to ∼60 g in 10–12 months. Synthetic rubies can be pro- (b) emeralds. duced using a PbF2 flux; rubies can grow to 600 g in 8 months. The synthetic crystals are ∼10% of the price of natural ones. The primary commercial manufacturer of TABLE 29.7 Fluxes Used for the Growth of Ceramics emerald and ruby in the United States is Chatham in San Francisco, which produces 20% (1 t/year) of the worldwide Material Flux production of synthetic emeralds and about 70% (700 kg/ Al2O3 PbF2 + B2O3 year) of the worldwide production of flux-grown rubies. B Pt The main advantage of the flux-growth method is BaFe2O4 Na 2CO3 that it can be used for a wide variety of materials. Single BaTiO3 Bi2O3 BeAl2O4 PbO, Li2MoO3, PbMoO4 crystals of materials that undergo phase transitions, melt CeO2 NaF + B2O3 incongruently, or have a high vapor pressure at their Fe2O3 Na 2B4O7 melting temperature can all be grown using flux growth. GaAs Ga, Sn The major disadvantages are as follows: GaFeO3 Bi2O3 + B2O3 GaP Ga  Impurities may be trapped in the crystal. Ge In, Sn + Pb  Growth is slow compared to melt-growth methods. GeO2 Li2Mo2O7, Li2W2O7  Growth of very large crystals is not possible. KNbO3 KF, KCl KTa xNb1−x O3 K 2CO3 For these reasons flux growth is a useful research MgFe2O4 Bi2O3 + B2O3 tool for growing small crystals (typical crucible volumes NiFe2O4 Na 2B4O7 PbZrO3 PbF2 between 50 and a few hundred cubic centimeters), but it SiC Si is not used widely for the production of industrial single TiO2 Na 2B4O7 + B2O3 crystals apart from gemstones. Many ceramics have been Y3Al5O12 PbO + B2O3, PbO + PbF2 produced as single crystals by the flux-growth process. Y3Fe5O12 PbO, PbO + PbF2, BaO + B2O3 The literature contains a large amount of information ZnO PbF2 ZnS ZnF2 about suitable fluxes for several thousand materials. Table ZnTe In, Ga, Sn, Bi, Pb 29.7 gives a few examples. 520 ............................................................................................................................................ G r o w i n g S i n g l e C ry s ta l s  Metal Catalyst Growing growing large diamonds is shown in the schematic diagram contact skin diamond crystal in Figure 29.16. The pyrophyllite (a hydrous aluminum silicate) tube is inserted into a ring of tungsten carbide through which the hydraulic pressure is applied. Pyro- phyllite is used because at high temperature and under high pressure it extrudes to form a gasket that bonds well to the tungsten carbide pistons and seals the tube to main- tain the applied pressure. Heating is achieved by passing an electric current through the tube. The temperature gra- Pyrophyllite Pyrophyllite heater dient within the tube is such that the center is between 10 heater Carbon and 30°C hotter than the ends. The carbon source (any source carbon-containing compound may be used, even peanuts) is dissolved in the solvent, often Ni, Fe, or an Ni–Fe alloy. The solvent forms a thin film on the surface of the seed Pyrophyllite and transport of carbon from the source to the crystal takes place by temperature-difference solution growth (similar to what happens in the hydrothermal process). The diamond seed crystals favor the formation of diamond instead of graphite. Growth rates depend on the solvent and the orientation of the seed crystal, but are 3 to 5 mm/day. 29.15 VAPOR TECHNIQUE: VAPOR–LIQUID–SOLID Pyrophyllite The VLS mechanism was first used to grow Si whiskers. FIGURE 29.16 Chamber for diamond growth. (Other whiskers were identified some years earlier.) The catalyst-mediated whisker-growth process is illustrated in Figure 29.17 for the growth of SiC whiskers. The process 29.14 SOLUTION TECHNIQUE: begins with melting a solid catalyst particle (e.g., steel), GROWING DIAMONDS so that it forms a liquid ball on a suitable surface (in this case, a graphite slab). The ball forms a liquid interface In addition to their importance in jewelry, diamonds also between the growing SiC whiskers and the vapor phase. have important industrial applications such as in diamond- Carbon (in the form of methane CH4) and silicon (in the impregnated cutting tools and as abrasives. The world use form of SiO) in the vapor feed are extracted by the liquid of diamonds is about 26 t (26 Mg) per year, of which about catalyst, which in turn becomes supersaturated. Crystal 16 t is synthetic. The synthetic diamond industry is a $1 growth occurs by precipitation from the supersaturated billion/year business. liquid at the solid–liquid interface. Whiskers produced by The carbon phase diagram was shown in Figure 8.7. the VLS process characteristically have a spherical cap. From this diagram you can see that diamond is in fact the metastable form of C under ambient conditions, with graphite being the stable form. Diamond is stable at pres- sures as low as 1 GPa if T is ∼25°C, although the rate of Vapor the transformation is extremely slow if the pressure is lower. However, diamonds can be synthesized from graph- ite at very high temperature (∼3300 K) and very high pres- SiC crystal sure (∼13 GPa). A more practical method involves the use of a solution (the flux again) and shares similarities with the other solution methods described above. Vapor Molten The credit for the first synthesis of diamonds goes to steel Bundy et al. of the General Electric Company, although 〈111〉 the Swedish company ASEA may have synthesized dia- monds in 1953. In each case, the product was diamond grit Graphite suitable for grinding and polishing uses. In 1970 research- Graphite ers at GE succeeded in synthesizing large (up to about 1 ct in weight) single-crystal diamonds. The arrangement for FIGURE 29.17 VLS process for growing SiC whiskers. 2 9.1 5 Va p o r Te c h n i q u e : Va p o r – L i q u i d – S o l i d ....................................................................................................... 521 One of the drawbacks of the VLS process is that it is and the products condense onto the cooler seed. The extremely slow. This leads to high production costs and process is carried out at a low argon pressure (200 Pa), limited availability, which together combine to make the allowing boules of 20 mm in length and up to 30 mm in whiskers extremely expensive ($800/kg in 1994). Also diameter to be produced at a rate of about 4 mm/h. although SiC has been classified as a nonhazardous mate- SiC wafers produced from the boules are very expen- rial, there are health concerns associated with very small sive. A single SiC wafer 30 mm in diameter and 0.3 mm whiskers. This problem may be even more important with thick can cost upward of $3000. By comparison, an Si the increasing production of the smaller whiskers known wafer of this size costs less than $20. as nanowires and nanotubes. The VLS mechanism has been identified in the growth of other ceramic whiskers including Al2O3, BeO, and B4C. 29.17 PREPARING SUBSTRATES FOR It has been proposed as a method for producing nanotubes, THIN-FILM APPLICATIONS and is often assumed to be the principal feature of such growth processes. Conversion of the boule into polished substrates requires several operations. The exact number and type of steps involved in this process depend on the material involved 29.16 VAPOR TECHNIQUE: SUBLIMATION and the application for the substrates. The following sequence would be typical for the preparation of single- Single crystal SiC is of interest for a number of applica- crystal substrates of ceramics. tions including high-temperature electronic devices and blue-light-emitting diodes. For these applications the  The top and bottom (sometimes called the seed and preparation of large high-quality boules is necessary from tang ends, respectively) of the boule are removed using which individual wafers can be sliced. At atmospheric a diamond-tipped saw. pressure SiC sublimes, so single crystals cannot be pro-  The surface orientation of the boule is determined by duced by melt growth techniques such as the Cz process. an X-ray method (typically Laue back-reflection). The However, a sublimation technique has been developed that boule is mounted in such a way that when it is cut the can produce boules up to 30 mm in diameter. The cross slices have the desired surface orientation. section of a reaction chamber is shown schematically in  Wafers are sliced from the boule using a diamond- Figure 29.18. A seed crystal and a polycrystalline source tipped saw or a set of diamond-coated wires. When the material are placed at opposite ends of a cylindrical wire saw is used many slices can be cut in one run container, along which a temperature gradient of 10– (like slicing a hard-boiled egg). The substrate thick- 20°C/cm is established (2300–2500°C at the source and ness essentially depends on the slicing operation, 2100–2200°C at the seed). SiC sublimes from the source although the final value depends on subsequent polish- ing operations.  The wafers are polished (see Section 18.12).  The wafers are diced up to produce individual sub- Insulation strates of the desired size. In some cases the substrates are cut so that the edge is aligned along a particular SiC crystallographic orientation. This orientation is also powder set by X-ray methods. (2400 °C) 29.18 GROWING NANOWIRES AND NANOTUBES BY VAPOR–LIQUID–SOLID AND NOT Porous graphite Dense graphite SiC single Insulation There is great interest in growing single crystals that are crystal (2200 °C) smaller than 100 nm in one, two, or three dimensions. The techniques being used are variations on those listed above SiC but deserve separate mention because of the special fea- seed tures involved. The detailed mechanisms involved in the crystal growth are not fully understood. The essential feature is that the “substrate” is small. The VLS technique has probably attracted most atten- tion. Essentially this is an extension of that used by Wagner FIGURE 29.18 Modified sublimation process for SiC single and Ellis to grow the original Si whiskers, which were crystals. themselves nanowires. Vapor–liquid–solid growth of 522 ............................................................................................................................................ G r o w i n g S i n g l e C ry s ta l s Si required a catalyst particle, but not all wire growth be grown by several methods include arc-discharge requires a heterogeneous catalyst. We can grow arrays of and pulsed-laser deposition; both methods can produce ZnO wires by depositing islands of catalyst on a substrate quite large quantities; it has been claimed that tons of and providing a vapor so that the wires will grow only high-quality nanotubes will be produced (which will be where the catalyst particle is. In some cases, it appears needed for the space elevator). For technological applica- that the catalyst may be solid throughout the process. In tions we might prefer to grow arrays of aligned tubes. other similar processes there is no catalyst. Nature grows We can do this using Fe-oxide particles as the catalyst rutile and asbestos fibers sing crystal anisotropy. and 9% acetylene in N2 as the feedstock; the growth tem- Carbon nanotubes started the excitement in nanotech- perature need only be ∼600°C. Such aligned structures nology, although the Nobel Prize was awarded for the can already be grown from the pores of mesoporous SiO2, buckyball (Chapter 7). We can construct these nanotubes on glass substrates, porous Si, porous alumina, etc. Ni by rolling the sheet of graphite shown in Figure 29.19a catalysts have been used with plasma-assisted CVD at (known as a graphene sheet) and joining the sides. Now 660°C. We can use the C nanotubes themselves as tem- we can join the sheets so that A meets B, or C meets D, plates (or substrates) to grow tubes (or wires) of other but we can also make A meet E. You will realize that this materials. corresponds to the formation of a screw dislocation that We can now grow tubes of many ceramics. The array runs along the tube and really does have a hollow core! of TiO2 nanotubes shown in Figure 29.19b was grown Then we could wrap other sheets around the first (not from a Ti foil placed in an electrolyte of 0.5% HF in water necessarily of the identical construction). The tubes can using a Pt cathode. The anodization voltage was kept at B E C D a2 a1 A (A) (C) (D) (B) FIGURE 29.19 (a) Graphene sheet illustrating how carbon nanotubes are formed. (b) TiO2 nanotubes. (c) and (d) IrO2 nanotubes. 2 9.18 G r o w i n g N a n o w i r e s a n d N a n o t u b e s b y Va p o r – L i q u i d – S o l i d a n d N o t .............................................. 523 ∼20 V and this structure was produced in ∼45 minutes. chemical properties of rutile. The nanotubes of IrO2 in The sample was cleaned in pure water and sintered at Figure 29.29c and d have a square cross section because up to 880°C transforming the as-grown anatase to rutile. they are single crystal with sides parallel to {001} planes. The resulting material has many possible applications We can grow nanotubes of other oxides such as MgO and (it resembles MCM-41 structurally) since it has all the NiO, and nanotubes of nonoxides such as BN. CHAPTER SUMMARY Many methods can be used to grow single crystals of ceramic materials. To produce large crystals the methods can be classified as melt growth, solution growth, or vapor growth. For solution growth a suitable solvent must be found for the material. Because it is possible to find a solvent for most materials (the literature contains solvents for several thousand materials), solution-growth techniques are applicable to a very wide range of ceramics. Melt-growth tech- niques generally require that the material melts congruently or nearly congruently—so knowl- edge of the phase diagram for the material is important—and this fact alone eliminates many materials from consideration. The significant advantage of melt-growth techniques is that, particularly in the case of the Cz method, very high quality crystals can be produced. Vapor growth of bulk material is generally used only to produce single crystals of ceramics like SiC that cannot be made by either melt or solution techniques, or for growing nanocrystals. Many of the methods used for thin-film growth produce single crystals—the emphasis in this chapter is that the crystals “stand alone.” PEOPLE IN HISTORY Bridgman, Percy Williams was born in Cambridge, Massachusetts in 1882 and joined the faculty of Harvard University in 1908. He is best known for his research on the effects of high pressure on materials and was awarded the Nobel Prize in Physics in 1946 “for the invention of an apparatus to produce extremely high pressures, and for the discoveries he made therewith in the field of high pressure physics.” Bridgman made contributions to many fields including crystallography and devised a method for growing single crystals, which bears his name. He died in 1961. Czochralski, Jan was born on October 23, 1885 in Kcynia, which is now in Poland. He was the eighth child of a carpenter (died 1953). He went to Berlin to study chemistry in 1904 and by 1910 was working on the processing of Cu. The story is that in 1913 he was writing up his notes on a study of crystallizing metals while sitting next to a crucible with molten Sn. Absentmindedly, instead of dipping his pen in the inkpot, he dipped it in the crucible and withdrew it quickly. He observed a thin thread of solidified metal hanging at the tip of the nib. His observation led to a new crystal growth technique, which he published in 1917. Verneuil, August Victor Louis (1856–1913) was a French chemist who reported his method for growing ruby in 1902. GENERAL REFERENCES Brice, J.C. (1986) Crystal Growth Processes, Blackie, Glasgow. A clear description of all the major (and most of the minor) techniques used to produce single crystals and a useful discussion on method selection. Elwell, D. and Scheel, H.J. (1975) Crystal Growth from High Temperature Solutions, Academic Press, New York. An excellent place to look for fluxes for crystal growth. Hazen, R.M. (1999) The Diamond Makers, Cambridge University Press, Cambridge. Fascinating; it reads like a novel. Hurle, D.T.J., Ed. (1994) Handbook of Crystal Growth, Vol. 2, Bulk Crystal Growth, North-Holland, Amsterdam. Journal of Crystal Growth. An international journal that publishes articles that deal with all aspects of crystal growth, from nucleation and growth theories to apparatus and instrumentation. Laudise, R.A. (1970) The Growth of Single Crystals, Prentice-Hall, Inc, Englewood Cliffs, NJ. The standard reference for crystal growth; summarizes materials grown by different methods. Nassau, K. (1980) Gems Made by Man, Chilton Book Company, Radnor, PA. An excellent and highly read- able account of the techniques used to produce artificial gemstones. Contains lots of history and back- ground information on the processes and their inventors. Nassau, K. and Nassau, J. (1980) in Crystals: Growth, Properties, and Applications, edited by H.C. Freyhardt, Springer-Verlag, New York. O’Donoghue, M. (1988) Gemstones, Chapman & Hall, London. The processing and properties of gemstones. Chapter 10 discusses synthetic and imitation stones. 524 ............................................................................................................................................ G r o w i n g S i n g l e C ry s ta l s  Scheel, H.J. and Fukuda, T. (2004) Crystal Growth Technology, Wiley, Chichester. In Chapter One, this text points out that Czochralski used the Bridgman technique in his laboratory and that the Cz technique should have been called the Teal–Little–Dash technique after the group who first produced large (nearly) dislocation-free crystals of Ge. SPECIFIC REFERENCES Aleksandrov, V.I., Osiko, V.V., Prokhorov, A.M., and Tatarintsev, V.M. (1978) in Current Topics in Materials Science, Vol. 1, edited by E. Kaldis, North Holland Publishers, Amsterdam, p. 421. Discussion of skull melting. Bundy, F.P., Hall, H.T., Strong, H.M., and Wentorf, R.H. (1955) “Man-made diamonds,” Nature 176, 51. First description of diamond synthesis. Hazen (1999) indicates that synthetic diamonds may have been made prior to this publication from GE. Ivanov, P.A. and Chelnokov, V.E. (1992) “Recent developments in SiC single-crystal electronics,” Semicond. Sci. Technol. 7, 863. On using SiC for blue LEDs. Keck, P.H. and Golay, M.J.E. (1953) “Crystallization of silicon from a floating liquid zone,” Phys. Rev. 89, 1297. First description of the FZ method. Khattak, C.P. and Schmid, F. (2001) “Growth of the world’s largest sapphire crystals,” J. Cryst. Growth 225, 572. Montforte, F.R., Swanekamp, F.W., and Van Uitert, L.G. (1961) “Radio-frequency technique for pulling oxide crystals without employing a crucible susceptor,” J. Appl. Phys. 32, 959. First application of the skull melting process combined with crystal pulling to produce single crystals. Nassau, K. and Van Uittert, L.G. (1960) “Preparation of large calcium-tungstate crystals containing para- magnetic ions for maser applications,” J. Appl. Phys. 31, 1508. Describes the first use of the Cz process to grow ceramic crystals (CaWO4). Pfann, W.G. (1952) “Principles of zone melting,” Trans AIME 194, 747. The zone refining process. Remeika, J.P. (1954) “A method for growing barium titanate single crystals,” J. Am. Chem. Soc. 76, 940. Growth of BaTiO3 by flux growth at Bell Labs. Schmid. F. and Viechnicki, D. (1970) “Growth of sapphire disks from melt by a gradient furnace technique,” J. Am. Ceram. Soc. 53, 528. Stockbarger, D.C. (1936) “The production of large single crystals of lithium fluoride,” Rev. Sci. Instr. 7, 133. Described improvements to the Bridgman process. Tairov, Yu.M. and Tsvetkov, V.F. (1978) “Investigation of growth processes of ingots of silicon carbide single crystals,” J. Cryst. Growth 43, 209; (1981) “General principles of growing large size single crystals of various silicon carbide polytypes,” J. Cryst. Growth 52, 146. Describing the sublimation technique for growing large boules. Teal, G.K. and Little, J.B. (1950) “Growth of germanium single crystals,” Phys. Rev. 78, 647. Teal and Little of Bell Telephone Laboratories were the first to produce single crystals of Ge and Si by the Cz method. Tomaszewski, P.E. Professor Jan Czochralski (1885–1953). http://www.ptwk.org.pl/art2.htm. Vergés, M.A., Mifsud, A., and Serna, C.J. (1990) “Formation of rod-like zinc oxide microcrystals in homo- geneous solutions,” J. Chem. Soc. Faraday Trans. 86, 959. Low-T growth of ZnO. Wagner, R.S. and Ellis, W.C. (1964) “Vapor-liquid-solid mechanism of single crystal growth,” Appl. Phys. Lett. 4, 89; (1965) “Vapor-liquid-solid mechanism of crystal growth and its application to silicon,” Trans. Met. Soc. AIME 233, 1053. The description of the VLS mechanism. Now used for more than Si. Ziegler, G., Lanig, P., Theis, D., and Weyrich, C. (1983) “Single-crystal growth of SiC substrate material for blue-light emitting diodes,” IEEE Transact. Electr. Dev. ED-30, 227. (See Tairov et al., 1978.) EXERCISES 29.1 Describe the Verneuil method for producing ruby. What are the advantages and disadvantages of this process? 29.2 Briefly describe how ruby could be produced by the Czochralski (Cz) process. Under what situations, if any, would it be preferable to use the Cz process rather than the Verneuil process for ruby growth? 29.3 Why are crystals of cubic zirconia grown by the skull melting technique? 29.4 There are several different geometries for the Bridgman–Stockbarger method. Comparing the vertical and horizontal geometries, what are the advantages and disadvantages of each? 29.5 Knowledge of phase diagrams is very important for understanding the growth of single crystals from the melt. Using the case of BaTiO3 explain the considerations involved when producing single crystals of incon- gruently melting solids using melt growth techniques such as the Cz method. 29.6 Why are flux growth methods widely used in the production of synthetic gems? Are there are disadvantages that you can think of in using these methods for this particular application? C h a p t e r S u m m a ry .......................................................................................................................................................... 525  29.7 A company wishing to start producing single crystals of AlN has called you in as a consultant. What advice would you give them concerning the type of methods that would be suitable? 29.8 Draw up a list of as many different substrate materials as you can that have been used in the growth of thin films of the high-temperature superconductors. In your list make note of the surface orientation (if it is given) and the surface condition (was it polished, cleaned, annealed, etc.) of the substrate. 29.9 Using the information you gathered for question 29.8 add to your list one method that could be used to produce each type of single crystal from which the substrates were obtained. 29.10 By carefully reviewing the literature, present a detailed discussion of the method of growing diamond using the “flux” method. You should give quantities, diagrams, and references. 526 ............................................................................................................................................ G r o w i n g S i n g l e C ry s ta l s  Part VII Properties and Applications  30 Conducting Charge or Not CHAPTER PREVIEW Ceramics show the widest range of electrical properties of any class of material. At one extreme we have high-temperature superconductors, which have no resistance to an electrical current. At the other extreme we have electrical insulators. Ceramic superconductors have not yet ful- filled many of the expectations and predications for useful applications, whereas insulating ceramics are used for a number of critical applications such as packages for integrated circuits. Without the use of insulating ceramics the development of powerful personal computers would not have been so rapid. Between the two extremes are ceramics that behave very much like metals, and there are the semiconductors, which are all ceramics. Ceramics with metal-like conductivity are used as electrodes and in thick-film resistors. Semiconductors such as SiC are important for high-temperature electronics. In this chapter we will explain why ceramics show such a diverse range of electrical properties. The important concepts are related to our earlier discussion of bonding and energy bands. In some ceramics the only species that can move in an applied electric field are the ions in the structure. Generally, the movement of ions is slow, but in a class of ceramics called fast ion conductors, they can move very rapidly. In cubic zirconia the diffusion of oxygen ions at high temperature is particularly fast, and this ceramic is used as the electrolyte in solid oxide fuel cells. Fuel cells are becoming a key part of a diverse energy plan for the twenty-first century. We will begin by describing the conduction mechanisms in ceramics and looking at some specific applications. We will finish by describing one of the most fascinating developments in ceramics—high-temperature superconductors. 30.1 CERAMICS AS important properties, many ceramics are actually very ELECTRICAL CONDUCTORS good electrical conductors and some are even super- conductors. Ceramics show the broadest range of electri- Ceramics are usually thought of as electrical insulators cal properties of any of the classes of material. The values and indeed a great many of of electrical conductivity them are. Since the first for ceramics vary over an uses of electricity it has ELECTRIC TOWN enormous range—over 24 been necessary to have In 1881 Godalming became the first town in the world orders of magnitude!—as good electrical insulators to have a public electricity supply. shown in Figure 30.1. to isolate current-carrying Table 30.1 lists the wires. The expansion of the electrical industry and, in important parameters that are used in discussions of elec- particular, the use of the electric telegraph required enor- trical conductivity. As we have done elsewhere in this book mous numbers of porcelain insulators for telegraph poles. we will use SI units (unless there is a good reason for not From 1888 ceramics based on steatite began to be used doing so, such as the use of electron volts for band gap for the same purpose. Today ceramics are still used to energies). If another system is widely used the appropriate provide insulating supports in the power lines that criss- conversion factor is given. Electrical conductivity is in cross the country. general a tensor of the second rank. Fortunately, the elec- The distinction between materials as electrical con- trical properties of materials can largely be understood by ductors and materials as insulators was made in the assuming that they are isotropic and σ is simply a scalar. eighteenth century. Although historically the insulating The conduction mechanisms in ceramics can be quite properties of ceramics have often been one of their most complex and may involve the movement of electrons, 3 0 .1 C e r a m i c s a s E l e c t r i c a l C o n d u c t o r s ............................................................................................................. 529  Application Conduction Application Material Ionic Electronic Material 106 BaPb1–xBixO3 Superconductor RuO2 Thick film resistors TiO LaCaO3 Catalyst Metal LaNiO3 Fuel cell electrode La1–xSrxCrO3 MHD electrode SnO2:In2O3 Transparent electrode 0 SrTiO3 Photoelectrode 10 Na/S battery NaβAl2O3 (300°C) Oxygen sensor YSZ (1000°C) V2O3–P2O3 Fast ion Semiconductor (glass) Li2OLiClB2O3 (300°C) conductor (glass) Primary battery KxPb1–xF1.75 TiO2–x Oxygen sensor 10-6 Fluorine ion LaF3EuF2 Solid specific electrode electrolyte Table salt NaCl TiO2 10-12 ZnO Varistor Insulator Insulator Al2O3 Substrate Passivation on SiO2 Si devices 10-18 FIGURE 30.1 Range of conductivities of ceramics. holes, and ions; in some cases they may be “mixed,” with In comparing values of σ and ρ it is useful to remem- more than one type of charge carrier responsible for ber the simple relationship between them: current flow. In the case of ceramic superconductors the current is carried by electron pairs (Cooper pairs). So this 1 σ= (30.1) is really very different and is discussed separately. ρ TABLE 30.1 Terms and Units Used Parameter Definition Units/value Conversion factor Eg Band gap energy eV 1 eV = 1.602 × 10 −19 J (eV is a much more convenient unit for Eg) Ef Fermi energy σ Conductivity S/m 1 S = 1 Ω−1 I Current A J Current density C m−2 s −1 v Drift velocity m/s ξ Electric field strength V/m μ Mobility m2 V−1 s −1 Subscripts e and h will be used to represent electron and hole mobility, respectively; the units are the same in both cases R Resistance Ω ρ Resistivity Ω·m V Voltage V q Electron charge 1.602 × 10 −19 C Sometimes e t Transference number Dimensionless K Boltzmann constant 1.381 × 10 −23 J/K T Temperature K or °C Tc Critical temperature K 0 K = −273°C for superconductivity 530 ........................................................................................................................................ Conducting Charge or Not 30.2 CONDUCTION MECHANISMS TABLE 30.2 Transference Numbers of Cations, t + , Anions, IN CERAMICS t - , and Electrons or Holes, te,h in Several Materials Ceramic T (°C) t+ t− te,h Electrical conductivity is given by NaCl 400 1.00 0.00 600 0.95 0.05 σ = nqμ (30.2) KCl 435 0.96 0.04 600 0.88 0.12 The importance of Eq. 30.2 is that it applies to all materi- KCl + 0.02% CaCl2 430 0.99 0.01 als and it shows that the two factors affecting σ are 600 0.99 0.01 AgCl 20–350 1.00 AgBr 20–300 1.00  Number of charge carriers, n BaF2 500 1.00  Their mobility, μ PbF2 200 1.00 CuCl 20 1.00 When we consider the effect of variables such as composi- 366 1.00 tion, structure, and temperature on σ we are concerned ZrO2 + 7% CaO >700 1.00 <10 −4 Na 2O·11Al2O3 <800 1.00 (Na + ) <10 −6 with their effect on n and μ. FeO 800 10 −4 1.00 If more than one type of charge carrier is contributing ZrO2 + 18% CeO2 1500 0.52 0.48 to σ then we can define a partial conductivity for each. ZrO2 + 50% CeO2 1500 0.15 0.85 For example, if σ were due to the movement of electrons Na 2O·CaO·SiO2 glass 1.00 (Na + ) and cations with a charge Z, then for electrons 15% 1500 0.1 (Ca 2+ ) 0.9 (FeO·Fe2O3)·CaO· SiO2·Al2O3 glass σe = μe (ne q) (30.3) and for cations σ+ = μ+ (n + Zq) The real band structure of a material is actually a (30.4) complex three-dimensional shape. Even so these simple The total is representations can be used to illustrate many of the important electronic properties of materials. When Eg is σtot = σe + σ+ (30.5) zero, as in the case of most metals, there are free electrons present at any temperature If a ceramic is an elec- above 0 K. The total TRANSFERENCE NUMBER tron conductor, i.e., te = 1, The transference or transport number is the fraction of number of free electrons is then to determine n we equal to the number of σtot contributed by each charge carrier. need to know Eg. We valence electrons per atom usually consider the three multiplied by the number For electrons: te = σe /σtot situations shown in Figure of atoms in the metal. For cations: t + = σ+ /σtot 30.2, where the band gap Eg in a metal is not is either zero, narrow, or zero, but it is very small. Table 30.2 lists examples of t. For example, if we have a wide. metal crystal consisting of 1023 atoms and the width of the energy band is 1 eV then the separation between the energy levels would be only 10−23 eV (1.6 × 10−42 J). This would be the minimum amount Energy of energy required to excite an electron into a vacant CB CB Unoccupied level. CB bands A narrow band gap is usually defined as being in the Partly range of 0.02 to about 2.5 eV. When Eg is toward the lowest VB occupied end of this range there is a significant fraction of electrons VB band VB in the conduction band. Materials with a narrow band gap are usually referred to as semiconductors. Occupied bands  Silicon: Eg = 1.12 eV  Gallium arsenide: Eg = 1.42 eV Metal Semiconductor Insulator FIGURE 30.2 Schematic of electron energy bands in solids. The valence band (VB) and conduction band (CB) are indicated. Both Si and GaAs are ceramics. 3 0 . 2 C o n d u c t i o n M e c h a n i s m s i n C e r a m i c s ............................................................................................................ 531  TABLE 30.3 Band Gap Energies for Various Ceramics Material Eg (eV) Material Eg (eV) Material Eg (eV) Halides AgBr 2.80 BaF2 8.85 CaF2 12.00 KBr 0.18 KCl 7.00 LiF 12.00 MgF2 11.00 MnF2 15.50 NaCl 7.30 NaF 6.70 SrF2 9.50 TlBr 2.50 Oxides Al2O3 (sapphire) 8.80 CdO 2.10 Ga 2O3 4.60 MgO (periclase) 7.7 SiO2 (fused silica) 8.30 UO2 5.20 CoO 4.0 CrO3 2.0 Cr 2O3 3.3 CuO 1.4 Cu2O 2.1 FeO 2.4 Fe2O3 3.1 MnO 3.6 MoO3 3.0 Nb2O5 3.9 NiO 4.2 Ta 2O5 4.2 TiO2 (rutile) 3.0–3.4 V2O5 2.2 WO3 2.6 Y2O3 5.5 ZnO 3.2 BaTiO3 2.8–3.2 KNbO3 3.3 LiNbO3 3.8 LiTaO3 3.8 MgTiO3 3.7 NaTaO3 3.8 SrTiO3 3.4 SrZrO3 5.4 Y3Fe5O12 3.0 Carbides and Nitrides AlN 6.2 BN 4.8 C (diamond) 5.33 SiC (α) 2.60–3.20a Chalcogenides PbTe 0.275 PbS (galena) 0.350 PbSe 0.400 CdTe 1,450 CdSe 1.850 CdS 2.420 ZnSe 2.600 ZnS 3.600 Materials with a wide band gap (>2.5 eV) are consid- the electrons can be distributed (i.e., the number of ered to be electrical insulators because the probability of allowed energy states). an electron being in the conduction band at room tempera-  P(E) is the Fermi–Dirac function giving the probabil- ture is extremely small. However, the probability is not ity of an electron being in the conduction band. zero and so we should think of these materials as wide- band-gap semiconductors. SiC (Eg = 2.6–3.0) is an example ⎧ ⎫ of a wide-band-gap semiconductor and is used in sensors ⎪ 1 ⎪ f (E ) = ⎨ ⎬ ( ) in aircraft and fuel cells that can operate in hostile envi- (30.7) ronments at temperatures up to 600°C where conventional ⎪ ⎡1 + exp E − Ef ⎤ ⎪ silicon-based electronics cannot function. ⎩ ⎣⎢ kT ⎥⎦ ⎭ Band gap energies for a number of ceramics are listed in Table 30.3. The evaluation of ni is quite straightforward if we make the following assumptions: 30.3 NUMBER OF 1. E − Ef >> kT. This is often the case since at room CONDUCTION ELECTRONS temperature kT ∼ 0.025 eV and E − Ef is usually >5 eV. We can now omit the +1 in Eq. 30.7. [We are in effect replac- This section follows directly from Section 4.8. The number ing Fermi–Dirac statistics by Boltzmann statistics.] of electrons in the conduction band, ni, is 2. The excited electrons occupy states near the bottom of the conduction band. Under these conditions they Etop behave as free particles for which the state distribution ni = ∫ N c ( E ) f (E )dE (30.6) Ec function is known. 3. The upper limit of the integration in Eq. 30.6 is taken as ∞ since the probability of occupancy of a state  Nc (E) dE is the density of states in the conduction band by an electron rapidly approaches zero as the energy and represents the number of energy levels over which increases through the band. 532 ........................................................................................................................................ Conducting Charge or Not  Under these assumptions we can write Ec − E F ⎞ 8 ni = N c exp ⎛ − (30.8) log σ ⎝ kT ⎠ Sm-1 Metals EF lies midway between E C and EV in an intrinsic material 4 (i.e., one that has few impurities) and since NC ∼ 1025 m−3 Semiconductors we can simplify Eq. 30.8 as 0 ⎛ Eg ⎞ ⎛ Eg ⎞ ni = N c exp ⎜ − ⎟ ~ 1025 exp ⎜ − ⎝ 2kT ⎟⎠ (30.9) ⎝ 2kT ⎠ -4 The important things to remember from this series of Insulators equations are that -8  n depends on Eg and T.  As we increase T we increase n. -12 30.4 ELECTRON MOBILITY -16 As electrons move through a solid under the influence of ξ they experience a number of collisions (in a process 300 T (K) 1000 called scattering) that decreases μ. There are three scat- FIGURE 30.4 Conductivity variations with temperature for the tering mechanisms: different classes of electrical conductor. The shading indicates the range of values at room temperature.  Phonon. This is the major factor affecting μ (of both electrons and holes). A phonon is the quantum unit of lattice vibrational energy as described later in Chapter ciently strong (small polaron) the electron may be 34. The higher the temperature the greater the trapped at a particular lattice site, reducing μ and vibrational amplitude of the atoms in the lattice and decreasing σ. the greater the number of phonons. As a result, scat- tering increases and μ decreases with increasing temperature. 30.5 EFFECT OF TEMPERATURE μ ∝ T −m (30.10) For a material where Eg = 0, i.e., one in which n does not  Electron–electron. At room temperature the mean dis- vary significantly with T, σ decreases with increasing tance between electron–electron collisions is about 10 temperature because of the decrease in μ: times that of electron–phonon collisions so electron– n phonon scattering is dominant. σ∝ (30.11)  Polaron. This mechanism occurs only in ionic crystals Tm and involves the interaction between the electron and the ions in the crystal. The electron can cause local For materials where Eg > 0 (i.e., materials that we would distortion of the lattice known as a polaron as illus- classify as semiconductors or insulators), σ rises with T trated in Figure 30.3. When the interaction is suffi- because of the temperature dependence of n as shown by Eq. 30.9: σ ∝ exp ⎛ − E ⎞ (30.12) R ⎝ 2kT ⎠ e- Figure 30.4 shows the typical T dependence of σ for the e- three broad classes of electrical behavior. Because it is possible to make practical use of the variation in σ or ρ with T it is often beneficial to classify materials based on this variation. (From a practical point of view we usually consider changes in ρ rather than (A) (B) changes in σ.) The temperature dependence of resistivity FIGURE 30.3 Illustration of (a) a large polaron of radius R, formed may be expressed by an empirical equation in a metal oxide MO and (b) a small polaron, showing the distortion of the lattice around an electron trapped at a metal. ρ2 = ρ1[1 + αR(T2 − T1)] (30.13) 3 0 . 5 E f f e c t o f Te m p e r at u r e ...................................................................................................................................... 533 where ρ1 is the resistivity at T1 and ρ2 is the resistivity at Metal T2. The parameter αR is known as the temperature coeffi- s and p cient of resistivity or TCR. For materials where Eg = 0 the bands TCR is typically positive. These materials are called posi- tive temperature coefficient (PTC) materials. Most materi- E als that show semiconducting or insulating properties are Metal negative temperature coefficient (NTC) materials. Some d band EF ceramics, for example BaTiO3, that do have energy band gaps are actually PTC materials. This type of behavior has nothing to do with conduction across the band gap but Eg is actually a grain boundary (GB) effect. O 2p Valence band 30.6 CERAMICS WITH METAL-LIKE CONDUCTIVITY (A) (B) The general electrical characteristics of metals are FIGURE 30.6 Energy bands of a transition metal oxide: (a) d band empty; (b) metallic oxide with d band partially filled.  σ ≥ 104 S/m  te = 1  n = 1022–1023 cm−3 much higher energy. The metal d orbitals form a band  dσ/dT is small and negative. below that of the metal s and p orbitals as illustrated in Figure 30.6. Remember that Ω−1 (ohm−1) The divalent titanium TRANSITION METALS is S (siemens). Some cer- ion, Ti2+ , in TiO has two Transition metals have partially filled d orbitals. amics, for example TiO 3d electrons and so the and VO, show metallic- metal d band shown in like electronic conductivity where the conduction is due Figure 30.6 is partially filled. It is this partially filled to the movement of free electrons. To explain this behavior band, which you will notice resembles the energy level we will consider the example of TiO. diagram for a metal shown in Figure 30.2, that leads to TiO has a structure based on rocksalt with vacancies metallic conductivity in TiO. Looking at Figure 30.6 it is in both the metal and oxygen sublattices. One-sixth of the easy to see why titanium dioxide, TiO2, is an insulator. In titaniums and one-sixth of the oxygens are missing as the formation of the Ti4+ ion, both the two 4s electrons illustrated in Figure 30.5. and the two 3d electrons The 2p orbitals from the are given up to form oxygen oxygen atoms form a filled ELECTRON CONFIGURATIONS ions. So the 3d band (the valence band. The bands Ti 1s22s22p63s23p63d24s2 conduction band in the formed by the 4s and 4p Ti2+ 1s22s22p63s23p63d2 solid) is empty at T = 0 K. orbitals on the Ti are at a Ti4+ 1s22s22p63s23p6 The band gap, Eg, in TiO2 is 3 eV. This is a relatively small Eg for an insulator and indicates some covalent character in the Ti–O bond. O So why aren’t MnO, CoO, and NiO, which are also monoxides of the first row transition metals and have the rocksalt structure, metallic-like conductors? Ti To answer this question we need to consider the inter- action between the d orbitals and the formation of the d band in metal oxides. In the rocksalt structure the d xy, dyz, and d xz orbitals (collectively known as the t2g orbitals) on adjacent metal atoms overlap. The extent of the overlap is less than it would be in the pure metal because in the Layer at z = 0 Layer at z = 1/2 oxides the metal atoms are not nearest neighbors. Conse- (A) (B) quently the d bands are narrower than they would be for the metal. (We are referring to the widths of the bands FIGURE 30.5 The structure of TiO. (a) The (100) plane. (b) The (200) plane. Both show the absence of alternate ions along <110> themselves and not the size of the band gap.) As we go directions. The resultant superlattice has a monoclinic unit cell as across the first row transition elements (from Ti to Ni) indicated by the shaded region. there is an increase in nuclear charge and a corresponding 534 ........................................................................................................................................ Conducting Charge or Not  mentioned, e.g., ReO3, TiO, CrO2, and ReO2, dσ/dT is 6 Ti small and negative, just like it is for most metals. E (eV) 4 Fe Co Ni Occupied 30.7 APPLICATIONS FOR 3d levels HIGH-s CERAMICS 2 Mn There are many applications for ceramics that have metal- 0 O 2p like conductivity. We will look at two examples: Valence band  Resistors FIGURE 30.7 Electronic energy levels of some 3d monoxides,  Electrodes deduced from spectroscopic measurements. The energy zero has been taken as the top of the oxygen 2p valence band. Resistors contraction in the size of the d orbitals. As the d orbitals The requirements for most resistors are that they are become smaller the extent of overlap decreases and the 3d band becomes narrower, eventually forming a localized  Ohmic state as illustrated in Figure 30.7.  Small TCR Some oxides of the second and third row transition elements also exhibit metallic-like properties, for example, Components with R in the range 103 –108 Ω are the ReO2 and ReO3. In these compounds the metal electron major requirements of the electronic industry. These are energy levels of interest are the 5d, rather than the 3d as fabricated from electronically conducting ceramics with in the case of the first row transition metals. σ in the range 105–106 S/m. Resistance is not an intrinsic Figure 30.8 shows the σ versus temperature behavior property of a material. It is influenced by the specimen for several oxides. For some of the oxides we have already configuration, i.e., its thickness and length. The relation- ship between R and σ is l 1000 500 250 167 T (K) 125 R= (30.14) σA σ (S cm-1) ReO3 where A is the cross-sectional area of the specimen per- 104 TiO CrO2 pendicular to the direction of the current flow and l is the VO V2O3 Fe3O4 distance between the two points at which the voltage is ReO2 measured. To make a 105-Ω resistor of length 10 cm from 100 NbO MnO2 a material with σ = 106 S/m would require a cross- MoO2 sectional area of 10−12 m2. Using a strip with a 1 μm2 Cr2O3 cross section would be possible, but it is not usually eco- Ti2O3 CoO VO2 nomically feasible. There are two methods that are used Mn3O4 10-4 to make high-resistance components using high-σ ceramics: 1. Increase the aspect ratio (length to width) of the con- 10-8 ductive layer by patterning 2. Mix the conductive phase with a highly resistive one FeO Thin-film resistors usually make use of the first 10-12 approach. For example, thin films (∼10 nm thick) of indium tin oxide (ITO) are deposited onto glass, or sometimes Fe2O3 steatite, substrates by sputtering or chemical vapor deposi- NiO tion (CVD). After deposition the films are patterned to 10-16 achieve a large aspect ratio. If the substrate is in the form of a rod a spiral groove is cut into the film. 0 2 4 6 103/T (K) 8 Thick-film resistors are made by diluting a conductive FIGURE 30.8 Temperature dependence of the electrical conduc- oxide with an electrical insulator such as glass. (The prac- tivity of several electronically conducting oxides. tical aspects of thick-film processing were described in 3 0 .7 A p p l i c at i o n s f o r H i g h - σ C e r a m i c s ................................................................................................................. 535 log (ρs ⁄Ω c-1) generators where the electrode had to withstand tempera- 6 tures up to 2000°C and the corrosive potassium atmo- 5 sphere in the generator. LaCrO3 has a melting temperature of 2500°C and σ = 100 S/m at 1400°C. MHD generators 4 are now of little interest, but LaCrO3 has been used as an 3 electrode in solid oxide fuel cells. LaCrO3 has the 2 perovskite structure that we described in Chapter 7. Porous. In humidity and gas sensors the electrode 1 must be electrically conductive, produce a porous coating 0 (to allow the vapors to reach the sensor), and be stable in TCR/ppm K-1 the sensing environment. RuO2 is used as an electrode in 800 humidity sensors. One example of the sensing element is a solid solution of TiO2 in MgCr2O4. This type of sensor is used in microwave ovens where it detects the rapid rise 0 in humidity corresponding to the onset of cooking. There is a fall in ρ when the ceramic is exposed to humid atmo- spheres, the result of dissociation of water molecules: -800 0 10 20 30 40 50 60 RuO2 wt. % 2H2O = H3O + + OH− (30.15) FIGURE 30.9 Electrical characteristics of RuO2 thick-film resistors. Several other materials have been developed for humidity sensors and the electrical responses of three different ones Chapter 27.) Ruthenium dioxide (RuO2) and mixed metal are shown in Figure 30.10. oxides containing ruthenium, such as Bi2Ru2O7, are widely Transparent. For applications in which a transparent used as the conducting component. These oxides have σ electrode is required metals are completely unsuitable. in the range of 105–106 S/m. The glass is usually a lead Metals, because of their very small Eg, can absorb all borosilicate of composition typically (in wt%) 52PbO– wavelengths of visible light and are, as a result, opaque in 35SiO2–10B2O3 –3Al2O3. The final thickness of the resistor the visible part of the electromagnetic spectrum. Only after processing is in the range of 10–15 μm. The resistors metal layers <1 μm will be transparent. A ceramic used as normally have high resistivities and negative TCRs for low a transparent electrode is indium tin oxide (ITO). A typical concentrations of the conductive component and low resis- electrode composition is 90In2O3 –10SnO2. Transparent tivities and positive TCRs for high concentrations as electrodes are important for many electrooptic devices, shown in Figure 30.9. This behavior is the result of a combination of the positive TCR of the conductive parti- cles and the negative TCR of the regions between them. 107 108 The distribution of the conductive particles and the contact between them also determines the resistance of Resistivity Resistivity Ω • cm Ω • cm the deposited film. Final resistance values are obtained MgCr2O4 -TiO2 either by sand blasting, where the thickness of the film is reduced, or by laser trimming, to increase the effective 107 length of the resistor. These procedures would be per- formed after the resistor has been fired, but before the application of the protective glaze coating. SiO2 -ZnO 106 106 Electrodes High-σ ceramics are used as electrodes in a number of ZnCr2O4 -LiZnVO4 applications: 105  Fuel cells  Humidity sensors  Displays 105 104 The question we need to ask ourselves again is: What is 0 20 40 60 80 100 special about ceramics? Relative Humidity (%) Temperature Stability. LaCrO3 was developed in the FIGURE 30.10 Electrical response of three ceramic humidity 1960s for electrodes in magnetohydrodynamic (MHD) sensors at room temperature and 1 kHz. 536 ........................................................................................................................................ Conducting Charge or Not liquid crystal displays (LCDs), light-emitting diodes not known and we make the (often incorrect) assumption (LEDs), and solar cells. that me = m*e = m*h, where me is the rest mass of the electron. If we use the subscript i to denote intrinsic carrier concentrations, we can write 30.8 SEMICONDUCTING CERAMICS ni = pi (30.20) Semiconductors have a small Eg as shown in Figure 30.2. In semiconductors σ is proportional to n and μ (for both and electrons and holes). In general, there are three ways free electrons and holes may be generated in ceramics: np = nipi = ni2 (30.21)  Excitation across the band gap (intrinsic semiconductors) Therefore  Introduction of impurities/dopants (extrinsic semiconductors) ⎛ Eg ⎞ ni = ( N c N v ) exp ⎜ − 1/ 2 ⎝ 2kT ⎟⎠ (30.22)  Departures from stoichiometry (nonstoichiometric semiconductors) If Nc = Nv then Most oxide semiconductors are either doped to create extrinsic defects or are annealed under conditions in which ⎛ Eg ⎞ ni = N c exp ⎜ − ⎝ 2kT ⎟⎠ they become nonstoichiometric. (30.23) The intrinsic conductivity is given by Intrinsic Semiconductors For every electron that is σi = qni (μe + μh) (30.24) excited into the conduction band, a hole is produced in MOBILITIES OF ELECTRONS AND HOLES the valence band. In ceramics these depend upon their interaction with the Equation 30.24 is similar to Eq. 30.2, but we are The number of elec- lattice. Typical values are very small (≤0.1 cm2 V−1 s−1): trons in the conduction now considering μe and orders of magnitude lower than in Si and GaAs. μh. band is The intrinsic conduc- tivity of many pure oxide semiconductors is generally very ⎛ Eg ⎞ low because of their large Eg compared to Si and GaAs. n = N c exp ⎜ − ⎝ 2 kT ⎟⎠ (30.16) To illustrate this point we will compare the room tempera- ture conductivities of Cu2O, a semiconducting oxide Similarly, the number of holes in the valence band is Eg = 2.1 eV, and GaAs, a III–V semiconductor Eg = 1.4 eV. The largest applications for semiconductors use extrin- ⎛ Eg ⎞ p = N V exp ⎜ − sic material. The entire electronic materials industry is ⎝ 2kT ⎟⎠ (30.17) built around doped silicon. However, there are applica- tions that require intrinsic semiconductors. One such The densities of states are given by application is X-ray detectors used on transmission electron microscopes (TEMs) and scanning electron microscopes (SEMs) for chemical analysis. Unfortunately 2πm*e kT ⎞ 3/ 2 Nc = 2 ⎛ (30.18) it is essentially impossible to produce pure silicon. ⎝ h2 ⎠ Even electronic grade silicon contains small amounts of boron (a p-type dopant). To create “intrinsic” material and a dopant is added that produces an excess of electrons that combine with the holes formed by the residual 2πm*h kT ⎞ 3/ 2 boron. The process involves diffusing lithium atoms Nv = 2 ⎛ (30.19) into the semiconductor. Ionization of the lithium ⎝ h2 ⎠ produces electrons that recombine with the holes. It is possible to produce germanium crystals with much where m*e and m*h are the effective masses of the electrons higher purity, and intrinsic Ge detectors are used on and holes, respectively. For many ceramics m*e and m*h are some TEMs. 3 0 . 8 S e m i c o n d u c t i n g C e r a m i c s ................................................................................................................................. 537 Extrinsic and WORKED EXAMPLE conductor is known as a p- Nonstoichiometric type semiconductor because Semiconductors 1. Calculate Nc and Nv (Eqs. 30.18 and 30.19) (density holes (or positively charged of states): species) act as the majority An extrinsic semiconduc- charge carriers. tor contains impurities that Cu2O: we will assume m*e = m*h = 9.11 × 10−32 kg At low temperatures the are present either acciden- ⇒ Nc = Nv = 2.49 × 1019 cm−3 number of charge carriers tally or, as is most often is determined by the donor GaAs: m*e = 0.067me = 6.10 × 10−32 kg, the case, that have been and acceptor ionization m*h = 0.48me = 4.37 × 10−31 kg ⇒ intentionally added. The energies. At sufficiently Nc = 4.31 × 1017 cm−3 and effect of these impurities high temperatures full ion- Nv = 8.26 × 1018 cm−3 on the energy band diagram ization of the impurities is is that they introduce 2. Calculate ni (Eq. 30.23): achieved and the carrier additional energy levels densities become indepen- Cu2O: ni = 45.11 cm−3; GaAs: ni = 2.85 × 106 cm−3 into the band gap as illus- dent of temperature. This trated in Figure 30.11. These 3. Calculate σ (Eq. 30.24): region is called the “exhaus- new energy levels are often tion” or “saturation” region. The last parameters we need before we can calculate ni close to the band edges. At even higher tempera- are μe and μh. In ionic solids these values are often not If the impurity level is tures the thermal energy is well known, but are several orders of magnitude lower just above the valence band enough to excite electrons than for the covalent semiconductors. the impurity is an “accep- across the energy band gap tor” because it can accept Cu2O: μe = 0.2 cm2 V−1 s−1 and μh = 0.1 cm2 V−1 s−1. and the material behaves electrons leaving holes in like an intrinsic semicon- the valence band. If the (Reasonable estimates.) For GaAs see Table 30.4. ductor. These three regions impurity can supply elec- Cu2O: σ = 2.17 × 10−18 S/cm; are shown in Figure 30.12. trons into the conduction GaAs σ = 5 × 10−9 S/cm Nonstoichiometric semi- band it is a “donor” and the conductors are very similar level is located just below These are room temperature values for “pure” to extrinsic semiconduc- the bottom of the conduc- materials. tors, and can really be con- tion band. If the impurity acts as an electron donor the semiconductor is known as an n-type semiconductor because the electrons (or nega- tively charged species) are the majority charge carriers. If the impurity acts as an electron acceptor then the semi- TABLE 30.4 Mobilities of Various Semiconductors Electron mobility Hole mobility Semiconductor (m2 V −1 s−1) (m2 V −1 s−1) α-SiC 0.04 ∼0.02 Si 0.15 0.049 Ge 0.39 0.18 GaAs 0.85 0.30 InAs 3.30 0.02 Conduction band InSb 8.00 0.17 e- e- e- Diamond 0.18 0.12 PbS 0.06 0.02 Εd ≈ 0.01 eV GaSb 0.30 0.065 Donor CdS 0.04 — states CdSe 0.065 — CdTe 0.12 0.005 GaP 0.015 0.012 Εg ≈ 1.1 eV AlN — 0.001 PbSe 0.09 0.07 PbTe 0.17 0.093 Acceptor AgCl 0.005 — states Εa ≈ 0.01 eV SnO2 0.016 — SrTiO3 0.0006 — + + + Fe2O3 10 −5 — TiO2 2 × 10 −5 — Valence Fe3O4 — 10 −5 band CoFe2O4 10 −8 10 −12 FeO, MnO, CoO, NiO ∼10 −5 FIGURE 30.11 Effect of doping on band structure. 538 ........................................................................................................................................ Conducting Charge or Not  log(σ) ZnO (900° C) log(n) Log log σ Intrinsic 1 4 Saturation Extrinsic Low PO2 High PO2 Lattice scattering μ∞T -3/2 μ∞T 3/2 log(μ) log PO2 Impurity FIGURE 30.13 Effect of oxygen pressure on the electrical High T scattering Low T conductivity of ZnO. 1/T FIGURE 30.12 Temperature dependence of σ for an extrinsic semiconductor. The dashed lines show the individual contributions of n and μ to σ. [Zni] = [e′] = KpO2−1/4 (30.26) Now σ will be vary with the oxygen partial pressure as sidered together. The main difference is that the electronic shown in the log–log plot in Figure 30.13: defects rather than being due to impurity atoms are the result of changes in the stoichiometry of the crystal. We σ ∝ pO2−1/4 (30.27) still use the designations n- and p-type to describe the majority charge carrier and the defect adds levels into the Figure 30.14 shows the energy band diagram for Zn1+xO band gap that lead to increased levels of conductivity, illustrating the positions of the donor levels. E1 and E2 are particularly at room temperature and below. Conduction 30.9 EXAMPLES OF EXTRINSIC band SEMICONDUCTORS Zinc Oxide: An n-Type Semiconductor In Section 11.7 we described the result of heating ZnO in Zn vapor. The excess Zn atoms occupy interstitial sites. E1 One electron is produced for every Zn interstitial as shown Mi using Kröger–Vink notation: E2 Zn(g) → Zni · + e′ (11.13) (Mi+)• The requirement of electroneutrality means that the con- centration of interstitials is equal to the concentration of electrons: [Zni] = [e′] = KpZn1/2 (11.14) Because σ depends on the number of charge carriers it will be proportional to the zinc vapor pressure: Valence σ ∝ pZn1/2 (30.25) band The oxygen dependence can be considered in a similar FIGURE 30.14 Schematic representation of the energy levels in way and gives Zn1+x O. 3 0 . 9 E x a m p l e s o f E x t r i n s i c S e m i c o n d u c t o r s ........................................................................................................ 539 the first and second ionization energies for Zn. At low temperatures the electrons would not be excited into the conduction band and would be localized at the donor level. log σ Cu2O (1000° C) As the temperature rises, the fraction of electrons in the conduction band increases. At a sufficiently high tempera- ture all the impurity atoms will be ionized. Copper Oxide: A p-Type Semiconductor 1 + If we start with stoichiometric Cu2O and remove a copper 7 atom to form a copper vacancy, the charge balance requires formation of a hole as shown using Kröger–Vink notation: Low PO2 High PO2 log PO2 (CuCu) X → Cu(g) + (VCu)′ + h· (30.28) FIGURE 30.16 Conductivity of Cu2O as a function of pO2. For a possible second ionization state (VCu)′ → (VCu)′′ + h· (30.29) (You will recognize Eq. 30.30 as being similar to Eq. The above processes are shown on an energy band diagram 11.8.) in Figure 30.15. Using the same approach that we used for ZnO we can We can also consider that a hole forms by the produc- obtain a relationship between pO2 and σ: tion of vacancies on the cation sublattice when pO2 is increased. The overall reaction can be represented as σ ∝ [h·] = K(T)1/4pO21/8 (30.31) 1/2O2 (g) → (OO) X + 2(VCu)′ + 2h· (30.30) Experimentally, as illustrated in Figure 30.16, σ is found to be proportional to pO21/7, which is in reasonable agree- ment with Eq. 30.31. There are many examples of impurity semiconductors Conduction and a partial list is given in Table 30.5. band 30.10 VARISTORS A varistor is used in an electric circuit as protection against large voltage pulses, i.e., a surge protector. Such devices are particularly important in protecting micro- electronic devices. ZnO is the most widely used and important material for varistors. (VM+–)˝ Under normal operating conditions a small current will flow through the varistor. If the voltage rises above some threshold value (for example, the result of a voltage E2 (VM+)´ TABLE 30.5 Partial List of Impurity Semiconductors E1 (VM++) n-Type TiO2 Nb2O5 CdS Cs2Se BaTiO3 Hg2S V2O5 MoO2 CdSe BaO PbCrO4 ZnF2 U3O8 CdO SnO2 Ta 2O5 Fe3O4 ZnO Ag2S Cs2S WO3 p-Type Valence band Ag2O CoO Cu2O SnS Bi2Te3 MoO2 Cr 2O3 SnO Cu2S Sb2S3 Hg2O MnO FIGURE 30.15 Schematic representation of energy levels in a NiO Pr 2O3 CuI deficit semiconductor such as Cu2−x O. 540 ........................................................................................................................................ Conducting Charge or Not spike in the power supply) a large current will flow through G.B. the varistor to ground before it can damage the circuit. To operate in this way a varistor must have a highly nonlinear Conduction band I–V relationship, as shown in Figure 30.17. EF (grain)  At low applied voltages the varistor behaves in an Donor ohmic manner, i.e., there is a linear I–V relationship. Acceptor states levels  When the applied voltage reaches a threshold value EF known as the breakdown voltage a large current flows, (G.B.) following a power law: Valence band I ∝ Vα (30.32) The exponent α is used as a figure of merit for the varistor G.B. and can be as high as 70 for ZnO, although values in the Barrier eφ range 25–45 are more typical. For SiC α ∼ 5. height A significant difference between a varistor and a diode Equilibrated is that varistors can be used in both ac and dc circuits. EF Compare the plot shown in Figure 30.17 with what would be seen for a Zener diode. Electron Electron The microstructure of a ZnO varistor is the key to its depletion depletion operation. Grains of about 15–20 μm in diameter are sepa- layer layer rated by a Bi-rich intergranular film (IGF) that varies in thickness from 1 nm to 1 μm, as illustrated in Figure 14.38. λ λ Varistor action is a result of a depletion region formed on (A) (B) either side of the IGF. To explain varistor behavior we use FIGURE 30.18 Proposed band diagram for two semiconducting an approach very similar to that used to describe Schottky ZnO grains separated by an IGF: (a) showing the location of barriers in metal–semiconductor junctions. acceptor sites in the IGF; (b) at equilibrium. Application of a Figure 30.18a shows an energy level diagram for two potential decreases the barrier height. ZnO grains separated by an IGF. The bismuth that segre- gates to the GB results in the formation of acceptor levels. The way that the bismuth dopants produce these sites is duction band electrons must surmount this energy barrier not well understood, but possibly they stabilize acceptor for conduction to occur. When a potential is applied across defects such as Zn vacancies at the GB. At equilibrium the varistor the size of the energy barrier is reduced. Con- the Fermi levels on each side of the boundary must line duction is provided by thermal activation of electrons up, as shown in Figure 30.18b. This requirement is neces- across the barrier (at low fields) or tunneling (high fields). sary because at equilibrium the probability of occupation At the breakdown voltage the energy barrier is zero and a of any quantum level must be independent of position. massive increase in electrical conduction occurs. When this occurs, the conduction and valence bands bend, Varistor breakdown is reversible and if the applied resulting in an energy barrier (height eφ) at the GB. Con- voltage is decreased below the breakdown value the varis- tor will return to ohmic behavior. The breakdown voltage is typically in the range of tens to hundreds of volts. Ohmic GBs Breakdown Ohmic grains Upturn  Single-crystal silicon diodes (avalanche or Zener) are Prebreakdown Nonlinear region region region used only for low-voltage applications. 3 ρgb~1010-1012 Ω-cm  ZnO varistors are used for both low- and high-voltage applications. Reciprocal slope = α 2 SiC 30.11 THERMISTORS Thermally sensitive resistors (thermistors) have high dc ρg~1-10 Ω-cm ac TCRs produced by one of the following mechanisms: 10-8 10-6 10-4 10-2 1 102 104 1. Excitation across the band gap—intrinsic semi- Amp/cm2 conductor behavior resulting in an exponential decrease FIGURE 30.17 Typical I–V characteristic for a ZnO varistor. in ρ over a wide temperature range (NTC). 3 0 .11 Th e r m i s t o r s ......................................................................................................................................................... 541  2. A structural phase transformation causing a change from semiconducting behavior to metallic conduction, 4 C which causes a large decrease in ρ over a small tempera- log (ρ/Ω m) ture range (NTC). 3. A change in the conductivity of the GB, which produces a large increase in ρ over a small temperature 3 range (PTC). D In semiconductors such as SiC where NTC behavior is 2 expected ρ varies with T according to ρ(T) = ρ∞ exp(B/T) (30.33) 1 ρ∞ is approximately independent of temperature and B is a constant related to the energy required to excite the electrons into the conduction band. By differentiation we 0 can obtain an expression for α: A B αR = dρ/ρdT = −B/T2 (30.34) -1 αR is usually expressed either as a percentage change in 0 100 Tc 200 T (°C-1) 300 resistivity, e.g., −3% K−1, or in terms of ppm changes per FIGURE 30.19 Typical characteristics of a PTC thermistor degree change in temperature, e.g., ppm/°C. Table 30.6 material. shows the properties of thermistors based on Mn3O4 with partial replacement of the Mn by Ni, Co, and Cu. NTC materials are used in many applications to either Above θc sense temperature or to respond to changes in tempera- Rgb ∝ exp ⎡ N ⎛ 1 − cw ⎞ ⎤ T ture. One application is temperature sensors to measure (30.36) the temperature of the cooling water in an automobile ⎣⎢ ⎝ T ⎠ ⎦⎥ engine. where N is a temperature-independent constant for the The behavior of PTC materials is very different from particular material and includes specific details about the NTC materials. Commercial PTC devices rely on the electronic structure of the grain boundary and Tcw is the changes associated with the ferroelectric Curie tempera- Curie–Weiss temperature (∼θc). ture (θc). Typical PTC behavior is shown in Figure 30.19. In regions AB and CD the material is showing NTC behavior. But at the Curie temperature (θc) there is a large 30.12 WIDE-BAND-GAP positive change in ρ. SEMICONDUCTORS Polycrystalline lanthanum-doped BaTiO3 (BLT) is one example of a PTC material. The effect is associated with Wide-band-gap semiconductors refer to materials that GBs and is not observed in single crystals. At the GB there have a band gap between about 2 and 5 eV. At present one is a potential barrier (φ) preventing electron movement of the most interesting wide-band-gap semiconductors is from one grain to an adjacent one (very similar to that SiC, which has an Eg from 2.4 to 5.1 eV. These materials caused by the IGF in ZnO). The GB resistance, Rgb is are important because they can be used at much higher temperatures than Si or GaAs because the thermal genera- Rgb ∝ exp(φ/kT) (30.35) tion of electron-hole pairs is much lower. SiC exists in a number of different polytypes each having different prop- erties as shown in Tables 30.7 and 30.8. TABLE 30.6 Properties of Thermistor Compositions Based on Mn3O4 at 25°C Composition (cat.%) TABLE 30.7 Summary of Band Structures for SiC −1 Polytypes Mn Co Ni Cu ρ25 /Ω·m B/K αR /%K 3C 6H 4H 2H 56 8 16 20 10 −1 2580 −2.9 65 9 19 7 1 2000 −2.2 Direct band gap (eV) 5.14 4.4 4.6 4.46 70 10 20 10 3600 −4.0 Indirect band gap (eV) 85 15 102 4250 −4.7 Experimental 2.39 3.0 3.26 3.35 94 6 103 4600 −5.1 Theory 2.4 2.4 2.8 3.35 542 ........................................................................................................................................ Conducting Charge or Not  TABLE 30.8 Summary of Properties for n-Type SiC then give σ in terms of D, which is what we did in (ND = 6 ¥ 1016 cm -3 ) at Room Temperature Section 11.15: Electron mobility ne2 D Polytype (cm2 V −1 s−1) ED (meV) m*|| /me m*/m | e σ= (11.53) kT 4H 700 33 0.19 0.21 15R 500 47 0.27 0.25 The following factors contribute to ionic mobility: 6H 330 95 1.39 0.35  Size. It is easier to move a small ion than a large one.  Charge. A highly charged ion will polarize, and be 30.13 ION CONDUCTION polarized by ions of opposite charge as it moves past them. This will increase EA. Ion movement can make a major contribution to σ, par-  Lattice geometry. Some structures contain channels ticularly if the material has a large Eg. Conductivity result- that facilitate the ion movement. A large number of ing from ion migration is important in several ceramics. vacant sites can help. It is also the major conduction mechanism in ionic salts such as the halides. When we describe the mobility of ions we often use 30.14 FAST ION CONDUCTORS the absolute mobility, B: Materials that show exceptionally high ionic conductivity v v are referred to as “fast ion” conductors or “superionic” B= = (30.37) F zeE conductors. The conductivities are comparable to those of electrolyte solutions, but are still low compared with where v is the drift velocity and F is the applied force metal-like electron conductivity. There are two important (which in this case is the electrical potential, i.e., F = Zqξ, types of fast ion conductor: where Z is the charge on the ion.) B is related to μ: 1. The β-aluminas: nonstoichiometric aluminates, for μ = ZqB (30.38) example  Na O · 11Al O (β-alumina) 2 2 3 Substituting Eq. 30.38 into Eq. 30.2 gives  Na O · 8Al O (β′-alumina) 2 2 3 σ = nZq2 B (30.39)  Na O · 5Al O (β′′-alumina) 2 2 3 The absolute mobility, and hence σ, is directly related to They all have a layer structure, as illustrated earlier in the diffusion coefficient, D, through the Nernst–Einstein Figure 7.12, that is composed of spinel blocks of close- equation: packed O2− ions with Al3+ in tetrahedral and octahedral D = kTB (30.40) interstices. Planes containing Na + and O2− ions separate the spinel blocks. It is within these planes that the mobility The diffusion coefficient is given by an Arrhenius of the Na + ions is high. The conductivity is highly aniso- equation, which means that there is an activation energy tropic; it is high within the Na + -containing planes and that must be overcome for the ions to move through negligible in the perpendicular direction. the material as illustrated in Figure 30.20. We can 2. Cubic stabilized zirconia stabilized usually with either CaO or Y2O3. ΕA These materials have oxygen ion transport numbers very close to 1.0. To understand how they are able to conduct large oxygen ions it is necessary to consider their (A) a defect structure. The correct composition of an oxide with the fluorite structure oxide would be MO2. The addition ΔΕA of CaO to ZrO2, for example, drops the metal-to-oxygen ratio below 2.0, and the formula of the oxide becomes Ca xZr1−xO2−x. As we showed in Section 11.7, the Ca2+ ions substitute for Zr4+ ions and we have compensating oxygen vacancies. For each substitutional Ca2+ , we must create (B) ξ one anion vacancy. The result of this enormous defect FIGURE 30.20 Potential energy barrier to ion movement. (a) In the population is to greatly increase the diffusion coefficient absence of an applied field and (b) with an applied field. EA is the for oxygen to the extent that this material becomes a very activation energy and a the jump distance between ion sites. fast oxygen-ion conductor. 3 0 .14 Fa s t I o n C o n d u c t o r s ......................................................................................................................................... 543  e e TABLE 30.9 Efficiency of Various Batteries Type Efficiency (Wh/kg) Seal Nickel–cadmium (Ni–Cd) 7–50 assembly Nickel–metal hydride (Ni–H) 20–100 Sodium–sulfur 75–200 Outer case (mild steel) Sulphur (in C-felt matrix) Figure 30.21. It is often convenient to place the S inside Na the β-alumina tube since the ceramic has far superior cor- Current rosion resistance to that of the mild steel outer casing. On collector connection to the external circuit the Na gives up electrons (coated Al) forming Na + ions. These diffuse through the β-alumina to react with the S to produce the sulfide according to the Separator ß-Al2O3 reaction tube Na flow- 2Na (l) + 5S (l) → Na2S5 (l) (30.41) rate limiter The reverse reaction occurs on recharging. The cell runs at about 300°C with both Na and S in the liquid state. Na The cell reaction is extremely energetic, and the heat reservoir required to maintain the cell at its operating temperature is readily supplied by the cell reaction itself. Despite being used by the Ford Motor Company in a FIGURE 30.21 Schematic of a “central sulfur” cell. Typically, the series of test vehicles the disadvantages of the Na–S electrolyte tube is some 300 mm long and 30 mm in diameter. battery, not least of all its cost (∼$50,000 each), have limited its adoption for electric vehicle applications. A different application Stable ceramics that proposed for Na–S batteries have completely ionic OTHER USES OF CERAMICS IN BATTERIES is for spacecraft. Since elec- conductivity can be used Hg battery—HgO is the cathode. trical power systems make up as solid-state electro- Ni–Cd battery—hydrated NiO (NiOOH · H2O) is the a major part of a spacecraft’s lytes. Two examples are cathode. weight and batteries are typi- the Na–S battery and the Li battery—MnO2 is the cathode. cally the largest component solid oxide fuel cell. of the power system, it is crit- ical to improve the efficiency of spacecraft batteries. Battery efficiency is measured in terms of specific 30.15 BATTERIES energy, or watt-hours of energy output per kilogram of battery weight (Wh/kg), and values for several batteries A battery operates on the principle of a Galvanic cell; a are given in Table 30.9. In 1996 an Na–S battery was flight chemical reaction is used to produce electricity. The mate- tested during a space shuttle mission. Although cost is not rials that are involved in the reaction form the electrodes as much of an issue with spacecraft as it is with automo- and the reaction takes place by the passage of ions through biles, there are still technological challenges in using an electrolyte. The formation of ions during the chemical Na–S batteries. One of these challenges is producing a reaction involves the transfer of electrons to or from the suitable casing. Steel containers, even with protective electrodes. In a galvanic cell these are not allowed to pass coatings, can easily be dented or scratched, leading to through the electrolyte but must travel around an external corrosion and rapid failure. circuit, driven by a potential difference created between the electrodes. It is the electron movement through the external circuit that can be used to do work. 30.16 FUEL CELLS β-Alumina is used as an electrolyte in high-energy- density Na–S batteries. The concept of a battery based on A fuel cell is another example of a galvanic cell and sup- the reaction of Na and S was first proposed in 1967 as an plies electrical energy in the same way as a battery. The alternative to the conventional lead-acid battery. The Na essential difference between the two types of cell is that and S are separated by a membrane of β-alumina, usually the electrodes of a fuel cell do not deteriorate chemically. in the form of a closed-end thin-walled tube as shown in Therefore, if a fuel cell is fed a constant supply of fuel it 544 ........................................................................................................................................ Conducting Charge or Not  TABLE 30.10 Fuel Cells and Their Applications Operating Fuel cell Electrolyte Anode fuel Cathode gas T(°C) Applications Alkaline fuel cell (AFC) KOH solution H2 O2 60–90 Spacecraft, submarines Proton exchange Proton conductive H2 O2 (in air) 60–90 Transportation vehicles, membrane fuel polymer membrane stationary power plants, cell (PEMFC) cogeneration plants, portable power supplies Direct methanol fuel Proton conductive Methanol O2 (in air) 90–120 Transportation vehicles, cell (DMFC) polymer membrane stationary power plants, cogeneration plants, portable power supplies Phosphoric acid fuel Phosphoric acid H2 O2 (in air) 200 Stationary power plants, cell (PAFC) cogeneration plants Molten carbonate fuel Molten alkaline H2, CH4, or coal gas O2 (in air) 650 Stationary power plants, cell (MCFC) carbonate cogeneration plants Solid oxide fuel cell Ceramic solid H2, natural gas, coal O2 (in air) 800–1000 Stationary power plants, (SOFC) electrolyte gas cogeneration plants will supply continuous electrical energy. The fuel is hydro- together in series. Commercially voltages up to ∼ 200 V gen or a hydrogen-rich source (e.g., methanol or formic can be attained. The current produced is proportional to acid). the area over which the reaction occurs. The best fuel The first practical fuel cell was developed in the 1950s cells at present provide a maximum current density of at Cambridge University in the UK. The cell used Ni 0.5–2 A/cm2. electrodes and an alkaline electrolyte. Pratt and Whitney MCFCs and SOFCs can be made by assembling indi- further modified the alkaline fuel cell as it was called in vidual plate cells into stacks, just like the design of the the 1960s for NASA’s Apollo program. The cells were original voltaic pile. For SOFCs producing 5–200 kW used to provide on board electrical power and drinking ceramic plates from 150 mm to 300 mm square are water for the astronauts. The alkaline fuel cell proved required. This requirement presents a problem because it successful, but it was an order of magnitude too expensive is difficult to produce large thin flat dense plates of cer- for terrestrial applications and demanded pure hydrogen amics. Siemens-Westinghouse developed an alternative and oxygen to operate. tubular design; it is straightforward to extrude long tubes Table 30.10 lists the different types of fuel cell that are (see Section 23.9). The disadvantage of the tube design being investigated together with some of their potential applications. Fuel cells are one of the leading research topics at the present time with the goal of reducing the dependence on fossil fuels and associated problems of e- global warming. Air O2- or There are two types of fuel cell that use ceramics: Fuel O 2- O2 2- O  Molten carbonate fuel cell (MCFC) O2 O2- O2  Solid-oxide fuel cell (SOFC) O 2- O2- 2- The main difference between the two types is in the O electrolyte. The MCFC uses a molten carbonate immobi- O2 O2- O2 lized in a porous LiAlO2 matrix. The SOFC uses a ceramic O2- membrane of cubic stabilized zirconia. An illustration of O2- the operation of a SOFC is shown in Figure 30.22. The cell reactions are O2- O2 O2- O2 Air − Cathode: O2 + 4e → 2O 2− Fuel Doped ZrO2 or Electrolyte O2 Anode: 2H2 + 2O2− → 2H2O + 4e− O2- Overall reaction: O2 + 2H2 → 2H2O Anode Cathode A single fuel cell supplies a dc voltage of < 1 V. If FIGURE 30.22 Simple representation of an SOFC using cubic larger voltages are required the cells must be stacked zirconia. 3 0 .16 F u e l C e l l s ........................................................................................................................................................... 545 is that it has high thermal inertia and a long warming time. O2-(2p) Fuel cells offer significant advantages over many other E power sources. They are EG ≈ 8eV  Silent  Low maintenance Mg+(3s)  Efficient (they are not limited to the Carnot effi- ciency—i.e., the maximum theoretical efficiency that can be obtained from an engine employing combustion) MgO  Nonpolluting (the product is distilled water) These advantages are the reasons for the continued research efforts. However, we still do not know whether Mg2+(2p) fuel cell technology can be made commercially viable (at the present time it is not). A principle similar to that used in the SOFC can be FIGURE 30.23 Energy band diagram for MgO. applied to oxygen sensors for applications including moni- toring of automobile exhaust emissions to increase engine efficiency and reduce emissions. Figure 11.17 can be com-  Predominantly ionic bonding pared to Figure 30.22 to see the similarities. Oxygen  Consist of atoms (ions) of low Z control is also important in several metallurgical pro- cesses such as gas carburizing and the bright annealing of Some ceramics having large values of Eg are listed in stainless steel. Table 30.3. No entirely satisfactory relationship has been established between the ionic character of the bond and the atom size on Eg. In a homologous series of oxides, such 30.17 CERAMIC INSULATORS as the oxides of the alkaline-earth metals, Eg increases with increasing ionic potential, φ, of the cation as shown More typically we think of ceramics as being good elec- in Figure 30.24. trical insulators and there are many ceramics that have In a series of isoelectronic compounds (i.e., compounds ρ > 1014 Ω·cm. Examples of common ceramic insulators with an identical total number of electrons) Eg increases include  Aluminum oxide (Al2O3) 8  Mullite (3Al2O3 · 2SiO2) MgO  Forsterite (2MgO · SiO2) EG (eV)  Beryllium oxide (BeO) CaO  Aluminum nitride (AlN) In an electrical insulator there is a wide energy gap between the bottom of the conduction band and the top of 6 SrO the valence band. Figure 30.23 shows the energy band diagram for MgO. The valence band is formed by the 2p energy levels of oxygen (O2− ions) and the conduction band is formed from the empty 3s orbitals of the Mg2+ ions. The energy band gap is ∼8 eV and the concentration BaO of thermally excited electrons in the conduction band of 4 MgO is low right up to its melting point, 2800°C. MgO is therefore an excellent high temperature insulator. Very wide energy band gaps (>6 eV) are associated with compounds that have high fractions of ionic character in their bonding. Ions have a stable noble gas electron configuration. To excite an electron from the valence band 2 to the conduction band involves making the electron con- 0.5 1 1.5 φ 2 figuration of the ions different from those of the noble relative gases. This process is energetically unfavorable. FIGURE 30.24 Effect of bond ionicity on Eg for metal oxides MO In general, compounds with wide band gaps have (φ = Z/r). 546 ........................................................................................................................................ Conducting Charge or Not  NaCl diagram for MgO, this time with the estimated defect 8 energy levels included. If the crystal contains oxygen Eg vacancies (i.e., it has been reduced) these can become (eV) ionized: (V Ox ) → (V Oi ) + e ′ (30.42) 6 You will notice that Kröger–Vink notation is useful for describing this process. The energy for ionization is 0.5 eV and can be represented as a level just below the bottom of the conduction band—the oxygen vacancy is behaving as 4 a donor. MgS The oxygen vacancy can become doubly ionized: AlP ( V Oi ) → ( V Oi i) + e ′ (30.43) 2 The energy for this second ionization process is ∼2 eV and can be represented as another donor level. Si In a similar way we can represent acceptor sites within the band diagram for MgO as being due to the oxidation 0 1 ΔEN 2 of MgO, i.e., the introduction of magnesium vacancies and FIGURE 30.25 Correlation of Eg and electronegativity difference (ΔEN). corresponding holes. The following reactions show the origin of the acceptor levels: with the increasing ionic character of the interatomic bond as shown in Figure 30.25. Understanding this relationship ′ ) + h⋅ (VMgx ) → ( V Mg (30.44) is quite straightforward. As the fraction of covalent char- acter in a bond increases the electrons in that bond are and more equally shared and hence electron transfer becomes easier. ′ ) → ( V ″Mg ) + h⋅ ( V Mg (30.45) The presence of point defects in the lattice can be viewed as being donor or acceptor species in the same way that we considered defects in semiconductor crystals. The energies for these two processes are 0.5 eV and ∼1.5 eV, Figure 30.26 shows another version of an energy band respectively. Even though these ionization energies are relatively small compared to the band gap, the concentra- tion of these defects is extremely low. Even at tempera- Conduction band tures >2000°C the number of cation and anion vacancies (Mg 3 s°) in MgO is only about one per billion lattice sites. The addition of substitutional and interstitial point x x VO AlMg defects can also introduce additional energy levels. Using ED ≈ 2 eV MgO as our example let us consider the incorporation of 0.5 eV Al2O3. There are two defect reactions we can envision: V° O → 2 (Al Mg ) + (3 OO ) + (VMg )′′ i Al 2 O3 ⎯MgO ⎯⎯ x Eg ≈ 8 eV (30.46) and 4.5 eV ≈ Eg – Ed – Ea → 2 ( Al Mg ) + (OO ) + O2 + 2 e ′ i Al 2 O3 ⎯MgO ⎯⎯ x (30.47) In Eq. 30.46 the incorporation of Al into Mg sites is com- VMg ˝ pensated for by the formation of a magnesium vacancy. This type of incorporation is termed ionically compen- EA ≈ 1.5 eV VMg ´ sated because an ionic defect has compensated for the 0.5 eV charge difference. The second reaction, given by Eq. 30.47, is electronically compensated because electrons (or Filled band (O 2p6) in some cases holes) are compensating for the charge dif- FIGURE 30.26 Defect levels in MgO. ference resulting from the substitution of a divalent cation 3 0 .17 C e r a m i c I n s u l at o r s ........................................................................................................................................... 547 for a trivalent one. Accep- CHARGE BALANCE Ceramics with high ρ tor levels are introduced by Reminder: Reactions expressed using Kröger–Vink are important for a number ionic compensation, and notation must be charged balanced, just like regular of applications, many of electronic compensation chemical reaction equations. which utilize more than just corresponds to the intro- the high ρ. Other properties duction of donor levels in such as high strength, sta- the energy gap. bility at elevated temperature, high thermal conductivity, Combining Eqs. 30.46 and 30.47 we can write and hermeticity (impervious to the environment) are also important. 2O2 + 2e′ ↔ (2Oo) x + (VMg)′′ (30.48) One application that you may be familiar with is the Stoichiometric oxides such as MgO are very difficult use of alumina ceramics as the insulator in spark plugs. to reduce and hence the reaction represented by Eq. 30.48 The insulator must be able to withstand a peak voltage of is strongly to the right throughout all accessible ranges of about 10 kV at each spark discharge, a pressure pulse of temperature and oxygen activity. Even highly doped com- about 10 MPa, and the thermal radiation from the combus- positions are not electrically conductive at room tempera- tion temperature that is typically 2000°C. This combina- ture. The defects with a positive effective charge are tion of requirements can be met only by a ceramic. donors; these have given up an electron to become ionized A very visible application of ceramic insulators is as positively relative to the perfect lattice site. Correspond- power line insulators. For this application the strength of ingly, defects with a negative effect charge are acceptors, the ceramic is very important because the insulator sup- having accepted electrons relative to the perfect lattice. ports a considerable weight. The insulator must also be Dislocations are defects that also create additional resistant to weather damage and to absorption of water, energy levels within the band gap. They act as acceptors which can lead to arcing. One ceramic used for this appli- as shown in Figure 30.27. Note that the dislocation-accep- cation is porcelain. A typical porcelain composition would tor levels are usually in the upper half of the band gap. lie in the following ranges: clays [e.g., kaolinite Dislocations are particularly deleterious to the behavior of Al2 (Si2O5)(OH) 4], 40–60 wt%, flux [e.g., orthoclase semiconductors. One of the main factors that limited the (KAlSi3O8)], 15–25 wt%, and quartz or bauxite filler, increase in the size of silicon wafers has been the need to 30–40 wt%. The porcelain is known as a “silicious porce- grow dislocation-free single crystals. At the beginning of lain” if quartz is used as the filler and an “aluminous the semiconductor industry in the 1960s wafer sizes were porcelain” if bauxite is used. limited to 2-inch-diameter wafers; now 18-inch-diameter The above applications are visible uses for ceramic wafers are possible because of better control of the growth insulators. The two applications that we are going to parameters. emphasize next may not be ones that immediately come To understand why dislocations act as acceptors con- to mind when you think of ceramic insulators, but they sider the illustration of a dislocation in silicon shown in are extremely important and, in fact, the development of Figure 12.11. The dislocation creates dangling bonds, personal computers and other electronic devices owes which act as electron traps to satisfy the requirement of much to the use of insulating ceramics. each silicon atom to achieve a noble gas electron configuration. 30.18 SUBSTRATES AND PACKAGES FOR INTEGRATED CIRCUITS Conduction band Substrates and packages for integrated circuits (ICs) con- Donor stitute the largest application for ceramic insulators. The Ec level following properties are required:  High ρ  High thermal conduction  Low dielectric constant Dislocation-  Hermetic acceptor Eg level Three ceramics are usually used for this application:  Al2O3 Ev  BeO  AlN Valence band Alumina ceramics dominate, but there are important FIGURE 30.27 Effect of dislocations on the energy band diagram reasons why BeO and AlN are used in certain applica- of a semiconductor. tions. Table 30.11 compares the properties of these three 548 ........................................................................................................................................ Conducting Charge or Not  TABLE 30.11 Physical Properties of Substrate Materials Property 96%Al2O3 99.5% Al2O3 BeO AlN Mullite Glass-ceramics Density (g/cm3) 3.75 3.90 2.85 3.25 2.82 2.5–2.8 Flexural strength (MPa) 400 552 207 345 186 138 Thermal expansion from 25 to 500°C 7.4 7.5 7.5 4.4 3.7 3.0–4.5 (ppm/°C) Thermal conductivity at 20°C (W m−1°C−1) 26 35 260 140–220 4 4–5 Dielectric constant at 1 MHz 9.5 9.9 6.7 8.8 5.4 4–8 Dielectric loss at 1 MHz (tan δ) 0.0004 0.0002 0.0003 0.001–0.0002 0.003 >0.002 ceramics and some others that have also been used as Dry oxidation is slow, but produces a uniform relatively substrates and packages. BeO and AlN are used in situa- defect-free layer that is electrically very reliable. Wet oxi- tions in which high thermal conductivity is needed. Heat dation is more frequently used for masking operations removal from power electronics and from integrated cir- because the growth rate is faster, however, the layers are cuits is determined mainly through the substrate; one not as uniform as those produced by dry oxidation. factor that influences the heat transfer rate is the thermal The oxide layer formed on the silicon surface is what conductivity of the substrate material. Effective thermal is known as a protective oxide. The growth rate initially management is important in improving the reliability of follows a linear rate law, i.e., the oxide thickness, x, electronic devices. increases linearly with time, t AlN has a theoretical thermal conductivity of 320 W m−1 K and values as high as 285 W m−1 K−1 have been experi- −1 x∝t (30.51) mentally measured for single crystals. Commercial AlN substrates are available with a thermal conductivity up to For the two processes the activation energies are about 200 W m−1 K−1 at room temperature. The thermal expansion of AlN (3.9 × 10−6 K−1) from room temperature EA = 1.96 eV for wet oxidation to 500 K is very similar to that of silicon (3 × 10−6 K−1) EA = 2.0 eV for dry oxidation over the same temperature interval, which helps to avoid cracking due to thermal misfit stresses between substrate These values are close to the energy required to break the and device. This consideration is particularly important Si–Si bond, 1.83 eV. for large silicon chips. AlN also does not have the inherent After a layer of approximately 100 nm has formed the toxicity problems associated with BeO. growth kinetics follow a parabolic rate law, i.e., the oxide thickness increases with the square root of time: 30.19 INSULATING LAYERS IN INTEGRATED CIRCUITS x∝ t (30.52) Layers of SiO2 have several uses in the production of silicon ICs: Diffusion through the oxide layer follows an Arrhenius law (Eq. 3.13):  Device isolation  Isolation of multilevel metallization EA = 1.24 eV for dry oxidation  Surface passivation EA = 0.71 eV for wet oxidation  The gate oxide in metal–oxide–semiconductor (MOS) structures These activation energies are close to those for the  Barrier layer during dopant incorporation. diffusivity of oxygen and water vapor through fused silica, respectively. Fused silica has a structure very similar to SiO2 layers can be obtained by direct oxidation by one of that of thermal SiO2. the following reactions: When very thin SiO2 layers are required such as a gate Dry oxidation: oxide in an MOS-field effect transistor (MOSFET) or when an SiO2 layer is required as an insulating layer Si (s) + O2 (g) → SiO2 (s) (30.49) between layers in a multilevel device the CVD process is used. The dielectric is an active component of the Wet oxidation: storage capacitor in dynamic RAMs, and its thickness determines the amount of charge that can be stored (see Si (s) + 2H2O (g) → SiO2 (s) + 2H2 (g) (30.50) Chapter 31). 3 0 .19 I n s u l at i n g L ay e r s i n I n t e g r at e d C i r c u i t s ................................................................................................ 549  In a complementary metal-oxide semiconductor (CMOS) device oxidation of polysilicon is necessary for electrical isolation. A thermal oxide can be produced on polysilicon in a manner similar to that produced on single crystal silicon. 30.20 SUPERCONDUCTIVITY There are two properties that a material must possess to be considered a superconductor: 1. ρ = 0 2. B = 0 (described in Chapter 33) Zero resistivity is observed in a superconductor at all FIGURE 30.29 Illustration of lattice distortion around a free electron, which leads to the formation of Cooper pairs. temperatures below a critical temperature, Tc, as illus- trated in Figure 30.28. At Tc the material changes from a state of normal conduction to the superconducting state. In the superconducting state an induced current will flow the better superconductors, albeit still at very low tem- indefinitely: without loss. This behavior has been demon- peratures. Low-temperature superconductors (LTSC) have strated experimentally when a current has been run a Tc up to about 20 K. High-temperature superconductors through a closed ring of a superconducting metal for over (HTSC) are usually defined as having a Tc above the two and a half years without any measurable decay. boiling temperature of liquid nitrogen. Superconductivity has been observed in all the classes The BCS theory (after Bardeen, Cooper, and Schrief- of materials: metals, ceramics, and polymers. Of all the fer) provides an explanation for superconductivity at low elements in the periodic table only 27 are known to become temperatures. The theory is complicated, but the basis is superconducting under ordinary pressure. Niobium is the that there exists an attractive force between electrons that element with the highest Tc, 9.2 K, whereas for tungsten Tc have about the same energy. This force causes them, under is only 0.0154 K. An interesting fact is that metals having the right circumstances, to move in pairs. These are the the highest σ, e.g., Cu, Ag, and Au, are not superconduct- so-called Cooper pairs. The criterion for superconductiv- ing even at extremely low temperatures, if at all. It is the ity is that this attraction should be greater than the natural metals that are the poorer electrical conductors that make repulsion between like charges. Tc corresponds to the binding energy needed to hold the Cooper pairs together in a superconducting state. The origin of the attractive force is that in a lattice of positive ions, an electron will attract the positive ions toward itself. In this region the lattice will be slightly ρ in Ω denser as shown in Figure 30.29. To a passing electron the local lattice distortion will appear as an increase in posi- tive charge density and it will be attracted toward it. The two electrons pair up in this way through their interaction with the lattice. If the lattice is vibrating through thermal effects pairing will not be possible, but at very low temperatures where the vibration amplitude is small, the attractive force can be dominant. The electrons are held together by a binding energy of only about 10−4 eV. The separation of the electrons in the pair (called the coherence length) for most LTSC is 100 nm. Interatomic spacings are on the order of 0.3 nm, so two bound electrons can be as far apart as 300 lattice spaces. The large coherence length means that defects such as dislocations, GBs, and impurities are too small to have much effect on superconducting behavior. Tc T in K The existence of these bound electron pairs alters the FIGURE 30.28 Plot of ρ versus T for a superconductor. energy band diagram for a superconductor by introducing 550 ........................................................................................................................................ Conducting Charge or Not  TABLE 30.12 Critical Temperatures of Some Ceramic Superconductors Δ Compound Tc (K) Ef La 2−x M x CuO4−y 38 M = Ba, Sr, Ca x ∼ 0.15, y small Nd2−x Cex CuO4−y (electron doped) 30 Ba1−x K x BiO3 (isotropic, cubic) 30 Pb2Sr 2Y1−x Ca x Cu3O8 70 Normal R1Ba 2Cu2+m O6+m Superconductor R: Y, La, Nd, Sm, Eu, Ho, Er, Tm, Lu metal m = 1 (123) 92 FIGURE 30.30 Band diagram for a superconductor. m = 1.5 (247) 95 m = 2 (124) 82 Bi2Sr 2Ca n−1Cu n O2n+4 n = 1 (2201) ∼10 a small gap at EF, known as the superconducting gap, Δ. n = 2 (2212) 85 The difference in the band structure of a material in the n = 3 (2223) 110 superconducting state and in the nonsuperconducting state Tl2Ba 2Ca n−1Cu n O2n+4 is illustrated in Figure 30.30. The energy of this gap cor- n = 1 (2201) 85 n = 2 (2212) 105 responds to the binding energy of the electron pairs. An n = 3 (2223) 125 energy 2Δ is needed to break a Cooper pair. The relation- ship between Δ and Tc is given by the BCS theory: 2Δ = 3.5 kTc (30.53) ture, which, as shown in Chapter 7, is the structural build-  For LTSC Δ ∼1 meV ing block of all presently known HTSC.  For HTSC Δ ∼1–10 meV The beginning of HTSC started in 1986 with the dis- covery of superconductiv- The BCS theory pre- CHEVREL PHASES ity in the compound dicts an ultimate limiting These are complex forms of MoS2 having the general La2BaCuO4, which has Tc value of Tc of 30 K for elec- formula M xMo6X8, where M is a metal and X is a chal- ∼38 K. This discovery was tron pairing via lattice cogen. PbMo6S8 has the highest Tc of the Chevral phases of monumental importance vibrations (phonons). This (Tc = 15 K). They are named after French scientist Roger because the classic BCS limit was enough to stop Chevrel. theory for superconductiv- many researchers from ity predicted a maximum pursuing careers in super- value of Tc of only 30 K! conductivity. But clearly the BCS theory, in its entirety, Many more HTSC were simply obtained by systematic cannot be applicable to HTSC where Tc >> 30 K. In these substitution of elements into the basic perovskite unit. materials pairing of the electrons still occurs, but the Certainly in the early days many scientists said that mechanism that allows this pairing needs to be research in HTSC was more akin to cooking than any area determined. of science! The elements yttrium and lanthanum are interchange- able in terms of chemical properties (they are in the same 30.21 CERAMIC SUPERCONDUCTORS group in the periodic table) although they differ in size. The same is true of strontium and barium in Group II of The earliest nonmetallic superconductors were NbO and the periodic table. The idea behind the substitution of the NbN. Both materials have a rocksalt crystal structure. large element for a smaller element was based on observa- What was significant about the discovery of superconduc- tions that Tc could be raised under an applied pressure. tivity in these materials (they are of no practical use) is Substitution of a larger element for a smaller one was that they linked the phenomenon to ceramics and cubic thought to produce an internalized pressure effect. Table crystal structures. 30.12 lists some of these compounds and their Tc. Superconductivity in a multicomponent oxide was first Tables 30.13 compares properties of HTSC and LTSC; observed in SrTiO3. Although Tc was determined to be v F is the velocity of propagation of conduction electrons only 0.3 K, SrTiO3 has the very important perovskite struc- through crystal. 3 0 . 21 C e r a m i c S u p e r c o n d u c t o r s .............................................................................................................................. 551  TABLE 30.13 Comparison of Superconductors in the Normal State Number of conduction Fermi Mean free electrons (n) velocity ( vF) path (l e) r (@ 100 K) c Material (electrons/cm 3) (m/s ) (nm) (mW · cm) (nm) Al 180 × 1021 2.0 × 10 6 130 0.3 1600 Nb 56 × 1021 1.4 × 10 6 29 3 38 LSCO 5 × 1021 0.1 × 10 6 ∼5 ∼100 ∼1.5 YBCO 7 × 1021 0.1 × 10 6 ∼10 ∼60 ∼1.0  The obvious difference is Tc. The fact that Tc ∼ 102 K larger than within the planes; hence charge hopping means that the binding energy is ∼10 meV, as compared between planes is much less efficient. to <1 meV in LTSC. There are many potential applications for HTSC, but  The ceramics have higher ρ than the metals at 100 K. the actual realization of these has in many cases not But ρ is comparable to some of the best ceramic elec- occurred. The major problem is being able to fabricate the trical conductors, such as CrO2 and TiO. ceramics into useful and usable shapes. Ceramics are  For HTSC χ is only ∼1.0 nm, which means that the inherently brittle and this alone makes the fabrication of pairing behavior is almost on an atomic scale and long wires and tapes extremely difficult. These would be the superconducting properties will be dependent on essential for domestic and industrial power transmission atomic scale defects. (Compare χ with the width of a (some limited progress has been made in this area as we dislocation or GB.) Such defects therefore scatter the describe in Chapter 37). The low χ also makes practical electron pairs and reduce the critical current density. applications more difficult to achieve because we have to For metals χ is large, e.g., χ = 1.6 μm in pure Al, χ = be concerned about defects. 38 nm in pure Nb. The most likely route to widespread practical applica-  χ is anisotropic. For YBCO χab ∼ 1.5 nm and χc ∼ tion is to use the HTSC in the form of a thin film and 0.4 nm. A major problem in HTSC is to find a crystal utilize the Josephson effect. The original observation of defect that pins the flux vortices, but does not disrupt this effect was made using a junction consisting of two current flow. superconductors separated by a very thin insulating layer (∼1 nm). In thin films the “insulating” region can be ori- We showed the structures of HTSC in Chapter 7. entation changes across a GB as shown in Figure 14.37. Superconductivity essentially takes place within the CuO2 The I–V characteristics of a Josephson junction are planes. The Cu–O chains can be considered as a “charge- very nonlinear as shown in Figure 30.31. The key features reservoir” that is needed to transfer charge into the CuO2 are as follows: planes. Charge carriers are added by doping: adding oxygen to YBa2Cu3O6, which enters the compound as O2−  When V = 0, a direct current flows. and forms Cu–O chains. To maintain charge balance,  When a small voltage is applied I = 0. electrons are removed from the Cu–O planes and the  At Vc the electrons are no longer paired and normal remaining holes are mobile (hence conduction) and form electron tunneling occurs with associated resistive Cooper pairs below Tc. losses. In LTSC Cooper pairs, with a charge of −2e, are responsible for current flow. In most of the HTSC the Cooper pairs have a positive charge, +2e. In other words I they are positive holes and the charge transfer process can be written as Ic Cu2+ + h + → Cu3+ (30.54) V One of the consequences of a hole-hopping process Vc involving a two-dimensional array of copper ions is that the superconducting current is very anisotropic. Hopping tends to occur between copper ions that have the smallest separation from each other, namely those in the plane. The distance between copper ions on adjacent planes is much FIGURE 30.31 I–V characteristics of a Josephson junction. 552 ........................................................................................................................................ Conducting Charge or Not  V If a Josephson junction is irradiated with microwaves 2 mV of frequency f, the I–V behavior shows a series of steps, called Shapiro steps, as shown in Figure 30.32. These steps correspond to supercurrents across the junction when the condition for the absorption of microwave photons is satisfied (this is called the ac Josephson effect). Similar behavior is seen when we expose the junction to a mag- netic field. How Josephson junctions can be used to detect 5 mA I very small magnetic fields is described in Chapter 33. FIGURE 30.32 Effect of incident microwave radiation on the I–V characteristics of a Josephson junction. CHAPTER SUMMARY We can explain the wide range of electrical properties shown by ceramics by considering their electron band structure. Some oxides show metallic-like levels of conductivity consistent with either a partially filled valence band or a small Eg. These materials are used as electrodes and conductors. Most ceramics fall into the category of having a medium to wide Eg. Semiconduct- ing ceramics are used in a variety of sensors. The most important application is to “sense” anomalous voltages. As with the more familiar Si and GaAs, which are also ceramics, the conductivity of all semiconductors can be changed by doping. Unlike Si and GaAs we can use stoichiometry changes to modify σ. Ceramics having the largest Eg usually show a significant degree of ionic bonding and any conductivity is mainly associated with ion transport. The important technological example is cubic ZrO2, which is the electrolyte in solid oxide fuel cells. Fuel cells are one of the key components of a “hydrogen economy.” We finished this chapter with superconductors. The structure of these materials is already familiar from Chapter 7 and the importance of GBs as weak links from Chapter 14. PEOPLE IN HISTORY Bardeen, John (1908–1991) received the 1972 Nobel Prize in physics with Cooper and Schrieffer for the BCS theory. It was his second Nobel Prize! He won his first in 1956 for his role in the invention of the transistor. Cooper, Leon Neil (1930– ) received the Nobel Prize in physics with Bardeen and Schrieffer for the BCS theory. Cooper pairs are named after him. Drude, Paul Karl Ludwig (1863–1906) was a German physicist who developed a theory for electron conduc- tion. Drude’s theory provided an atomistic basis for understanding electron motion in metals and ceram- ics. In its original version it contained several inaccuracies, which were corrected by the application of quantum mechanics. Grove, Sir William Robert (1811–1896) was a British scientist who in 1839 discovered the principle on which fuel cells are based. His cell, which was composed of two Pt electrodes both half immersed in dilute H2SO4, one electrode fed with O2 and the other with H2, was not a practical method for energy production. Onnes, Heike Kamerlingh (1853–1926) was a Dutch physicist who succeeded in liquefying helium in 1908 and discovered superconductivity in mercury in 1911. He wrote at the time: Mercury has passed into a new state, which on account of its extraordinary electrical properties may be called the superconducting state. He received the Nobel Prize in physics in 1913. Schrieffer, John Robert (1931– ) received the Nobel Prize in physics with Bardeen and Cooper for the BCS theory. GENERAL REFERENCES Cox, P.A. (1987) The Electronic Structure and Chemistry of Solids, Oxford University Press, Oxford. A very good description of electronic properties. C h a p t e r S u m m a ry .......................................................................................................................................................... 553  Cyrot, M. and Pavuna, D. (1992) Introduction to Superconductivity and High-Tc Materials, World Scientific, Singapore. A clear introduction to the field. Treats the theoretical models at a level above that used here but within the range of most upper division MSE undergraduates and graduate students. Duffy, J.A. (1990) Bonding, Energy Levels and Bands in Inorganic Solids, Longman Scientific and Technical, Harlow, Essex, UK. Straightforward description of energy bands in solids. Hench, L.L. and West, J.K. (1990) Principles of Electronic Ceramics, Wiley, New York. Comprehensive background to electronic ceramics. Moulson, A.J. and Herbert, J.M. (1992) Electroceramics, Chapman & Hall, London. An excellent account of the properties and applications of electroceramics. Owens, F.J. and Poole, C.P. Jr. (1996) The New Superconductors, Plenum Press, New York. SPECIFIC REFERENCES Bardeen, J., Cooper, L.N., and Schrieffer, J.R. (1957) “Theory of superconductivity,” Phys. Rev. 108, 1175. The BCS theory in all its technical detail. Josephson, B.D. (1962) “Possible new effects in superconductive tunneling,” Phys. Lett. 1, 251. The epony- mous junction. Nye, J.F. (1985) Physical Properties of Crystals, Clarendon Press, Oxford. This is the standard reference for tensor representation. Chapter XI covers transport properties including electrical conductivity. The representation of σ by tensors is not necessary to understand the electrical behavior of materials. Its significance becomes clear when we want to specify certain properties of anisotropic single crystals. JOURNALS Solid State Ionics. An international journal published by Elsevier. Journal of Electronic Materials. Published by ASM. Journal of Materials Science: Materials in Electronics. Published by Springer. JOURNALS DEVOTED TO SUPERCONDUCTIVITY AND ITS APPLICATIONS The field of high-temperature superconductivity experienced unprecedented growth during the late 1970s and 1980s. The important aspects of much of that research have been compiled in several books. Even so the field is still producing new developments, although of a much more incremental nature, and journals are the best place to find out what is happening. The following journals deal exclusively with superconductivity. Physica C. Published by Elsevier. Journal of Superconductivity since January 2006 renamed the Journal of Superconductivity and Novel Mag- netism. Published by Springer. Superconductor Science and Technology. Published by the Institute of Physics (IOP). OTHER JOURNALS REPORTING DEVELOPMENTS IN HTSC Many other journals have regular contributions in the area of HTSC. The major resources are listed below. Journal of Applied Physics. Published by the American Institute of Physics (AIP). Applied Physics Letters. Also published by AIP. Consists of three page papers covering important develop- ments in applied physics. A repository for many of the early papers covering processing of HTSC films. Physical Review B, Physical Review Letters, Japanese Journal of Applied Physics, Journal of Materials Science: Materials in Electronics. EXERCISES 30.1 Using Table 30.2 explain the following: (a) Why do t + and t− change for NaCl as the temperature is increased from 400 to 600°C. (b) How would you expect these numbers to change if the temperature was increased further to 700°C? (c) Why is te zero? 30.2 At what temperature would the probability of finding an electron in the conduction band of diamond be the same as the probability of finding an electron in the conduction band of silicon at 25°C? 30.3 Using appropriate sketches compare the ion arrangements in the electrical conductor TiO shown in Figure 30.5 to those in the electrical insulator MgO. 30.4 In glasses containing alkali metal oxides such as Na2O, the current is carried almost entirely by the alkali metal ion. (a). What is the transference number for alkali metal ions in this case? (b) Sketch the potential energy barrier for ion transport (i.e., redraw Figure 30.20 for a glass). (c) Why does your figure look different from Figure 30.20? 30.5 Calculate the probability of an electron being in the conduction band of MgO at a temperature of 2000°C. 554 ........................................................................................................................................ Conducting Charge or Not  30.6 The Hope diamond exhibited at the Smithsonian Institution in Washington, D.C. is a striking blue. Would you expect this stone to be electrically conducting? Explain how you arrived at your answer. Make sure to mention any assumptions you make. 30.7 What is the HTSC that currently has the highest Tc? Are there any practical problems related to the use of this material? 30.8 In ZrO2 (fluorite structure) ion conduction is the result of anion motion. In Li 2O (antifluorite structure) would you consider the anions or cations to be more mobile? (b). How might you increase ion conductivity in Li2O? In both cases explain how you arrived at your answer. (c) Now repeat (a) and (b) for MgO. 30.9 GaN is a wide-band-gap semiconductor. (a) What is Eg for GaN? (b) Describe some possible applications for GaN. 30.10 Dislocations have been shown to decrease the mobility of electrons in a semiconductor. Using the illustration of a dislocation in Figure 12.11 explain why you think they have a detrimental effect on μ. C h a p t e r S u m m a ry .......................................................................................................................................................... 555  31 Locally Redistributing Charge CHAPTER PREVIEW In this chapter we describe ceramic dielectrics. A dielectric is by definition an electrical insula- tor (ρ is high and Eg is large). That means that dielectric behavior is a property associated with certain ceramics and polymers but not a property associated with metals. We begin with a background section. Some of this material may have been covered before but perhaps not spe- cifically in terms of ceramics. Dielectrics in the context of this chapter are more than just passive insulators. For example, in BaTiO3 and related perovskites structural changes create permanent electric dipoles that cause the material to become polarized. Among other things, polarization allows the material to store large amounts of charge: this is a prerequisite for a capacitor. Without dielectrics, computers cannot function; some of today’s greatest challenges for the electronics industry concern dielectrics more than semiconductors. The following key topics are discussed in this chapter:  Dielectrics are polarizable: the separated charges cause an electric field that we characterize by the dielectric constant.  Dielectrics can be self-polarizing: this is the ferroelectric effect. These ceramics are used in capacitors because of their high dielectric constant.  The dimensions of a dielectric may change when it is polarized: this is the piezoelectric effect and is used in microelectromechanical systems (MEMS), sonar, and medical ultra- sound imaging.  The spontaneous polarization of a dielectric depends strongly on T; this is the pyroelectric effect that we use for infrared (IR) detection (e.g., intruder alarms and thermal imaging). 31.1 BACKGROUND ON DIELECTRICS Table 31.1 lists the important parameters discussed in this chapter and their units. All materials contain electrically charged particles. At a minimum these are the electrons and protons that are part of the constituent atoms. Many ceramics also contain ions, Polarization Mechanisms which are charged. In a dielectric, charges have a limited Even though no charge is transferred when a dielectric is mobility and they will move only when they have enough placed in an electric field there is a redistribution of charge, energy to overcome their inertia. When an insulator which occurs by the formation and movement of electric receives a charge, it retains that charge, confining it within dipoles. There is an associated dipole moment, μ, having the localized region in which it was introduced. However, both magnitude and direction a conductor allows charge to flow freely and redistribute itself within the material. The distinction between conduc- tors and nonconductors (and it is not always a clear one) μ = qd (31.1) arises from the relative mobility of charge within the material. where d is the separation of the positive and negative ends The terms “dielectric,” “nonconductor,” and “insula- of the dipole. The dipole direction is, by convention, taken tor” are often used interchangeably. However, we often to point from the negative end to the positive end. specify dielectrics as materials that are not only electri- When a dielectric material is placed in an electric cally insulating but also have a high dielectric constant, field the induced dipoles, and any permanent dipoles, κ. become aligned. The material is now polarized and 556 ............................................................................................................................... L o c a l ly R e d i s t r i b u t i n g C h a r g e  TABLE 31.1 Terms and Units Used to Describe Dielectric Behavior Parameter Definition Units/value Conversion factor C Capacitance F, farads 1 F = 1 C/V = 1 A 2 s4 kg−1 m−2 ε0 Permittivity of a vacuum 8.85 × 10 −12 F/m ε Permittivity F/m εr Relative permittivity (ε/εo) Dimensionless κ (same as εr) Dielectric constant Dimensionless P Polarization C/m2 Q Charge C, coulombs 1C = 1As μ Dipole moment C·m V Voltage V q or e Electron charge 0.16 aC D Dielectric displacement C/m2 D = Q/A θc Curie temperature K 0 K = −273°C Tcw Curie–Weiss temperature K Ec Coercive field V/m χ Dielectric susceptibility Dimensionless ξ Electric field strength V/m C Curie constant K the polarization (or dipole POLARIZATION MECHANISMS and may also change the moment per unit volume) A note: In some texts you will find that the polarization overall dimensions of the is given by mechanism occurring in BaTiO3 is described as dipolar material. The dipole and in others as ionic. We prefer the former because moment is usually small P = Nqd (31.2) because, once again, the BaTiO3 contains permanent dipoles (a condition of dipolar polarization) that are being oriented in an elec- displacements involved are where N is the number of very small. Typically the dipoles. tric field. Although the permanent dipoles in BaTiO3 are the result of ion displacements, the term ionic polariza- ion displacements are only There are four possible 10–100 am. polarization mechanisms tion refers to the movement of any ions in an electric in a dielectric: field (whether the material has a permanent dipole or not). Dipolar This mechan- ism is generally uncom-  Electronic mon in ceramics because  Ionic most of the permanent dipoles cannot be reoriented without  Dipolar (also called molecular or orientation)  Interfacial (also called space charge) These mechanisms are each illustrated in Figure 31.1. Electronic Electronic When an electric field is applied to an + + atom, there is a displacement of the electrons relative to the nucleus. The electrons will concentrate on the side of the nucleus near the positive end of the field. The atom acts E=0 E as a temporarily induced dipole. This effect occurs in all Ionic materials (because all materials contain atoms), but the + + magnitude is small because d is very small. Typical E=0 E displacements are ∼1 am giving μ ∼1.6 × 10−37 C·m. Dipolar Electronic polarization is the only possible mechanism in pure materials that are covalently bonded and does not contain permanent dipoles (e.g., diamond and silicon). E=0 E E=0 Interfacial E Ionic This occurs when an ionically bonded material + + + + + is placed in an electric field; it is common in many ceramics + + + + + (e.g., MgO, Al2O3, NaCl). The bonds between the ions are + + + + + + elastically deformed. Consequently the charge is minutely redistributed. Depending on the direction of the field, the + + + + cations and anions move either closer together or further FIGURE 31.1 Illustration of the different polarization mechanisms apart. These temporarily induced dipoles cause polarization in a solid. 31.1 Bac k g r o u n d o n D i e l e c t r i c s .............................................................................................................................. 557 destroying their crystal structure. But there are some very TABLE 31.2 Dielectric Constants of Various Ceramics important exceptions and it is these materials that will k at k at form a large part of this chapter. The prototypical example Material 1 MHz Material 1 MHz is barium titanate. The structure is shown in Figure 7.2. At room temperature the octahedrally coordinated Ti4+ ion is Diamond 5.5–6.6 Al2O3 8.8 displaced slightly from its ideal symmetric position causing SiO2 3.7–3.8 MgO 9.6 NaCl 5.9 BaTiO3 3000 the crystal structure to become tetragonal and permanently Mica 5.4–8.7 Pyrex glass 4.0–6.0 polarized. When an alternating electric field is applied to Soda-lime glass 7.0–7.6 TiO2 14–110 a crystal of barium titanate, the Ti4+ ion moves back and Steatite 5.5–7.5 Forsterite 6.2 forth between its two allowable positions to ensure that the (SiO2 + MgO + Al2O3) (2MgO · SiO2) polarization is aligned with the field. Cordierite 4.5–5.4 Mullite 6.6 (SiO2 +MgO + Al2O3) High-lead glass 19 Vycor glass 3.9 Interfacial A charge may develop at interfaces (such as grain or phase boundaries and free surfaces) normally as a result of the presence of impurities. The charge moves on the surface when the material is placed in an electric field. This type of polarization is not well understood, P = (κ − 1)ε0ξ = χε0ξ (31.8) although it has considerable practical interest because most real materials and, in particular, many ceramics, are not where χ is a measure of the ratio of the bound charge/free pure. charge (i.e., P/Q). For dielectrics that polarize easily κ The total P for the material is then the sum of all the will be large and, in turn, a large quantity of charge can individual contributions: be stored. Table 31.2 lists κ for a range of materials. Many ceram- P = Pelectronic + Pionic + Pdipolar + Pinterfacial (31.3) ics and glasses have κ in the range of 4–10. Polarization is electronic only in covalent ceramics such as diamond and is a combination of electronic and ionic in materials such as MgO. Some ceramics, in particular BaTiO3 and Relating P and k other titanates and zirconates, have very large κ due to The dielectric constant is an important materials property their permanent dipole moments. and is a measure of the ability of an insulating material to store charge when subjected to an electric field; as you Frequency Dependence of Polarization might expect, it is directly related to P. We can develop an equation relating P and κ by When a dielectric is placed in an alternating electric field beginning with a simple parallel plate capacitor. From the dipoles attempt to maintain alignment with the field. electromagnetic theory we know that the total charge This process requires a finite time that is different for each per unit area of a capacitor plate, D 0, is proportional to polarization mechanism. At the relaxation frequency the the applied electric field ξ. The constant of proportionality dipoles will only just be able to reorient themselves in time is ε0 : with the applied field. At this frequency the dielectic is “lossy” and energy is lost in the form of heat. The dielec- D 0 = Q/A = ε0ξ (31.4) tric loss is at a maximum when the frequency of the external field coincides with the relaxation frequency of a If we now place a dielectric between the parallel plates we given polarization mechanism. This is the principle behind write the microwave oven. It operates at the relaxation frequency of water molecules and the heat generated warms the D = εξ (31.5) food. At frequencies above the relaxation frequency the D is also known as the dielectric displacement and repre- dipoles will no longer be able to keep up with changes in sents the extra charge that can be stored because of the the applied field and the contributing polarization mecha- presence of the dielectric. So we can rewrite Eq. 31.5 as nism becomes effectively “frozen” and no longer contrib- utes. Figure 31.2 shows the variation of polarization with D = ε0ξ + P (31.6) frequency for a hypothetical material that exhibits all four of the polarization mechanisms. By substituting Eq. 31.5 into Eq. 31.6 we obtain  At optical frequencies only electronic polarization is εξ = ε0ξ + P (31.7) operative.  Dipolar and ionic contributions are small at high fre- By simple rearrangement we can write quencies because of the inertia of the molecules and 558 ............................................................................................................................... L o c a l ly R e d i s t r i b u t i n g C h a r g e  TABLE 31.4 Dielectric Strengths for Various Ceramics Material Dielectric strength (MV/cm at 25°C) Al2O3 (99.5%) 0.18 P Al2O3 (94.0%) 0.26 αinterfacial charge High-voltage porcelain 0.15 IR UV Steatite porcelain 0.10 Lead glass 0.25 αdipolar Lime glass 2.5 Borosilicate glass 5.8 Fused quartz 6.6 αionic Quartz crystal 6.0 NaCl [100], [111], [110] 2.5, 2.2, 2.0 Muscovite mica 10.1 αelectronic RF to μwave 100 104 108 1012 f (Hz) 1016 FIGURE 31.2 Frequency dependence of polarization. tric strengths are important in applications in which the thickness of the material is going to be small, e.g., in capacitors. Values of ions. The peaks occur- REAL AND IMAGINARY COMPONENTS OF e dielectric strength for ring at ∼1013 and The permittivity under an alternating field can be rep- several ceramics are given ∼1015 Hz are due to res- resented mathematically as the sum of real (ε′) and in Table 31.4. Note the very onance effects where imaginary (ε′′) parts: high value of mica, which the external field is is one of the reasons it was alternating at the ε = ε′ − jε′′ (Box 31.1) used in early ceramic disk natural vibrational fre- capacitors. quency of the bound In an alternating electric field the phase angle of the ions or electrons, electric flux density lags behind that of the electric field respectively. due to the finite speed of polarization. The delay angle Nonlinear Dielectrics δ is Nonlinear dielectrics have Dielectric Strength permanent dipoles that A dielectric will be able to tan δ = ε′′/ε′ (Box 31.2) interact to give a polariza- withstand a certain applied tion in the absence of an electric field strength The electric power loss per unit time (also called the applied electric field. These before it breaks down and dielectric loss) is proportional to tan δ. Typical values materials are the ferroelec- current flows. High dielec- are given in Table 31.3. trics. The topic shares many similarities with fer- romagnetism described in Chapter 33. For example, above TABLE 31.3 Dielectric Loss for Some Ceramics and a critical temperature, the Curie temperature θc, the spon- Glasses at 25°C and 1 MHz taneous polarization is destroyed by thermal disorder. A plot of P versus ξ is shown in Figure 31.3 and demon- Material Tan d strates hysteresis. This behavior is similar to that produced LiF 0.0002 by a ferromagnet when it is cycled through an alternating MgO 0.0003 magnetic field. The description is based on the domain KBr 0.0002 structure of ferroelectrics. NaCl 0.0002 TiO2 (储 c) 0.0016 When the dipoles in a crystal are randomly oriented TiO2 (储 a,b) 0.0002 there is no net P. When a field is applied, the dipoles begin Al2O3 (储 c) 0.0010 to line up with the electric field. The total dipole moment Al2O3 (储 a,b) 0.0010 changes either by the movement of the walls between BaO 0.0010 domains or by the nucleation of new domains. Eventually KCl 0.0001 Diamond 0.0002 the field aligns all of the dipoles and Ps is obtained. When Mg2SiO4 (forsterite) 0.0003 all the dipoles are aligned in the same direction the mate- Fused silica glass 0.0001 rial is “poled.” Vycor (96 SiO2–4B2O3) glass 0.0008 When the field is subsequently removed a remnant Soda-lime silica glass 0.0100 polarization Pr exists due to the coupling between adja- High-lead silica glass 0.0057 cent dipoles. The material is permanently polarized in the 31.1 Bac k g r o u n d o n D i e l e c t r i c s .............................................................................................................................. 559  P TABLE 31.5 Noncentrosymmetric Crystals Ps Noncentrosymmetric Pr Crystal system point groups Piezoelectric Pyroelectric Triclinic 1 Yes Yes Monoclinic 2 Yes Yes m Yes Yes Orthorhombic mm2 Yes Yes 222 Yes No Tetragonal 4 Yes Yes 4̄ Yes No 422 Yes No 4 mm Yes Yes -Ec Ec 4̄2 m Yes No 0 E Trigonal 3 Yes Yes 32 Yes No 3m Yes Yes Hexagonal 6 Yes Yes 6̄ Yes No 622 Yes No 6 mm Yes Yes 6̄m2 Yes No Cubic 23 Yes No 432 No No 4̄3 m Yes No FIGURE 31.3 Hysteresis curve for a typical ferroelectric. absence of an electric field. This property is the key to 31.2 FERROELECTRICITY ferroelectricity. When the direction of Ferroelectrics exhibit an ξ is reversed the dipole FERROELECTRICS electric dipole moment in orientation switches to Ferroelectrics do not contain iron. The term comes from the absence of an external become aligned with the the analogy with ferromagnetism, which also does not electric field. The direction new field direction. As the require iron. of the dipole moment may strength of the reverse field be switched by the applica- is increased, Ps will eventually occur with the opposite tion of an alternating field. This property of polarization polarization. As the field alternates a hysteresis loop is reversal and remanence cannot be predicted by looking produced. The area contained within the loop is related to only at the structure of a material; it must be determined the energy required to cause the polarization to switch experimentally. directions. Linear dielectrics (which is most of them) do Ferroelectricity is a property that is associated not only not show significant hysteresis in an alternating electric with ceramics. Certain polymers such as polyvinylidene field. fluoride (PVDF) and copolymers between PVDF and tri- There is a structural requirement for ferroelectricity. fluoroethylene are ferroelectric. PVDF is a semicrystalline There are a total of 32 different symmetry point groups, polymer. The crystalline conformation has an orthorhom- 21 of which do not possess a center of symmetry. Ferro- bic unit cell (mm2). electrics are part of a small subgroup of noncentrosym- A ferroelectric crystal consists of regions called metric crystals. Related properties are piezoelectricity and domains. Within each domain the polarization is in a pyroelectricity. Dielectrics belonging to all but one of the common direction, but in adjacent domains the polariza- groups of noncentrosymmetric crystals are piezoelectric. tion is in a different direction as illustrated in Figure 31.4. Pyroelectric crystals form a further subgroup of 10 types The net polarization then depends on the difference in of crystal having especially low symmetry as shown in volumes of the two domain orientations. If the volumes Table 31.5. are equal the material will not exhibit a net polarization. By etching in a suitable chemical we can see the domain  All ferroelectrics are pyroelectric and piezoelectric. structure. This is analogous to the process we described  All pyroelectrics are piezoelectric. in Section 12.3 to reveal dislocations.  All piezoelectrics are not pyroelectric. Domain walls separate adjacent domains and are  All pyroelectrics are not ferroelectrics. transition regions in which the direction of polarization 560 ............................................................................................................................... L o c a l ly R e d i s t r i b u t i n g C h a r g e  Curie- εr Weiss Law + + + + + + + + + + + + Tcw T FIGURE 31.6 Relative permittivity of a ferroelectric as a function P P of T. (A) (B) FIGURE 31.4 (a) Schematic showing ionic displacements in two  180° wall—polarization vectors in adjacent domains 180° ferroelectric domains. (b) Domain structure showing several are antiparallel. 180° domains of different sizes. The wall energy is of the order of 10 mJ/m2. This value can be compared to typical grain-boundary (GB) energies that range from 0.1 to 0.3 J/m2 for low-angle boundaries, 0.5–0.6 J/m2 for high-angle tilt boundaries, and 0.8– 0.9 J/m2 for high-angle twist boundaries. As a conse- quence, it is, in general, easier to move domain boundaries than it is to move GBs. Ferroelectricity depends on temperature. Above θc ferroelectric behavior is lost and the material becomes paraelectric. The change from the ferroelectric to the non- ferroelectric state is accompanied either by a change in crystal symmetry (e.g., as in BaTiO3) or by an order–dis- order transition such as in the organic ferroelectric com- pound triglycine sulfate (TGS). The relative permittivity shows a characteristic peak FIGURE 31.5 Illustration of a 180° domain wall. The width is at Tcw as shown in Figure 31.6 and falls off at higher tem- ∼0.2–0.3 nm. peratures following the Curie–Weiss law: εr − 1 = χ = C/(T − Tcw) (31.9) changes. They have a width on the order of one lattice Curie constants and Curie temperatures for several ferro- parameter (∼0.2–0.3 nm), but this varies with temperature electric ceramics are given in Table 31.6. and crystal purity. This is less than one hundredth as thick as the Bloch walls between magnetic domains in ferro-  For ferroelectrics that undergo a first-order transition magnets (see Chapter 33). Figure 31.5 illustrates a domain [e.g., BaTiO3, (Ba, Sr)TiO3, PbTiO3, and KNbO3] Tcw < wall in a ferroelectric. There are actually two types: θc. For example, experimental measurements on poly- crystalline BaTiO3 have shown that Tcw can be more  90° wall—polarization vectors are in adjacent domains than 10°C less than θc. A first-order transition involves at right angles. a discontinuous change in P with T. TABLE 31.6 Curie Temperatures and Curie Constants for Several Ferroelectric Ceramics Ceramic Structure q c (K) C (K) Oxide Structure q c (K) C (K) SrTiO3 Perovskite ∼0 7.0 × 104 LiNbO3 Ilmenite 1470 BaTiO3 Perovskite 393 12.0 × 104 LiTaO3 Ilmenite 890 PbTiO3 Perovskite 763 15.4 × 104 Cd2Nb2O7 Pyrochlore 185 7.0 × 104 CdTiO3 Perovskite 1223 4.5 × 104 PbNb2O6 Tungsten bronze 843 30.0 × 104 KNbO3 Perovskite 712 27.0 × 104 31. 2 F e r r o e l e c t r i c i t y ................................................................................................................................................. 561   For ferroelectrics that undergo a second-order transi- tion (e.g., triglycine sulfate, Rochelle salt, and dihydro- 9 pm gen phosphate) Tcw ∼ θc. The change in P is continuous [010] for a second-order transition. [001] 31.3 BaTiO3 : THE PROTOTYPICAL FERROELECTRIC 6 pm 6 pm Barium titanate (BaTiO3) was the first ceramic in which ferroelectric behavior was observed and is probably the most extensively investigated of all ferroelectrics. Its dis- covery made available κs up to two orders of magnitude greater than had been known before. This property was very soon utilized in capacitors and BaTiO3 remains the basic capacitor dielectric in use today (although not in its pure form). There are several reasons why BaTiO3 has been so widely studied: FIGURE 31.7 [100] projection of BaTiO3 showing ion displace- ments below θc (not to scale).  Relatively simple crystal structure  Durable  Ferroelectric at room temperature (θc = 120°C) There are other structural transformations that occur  Easily prepared as a polycrystalline ceramic, single in BaTiO3, these are shown in Figure 31.8. crystal, or thin film  Below 0°C the unit cell is orthorhombic with the polar axis parallel to a face diagonal. Application of an elec- Structure and Structural Transformations tric field along [011] causes the domains to adopt this Above θc the unit cell of BaTiO3 is cubic (point direction of Ti4+ off-centering. group m3m) with the ions arranged as shown in Figure  Below −90°C the structure is rhombohedral with the 7.2. polar axis along a body diagonal. The Ti4+ is off- Recap: Each Ba2+ is surrounded by 12 nearest- centered along [111]. neighbor oxygen ions; each Ti4+ has six oxygen-ion neigh- bors. Together the Ba2+ and O2− ions form a face- Because these transformations both occur below room centered cubic (fcc) arrangement with Ti4+ fitting into the temperature they are not commercially important. octahedral interstices. The octahedral site is actually The phase changes that occur in BaTiO3 are character- expanded because of the large Ba2+ ions (r Ba2+ = 0.136 nm). ized by an expansion of the original cubic lattice in the The Ti4+ ion is quite small (r Ti4+ = 0.064 nm) giving a direction of the spontaneous polarization and a contrac- radius ratio with oxygen of r Ti4+ /rO2− = 0.44. This value is tion in the perpendicular direction. The temperature close to the limiting value (≥0.414) for a coordination dependence of the lattice parameters of BaTiO3 in the four number of 6. The result is that the Ti4+ often finds itself phases is shown in Figure 31.9. off-centered within its coordination octahedron. This is why it is sometimes referred to as the “rattling” titanium ion (think back to Pauling’s rules). The direction of off- a centering may be along one of the 6 <001> directions, a one of the 8 <111> directions, or one of the 12 <110> a directions. 120°C a a At temperatures greater than θc the Ti4+ has no Cubic fixed nonsymmetrical position and hence there is no P c Orthorhombic 0°C c permanent dipole moment. The crystal is paraelectric; it a P can be polarized only while it is in an applied electric Tetragonal a Rhombohedral field. a a On cooling BaTiO3 below θc the structure spontane- -90°C P ously changes to the tetragonal form (point group 4 mm) a with a dipole moment along the c axis. The magnitude and direction of the ion displacements accompanying this FIGURE 31.8 BaTiO3 polymorphs showing direction of transformation are given in Figure 31.7. polarization. 562 ............................................................................................................................... L o c a l ly R e d i s t r i b u t i n g C h a r g e  0.404 cooling tion by the strain that accommodates switching of c and c a axes. a or c (nm) heating The almost horizontal portions of the hysteresis loop 0.402 cooling represent saturated states in which the crystal is a 3 c volume single domain during a cycle. Defects and internal strains heating within the crystallites impede the movement of domain 0.400 walls. Domain wall mobility has been found to decrease Rhombo- Orthorhombic a Cubic with time (even without an applied mechanical or hedral Tetragonal electrical stress or thermal changes). This is due to inter- a 0.398 nal fields associated with charged defects, redistribution of lattice strains, and accumulation of defects at domain -150 -100 -50 0 50 100 150 walls. T (°C) The hysteresis loop of a polycrystalline BaTiO3 ceramic FIGURE 31.9 Experimental measurements of lattice parameters of has a higher Ec and lower Pr than the single crystal. BaTiO3 as a function of T. Note the change in volume at each transition and the hysteresis in the lattice parameters. The size of the hysteresis loop also depends on tem- perature as shown in Figure 31.13. At low temperatures the loops are fatter and Ec is greater, corresponding to the larger energy required for domain reorientation. Properties of BaTiO3 CALCULATION OF THE DIPOLE MOMENT At higher temperatures Barium titanate is ferro- FOR BaTiO3 Ec decreases until at θc electric and, by implica- Using Eq. 33.1 we need to consider the distances that no hysteresis remains and tion, also pyroelectric and the Ti4+ and O2− ions are displaced from their regular the material becomes piezoelectric. The charac- (cubic) lattice positions (assuming the position of the paraelectric. teristic of a ferroelectric is Ba2+ ions is fixed). The charge is the product of q and Figure 31.14 shows the that it is polarized in the the ion charge. The dipole moments are then temperature dependence absence of an applied elec- of the dielectric constant tric field and the direction μ(Ti4+): (1.602 × 10−19 C) (4) (0.06 × 10−8 cm) of single-crystal BaTiO3. of polarization can be = 3.84 × 10−28 C·cm The high value of κ appears reversed. Figure 31.10 over a very short tempera- shows a rectangular hys- μ(O2− top): (1.602 × 10−19 C) (2) (0.09 × 10−8 cm) ture range, close to θc and teresis loop for a single- = 2.88 × 10−28 C·cm far from room tempera- domain single crystal of ture. For this reason pure BaTiO3. This loop was μ(O2− side): (1.602 × 10−19 C) (2) (0.06 × 10−8 cm) BaTiO3 is not particularly obtained at room tempera- = 1.92 × 10−28 C·cm useful as a dielectric. ture using a 50 Hz supply. Ideally κ must be Ec is 0.1 MV/m and Ps is Now we need to include the number of each of the types 0.27 C/m2. of ions per cell. There is a single Ti4+ /cell, there is a  High at room tem- In tracing out the hys- top-face O2− /cell, and there are two side-face O2− /cell. The total dipole moment per unit cell is perature teresis loop both 180° and  Stable over as wide a T 90° changes in domain orientation take place. The μ = μ(Ti ) + μ(O top) + 2μ(O side) 4+ 2− 2− range as possible −27 almost vertical portions of = 1.056 × 10 C·cm the loop are due to the There are several ap- reversal of spontaneous polarization as antiparallel 180° proaches that can be used to lower θc and increase κ at domains nucleate and grow as illustrated in Figure 31.11. room temperature: This process corresponds to the Ti4+ moving from one of its off-center sites along the c axis to the other site. There is a potential barrier to this movement as indicated by  A solid solution can be formed with an isostructural Figure 31.12. compound (see Section 31.4). The motion of domain walls in ferroelectrics is not  The grain size can be reduced as shown in Figure simple. In an electric field a 180° wall in BaTiO3 appears 31.15. to move by the repeated nucleation of steps by thermal  Mechanical stresses (compressive or tensile) in thin fluctuations along the parent wall. Domains misoriented films can be induced because of differences in the by 180° tend to switch more easily than 90° domain walls lattice parameter between the film and the substrate, since no net physical deformation is required; domains e.g., values of θc for BaTiO3 thin films on MgO and on misoriented by 90° are inhibited from changing orienta- Pt are lower than for bulk material. 31. 3 BaTi O 3 : Th e P r o t o t y p i c a l F e r r o e l e c t r i c ..................................................................................................... 563  P/C m-2 0.3 εr P/C m-2 10000 0.2 0.2 8000 0.1 0.1 6000 0 4000 -0.2 -0.1 0 0.1 0.2 -1.0 1.0 E/MV m-1 E/MV m-1 -0.1 2000 -0.1 -200 -160 -120 -80 -40 0 40 80 120 (A) T (°C) -0.2 -0.2 0.2 -0.3 Ps (Cm-2) (A) (B) 0.16 FIGURE 31.10 Hysteresis loops for BaTiO3. (a) Single-domain single crystal. (b) Polycrystalline ceramic. 0.12 0.08 0.04 P (B) -180 -120 -60 0 60 120 T (°C) E FIGURE 31.14 (a) Dielectric constant and (b) spontaneous polarization of single-crystal BaTiO3 as a function of T. (Compare to Figure 31.9.) FIGURE 31.11 Illustration of the growth of a ferroelectric domain in a field ξ. Relative permittivity 104 E 5x103 1μm 0 Displacement of Ti 4+ 3μm FIGURE 31.12 Potential energy wells for Ti4+ as a function of displacement within the octahedral site. 15μm 50μm 0 0 100 T (°C) 200 -175°C -65°C 0°C 30°C 90°C 120°C FIGURE 31.15 Effect of grain size on the dielectric constant of FIGURE 31.13 Hysteresis loops for BaTiO3 as a function of T. BaTiO3. 564 ............................................................................................................................... L o c a l ly R e d i s t r i b u t i n g C h a r g e  31.6 RELAXOR DIELECTRICS 400 θc (°C) BaTiO3 and most related compositions show little change in dielectric properties with frequency until the gigahertz 200 range is reached. Relaxor dielectrics are a class of perovskite ferroelectrics that shows significant changes in κ and tan δ with frequency. The classic high-κ relaxor is 0 lead magnesium niobate (PbMg1/3Nb2/3O3 or PMN), which was first synthesized in the late 1950s. In addition to the high κ of many relaxor compositions -200 they also have a broad peak in the permittivity versus SrTiO3 BaTiO3 PbTiO3 temperature range, even in the absence of additives and mol.% FIGURE 31.16 Effect of substitution on θc for BaTiO3 solid even in the form of single crystals. This behavior is attrib- solutions with SrTiO3 and PbTiO3. uted to nanoscale (∼10 nm)-ordered regions, which are too small to yield the sharp phase transition of normal ferro- electrics. As a result, spontaneous polarization and associ- ated ferroelectric properties are retained over a very broad temperature range. Another attractive feature of relaxors 31.4 SOLID SOLUTIONS WITH BaTiO3 is that dense polycrystalline ceramics are achievable at relatively low sintering temperatures (≤900°C), which BaTiO3 is rarely used in its pure form because, as men- allows a significant reduction in the amount of Pd used in tioned in the previous section, high κ occurs only over a Ag–Pd metallizations for electrodes in multilayer capaci- very short temperature range that is far from room tem- tors (see Section 31.7). perature. Solid solutions with an isostructural compound One of the difficulties with most relaxor compositions can broaden θc as well as shifting it to lower temperatures. containing Pb and Nb is that they have a tendency to form One important solid-solution phase is that formed between the lower κ pyrochlore-type rather than perovskite struc- BaTiO3 and SrTiO3. These solid solutions are often referred tures. The pyrochlore-type phase found in PMN has the to as BST. Solid solutions of BaTiO3 and PbTiO3 lead to composition Pb1.83Nb1.71Mg0.29O6.39. It has a room tempera- an increase in θc over that of pure BaTiO3. The effect on ture κ of 130 and is paraelectric. the substitution of either Sr2+ or Pb2+ for Ba2+ in BaTiO3 is There are a whole range of lead-containing relaxors shown in Figure 31.16. based on lead zinc niobate (PZN), lead iron niobate (PFN), lead iron tungstate (PFW), and solid solutions with each other and with BaTiO3 (BT), PbTiO3 (PT), and SrTiO3 31.5 OTHER FERROELECTRIC (ST). Some of the solid-solution phases are PMN-PT, CERAMICS PMN-PT-PZN, PMN-PZN, PFN-PFW, PFN-PMN, and PFW-PT. Table 31.7 lists some other ferroelectric ceramics, although it does not include the large number of solid-solution phases that are ferroelectric. Many ferroelectric ceramics 31.7 CERAMIC CAPACITORS have a perovskite structure above θc, but this is not a pre- requisite. For example, LiNbO3 has an ilmenite (FeTiO3) Capacitance is defined as the total charge stored by the structure and Cd2Nb2O7 has a pyrochlore structure (the capacitor divided by the applied potential: mineral pyrochlore is CaNaNb2O6F). C = Q/V (31.10) This depends on the  Dielectric between the conductors TABLE 31.7 Some Other Ferroelectric Ceramics  Area of each conductor, A Compound q c (°C)  Separation between them, d SrTiO3 −245 PbTiO3 490 For a parallel plate capacitor in a vacuum KNbO3 435 KTaO3 −260 C = ε0 A/d (31.11) Cd2Nb2O7 −85 PbNb2O6 570 When a dielectric is present polarization occurs and LiNbO3 1200 permits additional charge to be stored. The ability of the 31.7 C e r a m i c C a pa c i t o r s ............................................................................................................................................. 565 dipoles in the dielectric to polarize and store charge is  Stable capacitors for general electronic use in the fre- reflected by ε: quency range 1 kHz–100 MHz because of the stability of capacitance with temperature C = εA/d (31.12)  Microwave resonant cavities operating between 0.5 Or in terms of κ and 50 GHz because of their stability and low tan δ C = κε0 A/d (31.13) Class 2 capacitors consist of high dielectric constant There are three main types of capacitors: ceramics based on BaTiO3. The two main subclasses are Z5U and X7R after the scheme shown in Table 31.9 that  Ceramic was devised by the Electronics Industries Association  Paper or polymer film (EIA) in the United States for specifying the variability  Electrolytic (aluminum or tantalum) of capacitance with temperature in the range of practical interest. For maximum Frequency ranges in capacitance θc is shifted which these capacitor types NOTATION FOR C close to room temperature are usable and the capaci- We use C for capacitance and C for the Curie constant. and broadened. Shifters tance values of each type There is really no way around this potential confusion; form solid solution phases are shown in Table 31.8. fortunately both terms rarely occur in the same with BaTiO3. Depressor Ceramic capacitors occupy equation. additives result in broad- about 30% of the total ening of the peak and con- capacitor market with sales of over 80 billion discrete centrate at the GBs. The compositions and properties of units per year. some Z5U and X7R dielectrics are shown in Tables 31.10 We can distinguish three basic types of ceramic and 31.11, respectively. capacitors: Class 3 capacitors are based on either BaTiO3 or SrTiO3 (usually X7R type) and have very high “apparent” dielec-  Film capacitors used in memory devices tric constants (κ = 50,000–100,000), which are achieved  Single-layer discrete capacitors, usually disc by producing either a surface layer on the grains or at the capacitors GBs that is electrically insulating while the grains them-  Multilayer chip capacitors (MLCCs) selves are conducting or semiconducting. This can be achieved in two ways: Each of these types will be described separately. Film  The ceramic is first heated to a high temperature (900– capacitors that are used in memory devices are integrated with the other circuit components. However, disc capaci- 1000°C) under reducing conditions (usually a H2 /N2 tors and MLCCs are discrete components. mixture) that makes it semiconducting and then the surface layer is reoxidized by heating in oxygen at a lower temperature. Categories of Ceramic Capacitor Dielectric  The GBs can be made insulating by diffusing a low Ceramic capacitors are generally classified into three melting point mixture of metal oxides such as CuO, types (1, 2, 3 or I, II, III) based on their properties. MnO, and Bi2O3. The very thin (10 μm) insulating Class 1 or NPO capacitors have κ < 15 and are mainly layers and the high GB area produce very high used for electrical insulation such as substrates, power line capacitances. insulators, and spark plug insulators. Medium κ class 1 capacitors are used in the following: The properties of these dielectrics are similar to those in class 2, but their working voltages are between 2 and  High-power transmitter capacitors in the frequency range 0.5–50 MHz because of their low tan δ TABLE 31.9 EIA Coding of Class 2 Capacitors Temperature Capacitance Code range (°C) Code change (%) TABLE 31.8 Frequency and Capacitance Ranges for Capacitor Types X7 −55 to +125 D ±3.3 Maximum usable Range of capacitance X5 −55 to +85 E ±4.7 Capacitor frequency (Hz) values (mF) Y5 −30 to +85 F ±7.5 Z5 +10 to +85 P ±10 Mica 10 G 0.1–10 −6 R ±15 Paper/polymer 10 G 100–10 −6 S ±22 Ceramic 10 G 103 –10 −6 T +22 to −33 Al electrolytic 10 k 10 6 –0.1 U +22 to −56 Ta electrolytic 10 k 103 –0.1 V +22 to −82 566 ............................................................................................................................... L o c a l ly R e d i s t r i b u t i n g C h a r g e  TABLE 31.10 Composition and Properties of Z5U Dielectrics Composition (wt%) Component 1 2 3 Role BaTiO3 84–90 65–80 72–76 Base material CaZrO3 8–13 — — Shifter MgZrO3 0–3 — — Depressor SrTiO3 — 7–11 5–8 Shifter CaTiO3 — 7–11 4–6 Depressor BaZrO3 — 7–11 7–10 Shifter CaSnO3 — — 2–4 Shifter Other oxides (e.g., Nb2O5) 1–3 8–13 0–3 Acceptors κ (25°C, 1 kHz) 5700–7000 5500–6500 11,500–13,000 Tan δ ≤0.03 ≤0.03 ≤0.03 25 V. The big advantage is that simple disc capacitors can methods. The powder is mixed with between 5 and 10 vol% be produced with large capacitances >1 μF. of an organic binder and pressed into a disk. Alternatively they can be punched from extruded ribbon or tape. The Disk Capacitors green ceramic is then sintered at between 900 and 1300°C in air to produce a dense material. After sintering Ag paint Figure 31.17 shows an example of a ceramic disk capaci- is applied to the major surfaces and the discs are briefly tor. Disc diameters range from 2 to 30 mm and dielectric refired at 600–800°C. Tinned copper wires are soldered to thicknesses range from 50 μm to 2 mm. the metallized ceramic disc before the whole assembly is These capacitors are common, but from a practical immersed in a polymer (usually an epoxy resin). standpoint can store only a limited amount of charge. To Disc capacitors are made using all classes of capacitor increase the storage capacity it would be necessary to dielectric allowing a wide range of capacitances: increase the overall size or decrease the distance between the plates. The first option would make the component too 0.1–1000 pF using class 1 dielectrics bulky. The second option would increase the possibility 1000–100 000 pF using class 2 dielectrics of dielectric breakdown. 0.1–2 μF using class 3 dielectrics The first disc capacitors used mica sheets. Mica MLCC ADVANTAGES has a very high dielectric Small strength (see Table 31.4) Inexpensive Multilayer Chip and can readily be cleaved Good frequency response Capacitors (MLCCs) into thin sheets. Disk Can be surface mounted The largest class of ceramic capacitors are now made High capacitance capacitors produced, in from BaTiO3-based com- Easy to make numbers and in value, is positions using tradi- tional ceramic processing TABLE 31.11 Composition and Properties of X7R Dielectrics Composition (wt%) Component 1 2 3 Role BaTiO3 90–97 85–92 86–94 Base material CaZrO3 2–5 4–8 — Shifter BaCO3 0–5 — — Stoichiometry adjuster SrTiO3 — 3–6 — Shifter Bi2O3 5–10 Depressor, flux Other 2–5 1–4 2–6 κ (25°C, 1600–2000 1800 1400–1500 1 kHz) Tan δ <0.025 <0.025 <0.015 FIGURE 31.17 Ceramic disc capacitor. 31.7 C e r a m i c C a pa c i t o r s ............................................................................................................................................. 567 the MLCC. More than 80 billion “chips” are manufac-  Screen printing Ag–Pd electrodes. The cost of the elec- tured worldwide each year. trode materials is a big concern. In fact, the noble Figure 31.18 shows several MLCCs and a schematic of metals account for more than half the cost price of their structure. The external dimensions range from MLCCs. Alternative nonprecious metals such as copper 1.25 mm × 1 mm × 1 mm thick up to 6 mm × 6 mm × and nickel have been used. A different approach to 2.25 mm thick. The interelectrode spacing is typically reducing the cost of metallization is the “fugitive” about 20 μm. Capacitance values have been produced electrode process. The electrodes are made of carbon, from 1 pF up to 300 μF. Class 1 and class 2 dielectrics which is removed during sintering in air. The remain- are mainly used for MLCCs. Increased performance has ing cavities are then pressure infiltrated with either been obtained using relaxor dielectrics, such as PFN and molten lead or a tin–lead alloy to produce the PMN. electrodes.  Stacking the electroded sheets  Laminating Fabricating MLCCs  Dicing There are several different ways to make MLCCs. The  Burning out the binder. This step of the process must basic steps include the following: be very carefully controlled. There is a lot of binder to be removed and if burnout is too rapid the sheets may  Preparing the slurry. The slurry may contain up to delaminate. 35 vol% of liquid. Water-based slurries containing a  Sintering. Typical sintering temperatures are 1200– latex binder are often used, although for some powder 1400°C in air. If nonprecious metals are used the formulations an organic based slurry is required. furnace atmosphere must be very carefully controlled  Tape casting to avoid oxidation. Atmospheres of N2 and H2 + N2  Drying have been used.  Cutting dried sheets typically into 15-cm squares  Application of external electrodes. The ends of the chips can be dipped into an Ag–Pd ink. Pure Ag can be used (which is cheaper), but it must be coated with Ni to increase solder leach resistance and then by Sn to maintain solderability. 31.8 CERAMIC FERROELECTRICS FOR MEMORY APPLICATIONS An important potential application for ferroelectrics is their incorporation as thin films into dynamic random access memories (DRAMs). The majority of the memory in a computer is DRAM. Information is stored in millions of tiny capacitors, each representing a single bit. The capacitors used in DRAM chips are fabricated directly onto the silicon substrate. The dielectrics currently used in DRAMs are (A)  SiO2, which can be produced by thermal oxidation Ceramic of Si Electrodes  A combination of SiO2 and Si3N4 (which is often referred to as “ONO” because the dielectric consists of alternating layers of SiO2 and Si3N4) The bottom electrode is the doped (often n-type) silicon substrate; the top electrode is either polysilicon or aluminum. The limitation of both SiO2 and Si3N4 is that they have low κ. Termination The dielectric constant of SiO2 is 3.9. A 100-nm-thick SiO2 film will yield a capacitance of 3.4 × 10−16 F/μm2 (B) (31 fF/μm2). FIGURE 31.18 (a) Ceramic MLCC. (b) Schematic showing The dielectric constant of Si3N4 is 6. A 100-nm Si3N4 electrode structure. film will yield a capacitance of 53 fF/μm2. 568 ............................................................................................................................... L o c a l ly R e d i s t r i b u t i n g C h a r g e  To push memory densities beyond 64 Mbits using SiO2 Direct effect D = dT + εTξ (31.17) or ONO dielectrics it has been necessary to develop very Inverse effect S = s ξT + dξ (31.18) complicated three-dimensional structures such as trench capacitors. The only new variable Being able to use a STRESS AND STRAIN here is s, the material com- dielectric with a large κ would allow a decrease in We use S for the strain and T for the stress (not ε and σ, pliance (inverse of stiff- which are more typical) to avoid possible confusion with ness). The superscripts in the required surface area, would avoid stacking and permittivity, which is almost always represented by ε. Eqs. 31.17 and 31.18 denote the parameters that are trenching, and would allow held constant. For example, planar configurations. Such configurations are easier and s ξ is the compliance at constant ξ. cheaper to fabricate and provide high production yields. When written in matrix form these equations relate the Thin films of BST have been the most widely studied properties to the crystallographic directions. For ceramics dielectric for ferroelectric DRAMs (FRAMs or FeRAMs). and other crystals the piezoelectric constants are anisotro- The highest capacitance reported for a BST dielectric is 2 pic. For this reason, they are expressed in tensor form. The 145 fF/μm , which was achieved with a 20 nm film of a directional properties are defined by the use of subscripts. material having κ = 325. Prototype BST capacitor DRAMs For example, d31 is the piezoelectric strain coefficient were first reported in 1995, but have not been widely used where the stress or strain direction is along the 1 axis and commercially because of the advances in other storage the dielectric displacement or electric field direction is technologies. along the 3 axis (i.e., the electrodes are perpendicular to the 3 axis). The notation can be understood by looking at Figure 31.19. 31.9 PIEZOELECTRICITY Another important parameter of a piezoelectric is the electromechanical coupling coefficient, k, which is a Piezoelectricity is a reversible property possessed by a measure of the ability of the material to convert electrical select group of materials that does not have a center of energy to mechanical energy or vice versa. symmetry. When a dimensional change is imposed on the For the direct effect dielectric, polarization occurs and a voltage or field is created. This is the direct effect. When an electric field is mechanical energy converted to electrical energy applied to a dielectric, polarization may change its dimen- k2 = sions. This is the inverse effect, also called electrostric- input mechaniccal energy tion. Dielectric materials that display this reversible (31.19) behavior are piezoelectric. For the indirect effect The ξ produced by the stress T is electrical energy converted to mechanical energy k2 = ξ = gT (31.14) input electriccal energy (31.20) The strain, S, produced by ξ is Since the conversion of electrical energy to mechani- S = dξ (31.15) cal energy (or vice versa) is always incomplete, k2 is always The piezoelectric coefficients d and g are related by Young’s modulus, E: 3 Poling 6 E = 1/gd (31.16) axis  High-d coefficients are desirable for dielectrics that are utilized in motional or vibrational devices such as sonor and transducers in ultrasonic cleaners.  High-g coefficients are desirable for dielectrics used to produce voltages in response to mechanical stress, such as in gas igniters. 2 5 The equations of state that describe a piezoelectric 1 crystal in regard to its electric and elastic properties are, 4 in their general form: FIGURE 31.19 Notation of axes for a piezoelectric ceramic. 31. 9 P i e z o e l e c t r i c i t y .................................................................................................................................................. 569  TABLE 31.12 Properties of Some Piezoelectric Ceramics 2000 0.7 Piezoelectric constant Electromechanical εr kρ Material C/N coupling factor ( k) 0.6 −12 1500 Quartz (× cut) d 21 = 2.25 × 10 d 33 = 2.3 × 10−12 0.1 0.5 BaTiO3 d 31 = −75 × 10 −12 0.48 PZT d 33 = 374 × 10 −12 0.67 0.4 Lead metaniobate d 33 = 85 × 10−12 0.42 1000 Lithium niobate d 33 = −1 × 10−12 0.3 d15 = 68 × 10−12 0.4 Rochelle salt d14 = 870 × 10−12 0.78 (45° × cut) 500 0.2 0.1 <1, and so k is also <1. Values of k in piezoelectric ceram- ics range from 0.1 to 0.9 as shown in Table 31.12. Rochelle PbZrO3 PbTiO3 salt is the classic example of a piezoelectric because k is FIGURE 31.21 Dielectric constants and coupling coefficients for so large. PZT compositions near the MPB. 31.10 LEAD ZIRCONATE–LEAD TITANATE PZ : PT ratio is almost 1 : 1. At an MPB there is an abrupt (PZT) SOLID SOLUTIONS change in the structure with composition at a constant temperature. PZT compositions near the MPB have both Solid solutions between lead zirconate (PbZrO3) and lead high k and high κ as shown in Figure 31.21. This is where titanate (PbTiO3) are known by the acronym PZT and are commercial PZT compositions are chosen. the most widely used of all piezoelectric ceramics. PZT ceramics often contain dopants (in the range 0.05 Lead zirconate is orthorhombic at room temperature: to 5 at%) to modify the properties of the material for a = 0.588 nm, b = 1.176 nm, and c = 0.820 nm. It is antifer- specific applications. roelectric with θc = 231°C. The dipoles due to the displace- Examples: ment of the Zr4+ ion from the center of the octahedral site are in opposite directions in adjacent unit cells so that the 1. Donors, e.g., replacing Zr4+ with Nb5+ or replacing net P is zero. Pb with La3+ . To maintain electroneutrality the addition 2+ Lead titanate is isomorphous with BaTiO3 with a = of these dopants is usually compensated for by the forma- 0.390 nm and c = 0.415 nm. It is ferroelectric at room tion of Pb2+ vacancies. Donors enhance domain reorienta- temperature with a θc = 495°C (the highest known value tion, and materials produced with these additives are among perovskite ferroelectrics). characterized by rectangular hysteresis loops, low Ec, high The PZT phase diagram is shown in Figure 31.20. The Pr, high κ, maximum k, high tan δ, high elastic compli- significant feature of this phase diagram is the morpho- ance, and reduced aging. Typical applications are in areas tropic phase boundary (MPB) at a composition where the in which high sensitivity is required, such as hydrophones, sounders, and loudspeakers. 2. Acceptors, e.g, replacing Zr4+ with Fe3+ with the 500 concomitant formation of oxygen vacancies. Domain re- T (°C) Cubic orientation is limited, and hence acceptor additives lead to poorly developed hysteresis loops, lower κ, low tan δ, 400 θc Tetragonal low compliance, and high aging rates. Typical applications are in high-power devices such as sonar and ultrasonic 300 transducers. 3. Isovalent, e.g., replacing Pb2+ with Ba2+ or Sr2+ or Rhomb (high-T form) replacing Zr4+ with Sn4+ . The substituting ion is of the 200 Ortho same valence and approximately the same size as the replaced ion. Solid-solution ranges with these additives 100 Morphotropic PB are usually quite high and may result in lower θc. Hyster- R(low-T form) esis loops may be poorly developed without additional 1 0.8 0.6 0.4 0.2 0 additives. Other properties include lower tan δ, low com- PbZrO3 X PbTiO3 pliance, and higher aging rates. These ceramics are used FIGURE 31.20 The PZT phase diagram. in high-drive applications such as torpedo guidance. 570 ............................................................................................................................... L o c a l ly R e d i s t r i b u t i n g C h a r g e  PZT ceramics can be made by normal powder process- mechanical control there is a need for a variety of types ing methods. The main difficulty is the high volatility of of actuators. Examples include the positioning of circuit PbO. To retain as much PbO as possible sintering may be components during the fabrication of integrated and performed with the component surrounded by a lead-rich positioning of lenses and mirrors in precise optical equip- powder such as PZ and enclosed in a lidded crucible. Even ment. They are also used as positioners for atomic force with these precautions there is usually some (typically 2– microscopy (AFM) and scanning tunneling microscopy 3%) loss of PbO, which is (STM). compensated for by adding The natural resonance additional PbO to the start- MEDICAL ULTRASOUND IMAGING frequency of a piezoelec- ing batch. A note about FREQUENCY RANGES tric crystal may be used safety: lead is toxic and Abdominal, obstetrical, and cardiological applications: as a frequency standard. exposure to lead com- 2–5 MHz Quartz is the material of pounds has a cumulative Pediatric and peripheral vascular applications: choice. Quartz crystal res- effect. It is therefore nec- 5–7.5 MHz onators provide highly essary that evaporation is Small objects (e.g., the eye) and intracardiac and stable crystal-controlled controlled. intravascular applications: 10–30 MHz clocks and watches (con- As in other forms of microscopy, a higher frequency stant to 1 part in 109) and (lower λ) gives better resolution: ∼50 μm at 30 MHz control fixed frequencies in communications equip- 31.11 APPLICATIONS FOR ment. Other resonant uses include selective wave filters PIEZOELECTRIC CERAMICS and transducers for sound generation as in sonar. PZT ceramics also dominate the market for resonators for Applications for piezoelectric ceramics utilize one of the ultrasonic cleaners and drilling devices. two piezoelectric effects: Piezoelectric transducers are key components in medical ultrasound imaging and are used both as the Direct effect—a voltage is produced by means of a com- acoustic source and the detector (pulse-echo technique). pressive stress. The uses for ultrasound are numerous and include exami- Inverse effect—an applied ξ produces small movements. nation of the fetus in the mother’s womb as shown in In an alternating field the piezoelectric will vibrate. Figure 31.22 and high-resolution imaging of intravascular structures. PZT is the ceramic of choice for this applica- tion mainly because it has a high κ and is inexpensive Direct Effect compared to some of the other options such as polymer The first commercial piezoelectric BaTiO3 devices were piezoelectrics. phonograph pickups marketed by Sonotome Corporation in the mid-1940s. These used a so-called bimorph design in which an electrode layer separated two strips of the piezoelectric material. Bimorphs are no longer used for this application because they do not produce a high enough quality sound reproduction and most people use CDs now. The direct effect is used in high-voltage spark genera- tion for some gasoline engine ignition systems and manu- ally operated gas lighters. In the latter example, widely used to ignite natural gas water heaters and other gas-fired domestic appliances, lever-amplified hand pressure gener- ates the voltage. Two electroded piezoelectric cylinders are placed back to back and a force applied to the cylinders generates a spark across the electrodes. If this force is not applied quickly the voltage generated will disappear as the charge leaks away. Typical spark energies are ∼3 mJ. Indirect Effect Actuators are an important and growing market for piezo- FIGURE 31.22 Medical ultrasound image using ceramic piezoelec- electric ceramics. In applications requiring precise tric transducers. (Scale is in centimeters.) 31.11 A p p l i c at i o n s f o r P i e z o e l e c t r i c C e r a m i c s .................................................................................................. 571 31.12 PIEZOELECTRIC MATERIALS FOR PZT films can be prepared using physical vapor depo- MICROELECTROMECHANICAL SYSTEMS sition (PVD) methods such as sputtering, chemical vapor deposition (CVD), and Microelectromechanical solution processing. Vapor MEMS APPLICATIONS USING PIEZOELECTRIC systems (MEMS) are deposition provides THIN FILMS devices capable of sensing uniform films with good Accelerometers and responding to a step coverage and uses Acoustic sensors mechanical or an electrical methods that are standard Infrared detectors stimulus. One common in microfabrication facili- Hot-wire anemometers MEMS device that is in ties. However, there is Microvalves commercial production is often a problem with Micropumps the miniature accelero- obtaining films of the Stepper motors meter (a device used to correct stoichiometry be- measure acceleration) used cause of the high vapor to control the deployment of an automobile airbag. Ferro- pressure of PbO. Solution techniques such as sol-gel pro- electric and piezoelectric ceramics are materials that fit cessing are simple and inexpensive and give good stoichi- well into the field of MEMS because of their combined ometry control but result in poor step coverage. and related electrical/mechanical properties. The ceramic need not be both ferroelectric and piezoelectric. But if it is ferroelectric then polycrystalline material can be used because it can be poled before use. In nonferroelectric 31.13 PYROELECTRICITY piezoelectric materials such as ZnO it is necessary to use single crystals with a single domain orientation. Pyroelectric materials exhibit a spontaneous polarization The most widely studied ceramics for MEMS applica- that is a strong function of temperature because the dipole tions are the PZTs because of their high κ and high k. Thin moments vary as the crystal expands or contracts. films of PZT have been used in the fabrication of a range of This was observed in the mineral tourmaline in the sev- different MEMS and can be integrated with silicon IC pro- enteenth century. Pyroelectricity occurs in organic crys- cessing methods. Figure 31.23 illustrates some of the process tals such as triglycine sulfate (TGS), ceramics such as steps used to fabricate a LiTaO3, and polymers such cantilever beam microsen- as PVDF. sor such as an accelerome- PYROELECTRICS The electric field devel- ter. The actual processing LiTaO3 (single crystal): p = 230 μC m−2 K−1 oped across a pyroelectric sequence requires over 50 (Sr,Ba)Nb2O6 (single crystal): p = 550 μC m−2 K−1 crystal can be extremely individual steps. PZT (polycrystalline): p = 380 μC m−2 K−1 large when it is subjected Piezoelectric Recessed trench TiO2 Ti Silicon water Si wafer (A) (D) PECVD SiO2 Si wafer Si wafer (B) (E) Al SiN encapsulation FIGURE 31.23 Steps in the production of a Poly Si MEMS cantilever. (a) Create trench by etching; (b) deposit SiO2 layer by pressure-enhanced Structural chemical vapor deposition (PECVD); (c) deposit membrane Si3N4 followed by polysilicon; (d) deposit the (Si3N4) piezoelectric film on an electrode/diffusion barrier Si wafer Si wafer system; (e) pattern and etch; (f) apply metal (C) (F) contacts and sacrificial etch. 572 ............................................................................................................................... L o c a l ly R e d i s t r i b u t i n g C h a r g e to a small change in temperature. A pyroelectric coeffi- 31.14 APPLICATIONS FOR cient, p, can be defined as the change in D due to a change PYROELECTRIC CERAMICS in T: Pyroelectric ceramics can be used to detect any radiation ∂D that produces a change in the temperature of the crystal, p= (31.21) ∂T but are generally used for IR detection. Because of their extreme sensitivity a rise in temperature of less than one- For example, a crystal with a typical pyroelectric coeffi- thousandth of a degree can be detected. This property cient of 10−4 C m−2 K−1 and κ = 50 develops a field of finds application in devices such as intruder alarms, 2000 V/cm for a 1 K temperature change. thermal imaging, and geographic mapping. CHAPTER SUMMARY The uses of dielectrics range from capacitors for storing charge to ultrasound imaging for medical applications. We separate “dielectrics” from “insulators,” which we described in Chapter 30, because dielectrics have permanent electric dipoles. If the resultant polarization is spontaneous we have ferroelectrics. This topic is essentially exclusive ceramic materials. Although some polymers are ferroelectric they do not find as wide use as ceramics. And metals cannot be ferroelectric because the charge is not localized. The requirement of a permanent dipole moment limits useful dielectrics to a select few crystal structures. So the topic of crystallography is once again important, but we cannot predict ferroelectricity by considering only crystal structure. The most important of the ferro- electric crystals are perovskites. By now you should be gaining an appreciation of the signifi- cance of this crystal structure and we still have some important magnetic perovskites to describe in Chapter 33. PEOPLE IN HISTORY Hankel, Wilhelm Gottlieb (1814–1899) (father of Herman Hankel) proposed the word piezoelectricity in 1881. He taught for 10 years in Halle and then moved to Leipzig in 1849 where he was Professor for 40 years. His thesis was titled “De thermoelectricitate crystallorum”. Pierre and Jacques Curie had discovered piezoelectricity in 1880. Seignette, Pierre (1660–1719) was a French pharmacist who first prepared Rochelle salt in c. 1675. In the early literature the phenomenon of ferroelectricity was more often referred to as “Seignette-electricity” or “Rochelle-electricity.” Valasek, Joseph (1897–1993) discovered ferroelectricity in the 1920s during an investigation of the anomalous dielectric properties of Rochelle salt, NaKC4H4O6 · 4H2O. Rochelle salt is named after the town of La Rochelle (France) where it was first prepared. Valasek was on the faculty at the University of Minnesota from 1919 until he retired in 1965. Von Hippel, Arthur Robert (1898–2003) reported the ferroelectric properties of BaTiO3 in 1946. Since then over a hundred pure materials and many more mixed crystal systems that are ferroelectric have been found. He was on the faculty of MIT from 1936 until he retired in 1964. His starting salary was only $3,500 per year and he is reported to have sold textbooks to pay for medical bills for his children. The Materials Research Society has named one of its major awards in recognition of von Hippel’s contribution to “dielectrics, semiconductors, ferromagnetics, and ferroelectrics.” GENERAL REFERENCES Jaffe, B., Cook, W.R., Jr., and Jaffe, H. (1971) Piezoelectric Ceramics, Academic Press, London. Now a little dated in view of more recent developments in the field. But the basic science remains the same. Jona, F. and Shirane, G. (1993) Ferroelectric Crystals, Dover, New York. First published by Pergamon Press, Oxford, England and The Macmillan Company, New York in 1962 as Volume I in the International Series of Monographs on Solid State Physics. A comprehensive description of many types of ferroelectric crystal. Somewhat dated: the Dover edition was not updated from the 1962 Pergamon edition. Lines, M.E. and Glass, A.M. (1977) Principles and Applications of Ferroelectric and Related Materials, Clarendon Press, Oxford. Moulson, A.J. and Herbert, J.M. (1990) Electroceramics, Chapman & Hall, London. An outstanding and very readable coverage of the entire field of electronic ceramics including applications for capacitors. Highly recommended. C h a p t e r S u m m a ry .......................................................................................................................................................... 573  SPECIFIC REFERENCES Smolenskii, G.A. and Agranovskaya, A.I. (1958) “Dielectric polarization and losses of some complex com- pounds,” Sov. Phys. Tech. Phys. 3, 1380. The first synthesis of PMN relaxors. JOURNALS AND CONFERENCES DEVOTED TO FERROELECTRIC MATERIALS The Materials Research Society (MRS) has offered a number of symposia under the title Ferroelectric Thin Films. Integrated Ferroelectrics. An international journal published by Gordon and Breach since 1992 devoted to research, design, development, manufacturing, and utilization of integrated ferroelectrics. These are devices that combine ferroelectric films and semiconductor IC chips. Journal of Materials Science: Materials in Electronics. WWW www.uoguelph.ca/~antoon/gadgets/caps/caps.html A general site on capacitors: explains that NPO is “negative-positive-zero”, and emphasizes that all capacitors are polarized. EXERCISES 31.1 What technique would you use to obtain the data shown in Figure 31.9? 31.2 Explain why the hysteresis loops of single crystal and polycrystalline BaTiO3 shown in Figure 31.10 have different E c and Ps. Would you expect this behavior? 31.3 What would be the appropriate EIA code for a capacitor that is required to have a capacitance at room tem- perature that changes by no more than ±4.7% in the temperature range −55 to +125°C? 31.4 (a) The dielectric strength of lead glass has been measured at two temperatures, 25°C and 200°C. The values obtained are 0.25 MV/cm and 0.05 MV/cm. Explain why these values are different. (b) A similar study was performed using a 100-nm-thick Al2O3 film that had been obtained by anodizing Al. The dielectric breakdown was measured to be 16 MV/cm. Why is this value so much higher than that for the polycrystalline Al 2O3 ceramics listed in Table 31.4? 31.5 Describe how you would expect the polarization of the following ceramics to vary as a function of frequency. Start at 1 MHz and go up to visible light frequencies: (a) diamond, (b) Al2O3, (c) BaTiO3, (d) MgO, (e) AlN. 31.6 Explain the trend in the hysteresis loops shown in Figure 31.13. Sketch the situation at 150°C. 31.7 A parallel plate capacitor is required to store a charge of 50 μC at a potential of 5 kV. The separation between the electrodes is 500 μm. Determine the plate area if the following dielectrics are used: (a) mica, (b) MgO, (c) BaTiO3, (d) Al2O3. In each case would the dielectric be able to withstand the applied field? 31.8 Estimate the polarization of diamond. Diamond has a diamond-cubic structure with a = 0.357 nm. 31.9 Estimate the polarization of MgO. MgO has a rocksalt structure with a = 0.421 nm. 31.10 Write out using Kröger–Vink notation the effect of the donor and acceptor additions described in Section 31.10. 574 ............................................................................................................................... L o c a l ly R e d i s t r i b u t i n g C h a r g e  32 Interacting with and Generating Light CHAPTER PREVIEW In this chapter we examine four key properties of ceramic materials all of which we can clas- sify as optical. (1) Ceramics can be transparent, translucent, or opaque for one particular composition. (2) The color of many ceramics can be changed by small additions: additives, dopants, or point defects. (3) Ceramics can emit light in response to an electric field or illumi- nation by light of another wavelength. (4) Ceramics can reflect and/or refract light. We will discuss why these effects are special for ceramics and how we make use of them. The optical properties of ceramics result in some of their most important applications. In their pure form, most dielectric single crystals and glasses are transparent to visible light. This behavior is very different from that of metals and semiconductors, which, unless they are very thin (<1 μm), are opaque. Many ceramics and glasses also show good transparency to infrared (IR) radiation. This property has led to the use of glasses for optical fibers for high-speed communications. We can produce polycrystalline ceramics that are highly transparent. The ability to make translucent and transparent polycrystalline ceramics was developed in the 1960s when it was discovered that small additions of MgO to Al2O3 powder could produce a fully dense ceramic by sintering. This product is widely used in streetlights (the golden glow). If a transparent ceramic or glass is doped, for example, by the addition of transition metal ions, the material becomes colored. We will discuss the different types of colors that can be produced in ceramics. The doping of Al2O3 with Cr3+ produces ruby, which is used as an optical cavity in a solid-state laser. The ruby laser was the first solid-state laser. There are now many more examples of solid-state lasers using colored ceramics and glasses as the optical cavity. We will describe how solid-state lasers work and the different wavelengths of radiation that can be produced. Phosphors produce light as a result of excitation by, e.g., electron irradiation. Again, we are using doped ceramics for this application because, as we will see, doping changes the electronic band structure of the ceramic. 32.1 SOME BACKGROUND FOR shown in Figure 32.1. Radiation with a single wave- OPTICAL CERAMICS length is referred to as monochromatic; λ and f are related through c: Electromagnetic Spectrum, the Terminology c and Units f = (32.1) λ Table 32.1 lists some of the major terms, and their units, that we will encounter in this chapter. It also lists the The frequency never changes regardless of the density of important physical constants that are needed to describe the medium through which the monochromatic light the optical properties of materials. The electromagnetic passes; however, the velocity of propagation and λ do spectrum embraces a wide range of wavelengths, from the change. For a high-density medium, such as glass, the very short γ rays to the velocity is lower than it long radio waves. would be in a vacuum and, The portion of the l AND COLOR consequently, λ is propor- spectrum that the human Ultraviolet (UV) is short λ tionally smaller. (A dense eye can detect is quite Blue is 390 nm medium has a lower c.) small. To put this in Green is 550 nm The light waves are context, the full electro- Red is 770 nm retarded because of the magnetic spectrum is IR is long λ interaction of the electro- 3 2 .1 S o m e Ba c k g r o u n d f o r O p t i c a l C e r a m i c s ...................................................................................................... 575  TABLE 32.1 Terms and Units Used in Optics Parameter Definition Units/value Conversion factor λ Wavelength m 1 Å = 10 −10 m f Frequency Hz v Velocity m/s n Refractive index Dimensionless Δn Birefringence Dimensionless c Speed of light 2.998 × 108 m/s R Reflected light Dimensionless Ratio given by Eq. 32.6 T Transmitted light Dimensionless Ratio given by Eq. 32.2 Eg Band gap energy eV 1 eV = 0.1602 aJ I Intensity cd ε0 Permittivity of a vacuum 8.85 × 10 −12 F/m See also Section 31.1 R∞ Molar refractivity Directly proportional to electronic polarizability (see Section 31.1) No Avogadro’s number 6.022 × 1023 mol−1 rc Linear electrooptic coefficient m/V R Quadratic electrooptic coefficient m2 /V2 P Polarization C/m2 See also Section 31.1 Ec Coercive field V/m magnetic radiation and the electrons of the atoms that the wave propagation direction as shown in Figure 32.2. make up the material. Remember that a dielectric material reacts to electromag- netic radiation because the opposite electrical charges are The Nature of Light displaced in opposite directions; this dielectric property is the underlying reason for refraction and absorption in Maxwell’s equations describe how an electromagnetic wave glass. originates from an accelerating charge and propagates in free space with a speed of 2.998 × 108 m/s. An electromag- Absorption and Transmission netic wave in the visible part of the spectrum may be emitted when an electron changes its position relative to the The classical description of the absorption of electromag- rest of an atom, involving a change in dipole moment. Light netic radiation by materials indicates that it occurs by two can also be emitted from a single charge moving at high basic mechanisms: speed under the influence of a magnetic field: because the charge follows a curved trajectory it is accelerating and, as  Electronic transitions: electrons are excited from the a consequence, radiating. (The same principle is used to valence band into unfilled energy states in the conduc- produce high-energy X-rays at a synchrotron.) tion band. An electromagnetic wave in free space comprises an  Absorption: the light excites vibrational and rotational electric field E and a magnetic induction field B that lie vibrating modes in the dielectric material since it is in mutually perpendicular directions in a plane normal to associated with an oscillating electric field. Orange Yellow Green Violet Blue Red 4.3 4.8 5.2 5.7 6.4 7.1 x 1014 Hz Lower ν Visible Higher ν Near RF Microwave Far IR IR UV Vacuum UV X-rays, γ-rays log (ν/Hz) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 λ 3 km 3 m 30 cm 3 mm 0.03 mm 300 nm 3 nm 3 pm FIGURE 32.1 The electromagnetic spec- trum. The visible region has been expanded for clarity. It is actually a 700 620 580 530 470 420 nm very small part of the 1.43 1.61 1.72 1.89 2.13 2.38 x 104 cm-1 spectrum. 576 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t  function of λ. The variation of n with λ produces a disper- Wave propagation sion of the light: direction Dispersion = dn/dλ (32.4) The ability of a substance to refract or “bend” light waves is sometimes described as refringence. Crystals having one unique axis (optic axis) along which the index of refraction is different from the index along the other orthogonal axes are known as uniaxial birefringent crys- Polarizer tals. The magnitude of the difference between the two indices of refraction is referred to as the birefringence, or simply, Δn. It is defined as FIGURE 32.2 Polarization of light. Δn = ne − no (32.5) For a single-phase material we can express the fraction where ne is the index of refraction of a light wave vibrat- of light transmitted, T, as ing in a plane parallel to the optic axis but traveling in a direction perpendicular to the optic axis, no is the T = I/I0 = exp(−βx) (32.2) index of refraction of a wave vibrating parallel to either of the other axes and traveling in the direction of the optic where I is the transmitted intensity, I0 is the intensity of axis, o is the ordinary ray, and e is the extraordinary the incident light, x is the optical path length (the thick- ray. The value of the birefringence may be positive or ness as seen by the light beam), and β is the absorption negative. Glass cannot be birefringent because it is isotro- coefficient. Equation 32.2 is a mathematical representa- pic. Ceramics from all noncubic crystal systems do show tion of Lambert’s law, which simply states that the fraction birefringence. of light that is transmitted by a material does not depend Ceramic applications of refraction are numerous: from on the intensity of the incident light. The parameter β the glass spheres used in road signs to the sparkle in dia- varies with λ; this variation is important because it causes monds. The trilobite eye made use of refraction in calcite color when light is transmitted. If the absorption is due to (Section 32.16). a particular dopant ion then Eq. 32.2 is modified by setting β equal to εC; C is the concentration of the absorbing ion Reflection and ε is the absorption per unit concentration. This is the The amount of light reflected from a surface of a material Beer–Lambert law. In real life, we also have scattering by in air is determined by the refractive index of the reflect- defects in the bulk or at the surface. ing medium. At normal incidence, the fraction, R, of light Ultraviolet absorption corresponds to electronic reflected (in medium 1) from the interface between two transitions from the filled valence band to the unfilled dielectric materials (1 and 2) is given by Fresnel’s conduction band: the larger Eg is, the greater the equation: range of transparency in the UV. Infrared absorption occurs by elastic vibrations. R = (n2 − n1) 2 /(n2 + n1) 2 (32.6) Refraction For air (n1 ∼ 1) and “optical” glass (n2 ∼ 1.5) R is ∼4%, Refraction is the phenomenon that is responsible for whereas lead-crystal glass (n2 ∼ 2.1) gives an R of ∼13%. making lenses work. The ratio of the velocity of light in Equation 32.6 will be very important when we use dielec- a vacuum to that in any other medium is known as the trics as antireflection coatings (ARCs); we then have to refractive index, n. Expressed mathematically, n is given consider two interfaces. The thickness of the films and the by the simple equation nature of the reflecting surface will also be important. Ceramic applications of reflection are numerous but are c often linked to refraction. n= (32.3) cm 32.2 TRANSPARENCY where cm is the velocity of light in the material (the medium). Since cm is always less than c, values of n are Dielectrics generally show good transmission in the visible always greater than unity and range from 1.0003 (air) to part of the electromagnetic spectrum as shown in Figure approximately 3.0 for very dense solids. Clearly n is not a 32.3. In the UV, absorption corresponds to electronic constant for any ceramic, since it depends on cm; n is a transitions from the filled valence band to the unfilled 3 2 . 2 Tr a n s pa r e n c y ........................................................................................................................................................ 577  log λ (λ in μm) The refractive index of several ceramic materials is 10 4 2 0 -2 -4 given in Table 32.2. We have seen that the value of n is a k Metal function of λ. It normally decreases as λ increases and 8 this trend is illustrated for a range of ceramics in Figure 32.5. The reason for this behavior is that colorless solids 6 and glasses have characteristic frequencies in the UV Semiconductor where they become opaque. For example, the important Dielectric characteristic frequencies for glasses occur at λ ≈ 100 nm. 4 The dispersion as a function of λ for several ceramics is shown in Figure 32.6. Dispersion is important in creating Visible 2 “fire” in gemstones (see Chapter 36). Several factors 0 influence n. Radio IR UV X-ray γ-ray FIGURE 32.3 Comparison of the frequency variation of absorption  Ion size. Materials containing large ions have large for metals, semiconductors, and dielectrics. The visible region of values of n because large ions are more easily polar- the spectrum is shaded. ized than small ions. The Lorentz–Lorentz equation quantifies the relationship between polarizability, α, conduction band. Ceramics with large values of Eg are and n. transparent to shorter UV wavelengths. In the IR, absorp- tion by elastic vibrations is the result of loss of transpar- TABLE 32.2 Refractive Indices of Some Glasses and ency. This absorption occurs at longer wavelengths for Crystals materials that contain large ions held together by weak Average interatomic forces: large ions and weak bonds lead to low refractive index Birefringence frequencies, i.e., small f, which implies large λ, i.e., long Glass composition wavelength. Transparency in the microwave and radio fre- From orthoclase (KAlSi3O8) 1.51 quency (RF) region is critical for radomes that house the From albite (NaAlSi3O8) 1.49 guidance system on missiles. Ceramics are the only mate- From nepheline syenite 1.50 rials that are suitable for this application. Silica glass, SiO2 1.458 Vycor glass (96% SiO2) 1.458 Soda-lime–silica glass 1.51–1.52 32.3 REFRACTIVE INDEX Borosilicate (Pyrex) glass 1.47 Dense flint optical glasses 1.6–1.7 Arsenic trisulfide glass, As2S3 2.66 Refraction is the bending of a beam of light when it enters a dielectric. The physical reason for this is that the velocity Crystals of light is different inside the dielectric. We are used to Silicon chloride, SiCl4 1.412 this happening in water or glass but in crystals the situa- Lithium fluoride, LiF 1.392 Sodium fluoride, NaF 1.326 tion can be more complex when crystals are anisotropic. Calcium fluoride, CaF2 1.434 The classic example is calcite, which is illustrated in Corundum, Al2O3 1.76 0.008 Figure 32.4. Periclase, MgO 1.74 Quartz, SiO2 1.55 0.009 Spinel, MgAl2O4 1.72 Zircon, ZrSiO4 1.95 0.055 Orthoclase, KAlSi3O8 1.525 0.007 Albite, NaAlSi3O8 1.529 0.008 Anorthite, CaAl2Si2O8 1.585 0.008 Sillimanite, Al2O3 · SiO2 1.65 0.021 Mullite, 3Al2O3 · 2SiO2 1.64 0.010 Rutile, TiO2 2.71 0.287 Silicon carbide, SiC 2.68 0.043 Litharge, PbO 2.61 Galena, PbS 3.912 Calcite, CaCO3 1.65 0.17 Silicon, Si 3.49 Cadmium telluride, CdTe 2.74 Cadmium sulfide, CdS 2.50 Strontium titanate, SrTiO3 2.49 Lithium niobate, LiNbO3 2.31 Yttrium oxide, Y2O3 1.92 Zinc selenide, ZnSe 2.62 Barium titanate, BaTiO3 2.40 FIGURE 32.4 Birefringence in calcite: two images of one paperclip. 578 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t  3ε 0 n 2 − 1 M 3ε 0 10 -1 α= = R∞ (32.7) N 0 n2 + 2 ρ N0 Sapphire Fused SiO2 where M is molar weight and ρ is density. dn/dλ (μm-1) LiF The refractive index of SiO2 glass can be raised by CaF2 As2S3 adding GeO2. This has important implications in the NaCl fabrication of optical fibers (Section 32.11). 10 -2 AgCl  Structure. Less dense polymorphs of a particular mate- rial will have a more open structure and thus a lower n than their denser counterparts. We can illustrate this KBr with the case of SiO2, which can exist as a glass or in CsI several crystallographic forms: nglass = 1.46, ntridymite = 1.47, ncristobalite = 1.49, and nquartz = 1.55. 10 -3 ~0.7 μm 1.70 White light Red n Orange Si Yellow 1.65 Green Prism Blue ~0.4 μm Dense Violet Ge flint Visible 10 -4 1.60 glass 0.1 1.0 10 40 λ (μm) Light flint FIGURE 32.6 Dispersion as a function of wavelength for a number 1.55 glass of ceramics. The inset is the classic illustration of dispersion, a prism separating white light into its spectral components. Borosilicate 1.50 glass  Crystallographic direction. Glasses and crystals with Hydrogen F Sodium D Hydrogen C a cubic structure are optically isotropic. In all other crystal systems n is higher along close packed 1.45 0.4 0.6 0.8 λ (μm) directions. (A)  Stress. The application of tensile stress to an isotropic material causes an increase in n normal to the direc- 4.0 Ge tion of the applied stress and decreases n along the stressed direction. The situation is the exact opposite n if a compressive stress is applied. The change of n with Si applied stress is known as stress birefringence. 3.0 32.4 REFLECTION FROM CERAMIC SURFACES TiO2 a-Se Using Eq. 32.6 we can determine the reflectivity from the SrTiO3 As2S3 glass surface of various ceramics and glasses. The reflectivity AgCl is about 4% from a surface with n = 1.5 and about 10% 2.0 for a surface with n = 1.9. A high reflectivity is often MgO Calcite Sapphire CsBr important for aesthetic reasons. The high reflectivity, R = NaCl 13%, of lead “crystal” glass, glass that contains a high Fused silica LiF amount of PbO, is due to its high refractive index, n = 2.1. NaF CaF2 The reflectivity is more than twice that of normal silicate Quartz crystal glasses. High reflectivity is important for gemstones, 1.0 0.1 1.0 10 λ (μm) 60 where it affects the brightness and sparkle of the stone. (B) This is partly the result of the cutting skills of the jeweler and the fact that gemstones have high values of n. The FIGURE 32.5 (a) Change in n with λ for several commercial glasses. (Hydrogen F, Sodium D, and Hydrogen C refer to specific refractive index of diamond is 2.4. light sources that have λ = 589, 486, and 656 nm, respectively.) High reflectivity for glazes and enamels is also impor- (b) Change in n with λ for several ceramics and glasses. tant, and can be achieved by using glass formulations with 3 2 . 4 R e f l e c t i o n f r o m C e r a m i c S u r fa c e s ............................................................................................................... 579 I R I I I surface so that its thickness is one-quarter of the wave- length of the incident light. For an ARC optimized for green light (λ = 530 nm), which is in the center of the elec- tromagnetic spectrum (and where the eye is most sensi- tive), the thickness of the ARC should be about 130 nm (0.13 μm). Light reflected from the top surface of the FIGURE 32.7 Effect of surface roughness on reflectivity. I, incident; R, reflected. coating is exactly out of phase with light reflected from the glass surface, and so there is destructive interference and no net reflected beam. Magnesium fluoride (MgF2) is a a high PbO content. However, it is important to test the widely used ARC material and is usually applied onto the formulation carefully to make sure that high concentra- glass surface by a physical vapor deposition (PVD) process tions of Pb do not leach out into food and beverage items. such as evaporation. A single layer of MgF2 (d = λ/4) will (Hence there is a protocol for the leach-testing of glazes; reduce the reflectance of glass from about 4% to a little see Section 2.5). more than 1% over the visible spectrum. Antireflective The reflectivity of a glaze or enamel is reduced if the coatings are also applied to glass for architectural applica- surface is rough. Roughness causes considerable diffuse tions to help with radiation control (see Section 26.7). reflection from the surface as illustrated in Figure 32.7.  Specular reflection is light reflected at a single angle (conventional reflection). 32.5 COLOR IN CERAMICS  Diffuse reflection occurs when light is reflected through a range of different angles. We discussed colorants in history throughout Chapter 2, F centers in crystals in In some situations we Section 11.9, and the do not want a high reflec- A LIGAND origins of color in glass tivity. In fact, we want to A ligand is any molecule or ion that is bonded to a metal in Section 21.8; we will minimize the reflectivity ion. discuss color more in as far as possible. One very Chapter 36. effective way of reducing the reflectivity of a glass surface Most dielectric ceramics and glasses are colorless is to coat it with an antireflection (AR) coating (giving an because of their large Eg. They become colored when ARC). A good ARC can cut the percentage of light reflected energy states are added within the band gap. These new from >5% to <0.2%. One example is the purple colored levels allow electron transitions to occur within the visible ARC on binocular and camera lens. Catalogs for optical part of the electromagnetic spectrum. equipment will often indicate whether the lens has an ARC The most common way to color a ceramic is by adding applied. The principle behind how an ARCs works is illus- transition metals (TM), particularly Ti, V, Cr, Mn, Fe, Co, trated in Figure 32.8. The coating is applied onto the glass and Ni, where the 3d is partly filled. To explain how the addition of a TM to a colorless Incident Primary ceramic makes it colored we use the ligand field theory. wave i reflected In ceramics the most common ligand is oxygen, the O2− i wave ion. To understand the behavior of a transition metal once Secondary reflected wave it is placed in a ligand field we need to consider the shapes of the d orbitals (see Figure 3.2). There are five of them Surface and they are designated d xy, d xz, dyz, d x −y , and dz . In a free 2 2 2 ion, all the d orbitals are degenerate (i.e., they have the same energy). However, when the ion is put into a crystal ARC d the energy of the d orbitals is affected by the ligands. r Consider the case of the Ti3+ ion, which contains only a single 3d electron. If the Ti3+ ion is in an octahedral site Interface (i.e., it is surrounded by six anions arranged at the corners of an octahedron) the energy of the d x −y and dz orbitals 2 2 2 is raised relative to the free Ti3+ ion because of repulsion Secondary from the surrounding anions. The energy of the other Glass lens transmitted three orbitals is lowered, as illustrated in Figure 32.9a. If Primary wave transmitted the Ti3+ ion were placed in a tetrahedral site (i.e., it is sur- wave rounded by four anions arranged at the corners of a tetra- hedron), the energy of the d x −y and dz orbitals is lowered 2 2 2 with respect to the d xy, d xz, and dyz orbitals. The total split- FIGURE 32.8 Illustration of how an ARC works. ting for d orbitals is in the range of 1–2 eV, being lower 580 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t  dx2-y2,dz2 by the addition of RE ions to oxide glasses. Rare earth eg ions tend to color glass less strongly than do transition metal ions and the spectra usually consist of a large number of weak bands. dxy,dyz,dxz 0.6Δ Other sources of color in ceramics include the t2 following: Δ 0.4Δ E Δ  F centers in alkali halides, which result from heating dxy,dyz,dxz, 0.6Δ in alkali vapor. An F center in metal halides consists dx2-y2,dz2 0.4Δ of a halide ion vacancy that has trapped an electron. e dx2-y2,dz2 This process creates additional energy levels between t2g the valence band and the conduction band. A similar dxy,dyz,dxz situation is found in MgO heated in Mg vapor: the F Tetrahedral Free Octahedral center consists of two electrons trapped at an oxygen field ion field (A) vacancy. F centers are one example of so-called color centers. There are other types of possible color centers dx2-y2 in ionic materials involving electrons and holes. (See E dxy Section 11.9; F is Farben.)  Defects produced by X-ray or neutron bombardment. eg Irradiation of colorless quartz crystals with X-rays will t2g result in the formation of a dark brownish gray to black color of “smoky quartz.” Coloration is due to the for- dxz, dyz mation of a color center, a hole color center this time. Tetrahedral dz2 If the smoky quartz is heated to several hundred °C it Octahedral distorted Square Square field octahedral planar (a) planar (b) will become clear again.  Defect states produced as a result of nonstoichiometry. Distortion This occurs in, e.g., TiO2 and ZrO2. (B) FIGURE 32.9 (a) Splitting of the d orbitals in a ligand field. (b) Splitting of d orbitals in a distorted octahedral ligand field in corundum. 32.6 COLORING GLASS AND GLAZES for a tetrahedral ligand field than for an octahedral field. To color glass, TM oxides or RE oxides are added to the Hence absorption of light, associated with electronic tran- glass batch. Color is produced through selective light sitions between the lower and upper d levels, generally absorption by the TM or RE ion, which is incorporated occurs in the visible or near IR regions of the spectrum. into the glass structure. The mechanism essentially uses The situation is actually a little more complicated if a solution approach to coloring. The color results when the we consider corundum, because the octahedral sites are absorbing ion removes light of certain wavelengths, so we slightly distorted. This distortion produces further split- see the complementary color in transmission. ting of the energy levels as illustrated in Figure 32.9b. Uses for colored glass include not only the obvious We can use a similar argument to show how the addi- stained glass windows and Tiffany lampshades but also tion of rare earth (RE) elements, with incomplete f shells, the glazes used to seal and decorate cups and pots. Adding also causes color. Table 32.3 shows the colors produced Pb to make X-ray-absorbing glass is essentially the same process/motivation: the intent is to absorb the X-rays. TABLE 32.3 Optical Absorption of Rare Earth Ions in Oxide Glasses Number of f 32.7 CERAMIC PIGMENTS AND STAINS Ion electrons Color 3+ We color ceramics using inorganic pigments and stains Ce 1 Green that are relatively insoluble in the ceramic they are color- Pr 3+ 2 Green Nd3+ 4 Violet ing; they should also be unaffected chemically and physi- Sm2+ 6 Green cally. This is not the same approach used for glass. Eu2+ 7 Brown Table 32.4 shows the types of environment and tem- Dy2+ 10 Brown peratures that ceramic pigments must withstand. The col- Ho3+ 10 Yellow orant may be mixed directly with the ceramic body (this Er 3+ 11 Pink is called a body stain). An example is the coloring of 3 2 .7 C e r a m i c P i g m e n t s a n d S ta i n s .......................................................................................................................... 581  TABLE 32.4 Ceramic Environments for Colors T (°C) Environment Colorant type Use 700–900 Molten leaded/unleaded Enamel or overglaze colors Tableware, tile decoration borosilicate glass 900–1000 Molten lead/unleaded Low-temperature glaze stains, Tableware, wall and floor tiles borosilicate or alkali underglaze colors, colored pellets borosilicate glasses and granules 950–1200 Siliceous bodies Body stains, brick surface colorants, Tableware, floor tiles, fancies, colored pellets and granules bricks 1100–1350 Molten alkali/lime glasses Glaze stains Tableware, tiles, sanitary ware house bricks—not all PIGMENTS zirconium silicate, and house bricks are the same Much of the information is covered in the patent litera- the first patent for a zir- color. If the stain is used to ture. Zircon–vanadium blue was one of the most signifi- con-based pigment was produce a glaze then actu- cant innovations in color technology for several decades. issued in the 1930s. Zircon ally we are coloring a Seabright was also responsible for the praseodymium pigments fall into two glassy phase and coating yellow and the zircon–iron coral pink. categories. the ceramic. An example of this approach is the  Lattice type. The dopant ion replaces a Zr4+ ion in the glazing of sanitary ware and tiles (coloring whitewares). There are several classification systems for ceramic pig- zircon lattice, e.g., vanadium blue (V4+ replaces Zr4+) ments. One of the most widely used is that drawn up by and praseodymium yellow (Pr4+ replaces Zr4+).  Encapsulated type. Discrete particles of the colorant the Color Pigments Manufacturers Association (CPMA), formerly the Dry Color Manufacturers Association are trapped inside zircon crystals, e.g., the iron coral (DCMA), in the United States. This system provides a pink where very fine particles of red Fe2O3 are incor- structural classification of pigments as summarized in porated in zircon crystals. Table 32.5. Fourteen classes of pigment and over 50 broad pigment subcategories cover all the principal mixed-metal A different important class of pigments is the family oxide pigments manufactured today. However, it does not of cadmium pigments. These are substitutional solid solu- cover the full range of possible pigments. For example, tions between CdS and CdSe (both end members have the nonoxide compounds, such as the Cd-based pigments, are same crystal structure). Cadmium sulfide has a band gap not included. Eg = 2.6 eV. This provides absorption of violet and some In the CPMA classification, one commercially impor- blue but none of the other colors, leading to a yellow color. tant class of pigments is the zircon pigments. Zircon is CdSe has E = 1.6 eV and is black. When CdSe is added g to CdS the band gap of the material decreases and the color changes. This process is analogous to what we do in doping the III–Vs used to make light-emitting diodes TABLE 32.5 CPMA Classification of Mixed-Metal Oxide (LEDs) in Section 32.12. Inorganic Pigments The achievable colors range from the yellow of CdS, Pigment system, CPMA number Main components Color through orange, to bright red and maroon as the percent- age of CdSe is increased (Table 32.6). (The red is known I. Baddeleyite 1-01-4 Zr–V Yellow II. Borate 2-02-1 Co–Mg Red-blue III. Corundum-hematite 3-03-5 Cr–Al Pink IV. Garnet 4-07-3 Ca–Cr–Si Green V. Olivine 5-08-2 Co–Si Blue VI. Periclase 6-09-8 Co–Ni Gray TABLE 32.6 Colors in the CdSe–CdS System VII. Phenacite 7-10-2 Co–Zn–Si Blue CdSe (mol%) CdS (mol%) Color VIII. Phosphate 8-11-1 Co–Ni Gray IX. Priderite 9-13-4 Ni–Ba–Ti Primrose 12.6 87.4 Orange X. Pyrochlore 10-14-4 Pb–Sb Yellow 20.0 80.0 Orange-red XI. Rutile-cassiterite 11-15-4 Ni–Sb–Ti Yellow 36.0 64.0 Light red XII. Sphene 12-25-5 Cr–Sn–Si Pink 43.0 57.0 Dark red XIII. Spinel 13-26-2 Co–Al Blue 49.0 51.0 Brown XIV. Zircon 14-42-2 Zr–Si–V Blue 54.5 45.5 Dark brown 582 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t as selenium ruby.) The red color is particularly significant 100 because, for now, the only other additive that can produce 100 the red color in glass is the metal Au. The stability of the T (%) T (%) selenide pigment is somewhat limited; it will oxidize at 10 650°C with a resultant loss of color. But if the pigment is 2μ encapsulated in a zircon matrix then it has the properties 75 1 0.7μ of zircon and is stable to at least 1300°C and is relatively 1μ inert in many environments. 0.1 A problem, of course, with Cd-containing pigments (like Pb in glass) is the toxicity of Cd. In some countries, 0.01 e.g., Sweden, home of Orrefors and Kosta Boda, the use of 50 Cd is prohibited. There is increasing pressure worldwide to 0.001 0 0.01 0.02 0.03 0.04 reduce the use of potentially harmful or toxic species, such Volume Fraction Pores as Cd and Pb; there is therefore a growing need for devel- oping suitable alternatives. Even if these additives can be 2μ managed during processing, it is difficult to control them 25 during recycling; legislation can be aimed at the initial use 1μ (to protect the worker) or at recycling (e.g., so that heavy metals no longer enter the water supply). 0.7μ 0 0 0.01 0.02 0.03 32.8 TRANSLUCENT CERAMICS Volume Fraction Pores FIGURE 32.11 Effect of porosity on the transparency of polycrys- talline alumina. Polycrystalline ceramics are often opaque, even though the single crystal may be transparent and Eg is large. We can also make glass that is not clear or is even opaque. The loss of transparency is due to scattering of the inci- dent light, which can have several possible causes as illus- When the pore size is close to the λ of visible light trated in Figure 32.10. then the scattering is maximized. This scattering can be engineered by controlling the sintering conditions or by hot pressing. Table 32.7 shows examples of pro-  Porosity. The transmission decreases markedly with cessing conditions that have been shown to produce small increases in porosity as shown in Figure 32.11. translucent ceramics.  Differences in n. In general, light scattering can occur at grain boundaries (GBs) where refractive indices are discontinuous; this is especially easy for noncubic (i.e., Incident light anisotropic) structures. A similar situation can occur Diffuse scattering in multiphase materials, such as ceramics densified by liquid-phase sintering, where there may be an intergranular film (IGF). Matching refractive indices pore between different phases can reduce scattering losses. This approach is used in making high-quality bone GB china. precipitate  Grain size, r. The effect of grain size on scattering is shown in Figure 32.12. Scattering is at a maximum when r is close to λ of visible light. For grain sizes smaller than the wavelength of the incident radiation, grain IGF the scattering increases with r and is proportional to phase λ−4. Scattering decreases rapidly as r increases and for large r it reaches a constant value. Transmitted light FIGURE 32.10 Mechanisms for loss of transparency due to The oldest glass objects in museums are opaque. scattering. GB, grain boundary; IGF, intergranular film. Details of Frosted glass appears to be opaque because light is the individual defects are described in Chapters 12–15. scattered at the surface. 3 2 . 8 Tr a n s l u c e n t C e r a m i c s ....................................................................................................................................... 583  TABLE 32.7 Sintering Additives and Conditions of Various Translucent Ceramics Sintering additive Transmissivity l (mm) and specimen Ceramic (wt%) (%) thickness (mm) Sintering conditions Al2O3 MgO (0.25) 40–60 0.3 ∼ 2 (1) T = 1850–1900°C t = 16 hours Atmosphere: H2 Y2O3 (0.1), MgO 70 0.3 ∼ 1.1 (0.5) T = 1700°C (0.05) t = 5 hours Atmosphere: H2 MgO (0.05) 40 ∼0.9 T = 1700°C P = 0.06 Pa Y2O3, La 2O3, ZrO2 80 Visible light (∼1) T = 1700°C (0.1∼0.5), MgO Atmosphere: H2 (0.55∼1.0) MgO (0.05) 85–90 Visible light (0.75) T = 1725–1800°C t = 17–30 hours Atmosphere: H2 CaO CaF2 (0.2∼0.6) 40–70 0.4∼8 (1.25) T = 1200–1400°C t = 0.5–2 hours P = 0.5–0.8 GPa MgO LiF, NaF (1) 80–85 1∼7 (5) T = 1000°C t = 15 minutes P = 10 MPa in vacuo NaF (0.25) Clear Visible light T = 1600°C t = 111 hours Atmosphere: O2 32.9 LAMP ENVELOPES The requirements for the envelope material are therefore very stringent: it has to be transparent to visible light, An important application of transparent ceramics is found stable at high temperature, and must contain the corrosive in the familiar high-intensity yellow streetlights that are Na plasma. It needs to be inexpensive because about 16 common along major highways. These lamps are known million units are made each year. The sodium-vapor lamp as sodium-vapor lamps because during operation they was made possible by the development of very dense contain sodium vapor that is being heated to a high tem- perature. Figure 32.13 shows the construction of a typical sodium-vapor lamp. The plasma temperature inside the Silica glass jacket Xe or Ne lamp is 3700°C and the lamp envelope reaches a peak temperature of 1200°C; the Na vapor pressure is ∼100 torr. Al2O3 sealing Ni wire frame Nb feedthrough Base buttons 160 Electrode W electrode Scattering coefficient For NaD line (λ = 589 nm) Al Al22OO33 envelope cm-1 Glass 120 stem Ba getter Na-Hg amalgam Calcium aluminate (A) Vacuum sealing frit 80 40 0 (B) 0 1 2 3 4 5 6 7 8 Particle diameter (μm) FIGURE 32.13 (a) Construction of an Na-vapor lamp. (b) An actual FIGURE 32.12 Effect of particle size on the scattering of light. lamp. 584 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t  TABLE 32.8 Fundamental Properties of Candidate Lamp-Envelope Materials Property Al2O3 Y2O3 MgO 3Al2O3 · 2SiO2 MgAl2O4 Y3 Al5O12 EG (eV) 7.4 5.6 >5 ≥5 >5 >5 σ (S/m) <2 × 10−12 Low Low <10 −7 Low Low α (10 −6 K−1; 300–1300 K) 8.2 7.9 13.5 5.3 9.0 8.6 Strength (MPa) 310 150 206 270 184 410 E (GPa) 405 164 307 220 277 290 k at 300 K (W m−1 K−1) 29 13 25 6 15 13 RTS 2707 1508 1242 1389 1077 2137 TM (K) 2323 2737 3073 2101 2408 2243 Vapor pressure 3 × 10 −9 1 × 10 −10 2 × 10 −5 2 × 10 −5 2 × 10 −6 — (Pa at 1500 K) Relative emissivity 5.56 7.9 8.2 4 5.7 5.8 (∼λ0.75) (μm) ceramic envelopes that did not contain any light-scattering difference in energy causing heating in the sample. Many porosity. The addition of small amounts of magnesia naturally occurring minerals show fluorescence, but only (MgO) allows us to sinter a compact of fine Al2O3 powder some are spectacular. to theoretical density—free of porosity. Table 32.8 compares the properties of Al2O3 to some Calcite, halite (with Mn) red of the other materials evaluated as candidate lamp- Fluorite, opal green envelope materials. In addition to satisfying the materials Adamite yellow/green selection criteria given above, Al2O3 also has a significant Willhemite green advantage over the other materials listed in Table 32.8 Scheelite blue because it has superior thermal shock resistance. Scapolite yellow Scapolite has a complicated crystal structure and is 32.10 FLUORESCENCE formed by the alteration of plagioclase feldspars. Inciden- tally, diamond, sapphire, and ruby all fluoresce, but as Fluorescence occurs when light that is incident on a speci- with the materials above, the color depends on the UV men causes the emission of light of another color; the wavelength used. A given specimen can also show differ- effect is shown in Figure 32.14. This is most dramatic ent colors depending on the distribution of impurities. when the incident light is UV (and the observer is in a Trace elements can be included in synthetic gemstones to darkened room), but it also occurs with other wavelengths. make them fluoresce and thus be easily identifiable. Short wavelength UV is 254 nm; long wavelength UV is Phosphorescence. UV radiation excites electrons to a 300–388 nm (IR would be >780 nm). The wavelength of higher energy state. When the UV is removed, the decay the emitted radiation is longer than that of the illuminating to the ground state usually takes seconds but can take light; this is known as Stokes’ law of fluorescence. The years. A material that phosphoresces for 12 hours would energy of the emitted light is therefore lower, with the have many uses (see Section 32.12). Flash is the initial color produced when a UV lamp is first directed at certain fluorescent samples. The emitted Willemite wavelength then changes as exposure continues. Thermoluminescence. This is essential fluorescence caused by heating a mineral to allow electrons that are trapped in high-energy states to drop back to the ground state. Heating chlorophane, a variety of fluorite, can produce a green light but only once. Triboluminescence. Light can be produced by rubbing or striking a ceramic. Fracturing mica or rubbing a sphal- erite crystal causes light emission. Cathodoluminescence. Instead of UV radiation, this luminescence is produced by irradiating the sample with electrons (and therefore it usually occurs in a vacuum). This is the phenomenon used in cathode ray tubes (CRTs) Calcite (including old TV screens) that were coated on the inside FIGURE 32.14 Fluorescent minerals. with a ceramic phosphor. 3 2 .10 F l u o r e s c e n c e ...................................................................................................................................................... 585 32.11 THE BASICS OF OPTICAL FIBERS 1988 and the Pacific Ocean by 1996 (but STL had disap- peared). The first low-loss fibers were made at the Corning Light is transmitted from one end of an optical fiber to the Glass Works. The fibers were made by a CVD process other by total internal reflection (TIR) as illustrated in known as outside vapor-phase oxidation (OVPO) and pro- Figure 32.15. Modern optical fibers use a composite con- duced an early fiber with a loss of 20 dB/km (which means struction with a core of refractive index n1 and a cladding that 1% of the light remains after traveling 1 km). with a lower refractive index, n2, such that (n1 − n2) is typically in the range of 0.005–0.05. Light will remain in Materials the fiber when the critical angle of incidence, ic, is met or exceeded. To determine ic we make use of Snell’s law  Processing: how to make the fibers (which can be derived from Maxwell’s equations):  Applications: how they work and what goes wrong  Materials: which glasses to choose n2 /n1 = sin i/sin r (32.8) There are four classes of glass optical fiber. At ic the angle of refraction, r, must be 90° and so we can write 1. Pure fused silica and doped silica glasses are used for telecommunications because of the requirement of very n2 /n1 = sin ic /sin 90° = sin ic /1 (32.9) low transmission loss over long distances. These now form the backbone for trunk transmission in most developed The requirement for TIR sets a limit on the angle of countries, and in undersea intercontinental routes, and the light incident on the fiber that will be trapped in the many millions of kilometers have been installed through- core of the fiber. This condition is expressed in terms of out the world. For applications in laser surgery pure silica- the numerical aperture (NA) of the fiber, defined as the based glass fibers are used as they have a low transmission sine of the acceptance angle for incident radiation. loss at 1.06 μm and have high strength and durability. 2. Multicomponent oxide glasses such as Na2O–CaO– sin ic = (n22 − n12)1/2 (32.10) SiO2 (NCS) and Na2O–B2O3 –SiO2 (NBS) are used for applications requiring light transmission over short dis- Although light can be transmitted along a glass fiber tances such as in image bundles, in optical faceplates on in air, there are large losses due to scattering arising from CRTs, and in IR imaging devices. The glass is of lower surface defects on the fiber. The most important optical optical quality than silica glass, but can be processed in fibers consist of a high-purity glass core encased in an bulk by conventional melting techniques and is relatively equally high-purity cladding. In most cases the cladding cheap. is glass, but polymer claddings are also used when a suit- 3. Fluoride glasses based on ZrF4 –BaF2–LaF3 –AlF3 – able glass cladding is not available or when it is important NaF (ZBLAN) have been widely investigated because to reduce costs. they have potentially very low losses. The ultimate attenu- Kao and Hockham suggested the concept of sending ation has been calculated to be ∼10−2 dB/km at 2.5 μm. optical signals along glass fibers in 1966. Initiated at the Heavy-metal fluoride glasses are made by melting together Standard Telecommunications Laboratory (STL) in the high-purity fluoride powders at ∼800°C and casting pre- UK, optical fibers were crossing the Atlantic Ocean by forms. The impurity levels (∼10–1000 ppb) have meant that the very low losses have not yet been achieved. 4. Chalcogenide glasses based on AsGeS have been 100 μm investigated. The raw materials used to make these glasses (A) are volatile and so the glasses are usually made in sealed silica ampoules in a rocking furnace. The resulting glass RI 140 μm Cladding Core is reasonably stable and can be machined into preforms or (n) drawn in a fiber from the melt. ~65 μm (B) Fabrication 125 μm Three methods are used to make glass optical fibers: 10 μm  Double crucible method (C)  Rod-in-tube method followed by drawing  Chemical vapor deposition (CVD) techniques to make 125 μm preforms followed by drawing FIGURE 32.15 Total internal reflection (TIR) along an optical fiber. (a) Step index fiber; (b) graded index fiber; (c) single mode fiber. The double crucible method and the rod-in-tube The plot on the left is a variation of RI (= n). method are used primarily for higher-loss fibers made 586 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t from multicomponent glasses, such as those used in mounted in a special lathe. The core, which must have a imaging bundles. Pure fused silica and doped silica fibers higher n than the cladding, is formed inside the tube by are drawn from a preform that has been made using a the following reactions: CVD process. The double-crucible method: The glasses for the core SiCl4 + O2 → SiO2 + 2Cl2 (32.11) and cladding are made by melting together the constituent oxides (or fluorides) and then pulling the fiber. This tech- and nique is suitable for glasses that have low working tem- peratures (<1200°C) such as NBS and NCS glasses. GeCl4 + O2 → GeO2 + 2Cl2 (32.12) The rod-in-tube method: A preform consisting of a rod of the core glass is formed inside a tube of the cladding The burners that traverse the tube heat the vapors and glass. The preform can be made either by drawing a rod oxidize the halides. Glass particles are deposited on the of core glass and a tube of cladding glass from the melt, wall of the tube and are remelted to give clear glassy or by machining a rod and tube from bulk glass. The layers. The deposition rate is typically 1 g/min. When suf- preform is then drawn into a fiber by elongation in a ficient deposit has been achieved the tube is collapsed to furnace. Glass is drawn into a fiber when the viscosity is give a preform. The GeO2 has the effect of lowering n. in the range of 103 – 105 d Pa s. The drawing process, which Adding 10 mol% GeO2 to pure SiO2 raises n by 0.012. By is normally performed vertically downward, is a balance varying the ratio of GeCl4 to SiCl4 in the gas stream with between the downward viscous forces and the surface time it is therefore possible to produce graded-index tension of the molten region. fibers. Several variations of the CVD process are used to make preforms: Drawing the Preform  MCVD—modified chemical-vapor deposition The preform is drawn in a carbon-resistance furnace or  OVD—outside vapor deposition zirconia induction furnace; these furnaces can provide the  VAD—axial vapor deposition required temperature (>2000°C) while still having a rea- sonable operating life. The temperature required for The MCVD process was developed by Bell Laborato- drawing optical fibers is much greater than for conven- ries in the United States and became the standard method. tional glass fibers because of their higher purity (the clad- The other processes are very similar except for the details ding is pure SiO2). The furnace is mounted in a tall tower of the geometry. The MCVD process is illustrated in with a preform feed-screw mounted above. Drawing is Figure 32.16. The cladding is a tube of pure silica that is achieved using a capstan, with the fiber being wound onto a drum that can hold several kilometers of fiber. A coating applicator is mounted above the capstan and fibers are Rotation Silica tube coated on-line with a polymer to give mechanical protec- Reactants (SiCl4, GeCl4) Exhaust tion. Drawing speeds of >10 m/s are possible in produc- Oxygen tion; the drawing speed is mainly limited by the stability (O2) of the polymer coating process. A single preform can yield Deposited up to 100 km of fiber. A schematic of a typical fiber glass layers drawing apparatus is shown in Figure 32.17. Collapse Silica fibers may be joined in an electric arc. The two process ends are aligned and the arc is struck. The fibers are fed Oxy-hydrogen burner toward each other at a controlled rate so they are fused Cladding part (SiO2) with minimal distortion of the core; joint losses can be very low (<0.1 dB). We then have to polish the ends of the Core part fiber. (SiO2-GeO2) Preform rod Drawing process Operation An important characteristic for optical fibers is loss or Fiber attenuation. Attenuation in fibers is normally measured in decibels per kilometer (dB/km). The optical loss, in dB, Preform rod Carbon measured over 1 km is written as 10 log Iin /Iout where Iin furnace and Iout are the input and output optical power. FIGURE 32.16 Steps in the metalorganic chemical vapor deposi- The optical signal can be attenuated primarily by two tion (MOCVD) process for forming optical fiber preforms. factors. 3 2 .11 Th e Ba s i c s o f O p t i c a l F i b e r s ......................................................................................................................... 587  1. Absorption. Photons interact with electronic and 1.0 vibrational transitions in the glass in the UV and IR Loss (db/km) Total regions, respectively. In the UV, absorption is due to elec- loss tronic transitions across the band gap. Absorption occurs 0.5 at shorter wavelengths for a larger band gap. In the IR, absorption is due to a coupling of the electromagnetic field 0.3 to lattice vibrations. 2. Scattering. Fluctuations in composition and density 0.2 Rayleigh of the glass occur as it cools down below Tg; the resulting scattering scattering is a form of Rayleigh scattering. We can describe the intrinsic loss, L, mathematically by 0.1 Phonon absorption −4 L = A exp(e/λ) + B exp(−g/λ) + Cλ (32.13) 0.05 Absorption due to electronic transitions where A, B, C, e, and g are constants characteristic of the glass. These loss mechanisms combine to give a loss spec- 0.03 Extrinsic trum as shown in Figure 32.18. For silica the minimum loss imperfections 0.02 of 0.15 dB/km occurs at a wavelength of 1.55 μm. ZBLAN 1.2 λ (μm) 1.5 1.8 is a fluoride glass with even lower loss, 0.02 dB/km at FIGURE 32.18 Loss spectrum for fibers. 2.55 μm. These losses are theoretical minima and difficult to achieve in practical situations. There are many extrinsic sources of loss:  Absorption caused by the OH group  Absorption caused by transition metal impurities (e.g.,  Scattering caused by defects in the glass such as par- Fe, and Cu) ticulate contamination and bubbles  Scattering caused by manufacturing defects such as changes in the fiber diameter along its length and frozen-in stresses Feeder The minimum loss in commercial silica fibers used for Preform assembly optical communications is typically 0.2 dB/km at 1.55 μm. In fluoride fibers the lowest reported loss is 0.4 dB/km at 2.35 μm. Carbon Heater furnace 32.12 PHOSPHORS AND EMITTERS Diameter When a material is placed in an electric field or irradiated gauge with light, it may itself radiate light: either electric or Coating optical energy is absorbed and optical energy is then radi- Pressure material coating die ated. A material that exhibits this phenomenon is called a Read phosphor and the light radiated is called luminescence diameter (see Section 32.10). Luminescence can be fluorescence or phosphorescence. The difference is the time for which P.I.D. emission occurs. controller Tubular curing oven  Fluorescence occurs very quickly: <10−8 s.  Phosphorescence is slow emission over ∼1 s or even Control longer. pull speed Table 32.9 lists the applications of various phosphors. Light-emitting diodes and III–V lasers are devices that use a direct-band-gap semiconductor to convert electrical Dancer energy into visible light. They have long been used for Capstan Take-up materials with Eg ∼ 1 eV (the familiar red), but now GaN drum (with a wider band gap, large ν, and smaller λ) gives us a FIGURE 32.17 The fiber drawing tower. blue emitter. 588 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t  TABLE 32.9 Applications of Various Phosphors Applications Excitation methods Phosphors Color Color TV 18–27 kV e-beam ZnS: Ag, Cl Blue ZnS: Cu, Au, Al Green Y2O2S: Eu Red Cathode ray tube 1.5–10 kV e-beam Zn2SiO4: Mn Green Electron microscope 50–3000 kV e-beam (Zn,Cd)S: Cu, Al Green Numerical display ∼20 kV e-beam ZnO Green Fluorescent lamps 254 nm UV Ca10 (PO4) 6 (F,Cl) 2 : Sb, Mn White Fluorescent Hg lamps 365 nm UV Y(V,P)O4: Eu Red Copying lamps 254 nm UV Zn2SiO4: Mn Green X-ray multipliers X-ray CaWO4 Blue/white Gd2O2S: Tb Yellow/green Scintillators Radiation NaI: Tl Blue Electroluminescence 10–5 × 10 ac/dc ZnS: Cu, Mn, Cl Green Solid-state lasers Visible light (near UV – near IR) Y3Al5O12:Nd (YAG) IR 32.13 SOLID-STATE LASERS Ruby Flashtube The word “laser” was originally an acronym for “light Laser amplification by the stimulated emission of radiation”; beam now it is just a word—so there is no capitalization. A laser produces coherent (in phase) monochromatic (single λ) radiation. It consists of the active medium, called the optical cavity, which in the case of a solid-state laser is an insulating crystal or glass containing a specific Reflector Mirror dopant. The optical cavity is typically 10 cm long FIGURE 32.19 Schematic of the components of a ruby laser. and 1 cm in diameter. One end is coated to form a partially transparent mirror while the other end is fully reflecting. The operation of the laser is based on electronic excitation of the active medium using a pump source, 2. The Nd–YAG laser uses a single crystal of Y3Al5O12 which is usually a flash lamp or flash tube, as shown containing 1.4 × 1020 Nd3+ /cm3. The active electronic in Figure 32.19, or another laser. The excited electrons states are the f levels of Nd3+ . relax back to the ground state by emitting light. As light is reflected to and fro between the mirrors it is The properties of the ruby and Nd–YAG laser are sum- amplified. marized in Table 32.10. The Cr3+ transition is a three-level The two most impor- system: the laser transition tant solid-state lasers are: returns the electrons to the NOTATION ground state. The emission 4 1. The ruby laser uses a I11/2 is an example of a term symbol having the form occurs in the red part of 2S+1 single crystal of Al2O3 L J, which is used to describe arrangements of elec- the visible spectrum (λ = containing about 1.6 × trons in orbitals. The superscript is 2S + 1 where S is 694 nm). The Nd3+ transi- 10 19 3+ 3 Cr /cm . The the overall spin S = Σ m s . The symbol is the overall L = tion is a four-level system: active electronic states Σ ml. The subscript is a quantum number, J, that con- emission occurs near are d levels of the siders spin-orbit coupling; J has values from L + S, 1.06 μm and the terminat- Cr3+ . L + S − 1, to |L − S|. ing state lies above the TABLE 32.10 Characteristics of Typical Solid-State Laser Crystals Concentration Spontaneous of active centers fluorescence Crystal Active center (cm −3) lifetime Wavelength Ruby Cr 3+ 1.6 × 1019 3 ms 694.3 nm YAG : Nd Nd3+ 1.4 × 1020 230 μs 1.061 μm, 1.064 μm, 1.839 μm (77 K), 0946 μm (77 K), 1.318 μm NaF–(F+2) (F2+) color center 2 × 1017 40 ns Tunable, 0.99–1.22 μm Nd 0.5La0.5P5O4 Nd3+ 2 × 1021 150 μs 1.05 μm 3 2 .13 S o l i d - S tat e L a s e r s ............................................................................................................................................ 589 ground state. The four-level system is shown schemati- 32.14 ELECTROOPTIC CERAMICS FOR cally in Figure 32.20. OPTICAL DEVICES Doped oxide glasses are also used as the optical cavities in solid-state lasers. A wide range of dopants and glasses Electrooptic Effect can be used as indicated in Table 32.11. The advantages of using glass as a laser medium is that glass is optically iso- By applying an E field the optical properties, especially n, tropic and producible in a variety of sizes and shapes of high of electrooptic (EO) materials can be changed. Many optical quality. In addition, its chemical composition can be transparent solids and liquids show EO effects, but only a varied to tailor laser parameters for specific applications. few of these are useful for practical applications. However, because the thermal conductivity of glass is usually poor compared to its crystalline counterparts, If an electrooptic ceramic is noncentrosymmetric then δn glass lasers are limited to pulsed and low average- is proportional to E. Examples of such materials include power operation. Crys- piezoelectric crystals and some talline lasers are more poled ferroelectric ceramics; appropriate for contin- POLING this is known as the linear or uous and high-average- Poling is the process of polarizing a ferroelectric mate- Pockels effect. If the material is power operation. rial by applying a high electric field for a short time. initially centrosymmetric, then δn is proportional to E2; this is known as the quadratic or Kerr ~0.6 5d-6s band 1 effect. Such materials include isotropic crystals, unpoled ferroelectric ceramics, and all liquids. E (aJ) Population We saw in Section 32.1 that EO materials are birefrin- inversion gent: i.e., they have two orthogonal optic axes that are ~ ~ transition characterized by different indices of refraction; Δn is 4 F referred to as the birefringence in Eq. 32.5. The value of 2 Δn may be positive or negative. If an E field is applied parallel to one optic axis, then one refractive index is 0.2 Laser changed with respect to the other. As a result Δn is changed Pump transition and the state of polarization of light propagating through ~1064 nm the material is altered. Quadratic EO materials are not 0.15 generally birefringent unless they are subjected to a prop- 4 I15/2 erly aligned E field. The general relationship between Δn and E is 0.1 4 I13/2 Δn = n3 (rcE + RE2) (32.14) 0.05 4 I11/2 3 To Table 32.12 lists the values of r and R for several EO ground 4 state ceramics. The higher the EO coefficient, the lower the 0 I 4 applied voltage necessary to perform a particular 9/2 FIGURE 32.20 The four-level system for lasers. function. TABLE 32.11 Glass Laser Ions and Hosts Ion Transition Wavelength (mm) Sensitizer Host glasses Nd3+ 4 F3/2 → 4I9/2 0.92 Borate, silicate (77 K) 4 F3/2 → 4I11/2 1.05–1.08 Mn2+ , UO2+ 2 Borate, silicate, phosphate, fluorophosphates, germanate, tellurite, fluoroberyllate 4 F3/2 → 4 I13/2 1.32–1.37 Borate, silicate, phosphate Tb 3+ 5 D4 → 7 F4 0.54 Borate Ho3+ 5 I7 → 5 I8 2.06–2.08 Yb3+ , Er 3+ Silicate Er 3+ 4 I13/2 → 4 I15/2 1.54–1.55 Yb3+ Silicate, phosphate, fluorophosphate Tm3+ 3 H4 → 3 H6 1.85–2.02 Yb3+ , Er 3+ Silicate Yb3+ 2 F5/2 → 2 F7/2 1.01–1.06 Nd3+ Borate, silicate 590 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t  TABLE 32.12 Electrooptical Properties of Several Ceramics Material k n at 633 nm rc m/V R m 2 /V 2 Ceramic PLZT 8.5/65/35 5000 2.50 — 38.6 × 10 −16 PLZT 9/65/35 5700 2.50 — 3.8 × 10 −16 PLZT 9.5/65/35 5500 2.50 — 1.5 × 10 −16 PLZT 8/70/30 5400 2.48 — 11.7 × 10 −16 PLZT 8/40/60 980 2.57 1.02 × 10 −10 — PLZT 12/40/60 1300 2.57 1.20 × 10 −10 — PLZT 14/30/70 1025 2.59 1.12 × 10 −10 — Single crystal LiNbO3 (r 33) 37 2.20 0.32 × 10 −10 — LiNbO3 (r13) 37 2.29 0.10 × 10 −10 — BaTiO3 (r 33) 373 2.36 0.28 × 10 −10 — BaTiO3 (r51) 372 2.38 8.20 × 10 −10 — KNbO3 (r 33) 30 2.17 0.64 × 10 −10 — KNbO3 (r42) 137 2.25 3.80 × 10 −10 — Strontium barium 119 2.22 0.56 × 10 −10 — niobate (T = 560 K) Strontium barium 3400 2.30 13.40 × 10 −10 — niobate (T = 300 K) Ba 2NaNb5O15 86 2.22 0.56 × 10 −10 — Solid Solutions in the PLZT System La 0 at. % FErh The most important EO ceramics are solid-solution phases 5 AFE A in the PbZrO3 –PbTiO3 –La2O3 system known collectively FEtet B as PLZT materials. 10 C  The general chemical formula is 15 Pb1−xLa x (ZrzTi1−z)1−x/4O3. 20  The structure of PLZT is based on the perovskite, PEcubic ABO3 (see Section 7.3). 25 The linked network of oxygen octahedra has B ions 30 (Ti4+ , Zr4+) occupying the sites within the oxygen octahe- Mixed phases dra (B sites) and A ions (Pb2+ , La3+) situated in the inter- 100 80 60 40 20 0 stices (A sites) created by the linked octahedra. When PbZrO3 PbTiO3 off-valent ionic substitutions are made into this structure (e.g., La3+ for Pb2+) electrical neutrality is automatically FIGURE 32.21 The PLZT phase diagram. A, memory; B, linear; C, quadratic. maintained by the creation of A-site or B-site vacancies. The PLZT phase diagram at room temperature is shown in Figure 32.21. The compositions are specified by three successive numbers, values are low because of e.g., 8.5/65/35, which the low distortion of the PLZT COMPOSITION represent, from left to unit cell. In their ferroelec- When expressed as 8.5/65/35, the PLZT contains 8.5 right, the La, Zr, and Ti tric (FE) state the polar at% La and the Zr/Ti ratio is 65/35. atomic concentrations. c axis is typically only Ferroelectric PLZT about 1% longer than the a ceramics possess crystalline phases that belong princi- axis, which is why domain reorientation is easy in these pally to the tetragonal and rhombohedral crystal systems. materials. Domain reorientation produces a change in the These materials are classified as uniaxial, because they optical properties. The magnitude of the observed EO have two or more crystallographically equivalent direc- effect is dependent on both the strength and direction of tions lying in a plane that is perpendicular to the 4-fold the E field. (tetragonal case) or 6-fold (rhombohedral case) axis. They PLZT ceramics display optically uniaxial properties are also optically negative (i.e., ne –no < 0), with Δn values on both a microscopic and a macroscopic scale once typically ranging from about −0.018 to near zero. These polarized. The optic axis coincides with the polarization. 3 2 .14 E l e c t r o o p t i c C e r a m i c s f o r O p t i c a l D e v i c e s ............................................................................................. 591  TABLE 32.13 Transparent Electrooptical Ceramics Composition Notation Composition Notation (Pb,La)(Zr,Ti)O3 PLZT (Pb,La)(Hf,Ti)O3 PLHT (Pb,Ba,Sr)(Zr,Ti)O3 PBSZT (Pb,Sn)(In,Zr,Ti)O3 PSIZT (Pb,Ba,La)Nb2O6 PBLN (Pb,La)(Zn,Nb,Zr,Ti)O3 PBLNZT K(Ta,Nb)O3 KTN Pb(Sc,Nb)O3 PSN (Pb,La)(Mg,Nb,Zr,Ti)O3 PLMNZT (Ba,La)(Ti,Nb)O3 BLTN (Pb,La,Li)(Zr,Ti)O3 PLLZT (Sr,Ba)Nb2O6 SBN The macroscopic or effective birefringence is designated – ation of Δn is usually plotted in terms of the normalized – – by Δn. On a macroscopic scale, Δn is equal to zero before remnant polarization Pr/PR because Pr is an easily meas- electrical poling and has some finite value after poling, ured parameter that depends on domain switching. Inter- depending on the composition and the degree of polariza- mediate remnant states can be achieved by removing the – tion. The Δn value is an important quantity because it applied E field prior to reaching Ec. is related to the optical phase retardation, Γ, of the 2. Linear (Pockels effect). This effect is characterized material. by a square hysteresis loop having a large Ec. It occurs for The phenomenon of optical phase retardation in an EO tetragonal type compositions at the PbTiO3-rich end of the poled ceramic occurs when entering linearly polarized – solid-solution range such as 8/36/60. Δn is linear with monochromatic light is resolved into two perpendicular respect to E; from a practical point of view, grain size has components c1 and c2. Because of the different refractive a very significant effect on the linearity. indices, ne and no, the propagation velocity of the two 3. Quadratic (Kerr effect). A slim hysteresis loop with components will be different and will result in a phase zero, or very low Pr, is obtained between the FE and para- – shift or “retardation.” Γ is a function of both Δn and the electric (PE) compositions; a typical composition is path length t: 9.5/65/35. At room temperature they are essentially cubic, but the application of E enforces a transition to the rhom- Γ = Δnt – (32.15) bohedral or tetragonal FE phase, and the optical anisot- ropy increases with E2. Although at present PLZT is the most important EO ceramic, there are other transparent ceramics that exhibit EO characteristics; some of these are listed in Table 32.13. P/C m-2 0.3 I Many of these ceramics are based on solid solutions in the lead zirconate–lead titanate (PZT) system and are struc- turally related to PLZT. Notable exceptions are the nio- -2 -1 1 2 E/MV m-1 bates, such as KTN (potassium tantalum niobate or KTa1−xNbxO3 with x ∼ 0.35), which are also based on the -0.3 perovskite structure. NTT has shown n for KTN changing E (A) by a factor of 20× the change produced in LiNbO3 using an applied field of 60 V/mm2 (achieved by applying 1.2 V 0.3 I across a 20-μm sample), but the limiting factor is the growth of high-quality crystals. -2 -1 1 2 Electrooptic Characteristics of -0.3 E PLZT Ceramics (B) I Depending on composition PLZT ceramics display one of the three major types of EO characteristics shown in 0.3 Figure 32.22. -2 1 2 1. Memory. The P versus E hysteresis loop is narrow, indicating low Ec. This characteristic occurs for the rhom- -0.3 E bohedral FE phase; a typical composition is 8/65/35. The (C) – EO memory effect depends on the fact that Δn can be set FIGURE 32.22 Electrooptic characteristics of PLZT: (a) memory, to different values by applying (and removing) an E field. (b) linear, (c) quadratic. I is the light output versus applied field E – Once set, Δn remains constant as long as E = 0. The vari- (see A, B, and C in Figure 32.21). 592 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t Making Transparent PLZT Ceramics Polarizer White Optic axis For a ceramic to be useful as an EO material it must be light source transparent. In single-crystal form ferroelectric materials PLZT possess high optical transparency and useful EO proper- ties. In the form of polycrystalline ceramics they can also Analyser possess such properties if special precautions are taken during processing. To create a transparent ceramic it is necessary to limit the amount of sources that can lead to light scattering (the main culprits were discussed in Section 32.8). Hot pressing can produce a high-density product with low porosity. If the pore size is reduced to a value less than the wavelength of light (λyellow ∼ 0.5 μm) then the pores will have only a minor scattering effect. 380 μm Control The presence of impurities can be reduced by using high PLZT purity starting materials or by preparing the powders by a sol-gel process using metal alkoxides (see Chapter 22). 1 mm The use of liquid or solution techniques also helps to ensure good intermixing between the various components. 50 μm As noted above, for noncubic materials light scattering can occur at GBs, where refractive indices are discontinu- 10 cm ous. In PLZT the optical anisotropy is reduced by doping with La, which brings the ratio between c and a lattice parameters close to unity. Applications Using PLZT FIGURE 32.23 Illustration of the operation of flash goggles and Electrooptic Ceramics the interdigitated electrode arrangement. There are several applications for EO ceramics and two basic modes of operation for EO devices.  Transverse—the E field is applied in a direction normal quadratic material of typical composition 9.2/65/35, with to the light propagation direction. almost zero birefringence when E = 0.  Longitudinal—the E field is applied along the light This application uses an arrangement similar to that propagation direction. used for a voltage-controlled color filter. Now a variable voltage is used that determines what part of the visible Linear materials are used primarily for high-speed spectrum is blocked. When the applied voltage is zero no modulation of the intensity, amplitude, phase, frequency, light is transmitted. At the voltage at which the green light or direction of a light beam. Quadratic materials are used is retarded by λ/2 “white” light is transmitted (i.e., green principally for light valves and shutters. plus part of everything else). Further increases in the Here we will briefly describe four applications for voltage produce conditions at which the blue is extin- PLZT ceramics. guished resulting in the transmission of yellow light (i.e., red and green are transmitted). In a similar way voltage 1. Flash goggles are used by military pilots to prevent conditions can be reached at which either the red or the them from being blinded by a very bright flash! The green is excluded and the resulting colors are transmitted. arrangement consists of three components as illustrated in Again the PLZT is of the slim-loop quadratic variety. Figure 32.23. Under normal illumination the PLZT plate 2. PLZT elements can be used in reflective displays as allows the plane of polarization to be turned by 90° when shown in Figure 32.24. P1 and P2 are polarizers that are a voltage of ∼800 V is applied to the interdigitated gold set up in the parallel position. When no voltage is applied electrodes. The light passes through the analyzer and into to the indium tin oxide (ITO) electrodes, light passes the pilot’s eyes. An intense flash of light is detected by a through both polarizers and the PLZT plate and is reflected photodiode that forms part of the circuit connected to the from the reflecting surface into the eye. If a voltage PLZT plate, and removes the voltage applied to the elec- (∼200 V) is applied to the PLZT the light experiences a trodes. The plane of polarization of the incident light is retardation of λ/2 and is extinguished at P2. The activated not rotated and the analyzer blocks most of the light. The segments appear dark against a light background. The switching times are ∼100 μs and transmission ratios are PLZT is again of the 9.5/65/35 type, so it has a slim-loop 1000 : 1. For this application the PLZT is a slim-loop quadratic. PLZT displays are much more expensive and 3 2 .14 E l e c t r o o p t i c C e r a m i c s f o r O p t i c a l D e v i c e s ............................................................................................. 593  Patterned Buffer ITO l layer electrode 1 4 P1 g φ PLZT tw 2 3 P2 th Reflecting surface PLZT tf FIGURE 32.24 Basic layout of a PLZT reflective display. Sapphire require much higher operating voltages (>100 V) than FIGURE 32.26 An example of a PLZT thin film optical switch on the liquid crystal variety, but offer faster switching times. sapphire. The main applications are in military and automotive markets. When there is no voltage applied to the metal electrodes 3. Figure 32.25 shows an image storage device using light entering at 1 will exit at 3. If a large enough voltage V PLZT that operates on the basis of light scattering by is applied, total internal reflection (TIR) of the light will domain boundaries in the unpoled material. The PLZT is occur between the electrodes causing the signal to now exit of the memory type with a composition 7/65/35 and a at 4. TIR occurs because the voltage reduces n. grain size of ∼4.5 μm. To start, the device is uniformly The critical angle for TIR is irradiated and the PLZT is poled to Pr. The image to be stored is focused onto the photoconductive film (e.g., CdS θc = sin−1(1 − 0.5n2 RV 2) (32.16) or ZnS) while a voltage (∼200 V and opposite to that of the poling voltage) is applied across the transparent elec- The change in n causing TIR is regarded as being due to trodes. This causes regions of the ferroelectric to become the Kerr effect. If we use a 9/65/35 quadratic PLZT with depoled. The image can then be read by passing light R = 380 nm2 /V 2, n = 2.5, and with a 2° angle between through the plate and focusing the unscattered light so that the guides (i.e., θc = 88°) then the switching voltage is it passes through an aperture and onto a film. Regions that 1.4 V. have become depoled scatter the light to a greater extent than the poled regions. Repoling the PLZT can erase the 32.15 REACTING TO OTHER PARTS OF display. THE SPECTRUM 4. Optical signals in telephone systems are routed by first converting them to their electronic equivalents, So far we have concentrated on how ceramics interact with switching them electronically, and then reconverting them light in the UV, visible, and IR parts of the spectrum. This to the optical form. Thin-film optical switches allow the emphasis is because these interactions are often the most process of switching to be done optically, avoiding the useful and the ones that we are likely to notice. The need for electronic conversion. An example of a thin film response of ceramics to γ-rays is becoming of increased optical switch using PLZT is shown in Figure 32.26. The interest because of their use for radiation detectors (pri- PLZT layer can be deposited onto the sapphire substrate marily aimed at locating radioactive material that might by a variety of methods including sputtering, CVD, and be used for “dirty bombs”). Ceramics have long been used sol-gel. The lattice mismatch between the (0001) plane of to detect high-energy radiation. One example is Tl-doped sapphire and (111) plane of the PLZT is quite small (∼2%), NaI used as a scintillation detector on early X-ray dif- and this facilitates the formation of an epitactic layer with fractometers. The thallium causes the crystal to fluoresce the planar relationship (0001) s||(111) PLZT. in the violet part of the spectrum (λ = 420 nm). The goal is to make lower cost devices that can be portable, for example, incorporated into pagers and cell phones. Light Transparent The basic requirements of a scintillator for γ-rays are Photoconductor electrode as follows:  High light yield (>20 k photons generated per incident + - PLZT γ-ray)  A fast response time (<100 ns) PMMA  High density and high Z FIGURE 32.25 Schematic of an image storage device using a  Scintillation λ matches that of the light sensor (usually field-induced polarized PLZT film. an Si diode or photomultiplier) 594 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t (A) Light c-Axis (B) Correcting Correcting structure structure operative ignored Sea water Oriented calcite Intralensar bowl Focal plane Body fluid (C) FIGURE 32.28 The brittlestar lens: (a) plan view of an array; (b) cross section. FIGURE 32.27 Trilobite eye. Ce-doped YAG (which is yellow) is one ceramic that shown here is an array of calcite crystals, which direct the meets these requirements and the estimated cost for single light to a point. So at least some of the trilobites could see crystals is <$0.05 mm−3. because their eyes were inorganic crystals. We may think of this as being an oddity because the trilobites are extinct (although they did survive for ∼300 million years). 32.16 OPTICAL CERAMICS IN NATURE However, it has now been shown that brittlestars use a similar structure to detect light. The scanning electron We will use many of the concepts introduced in this microscopy (SEM) image in Figure 32.28 shows an array chapter when we discuss gemstones in Chapter 36. Nature of calcite lenses on the surface of the dorsal arm plate. does make use of these The cross section through concepts in surprising one of these lenses demon- ways. Figure 32.27 shows ECHINODERMATA strates how the light is the eye of a trilobite. Trilo- This is a group of animals that includes sea urchins and focused onto the nerve and bites existed for over 300 sea stars, one of which is the brittlestar (Ophiocoma even how the spherical million years. The eye wendtii). aberration is corrected. 3 2 .16 O p t i c a l C e r a m i c s i n N at u r e .......................................................................................................................... 595  CHAPTER SUMMARY At the simplest level the optical properties of ceramics are critical to society because glass is transparent, diamonds are not opaque, the development of television required phosphors, nearly all lighting depends on glass, the future of communications relies on glass fibers and periodic amplifiers, etc. Microscopy developed using glass lenses and led to our understanding of biology. We tend to use color when glazing (or there are no patterns). The general idea is that light affects and is affected by the electrons in the ceramic and this interaction is determined by the bonding in the ceramic. The interaction actually causes the speed of light to change inside a ceramic. The key properties of the material are then described by average quantities such as the dielectric constant and the refractive index. Crystallography comes in again because many ceramics are anisotropic; one particularly well-known case is calcite. PEOPLE IN HISTORY Coble, R.L. (Bob) (1928–1992) developed Lucalox®, a transparent polycrystalline alumina (Al2O3) ceramic, at the GE laboratory in Schenectady in 1961; GE is still a major supplier of lamp envelopes but Silvania, Osram and others also manufacture the envelopes now. Maxwell, James Clerk (1831–1879) developed the electromagnetic wave theory of light. Seabright, Clarence A. (1914–2002) in the United States was one of the key contributors to the development of ceramic pigments: (1948) Ceramic Pigments, US Patent 2,441,367; (1961) Yellow Ceramic Pigments, US Patent 3,012,898; (1965) Iron Ceramic Pigment, US Patent 3,166,430. van Royen, Willebrod Snell (1581–1626), the Dutch scientist, first described Snell’s law; the derivation is given in standard textbooks on electromagnetism (Panofsky and Philips, 1961) or optics (Born and Wolf, 1970). GENERAL REFERENCES Aggarwal, I.D. and Lu, G. (Eds.) (1991) Fluoride Glass Fiber Optics, Academic Press, Boston. Contains a series of chapters written by leading experts in the field detailing the structure, processing, and properties of fluoride glasses and their application as optical fibers and use in other optical devices. Agulló-López, F., Cabrera, J.M., and Agulló-Rueda, F. (1994) Electrooptics: Phenomena, Materials, and Applications, Academic Press, London. Gives a very detailed description of all aspects of electrooptic materials. Two of the chapters cover applications. It also provides information about how electrooptic coefficients are determined experimentally. Born, M. and Wolf, E. (1970) Principles of Optics, 4th edition, p. 110, Pergamon, Oxford. Standard optics text. Haertling, G.H. (1991) “Electrooptic ceramics and devices”, in Engineered Materials Handbook Volume 4: Ceramics and Glasses, ASM International, p. 1124. Haertling and Land (1971) developed the PLZT system of transparent ferroelectric ceramics. Kingery, W.D., Bowen, H.K., and Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd edition, Wiley, New York. Chapter 13 covers the optical properties of ceramics and glasses. Moulson, A.J. and Herbert, J.M. (1990) Electroceramics, Chapman & Hall, London. Covers the entire field of electronic ceramics. Chapter 8 is devoted to electrooptic ceramics. Highly recommended. Robbins, M. (1994) Fluorescence, Geoscience Press Inc., Phoenix, AZ. Many examples including color illustrations and a comprehensive bibliography. Taylor J.R. and Bull, A. (1986) Ceramics Glaze Technology, Pergamon, Oxford. Great book for information on glazes with examples. Warren, T.S., Gleason, S., Bostwick, R.C., and Verbeek, E.R. (1999) Ultraviolet Light and Fluorescent Miner- als: Understanding, Collecting and Displaying Fluorescent Minerals (Rocks, Minerals and Gemstones), Gem Guides Book Co. SPECIFIC REFERENCES Aizenberg, J. and Hendler, G. (2004) “Designing efficient microlens arrays: Lessons from nature,” J. Mater, Chem. 14, 2066. This and the earlier papers make fascinating reading. Burchfield, R.W. (1998) The New Fowler’s Modern English Usage, revised 3rd edition, Clarendon Press, Oxford, p. 371. Explains why we prefer electrooptic. Coble, R.L. (1961) “Sintering crystalline solids: I. Intermediate and final stage models; II. Experimental test of diffusion models in powder compacts,” J. Appl. Phys. 32, 787. DCMA (1982) Classification and Chemical Description of the Mixed Metal Oxide Inorganic Colored Pig- ments, 2nd edition, Metal Oxides and Ceramic Colors Subcommittee, Dry Color Manufacturers Associa- tion, Arlington, VA. Now called the Color Pigments Manufacturers Association (CPMA). 596 ............................................................................................................... I n t e r ac t i n g w i t h a n d G e n e r at i n g L i g h t  Haertling, G.H. and Land, C.E. (1971) “Hot-pressed (Pb,La)(Zr,Ti)O3 ferroelectric ceramics for electrooptic applications,” J. Am. Ceram. Soc. 54, 1. This is the original citation for transparent PLZT ceramics. Kaiser, P. (1973) “Spectral losses of unclad fibers made from high-grade vitreous silica,” Appl. Phys. Lett. 23, 45. Developed the MCVD process. Kao, K.C. and Hockham, G.A. (1966) “Dielectric-fiber surface waveguides for optical frequencies,” Proc. IEE 113, 1151. Kapron, F.P., Keck, D.B., and Maurer, R.D. (1970) “Radiation losses in glass optical waveguides,” Appl. Phys. Lett. 17, 423. Report of the first low-loss optical fibers. Kerr, J. (1875) Wied. Ann. 18, 213. The “Kerr” effect. Miyauchi, K. and Toda, G. (1975) “Effect of crystal-lattice distortion on optical transmittance of (Pb,La)(Zr,Ti)O3 system,” J. Am. Ceram. Soc. 58, 361. Doping PLZT with La to reduce the optical anisotropy. Nassau, K. (1980) Gems Made by Man, Chilton Book Company, Radnor, PA. Nassau, K. (1983) The Physics and Chemistry of Color: The Fifteen Causes of Color, Wiley, New York. The classic book on the sources of color in ceramics. Panofsky, W.K.H. and Philips, M. (1961) Classical Electricity and Magnetism, Addison-Wesley, Reading, MA. Pockels, F. (1884) Abh. Gottinger Ges. d. Wiss. 39, 169. The “Pockels” effect. Tilley, R. (2000) Colour and the Optical Properties of Materials, Wiley, New York. Strongly recommended. WWW Saphikon (www.saphikon.com) gives current examples of using alumina fibers in medicine. EXERCISES 32.1 Explain why BaTiO3 is a linear electrooptic material below Tc but a quadratic electrooptic material above Tc. 32.2 PLZT ceramics belonging to either the tetragonal or rhombohedral crystal systems are classified as optically uniaxial. Which other crystal system or systems are also optically uniaxial? 32.3 Several methods have been used to produce PLZT thin films. Try to find as many methods as you can and discuss the pros and cons of each. 32.4 Prior to the development of transparent alumina ceramics the material of choice for the lamp-envelope market was silica-based glass. Explain why such materials are not suitable for use in the sodium vapor lamp but dominate the incandescent, fluorescent, and electric discharge lamp-envelope market. 32.5 With the increasing demand for optical fiber communication systems new glass and fiber processing methods are being investigated. One such example is the sol-gel route for silica fibers. What advantages do you think the sol-gel route would offer over the present CVD processes? Can you think of any disadvantages of the sol-gel route? 32.6 The single crystals required for solid-state lasers are often made by the Czochralski process. Describe the advantages and disadvantages of using this process for producing single crystals of ruby and YAG. 32.7 Explain briefly why the transparency range of single crystal NaCl is much greater than for single crystal MgO. 32.8 Why are house bricks different colors? (You can answer this in 2 minutes or 2 hours.) 32.9 How is the numerical aperture (NA) of a fiber linked to the NA of a camera lens? 32.10 What causes refraction in glass? C h a p t e r S u m m a ry .......................................................................................................................................................... 597  33 Using Magnetic Fields and Storing Data CHAPTER PREVIEW If you were asked to give an example of a magnetic material instinctively you would probably say iron. It is a good example, but in its pure form iron is not a very useful magnet. Ceramics can be magnetic too and they were the first magnets known to humans. About 600,000 t of ceramic magnets are produced each year making them, in terms of volume, commercially more important than metallic magnets. The largest market segment is hard ferrites (permanent magnets) that are used in a range of applications including motors for electric toothbrushes and windshield wipers in automobiles, refrigerator door seals, speakers, and stripes on the back of the ubiquitous credit and ATM cards. Soft ferrites can be magnetized and demagnetized easily and are used in cell telephones, transformer cores, and, now to a somewhat lesser extent, magnetic recording. Ferrite is a term used for ceramics that contain Fe2O3 as a principal component. Magnetism has probably fascinated more people, including Socrates and Mozart (listen to Così fan tutte), over the years than any other materials property. For over four thousand years the strange power of magnets has captured our imagination. Yet it remains the least well understood of all properties. In this chapter we will start by describing some of the basic characteristics of magnetic materials, which often contain one of the first row transition metals, Fe, Co, or Ni. The electron arrangement in the 3d level of these atoms is the key. The manga- nates are a very interesting class of magnetic ceramic. Although they are not new, the recent discovery that they exhibit colossal magnetoresistance (just like the giant magnetoresistance observed in metal multilayers only much bigger) has renewed interest in these materials. Struc- turally the manganates are very similar to the high-temperature superconductors (HTSCs). The similarity may be more than coincidental. 33.1 A BRIEF HISTORY OF polished bronze plate. The rounded bottom of the spoon MAGNETIC CERAMICS swivels on the plate until it points south. Although this compass has been found to work it was used apparently Applications of magnetism began with ceramics. The first for quasimagical rather than navigational purposes. magnetic material to be discovered was lodestone, which Magnetite is found in many parts of the world and is is better known now as magnetite (Fe3O4). In its naturally an important iron ore used for steel making. The word occurring state it is permanently magnetized and is the magnet comes from the Greek word magnes, which itself most magnetic mineral. The strange power of lodestone may derive from the ancient colony of Magnesia (in was well known in ancient times. In c. 400 bce Socrates Turkey). Magnetite was mined in Magnesia 2500 years dangled iron rings beneath a piece of lodestone and found ago. Today, large deposits of magnetite are found at Kiruna that the lodestone enabled the rings to attract other rings. in Sweden and in the Adirondack region of New York. They had become magnetized. Even earlier (∼c. 2600 bce) Commercial interest in ceramic magnets really started a Chinese legend tells of the Emperor Hwang-ti being in the early 1930s with the filing of a Japanese patent guided into battle through a dense fog by means of a small describing applications of copper and cobalt ferrites. In pivoting figure with a piece of lodestone embedded in its 1947 J.L. Snoeck of N.V. Philips Gloeilampenfabrieken outstretched arm. The figure always pointed south and was performed a detailed study of ferrites, and the following probably the first compass. The term lodestone was coined year Louis Néel published his theory of ferrimagnetism. by the British from the old English word lode, which This latter study was particularly important because most meant to lead or guide. of the ceramics that have useful magnetic properties are Figure 33.1 shows an ancient Chinese compass. The ferrimagnetic. The first commercial ceramic magnets were spoon or ladle was carved out of lodestone and rests on a produced in 1952 by researchers at the Philips Company, 598 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data  Direction of N current Nucleus e- + e- or e- Direction of electron motion Direction of electron spin N N (A) (B) FIGURE 33.2 Generation of atomic magnetic moments by (a) electron orbital motion around the nucleus; (b) electron spin around its axis of rotation. netic dipoles are small internal magnets with north and south poles. FIGURE 33.1 An ancient Chinese compass.  Orbital motion. Equiva- the same company that MAGNETIC MOMENTS lent to a small current introduced the compact The fundamental magnetic moment is the Bohr magne- loop generating a very audiocassette in 1963. ton, μB, which has a value of 9.27 × 10−24 A·m2. small magnetic field. The The orbital magnetic moment, μorb, of a single elec- direction of the magnetic tron is moment is along the orbit axis as illustrated in 33.2 MAGNETIC DIPOLES μ orb = μ B [l (l + 1)] (Box 33.1) Figure 33.2a.  Spin. Origin of the l is the orbital shape quantum number (see Chapter 3). fourth quantum number, The Danish physicist Hans The spin magnetic moment of an electron is ms, that we used in Christian Oersted discov- Chapter 3. The magnetic ered that an electric current μ s = 2μ B [ms ( ms + 1)] (Box 33.2) moment is along the (i.e., moving electrons) In ceramics where the magnetic behavior is due to the spin axis as shown in gives rise to a magnetic presence of transition metal ions with unpaired electron Figure 33.2b and will be force. In an atom, there spins in the 3d orbital the magnetic moment of the ion either up (ms = +1/2) or are two possible sources due to electron spin, μion, is in an antiparallel down of electron motion that can direction (ms = −1/2). create a magnetic dipole and produce the resultant μ ion = 2μ B [ S ( S + 1)] (Box 33.3) The magnetic moment macroscopic magnetic pro- S = ∑ ms due to electron spin is, perties of a material. Mag- when present, dominant TABLE 33.1 Magnetic Moments of Isolated Transition Metal Cations Calculated moments Measured Cations Electronic configuration using Eq. B3 moments (m B) Sc3+ , Ti4+ 3d 0 0.00 0.0 4+ 3+ V , Ti 3d1 1.73 1.8 3+ 2 V 3d 2.83 2.8 V2+ , Cr 3+ 3d3 3.87 3.8 Mn3+ , Cr 2+ 3d4 4.90 4.9 2+ 3+ Mn , Fe 3d5 5.92 5.9 Fe2+ 3d 6 4.90 5.4 2+ Co 3d7 3.87 4.8 2+ 8 Ni 3d 2.83 3.2 Cu2+ 3d9 1.73 1.9 + 2+ 10 Cu , Zn 3d 0.00 0.0 3 3 . 2 M ag n e t i c D i p o l e s ................................................................................................................................................ 599  TABLE 33.2 Terms and Units Used in Magnetism Parameter Definition Units/value Conversion factor H Magnetic field strength A/m 1 A/m = 4π × 10 −3 oersted (Oe) Hc Coercive field A/m H cr Critical field A/m M Magnetization A/m B Magnetic flux density T T = Wb m−2 = kg A−1 s2 = V s m−2 Magnetic induction = 104 gauss (G) μo Permeability of a vacuum 4π × 10−7 H/m 1 H = 1 J s2 C−2 μ Permeability H/m 1 H/m = 1 Wb m−1 A−1 μr Relative permeability Dimensionless χ Susceptibility Dimensionless μion Net magnetic moment of an atom or ion A·m2 μs Spin magnetic moment A·m2 μorb Orbital magnetic moment A·m2 μB Bohr magneton 9.274 × 10 −24 A·m2 θc Curie temperature K 0 K = −273°C θN Néel temperature K Tc Critical temperature for superconductivity K C Curie constant K over that due to orbital motion. Table 33.1 lists values of where N is the number of turns of wire per meter. The μion calculated for some first row transition metal ions magnetic induction or magnetic flux density, B, is related using Eq. Box 33.3. You can see that, in general, the cal- to H by culated values agree well with the experimental values. This agreement shows that we are justified in considering B = μ0 H (33.2) only the contribution of the spin magnetic moment to the overall magnetic moment. μo is a universal constant. When an electron orbital in an atom is filled, i.e., all When a material is placed inside the coil, as shown in the electrons are paired up, both the orbital magnetic Figure 33.3b, it becomes “magnetized.” The magnetic moment and the spin magnetic moment are zero. 33.3 THE BASIC EQUATIONS, THE I I WORDS, AND THE UNITS Table 33.2 lists the important parameters used in this chapter and their units. The situation regarding units is more complicated for magnetism than for almost any other property. The reason is that some of the older units, in particular the oersted (Oe) and the gauss (G), are still in widespread use despite being superceded, in the SI system, l by A/m and T, respectively. The properties of most interest to us in the description of magnetic behavior are  μ  χ These terms are, of course, related to each other and by N turns considering the role of H to macroscopic measures such as M and B. I I The usual starting point to arrive at expressions for μ and χ is to consider a coil of wire in a vacuum as illus- trated in Figure 33.3a. A current, I, passed through the wire generates a magnetic field H (A) (B) FIGURE 33.3 Generation of a magnetic field by current flowing in H = IN (33.1) a coil of wire (a) in a vacuum; (b) with a material present. 600 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data moment produced in the material by the external field nature of the dipoles and their origin is very different. In changes B: the case of a dielectric, the dipoles are electric; there is a separation of positive and negative charges. These dipoles B = μ0 H + μ0 M (33.3) can be permanent or induced. In a magnetic material, the dipoles are, of course, magnetic in origin and are due to M represents the response of the material to H, which is electron motion. linear, and the ratio gives A note on terminology: In most materials science text- books, as we have done here, H is defined as the magnetic χ = M/H (33.4) field or the applied magnetic field and B as the magnetic flux density. In many physics textbooks B is referred to as By simple substitution we get the magnetic field and H is often ignored. The physics convention is adopted for purely historical reasons, but it B = μ0 (1 + χ)H (33.5) does have the advantage of reducing the number of terms we need to consider. Also H has nothing to do with a B/H is then the permeability: material whereas B is a measure of the response of a mate- rial to an applied magnetic field. Another point to note is B/H = μ0 (1 + χ) = μ (33.6) that B and H are both vector quantities and because the magnetic properties of a material are anisotropic (differ- The ratio of the permeabilities gives us the relative ent along different directions in the crystal) they should permeability: actually be represented by a second-rank tensor. μ = 1 + χ = μr (33.7) 33.4 THE FIVE CLASSES OF μ0 MAGNETIC MATERIAL There are many quali- tative similarities between There are five main types magnetic parameters and c AND m of magnetic behavior and those we used to describe Susceptibilities are generally used when the response to these can be divided into dielectrics in Chapter 31. an applied magnetic field is weak (of interest only to two general categories: In the former case, the physicists!). Permeabilities are used when the response  Induced material is responding to is large—of great interest to engineers!  Spontaneous an applied magnetic field, and in the latter case, it is responding to an applied electric field. Table 33.3 summarizes the properties of the five classes. We can find examples of each in ceramics.  H and the electric field strength ξ (V/m). Both are the external driving force, which causes the orientation of either magnetic or electric dipoles resulting in magne- 33.5 DIAMAGNETIC CERAMICS tization or polarization, respectively.  B and the polarization P (C/m 2). Both correspond to Most ceramics are diamagnetic. The reason is that all the the total field after dipole orientation. electrons are paired during bond formation and as a result  χ and dielectric constant, κ. Both are dimensionless the net magnetic moment due to electron spin is zero. “constants” that describe the magnitude of a material’s Table 33.4 lists χ for several diamagnetic materials. Cu, response to the applied field. They are both properties Au, and Ag are diamagnetic even though their atoms have of a material and depend on the types of atoms, the unpaired valence electrons. When the atoms combine to interatomic bonding, and, the crystal structure. form the metal the valence electrons are shared by the  μ and the permittivity of a vacuum ε are constants. crystal as a whole (to form the electron gas) and, on o 0 They are reference values to establish the strength of average, there will be as many electrons with ms = +1/2 a materials response to H or ξ, respectively. as with ms = −1/2. Most diamagnetic ceramics are of no commercial sig- The similarities described above are not surprising. nificance and of little scientific interest, at least not for In both cases, we are con- their magnetic behavior. cerned with the relation- The one exception is the ship between an external MAXWELL EQUATIONS ceramic superconductors, field and the dipoles within The magnetic, electric, and optical properties of a mate- which are perfect diamag- a material. Despite these rial are all related mathematically through the Maxwell nets below a critical mag- similarities the physical equations. netic field. 3 3 . 5 D i a m ag n e t i c C e r a m i c s ........................................................................................................................................ 601  TABLE 33.3 Magnetic Classification of Materials Critical Temperature Spontaneous Class temperature c variation of c magnetization Structure on atomic scale Diamagnetic None −10 −6 to −10 −5 Constant None Atoms have no permanent dipole moments Paramagnetic None +10 −5 to +10 −3 χ = C /T None Atoms have permanent dipole moments; neighboring moments do not interact Ferromagnetic θC Large (below θC) Above θC, Below θC, M s (T )/M s (0) Atoms have permanent dipole χ = C /(T − θ), against T/θC follows a moments; interaction produces with θ ≈ θC universal curve; above parallel alignment θC, none Antiferromagnetic θN As paramagnetic Above θN, None Atoms have permanent dipole χ = C /(T ± θ), moments; interaction produces with θ ≠ θN, antiparallel alignment below θN, χ decreases, anisotropic Ferrimagnetic θC As ferromagnetic Above θC, Below θC, does not Atoms have permanent dipole χ ≈ C /(T ± θ), follow universal curve; moments; interaction produces with θ ≠ θC above θC, none antiparallel alignment; moments are not equal 33.6 SUPERCONDUCTING MAGNETS The net effect is that the whole of the magnetic flux appears to have been sud- When a superconductor in LONDON PENETRATION DEPTH denly ejected from the its normal (i.e., nonsuper- Although there is no magnetic field in the bulk of a material and it behaves as conducting) state is placed superconductor it does penetrate below the surface to a a perfect diamagnet. This in a magnetic field and depth of between 0.2 and 0.8 μm. phenomenon is known as then cooled below its criti- the Meissner effect and is cal temperature the induced CRITICAL MAGNETIC FIELDS FOR YBCO usually demonstrated by magnetization, M, exactly Hc1 (T) || c ∼0.1 || a,b ∼0.01 suspending a magnet above opposes H and so from Eq. Hc2 (T) || c ∼50 || a,b ∼200 a cooled pellet of the 33.3, we can write || c field along the c axis of the unit cell superconductor. || a,b field in the basal plane There is an upper limit These Hc2 values are enormous. The world’s most pow- to the strength of the mag- B=0 (33.8) netic field that can be erful magnet is about 40 T. applied to a superconduc- tor without changing its TABLE 33.4 Magnetic Susceptibilities for Several diamagnetic behavior. At a critical field Hcr the magnetiza- Diamagnetic Materials tion goes toward zero and the material reverts to its normal Material c (ppm) state. For most elemental superconductors M rises in mag- Al2O3 −37.0 nitude up to Hcr and then abruptly drops to zero; this is Be −9.0 Type I behavior. BeO −11.9 A few elemental and most compound superconductors, Bi −280.1 including all HTSCs, exhibit Type II behavior. Above a B −6.7 certain field, Hc1, magnetic flux can penetrate the material CaO −15.0 CaF2 −28.0 without destroying superconductivity. Then at a (usually C (diamond) −5.9 much) higher field, Hc2, the material reverts to the normal C (graphite) −6.0 state. These two behaviors are compared in Figure 33.4. Cu −5.5 When a Type II superconductor is in the “mixed” state Ge −76.8 it consists of both normal and superconducting regions. Au −28.0 Pb −23.0 The normal regions are called vortices, which are arranged LiF −10.1 parallel to the direction of the applied field. At low tem- MgO −10.2 perature the vortices are in a close-packed arrangement Si −3.9 and vibrate about their equilibrium positions, in the same Ag −19.5 way that atoms in a solid vibrate. If the temperature is high NaCl −30.3 enough the vortex motion becomes so pronounced that the 602 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data -M TABLE 33.5 Magnetic Susceptibilities for Several Paramag- netic Materials Type I Material c (ppm) Al +16.5 Ca +40.0 Ce +2450 Type II CeO2 +26.0 Cr +180 Cr 2O3 +1965 Mixed state Li +14.2 Mg +13.1 Hcl Hcr H Hc2 Na +16.0 FIGURE 33.4 Magnetization behavior of Type I and Type II Ti +153.0 superconductors as a function of the applied field. TiO2 +5.9 arrangement randomizes and the vortex lattice “melts.” to the underlying geological structure (e.g., thickness Defects in the material can trap or pin vortices in place of the crust, movement of magnetic poles over time, and higher temperatures are then needed to cause etc.). “melting.” Pinning is of considerable practical importance  Magnetic imaging using scanning SQUID microscopy. because it enables higher currents to flow through the This allows local magnetic fields to be measured at the material before superconductivity is lost. surface of a sample. One of the most exciting potential applications of  Searching for submarines. When a submarine moves the Meissner effect is magnetic levitation (maglev) for through the water, the metal hull slightly disturbs the advanced high-speed transportation. Pilot maglev trains earth’s magnetic field and this small distortion can be that can reach speeds of more than 550 km/h have already measured. been developed in Japan, and other countries have plans  The human brain can be imaged by detecting small to develop maglev train services. The first U.S. maglev magnetic fields produced as a result of the currents due train was scheduled for the campus of Old Dominion to neural activity. This area of research is called University in Virginia with plans to complete construction magnetoencephalography (MEG) and is being used to by 2003. But the project has suffered a continuation of study epilepsy. major setbacks since then. Although ceramic superconductors have not been used for the generation of large magnetic fields, because it is difficult to form them into long wires, they have been 33.7 PARAMAGNETIC CERAMICS made into superconducting quantum interference devices (SQUIDs). The essential component of a SQUID is the The magnetic moment is due to unpaired electron spins. Josephson junction, a thin (∼1 nm) insulating layer between Magnetic susceptibilities are positive as shown in Table two superconductors through which weak supercurrents 33.5, because the magnetic moments line up with H and consisting of Cooper pairs can tunnel without an applied this leads to an increase in B. However, adjacent magnetic voltage. The insulating barrier can be a deposited thin film dipoles essentially behave independently; there is no inter- or, in the case of some of the ceramic superconductors, a action between them. It is this lack of an interaction that high-angle grain boundary (GB), such as that shown in separates paramagnetic materials from ferromagnets. Figure 14.37, which works well. Most first row transition metals, e.g., Ti and Cr, are A SQUID can be used paramagnetic because they to detect very small REFERENCE POINTS have unpaired electrons in (∼10−15 T) changes in B. −12 B = 10 T at the Earth’s surface. their 3d orbitals (see Table When a Josephson junc- 33.1). The number of tion is exposed to a mag- The human body produces a magnetic field of ∼10−10 T. unpaired electrons per netic field steps are atom is determined using produced in the I–V behavior. This is similar to what Hund’s rule (Section 3.5). happens when the junction is irradiated with microwaves Nontransition metals, e.g., Na, may be paramagnetic (as we showed in Chapter 30). Each step corresponds to due to the alignment of the spin moment of some of the a quantum change in B. Uses for SQUIDs include the valence electrons with the applied field. This effect, known following: as Pauli paramagnetism, is much weaker than that due to unpaired 3d electrons and involves electrons moving into  They can detect small changes in magnetic field a higher energy level and changing their spin direction. strength at the earth’s surface that can then be related This process can happen only if the gain in magnetic 3 3 .7 Pa r a m ag n e t i c C e r a m i c s ...................................................................................................................................... 603  + Co Fe Exchange χmag Interaction Ni 0 1.5 2.0 D d Mn - H FIGURE 33.6 The Slater–Bethe curve showing the magnitude and sign of J as a function of D/d. the sample by the magnetic field (as in the Gouy method) 0 T or on detecting currents induced in a circuit placed close FIGURE 33.5 Schematic showing how χ varies with T for a to the magnetic material. The main disadvantage of the paramagnetic solid. The insets indicate the direction of the Gouy method is that it requires quite a large sample (∼ magnetic dipoles in the solids. grams). energy is more than the energy needed for electron promo- 33.9 FERROMAGNETISM tion. Some oxides containing transition metal or rare earth ions, such as CeO2 and Cr2O3, are also paramagnetic. The origin of ferromagnetism, like paramagnetism, is the The temperature dependence of paramagnetic sus- presence of unpaired electron spins. However, in a ferro- ceptibility is shown in Figure 33.5 and follows the Curie magnetic material there is an interaction between adjacent law: dipoles. Of the first row transition metals only Fe, Co, and C Ni are ferromagnetic. So why is Cr paramagnetic not fer- χ= (33.9) romagnetic? The reason is due to a quantum mechanical T exchange interaction between the 3d orbitals on adjacent There are currently no commercial applications for atoms, which is represented mathematically by the paramagnetism. exchange integral, J. If J > 0 there is an interaction between adjacent magnetic dipoles causing them to line up and the 33.8 MEASURING c material is ferromagnetic (below the Curie temperature, θc). If J < 0 adjacent dipoles are antiparallel and the mate- The most straightforward way to obtain χ is the classical rial is antiferromagnetic (below the Néel temperature, Gouy method. The material, in the form of a rod, is θN). attached to one arm of a sensitive balance. It is then placed The magnitude and the size of J depend on the inter- between the poles of a magnet. If the sample is paramag- atomic separation, D, and the diameter, d, of the electron netic its energy is lower when it is inside the magnetic orbital under consideration as shown in Figure 33.6 (the field, and so there is a force, F, drawing it into the field. Slater–Bethe curve) for the case of the 3d orbitals of Fe, If the sample is diamagnetic its energy is less if it is Co, and Ni. outside the field, and so F is in the opposite direction. D can be determined simply by looking up the atomic Qualitatively the sign of χ can be determined by radius of the element and doubling it, e.g., for Fe r = whether the force on the sample (the apparent weight 0.124 nm and D = 0.248 nm. The value of d can be esti- change measured by the balance) is positive or negative. mated using Eq. Box 3.2 in Section 3.2. For the 3d orbitals We can quantify the value of χ using Eq. 33.10: of Fe r = 0.159 nm. Hence D/d is 1.56, as shown in Figure 33.6. J is more difficult to determine. It is related to the 1 overlap of the electron orbitals and involves integrating F = AχH 2 (33.10) the products of the wavefunctions for the electron orbitals 2 on adjacent atoms. where A is the cross-sec- If there is significant tional area of the sample. overlap of the 3d orbitals Other methods can be MEASURING c then, by the requirements used to determine magne- It is important to determine χ to know if a material is a of the Pauli exclusion prin- tization and susceptibility, superconductor. Having a very low electrical resistivity ciple, the spins must be but all rely either on mea- or an abrupt drop in resistivity is not a defining criterion. antiparallel (J < 0). If the suring the force exerted on A strong magnet has a large value of χ. separation is too large then 604 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data  1.0 Paramagnetic Paramagnetic χmag χ Msat (T) Msat (T=0) Paramagnetic Feromagnetic Feromagnetic 0 θc T 0 T 1.0 Antiferromagnetic θc (antiparallel spins) (A) (B) FIGURE 33.7 Schematic showing how (a) χ varies with T; (b) M varies with T for a ferromagnet. θN T FIGURE 33.8 Schematic showing how χ varies with T for an there is no appreciable interaction. However, in the case antiferromagnetic material. At θN it becomes paramagnetic. of iron, cobalt, and nickel the exchange interaction is large and positive and the electron spins are parallel. The magnetic susceptibility of a ferromagnetic mate- They all have the rocksalt (NaCl) structure and magnetic rial varies with temperature (Figure 33.7a) according to dipoles on adjacent {111} planes are antiparallel. The the Curie–Weiss law: magnetic interaction between the cations occurs indirectly through the oxygen ions and is known as a “superex- χ = C/(T − θc) (33.11) change” interaction. Along <100> there is overlap of the Ni dz2 orbitals and the O pz orbital as illustrated in Figure You will recognize this type of variation as being very 33.9. The Pauli exclusion principle governs the spin direc- similar to an order–disorder transition. Above θc the tion in the overlapping orbitals and, as a result, the adja- material become paramagnetic because of randomization cent Ni ions have opposed spins. of the spin magnetic moments. M decreases from its We have direct evidence of the orientation of the spin maximum value at 0 K and vanishes at θc as shown in magnetic moments in antiferromagnetic materials from Figure 33.7(b). neutron diffraction studies. Neutrons have a magnetic Chromium dioxide (CrO2) is at present the most impor- dipole moment. In neutron diffraction the neutron beam is tant ferromagnetic ceramic. It is used as magnetic media responding not only to atom positions but also to their in audio and video recording tapes. In this application, the magnetic moments. (X-rays give us information on atom CrO2 is not in the pure form but is usually doped to positions and electron distribution.) Above θN, the neutron improve its properties. diffraction pattern consists of reflections due to the peri- CrO2 has the rutile (TiO2) structure (Figure 6.11). The odic arrangement of the crystal structure. Below θN extra Cr4+ ions are located at the corners of the unit cell and reflections appear in the pattern because the neutrons there is a distorted CrO6 octahedron in the center. The are “seeing” two sets of cations, with different magnetic lattice parameters are a = 0.437 nm and c = 0.291 nm. CrO2 moments. The magnetic unit cell is therefore twice the size does not occur in nature and is usually manufactured by of the crystallographic unit cell as shown in Figure 33.10. thermal decomposition of CrO3 at ∼500°C under high Antiferromagnetism is not limited to oxides with a pressure (>200 MPa) in the presence of water. rocksalt structure. The following antiferromagnets have a corundum structure: 33.10 ANTIFERROMAGNETISM AND V2O3 (θN = 173 K) Ti2O3 (θN = 660 K) COLOSSAL MAGNETORESISTANCE α-Fe2O3 (θN = 950 K) Although the ceramics we have mentioned so far in In an antiferromagnet there is exact cancellation of the this section have no applications that use their magnetic magnetic moments. We can think of an antiferromagnetic material as consisting of two ferromagnetic lattices in which the spin magnetic moments are equal in magnitude [100] but opposite in direction. Above θN the antiferromagnetic spin alignments are randomized and the material becomes paramagnetic. The temperature dependence of the mag- netic susceptibility is shown in Figure 33.8. O The following oxides are antiferromagnetic: Ni Ni dz2 pz dz2 MnO (θN = 122 K) NiO (θN = 523 K) FIGURE 33.9 Overlap between Ni dz2 orbitals and O pz orbitals in CoO (θN = 293 K) FeO (θN = 198 K) Ni. 3 3 .10 A n t i f e r r o m ag n e t i s m a n d C o l o s s a l M ag n e t o r e s i s ta n c e ........................................................................ 605  Ferromagnetic: A A A A B B B Antiferromagnetic: A A A Ferrimagnetic: Magnetic unit Chemical unit cell length 2a cell length a A B A B A B A FIGURE 33.11 Schematic comparing dipole alignments in ferromagnetic, antiferromagnetic, and ferrimagnetic materials. FIGURE 33.10 Comparison of structural and magnetic unit cells of NiO. the magnetic moments are not of the same magnitude they only partially cancel each other and the material has a net M. Ferrimagnetism has several similarities to ferromagne- properties, there are manganate ceramics in the tism in that the cooperative alignment between magnetic La1−xA xMnO3 (0 ≤ x ≤ 1; A = Sr, Ca, Ba) system that are dipoles leads to a net magnetic moment even in the absence antiferromagnetic and exhibit colossal magnetoresistance of an applied field. Ferrimagnetism is lost above θc. The (CMR). In CMR the resistance drops dramatically in an difference between ferromagnetism, antiferromagnetism, applied magnetic field. It is related to, but much greater and ferrimagnetism in terms of the spin alignments is than, giant magnetoresistance (GMR) found in multilayers illustrated in Figure 33.11. of ferromagnetic and The easiest way to con- nonferromagnetic metals sider what happens in a (e.g., 30 Co/Cu bilayers). ZnFe2O4 ferrimagnet is to look at III II III 3+ In these structures there is In ZnFe 2O4 [Fe (Zn Fe )O4] all the magnetic Fe are the prototypical ferromag- an interaction between the on octahedral sites and are separated by a plane of O2− netic material, magnetite. ferromagnetic layers that ions. The material is antiferromagnetic because the Magnetite has an inverse can cause antiferromag- superexchange interaction involving the two Fe3+ ions spinel structure (Section netic ordering of magnetic resembles that shown in Figure 33.9. 7.2). The formula can be moments in adjacent layers. written as FeIII(FeIIFeIII)O4, So individually each Co layer is ferromagnetic, but the i.e., in the classic spinel form AB2O4. The Fe2+ ions and multilayer structure is actually antiferromagnetic. The half of the Fe3+ ions are in octahedral sites and the other extent of the interaction depends on the thickness of the half of the Fe3+ cations are in tetrahedral sites. The spins nonferromagnetic layer and H. All current hard disk drives of the Fe ions on the octahedral sites are parallel, but of make use of this technology. a different magnitude. The spins of the Fe ions on the The manganates have the layered perovskite structure tetrahedral sites are antiparallel to those in the octahedral similar to that found in the YBCO superconductor (see sites. The situation is illustrated in Figure 33.12, which Section 7.16). This similarity is particularly interesting shows one-eighth of the magnetite unit cell. The align- and may lead to increased understanding of both types of ment of the spins is the result of an exchange interaction material. The nature of the interactions in the manganites involving the O2− ions. The antiparallel alignment of the is complicated. They show a metal–insulator transition Fe3+ ion in the octahedral site and the Fe3+ ion in the tet- and a ferromagnetic–antiferromagnetic transition associ- rahedral site is usually explained by a superexchange reac- ated with CMR. tion similar to that used to explain antiferromagnetism. A mechanism to account for the parallel spin align- ment between the Fe3+ in the octahedral site and the octa- 33.11 FERRIMAGNETISM hedrally coordinated Fe2+ was proposed by Zener and is called the “double exchange” mechanism. The idea is that In a ferrimagnet the magnetic moments of one type of ion an electron from the Fe2+ ion (3d6) is transferred to the on one type of lattice site in the crystal are aligned anti- oxygen in the face-centered position of the subcell shown parallel to those of ions on another lattice site. Because in Figure 33.12. At the same time there is transfer of an 606 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data  Fe2+ (3d6) O2– (2p6) Fe3+ (3d5) Fe3+ (5μB)oct Fe2+ (4μB) Before Fe3+ (3d5) O1– (2p5) Fe2+ (3d6) O2– After FIGURE 33.13 Illustration of the double exchange interaction in magnetite. Fe3+ (5μB)tet spinels and their properties. The magnetic moments in this 0.419 nm table were calculated taking account of only the number FIGURE 33.12 Subcell of magnetite showing the location of Fe of unpaired 3d electrons; the units are Bohr magnetons ions and their spin moments. and the minus sign denotes an antiferromagnetic coupling. The most important and widely studied magnetic electron with parallel spin to the Fe3+ ion. The process is garnet is yttrium–iron garnet (YIG), which has the formula illustrated in Figure 33.13 and shares similarities with the Y3Fe2 (FeO4)3 [remember garnet is Ca3Al2 (SiO4)3]. We electron-hopping model of conduction in transition metal can write the formula of YIG as Y3c Fea2 Fed3O12 where oxides. (Note: a requirement of Zener’s model is that the the superscripts refer to the type of lattice site occupied cations have different charges.) by each cation. The cell shown in Figure 33.14 is actually Ferrimagnetic ceramics have the spinel (almost exclu- one of the eight subcells that form the YIG unit cell, sively inverse), the garnet, or the magnetoplumbite struc- which contains 160 atoms. In the subcell the a ions are ture. Table 33.6 lists some examples of ferrimagnetic in a body-centered cubic (bcc) type arrangement with the TABLE 33.6 Magnetic Properties of Several Ferrimagnetic Ceramics Calculated moments B sat (T) Material q c (K) at RT T site O site Net Experimental Spinel ferrites [AO · B2O3 ] Fe3+ [Cu2+ Fe3+ ]O4 728 0.20 −5 1.73 + 5 1 1.30 Fe3+ [Ni2+ Fe3+ ]O4 858 0.34 −5 2 + 5 2 2.40 Fe3+ [Co2+ Fe3+ ]O4 1020 0.50 −5 3 + 5 3 3.70–3.90 Fe3+ [Fe2+ Fe3+ ]O4 858 0.60 −5 4 + 5 4 4.10 Fe3+ [Mn2+ Fe3+ ]O4 573 0.51 −5 5 + 5 5 4.60–5.0 Fe3+ [Lio.5Fe1.5]O4 943 −5 0 + 0.75 2.60 Mg 0.1Fe0.9 [Mg 0.9Fe1.1]O4 713 0.14 0–4.5 0 + 5.5 1 1.10 Hexagonal ferrites BaO : 6Fe2O3 723 0.48 1.10 SrO : 6Fe2O3 723 0.48 1.10 Y2O3 : 5Fe2O3 560 0.16 5.00 BaO : 9Fe2O3 718 0.65 Garnets YIG{Y3 }[Fe2]Fe3O12 560 0.16 5 4.96 (Gd3)[Fe2]Fe3O12 560 16 15.20 Binary oxides EuO 69 6.8 CrO2 386 0.49 2.00 3 3 .11 F e r r i m ag n e t i s m ................................................................................................................................................... 607  and d ions. For every two Fe3+ on a sites, there are three Fe3+ ions on d sites giving a measured magnetic moment of ∼5 μB. Tetrahedron The mineral magnetoplumbite has the approximate composition PbFe7.5Mn3.5Al0.5Ti0.5O19. The commercially Fe ion important ferrimagnetic ceramic barium hexaferrite (BaO · 6Fe2O3) is isostructural with magnetoplumbite. A Fe ion schematic of the crystal structure of BaO · 6Fe2O3 is shown in Figure 33.15. The hexagonal unit cell is very large and contains 64 atoms. Magnetization is easiest along the c axis. Also shown in Figure 33.15 is a simplified repre- sentation of the spin magnetic moments of the Fe3+ Octahedron ions in BaO · 6Fe2O3. The actual arrangements are more Dodecahedron complicated. FIGURE 33.14 Structural units in a subcell of YIG. For clarity not There is a range of hexagonal ferrimagnetic ceramics all the atoms are shown and only one of each example of the containing BaO. These are usually classified based on polyhedra is shown. their chemical formula: c and d ions lying on the cube faces. Each a ion is in an  M-type compounds, (MO)(Fe2O3) 6, e.g., octahedral site, each c ion is on a dodecahedral site, and (BaO)(Fe2O3) 6 each d ion is on a tetrahedral site as illustrated in Figure  W-type compounds, (BaO)(MO) 2 (Fe2O3) 8 or M2W, 33.14. e.g., (BaO)(CoO) 2 (Fe2O3) 8 The net magnetic moment in YIG, as in other ferri-  Y-type compounds, (BaO)2 (MO) 2 (Fe2O3) 6 or M2Y, magnetic ceramics, arises from an uneven contribution e.g., (BaO) 2 (MnO)2 (Fe2O3) 6 from antiparallel spins; the magnetic moments of the a  Z-type compounds, (BaO)3 (MO) 2 (Fe2O3)12 or M2Z, and d ions are aligned antiparallel as are those of the c e.g., (BaO)3 (MgO) 2 (Fe2O3)12 5μB Hexahedral site 5μB Fe3+ A Tetrahedral site B Fe3+ A A Fe3+ C Orientation of the B B spin moments Octahedral site 5μB A A A C C B B B 0001 B A A A A Cubic z C A C Ba2+ c = 2.32 nm z A Stacking the Cubic oxygen planes C B A B Ba2+ Hexagonal A Hexagonal B A A A B B x a = 0.588 nm A A A x B B B A A A A FIGURE 33.15 Schematic of the barium ferrite crystal structure showing the structural units and the magneti- zation directions. 608 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data  TABLE 33.7 Magnetic Properties of Fe in Magnetic Ceramics Ion Number Site Spin direction Ion moment (μB) Total moment (μB) Fe2+ 1 Octahedral 4 4 Fe3+ 1 Octahedral 5 5 Fe 3+ 1 Tetrahedral 5 −5  X-type compounds, (BaO) 2 (MO) 2 (Fe2O3)14 or M2X, therefore they are often named after him. Within each e.g., (BaO)2 (FeO) 2 (Fe2O3)14 domain the direction of magnetization is the same. When  U-type compounds, (BaO) 4 (MO) 2 (Fe2O3)18 or M2U, the material is in its unmagnetized state the net magneti- e.g., (BaO) 4 (ZnO) 2 (Fe2O3)18 zation is zero, i.e., there are as many domains magnetized in one direction as there are in the antiparallel direction. 33.12 ESTIMATING THE MAGNETIZATION This situation is illustrated for several different domain OF FERRIMAGNETS structures in Figure 33.16. The energy of the material is lowered when the domains are smaller. For the configura- We can estimate saturation values of M and B by knowing tions shown in Figure 33.16 the overall energy decreases the crystal structure and lattice parameter of the material from left to right. The triangular domains are called and the orientation of the spin magnetic moments. We will closure domains and complete the magnetic flux path with illustrate this approach for magnetite. The magnetic the solid; this also lowers the overall energy. moments of each type of In the boundary region ion are summarized in between the different DOMAIN WALL domains there is a gradual 3+ Table 33.7. The Fe ions Typically the domain wall has a thickness of about −3 change in magnetic dipole interact antiferromagneti- 100 nm and an energy of ∼10 J/m . 2 orientation as illustrated in cally and the net magnetic moment is due only to the Figure 33.17. The bound- Fe2+ ions. Using Eq. Box 33.3 we can calculate the mag- ary regions are known as domain walls or Bloch walls after netic moment of an Fe ion as 4.9 μB. There are eight Fe 2+ 2+ the man who did much of the early work on this subject. ions per unit cell so the total magnetic moment per cell is The thickness of the domain wall is a tradeoff between the 8 × 4.9 = 39.2 μB. requirement for a small angle between adjacent spins, M is therefore which would necessitate a thick wall, and the tendency for the magnetic dipoles to be aligned with a specific crystal- 39.2 [μB] × 9.27 × 10−24 [A·m2 μB−1]/(0.837 × 10−9 [m])3 lographic orientation, requiring a thin wall. = 6.17 × 105 A/m There is also a domain structure in antiferromagnetic materials, with wall separating each domain: which is in fairly good agreement with the measured value of 5.3 × 10−5 A/m.  In S walls the magnetization direction is rotated across B is the wall.  In T walls there is a change in orientation characteris- −7 BS = μ0 Ms = 4π × 10 × 6.17 × 10 = 0.78 T 5 tic of twinning. This value is close to the measured value of 0.6 T. An interesting characteristic of both these values is that if the classical value of the spin magnetic moment is taken for Fe2+ , i.e., 4 μB, then both M and B are closer to the mea- sured values, even though for isolated cations Eq. Box 33.3 provides much better agreement with the experimental data. The reason for this discrepancy is not obvious. 33.13 MAGNETIC DOMAINS AND BLOCH WALLS A ferromagnetic or a ferrimagnetic material is divided into many small regions or domains. Pierre Weiss was the FIGURE 33.16 Examples of domain structures, each having zero first to recognize the presence of magnetic domains and net magnetization. 3 3 .1 3 M ag n e t i c D o m a i n s a n d B l o c h Wa l l s ........................................................................................................... 609  Domain wall Domain wall N N N N FIGURE 33.18 Magnetic domains on the basal surface of a hexagonal ferrite, Co2Ba2Fe28O46, revealed by the Bitter technique. FIGURE 33.17 Change in magnetic dipole orientation through a domain wall. All moments lie in the plane of the wall. The effect of M on the reflected light intensity is known as the Kerr effect. The polar Kerr effect refers to a situa- 33.14 IMAGING MAGNETIC DOMAINS tion in which the sample has a component of M normal to the surface and normal incidence illumination is used. There are many different ways to image magnetic domain The longitudinal Kerr effect is used when M is parallel to structures in a material. All the “microscopy” techniques the surface and the illumination is oblique. we described in Chapter 10 can be used, although, in some cases, deviations from the usual operating procedure are necessary to obtain the desired images. It is also possible Magnetic Force Microscopy (MFM) to use X-ray topography to study magnetic domains. In Magnetic force microscopy is closely related to scanning this section, we will briefly describe three techniques: the tunneling microscopy (STM) and atomic force micro- oldest, one of the newest, and the trickiest. scopy (AFM). In MFM the tip is coated with a ferromag- netic thin film that detects magnetic force variations on Visible Light Microscopy (VLM) the sample surface. The tip is scanned over the surface of Examination of a magnetic material by simple VLM will the sample (it does not actually touch) as in STM. Interac- not reveal any information about the domain structure tions between magnetic domains in the sample and the because the direction of magnetization does not change ferromagnetic coating result in a force on the tip, which the appearance of the surface in any way. Transmitted light requires that the specimens are transparent and so very thin (<0.1 μm) samples must be used. The first approach, known as the Bitter technique, “decorates” the domain boundaries with magnetic particles suspended in a liquid. The particles are attracted to where the domain boundaries intersect the surface and this allows the domain pattern to be observed. The Bitter technique is applicable to all types of magnetic material, but specimen preparation is impor- tant to avoid introducing surface strains that can distort the domain structure. A Bitter pattern obtained in the hexago- nal ferrite Co2Ba2Fe28O46 is shown in Figure 33.18. An alternative means of observing magnetic domain structures in the VLM is to use polarized light. Domains magnetized in opposite directions will rotate the plane of polarization in opposite senses. Using an appropriate ana- lyzer it is possible to vary the intensity of the light coming from each domain and produce corresponding intensity changes in the image. The effect of M on the transmitted light intensity is called the Faraday effect. The Faraday effect in a thin film of a substituted YIG, (BaTb)3 (FeGa)5O12, FIGURE 33.19 Domain pattern in a YIG thin film revealed by the is shown in Figure 33.19. Faraday effect. The stripes are 12 μm wide. 610 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data  Saturation B – =μ B Permeability = H Random Domains rotate B increases slowly zed neti ly mag ack Slope = μmax form n tr Uni itte Wr Domains grow faster zed B increases faster neti ly mag form Uni Random Slope = μinitial FIGURE 33.20 Schematic of MFM of a magnetized pattern on a B increases slowly hard drive. H FIGURE 33.21 The effect of H on B. The ratio is μ. depends upon the orientation of the domains. Different orientations produce a different force and this is how the When the field is removed, there is a resistance to different magnetized regions can be determined. Figure domain wall motion preventing reorientation of the 33.20 illustrates how an MFM image of a magnetic tape domains. As a result there is a residual magnetization, would appear. The bright and dark stripes in the center of known as remanence (Br), and the material acts as a per- the image are regions where the direction of magnetiza- manent magnet. tion is different. If H is then applied in a direction opposite to what was originally used then domains grow with an alignment in Transmission Electron Microscopy (TEM) the new direction. A certain field, called the coercive field, Hc, is needed to completely randomize the domains. Because electrons are charged they experience a force— Further increases in H eventually align the domains to the Lorentz force—as they move through a magnetic field. saturation in the new direction. The behavior of a ferro- This force causes them to be deflected by a small angle. magnetic or a ferrimagnetic material in an alternating The deflections are in different directions in different magnetic field is shown in Figure 33.22. The size of the domains. The domain walls cannot be imaged under normal bright-field imaging conditions but they can be seen by either underfocusing or overfocusing the image 3 (Fresnel images) or by displacing the objective aperture 4 B (Foucault images). Bs BR 33.15 MOTION OF DOMAIN WALLS AND HYSTERESIS LOOPS 5 2 When an external magnetic field is applied to a ferromag- Coercive netic or ferrimagnetic material the domain boundaries field begin to move. They move in such a way that domains in -H H H which the magnetization direction is aligned with H grow at the expense of the unaligned domains. The change in B with H is shown in Figure 33.21. Initially the movement 6 1 of the domain walls is reversible and B increases only slightly with increasing H. As the field increases the favor- ably oriented domains grow more easily and μ increases. -BR At very large H the unaligned domains will rotate and FIGURE 33.22 The variation of B as H alternates. The insets saturation will be reached in which all the domains are illustrate the domain structure at various points along the aligned in the same direction. hysteresis curve. 3 3 .1 5 M o t i o n o f D o m a i n Wa l l s a n d H y s t e r e s i s L o o p s ...................................................................................... 611  TABLE 33.8 Classes of Magnetic Ceramic Structure Composition Applications Spinel (cubic ferrites) 1 MeO : 1Fe2O3 Soft magnets MeO = transition metal oxide, e.g., Ni,Co, Mn, Zn Garnet (rare earth 3 Me2O3 : 5Fe2O3 Microwave devices ferrites) Me2O3 = rare earth metal oxide, e.g., Y2O3, Gd2O3 Magnetoplumbite 1 MeO : 6Fe2O3 Hard magnets (hexagonal ferrites) MeO = divalent metal oxide from group IIA; e.g., BaO, CaO, SrO hysteresis loop, i.e., the values of Br and Hc, vary from magnetic domains (by, for example, controlling the grain material to material. size so that each grain becomes a single domain). Barium ferrite and oxides with a magnetoplumbite structure are  When Hc is small (typically <103 A/m) the material is the preferred choice. a soft magnet. Philips introduced ferrite magnets commercially in  When Hc is large (typically >>103 A/m) the material is 1952 under the trade name “Ferroxdure.” About 550,000 t a hard magnet. of hard ferrites are produced annually (>95% of the hard magnet market). This is more than metallic magnets. Hard and soft do not have any connection to the mechani- There are a number of reasons why ferrite magnets are cal properties of the material. There are examples of commercially so important, not least of which is that the metals and ceramics that exhibit hard and soft behavior. raw materials are relatively cheap and widely available and the manufacturing processes are simple. Hard ferrite magnets are found in the following: 33.16 HARD AND SOFT FERRITES  Starter motors in automobiles The important ferrimagnetic ceramics form three groups  Loudspeakers depending on their crystal structures as summarized in  Rotors for cycle dynamos Table 33.8. When we are considering possible applications  Windscreen wiper motors it is more useful, at least to the engineers who are design-  Mixed with a flexible polymer in door-catches and ing and building magnetic components, to specify the decorative magnets for refrigerators materials as hard or soft. These designations, as men- tioned in Section 33.15, are based on the size of the B–H hysteresis loop, i.e., on the difficulty in reversing the direc- tion of magnetization for the material. Hysteresis loops for B hard and soft magnetic materials are compared schemati- cally in Figure 33.23. Hard Convention: magnetic oxides that contain Fe3+ ions are called ferrites. This terminology does not distinguish Soft between the crystal structures; do not confuse it with the chemical name. We often say that ferrites contain Fe2O3 as a principal component. H Hard Ferrites Hard ferrites, which are used to fabricate permanent magnets, must have large  Hc  Br To satisfy these requirements, it is necessary to use materials with crystal structures that exhibit a large mag- FIGURE 33.23 Comparison of the size and shape of hysteresis netic anisotropy and to prevent the growth and rotation of loops for hard and soft magnets. 612 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data  TABLE 33.9 Properties of Several Hard Magnets Composition Hc (BH) max Material (wt%) B r (T) (A-turn m −1) (kJ/m 3) q c (°C) r (W · m) Tungsten steel 92.8 Fe 0.95 5,900 2.6 760 3.0 × 10 −7 6W 0.5 Cr 0.7 C Cunife 20 Fe 0.54 44,000 12 410 1.8 × 10−7 20 Ni 60 Cu Sintered alnico 34 Fe 0.76 125,000 36 860 — 7 Al 15 Ni 35 Co 4 Cu 5 Ti Sintered ferrite BaO–6Fe2O3 0.32 240,000 20 450 ∼104 Cobalt rare earth SmCo5 0.92 720,000 170 725 5.0 × 10 −7 Sintered neodymium– Nd2Fe14B 1.16 848,000 255 310 1.6 × 10 −6 iron–boron  DC motors in fuel pumps the presence of inclusions or pores within the grains,  Household appliances such as electric shavers, food impurity levels, and stresses all reduce domain wall mixers, and coffee grinders motion. Porosity is particularly common in many sintered  Magnetic strips on credit cards, ATM cards, etc. ceramics and ferrites are certainly no exception. As a result magnetization rotation plays an important role in Table 33.9 compares some of the important properties reaching Bs. Soft ferrites should also have high electrical of hard ferrites with hard metal alloy magnets such as resistivities (not a problem for most ceramics!) because alnico and high-energy (BH ≥ 80 kJ/m3) rare earth magnets this limits eddy current losses. such SmCo5. Soft ferrites are generally used in applications in which the direction of H is frequently changing such as high- frequency inductors and transformers and magnetic ele- Soft Ferrites ments in microwave components. There are plenty of The prime requirement for a soft ferrite is that a high M household examples in which soft ferrites are used: can be produced using a small H. This means that soft ferrites should have  Magnetic recording and data storage media  Transformer cores in telephones  High μ  Numerous applications in radios and televisions, such  Low Hc as line transformers, deflection coils, tuners, and rod antennas Soft ferrites therefore have narrow hysteresis loops. During changes in field direction the domains are rapidly Table 33.10 compares some of the relevant properties and easily realigned with the changing magnetic field. of metal and ceramic soft magnets. Spinel ferrites based Consequently, domain wall motion and/or magnetization upon the (Mn,Zn,Fe)O4 system are examples of commer- rotation must be easy. Domain wall motion is particularly cially important soft magnets. The market for soft ferrites sensitive to the microstructure of the material and charac- is about 50,000 t per year. These are usually marketed teristics such as grain size and grain-boundary structure, under the trade name Ferroxcube. TABLE 33.10 Properties of Several Soft Magnets Hysteresis Material Composition (wt%) mi B s (T) loss/cycle (J/m 3) r (W · m) Iron 99.95 Fe 150 2.14 270 1.0 × 10 −7 Silicon-iron 97 Fe, 3 Si 1,400 2.01 40 4.7 × 10−7 (oriented) 45 Permalloy 55 Fe, 45 Ni 2,500 1.60 120 4.5 × 10 −7 Supermalloy 79 Ni, 15 Fe, 5 Mo, 0.5 Mn 75,000 0.80 — 6.0 × 10 −7 Ferroxcube A 48 MnFe2O4, 52 ZnFe2O4 1,400 0.33 ∼40 2,000 Ferroxcube B 36 NiFe2O4, 64 ZnFe2O4 650 0.36 ∼35 107 3 3 .16 H a r d a n d S o f t F e r r i t e s ................................................................................................................................... 613  Garnets also tend to be soft magnets but are not as 3 mm). As they travel along the waveguide their behavior widely used as the cubic ferrites: they are more expensive. is modified. There was a great deal of interest in the late 1960s and An important example is known as Faraday rotation, 1970s in magnetic garnets for use in bubble memory. A which involves the rotation of the plane of polarization of magnetic bubble is a small (from about 0.05 μm up to a plane wave as it travels through the waveguide. A plane- 10 μm) cylindrical region, which has M in the opposite polarized wave is equivalent to two circularly polarized direction to H. waves, polarized in opposite senses (i.e., a right-polarized A bubble memory is nonvolatile, which means that and a left-polarized component). Each component inter- once information is stored it remains even when the power acts very differently with the precessing spins and encoun- is removed (just like current hard drives). Bubble memo- ters different permeabilities, which affect the velocities of ries used a thin layer (usually about 4 μm) of a magnetic the two waves. The left component is retarded relative to garnet (a typical formulation being Y2.6Sm0.4Ga1.2Fe3.8O12) the right, causing a clockwise rotation of the plane of deposited by liquid phase epitaxy onto a substrate of gado- polarization. linium gallium garnet (GGG). The strain induced by the The most direct application of Faraday rotation is to lattice misfit and differences in the coefficient of thermal use waveguides in the same way that polarizers and ana- expansion between the two garnets resulted in an aniso- lyzers are used in light optics: to accept or reject plane tropic axis normal to the film. polarized waves. By the mid-1970s most of the large electronic compa- There are several different types of microwave devices. nies were working on bubble memories and by the late Isolators allow transmission of microwave radiation in one 1970s there were several commercial products. By the direction (they are used to prevent unwanted reflected 1980s the bubble memory market was dead. One of the signals). Gyrators are used to rotate the plane of reasons was the introduction of larger and faster hard polarization. There are other, more complicated devices, drives. such as phase shifters and circulators. Garnets are widely used in microwave engineering because their properties can be tailored for the specific application. A 33.17 MICROWAVE FERRITES garnet that is currently used in radar phase shifters is Y2.66Gd0.34Fe4.22Al0.68Mn0.09O12. When a magnetic field is applied to a spinning electron it Microwave ferrites are used in radar-absorbing paint, precesses around the field direction in much the same way which is used to make planes such as the F-117 Nighthawk that a spinning top precesses around the direction of a and the B-2 Spirit “stealthy.” gravitational field. In ferromagnetic and ferrimagnetic materials the electron spins are coupled and the magneti- zation vector, M, will precess around the field direction as 33.18 DATA STORAGE AND RECORDING shown in Figure 33.24. The interaction between electro- magnetic waves and the precessing spin magnetic moments Magnetic recording is a major technology for electronic in the ferrite has been used to make waveguides for micro- information mass storage. Its presence is ubiquitous in waves. Microwaves are electromagnetic radiation with audio and video cassette tapes, floppy disks, computer frequencies in the range of 1–300 GHz (λ = 30 cm to hard disks, credit cards, etc. The magnetic audio recorder was invented in 1898. Video recorders were first introduced in 1955 primarily for use by broadcasters before they became widely available for commercial use. H Hz Now magnetic recording equipment has spread to almost every household with sales exceeding $50 billion per year. Hrf Magnetic recording materials such as magnetic tapes and floppy disks are collections of very fine magnetic particles supported on a flexible polymer such as polyeth- Spiralling Maintain ylene terephthalate (PET). The basic features of magnetic into line M with recording are illustrated in Figure 33.25. A minute part of as energy applied M dissipates rf energy the magnetic tape is magnetized by a signal from a mag- netic head and data are stored in a form of the magnetiza- tion direction. The properties of the material used for this θ θ purpose are quite specific:  Hc must be high enough to maintain magnetization but FIGURE 33.24 Illustration of the precessional motion of the sufficiently low to allow stored data to be erased magnetization vector.  Chemically stable 614 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data  Direction of tape movement much higher Hc than γ-Fe2O3. This makes CrO2 more suit- able for high-density recording. It also has a high M giving a large range of response and thus a high quality of repro- duction. The small particle size and the very uniform particle size distribution mean that CrO2 tapes have much Width Ferrite particles Gap lower noise (less background hiss on audio tapes; less Read/Write Head “snow” on video pictures). Chromium dioxide is widely used in tapes for videocassettes and for professional audio- FIGURE 33.25 Illustration of the principal features of longitudinal tapes. The drawbacks of CrO2 are recording.  Low θc  Toxicity  Small (<1 μm), uniformly distributed acicular  It is abrasive to some types of recording head particles  Magnetic properties degrade slowly with time  Uniform distribution of particles  Cheap But the main drawback that prevented its more widespread Three types of ceramic particles are currently used as use in audiotapes is that it is more expensive than magnetic media: γ-Fe2O3, Co-γ-Fe2O3, and CrO2. Their γ-Fe2O3. properties are given in Table 33.11. Iron oxide particles Ferrites can be used to store a considerable amount of were first used in magnetic recording in the 1930s and information, but in many applications are being replaced now account for 90% of this market. The standard method by optical information storage such as CDs and DVDs. for making γ-Fe2O3 involves dehydrating goethite (α- Magnetic materials are used in the read and write FeOH) to hematite (α-Fe2O3) followed by reducing the heads of magnetic storage drives. The most significant hematite to magnetite (Fe3O4) and finally oxidizing the change since the beginning of this technology and the use magnetite to maghemite (γ-Fe2O3). of conventional recording heads using magnetic induc- Various experimental tance was the introduction modifications have been of magnetoresistive (MR) made to the process over MAGHEMITE and then GMR recording the years to produce γ- The name maghemite was first suggested in 1927. It is heads. These allowed data Fe2O3 particles that have a combination of the first syllables of magnetite, which to be stored more densely the required shape and has the same structure, and hematite, which has the and read more quickly. uniformity for use as mag- same composition. GMR is now used in most netic media. The γ-Fe2O3 modern hard drives. particles typically have lengths in the range of 100–700 nm Ceramic CMR materials may produce the next big change. and aspect ratios up to 10. Hc of γ-Fe2O3 is at the low end In CMR resistance does not change by a few percent but of the useful range for magnetic recording. As a result it by orders of magnitude. Applications for these materials is more useful at recording signals in the low frequency are being developed. range. Cobalt-modified γ-Fe2O3 particles were developed The use of barium ferrite for high-density recording to increase Hc. These particles were widely used in audio- applications has been investigated because it is chemically cassette tapes (before the advent of CDs and iPods) and stable and can have Hc ∼480 kA/m. The hexagonal parti- also on some videocassette tapes. The reason for the cles can, in principle, be oriented with their c axis normal higher Hc is not well understood. to the tape surface as shown in Figure 33.26. This is The process for producing chromium dioxide (CrO2) known as a perpendicular medium and can give very high particles for magnetic media was developed by the DuPont recording densities. Hexagonal ferrites are used in the Company in the 1960s. Because of the higher uniformity magnetic strips on credit cards and ATM cards. In these in size and shape of the particles CrO2 tends to have a applications we want the data to be permanent. TABLE 33.11 Physical and Magnetic Properties of Magnetic Particles Magnetic Particle Specific surface particle length (mm) Aspect ratio area (m 2 /g ) H c (kA/m ) B s (T) q c (°C) γ-Fe2O3 0.3–0.6 10 20–30 20–32 0.5 675 Co–γ-Fe2O3 0.3–0.4 10 20–30 30–70 0.5 400 CrO2 0.2–0.7 10–20 24–40 30–50 0.5 113 Fe (metal) 0.2–0.4 ∼6 40–50 75–130 2.0 770 3 3 .18 Data S t o r ag e a n d R e c o r d i n g ......................................................................................................................... 615  easy M +, M –: magnetization axis Ba-ferrite hexagonal M+ platelet – M 80 nm + M M– Hd λ FIGURE 33.27 Diagram of a viral-induced nanoassembly of magnetic nanoparticles. H d: demagnetization field 33.27. Iron oxide particles (∼50 nm in diameter) with a dextran coating are covered with antibodies. The antibod- FIGURE 33.26 The principle of perpendicular recording. ies are chosen for a specific virus (e.g., herpes simplex virus or adenovirus). When these specially coated nanoparticles are then exposed to the virus they will form 33.19 MAGNETIC NANOPARTICLES clusters that would be large enough to be visible on a nuclear magnetic resonance (NMR) or magnetic reso- Magnetic ceramic nanoparticles are becoming of increas- nance imaging (MRI) scan. This approach has already ing interest in a number of areas. One of these areas is been demonstrated in the laboratory using viral particles using them for the location and detection of viruses: a in solution. The idea is that it might eventually be used to viral nanosensor. The approach is illustrated in Figure detect viruses in human body fluid or tissue. CHAPTER SUMMARY In this chapter we described the different magnetic properties of ceramics. Most ceramics are diamagnetic, a very weak and commercially unimportant property. The most important mag- netic properties of ceramics arise because of the presence of unpaired electron spins, primarily in the 3d orbitals of Fe. Ferrites, a class of magnetic ceramics containing Fe2O3, are used in a wide variety of applications, and their production constitutes a multibillion dollar industry. Ferrites can be classified according to their structure, and there are three structural types: spinel or cubic ferrites, garnets, and hexagonal ferrites. The cubic ferrites, of which γ-Fe2O3 (maghemite) is the most ubiquitous example, are soft magnetic materials and hence the direc- tion of magnetization can be relatively easily changed in an alternating magnetic field. Maghemite was used extensively in audiotapes and floppy disks (which have now largely been replaced by iPods and CDs). The magnetic garnets are used in microwave applications includ- ing ingredients on radar-absorbing paint for stealthy airplanes. The hexagonal ferrites, such as BaO · 6Fe2O3, are hard or permanent magnetic materials. They are more difficult to demagne- tize. Barium hexaferrite is used in many applications from small electric motors in automobiles, to the magnetic seal on a refrigerator, to the magnetic strip on credit cards. Manganates, which have the technologically important layered perovskite structure, exhibit a property called colos- sal magnetoresistance and offer potential in a number of technologies from read/write heads in magnetic recording, sensors, and spin-polarized electronics. PEOPLE IN HISTORY Bitter, Francis (1902–1967) was born in Weehawken, New Jersey. In 1931 he discovered a method for visual- izing magnetic domains. In 1934 he joined the Department of Mining and Metallurgy at M.I.T (where he spent most of his career) and helped establish a high field magnet laboratory. During WW II, he worked in England on methods to demagnetize German mines in the English Channel. His work after the war led to the establishment of the National Magnet Laboratory, which after his death was renamed the Francis Bitter National Magnet Laboratory. Bloch, Felix (1905–1983) was born in Zurich, Switzerland. He received his Ph.D. in 1928 from the University of Leipzig where he worked with Heisenberg. Upon Hitler’s rise to power Bloch left Europe and moved to the United States where he accepted a position at Stanford University. He was awarded the 1952 Nobel Prize in Physics for the development of the NMR technique. 616 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data  Curie, Pierre (1859–1906) was born in Paris. In 1895 he obtained his Doctor of Science degree and was appointed Professor of Physics at the Sorbonne. In his early studies on crystallography, together with his brother Jacques, he discovered the piezoelectric effect. Later, he turned his attention to magnetism and showed that the magnetic properties of a given substance change at a certain temperature (the Curie temperature). He was awarded the Nobel Prize in physics in 1903 (together with his wife Marie) for their work in radioactivity. On April 19, 1906 he was killed in a street accident in Paris. GMR was discovered in 1988; CMR was discovered in 1993. Josephson, Brian David (1940– ) was born in Cardiff, Wales and discovered the Josephson effect while a 22- year-old graduate student at the University of Cambridge. He won the Nobel Prize in physics in 1973 for his discovery. Lenz (pronounced lents), Heinrich Friedrich Emil (1804–1865) was born in Dorpat, Russian Empire (now Tartu, Estonia) and formulated his eponymous law of electromagnetism in 1833. He participated in a round-the-world expedition in 1823–1826 and made extremely accurate measurements of the properties of seawater. London, Fritz (1900–1954) was born in Breslau, Germany (now Wroclaw, Poland). He fled Nazi Germany in 1933 and came to the United States in 1939 where he became naturalized in 1945. Together with his younger brother Heinz he formulated the London equations of superconductivity. Meissner, Walther (1882–1974) and his graduate student Robert Ochsenfeld (1901–1993), both Germans working in Berlin, discovered in 1933 that a superconducting material repels a magnetic field—behaving as a perfect diamagnet. The effect became known as the Meissner (or Meissner–Ochsenfeld) effect. Oersted, Hans Christian (1777–1851) was a Danish physicist and philosopher. He demonstrated the funda- mental relationship between electricity and magnetism on July 21, 1820 during a lecture on electricity at the University of Copenhagen. He showed that a compass needle is deflected when a wire carrying an electric current is placed near it. In addition to his work in electricity and magnetism, Oersted was the first to prepare pure metallic aluminum (1825). Weiss, Pierre Ernest (1865–1940) was born in Mulhouse in the Alsace region of eastern France. He proposed the domain theory of ferromagnetism in 1907 while he was working at the Polytechnic Institute in Zurich. GENERAL REFERENCES Cullity, B.D. (1972) Introduction to Magnetic Materials, Addison-Wesley, Reading MA. A standard, but now dated, text on magnetism. Jakubovics, J.P. (1994) Magnetism and Magnetic Materials, The Institute of Materials, London. A good overview (and brief), it includes more methods for measuring magnetic susceptibility. Kittel, C. (1986) Introduction to Solid State Physics, 6th edition, Wiley, New York. Chapter 14 describes diamagnetism and paramagnetism and Chapter 15 describes ferromagnetism and antiferromagnetism. The approach is quite mathematical and goes deeper into the fundamentals than we do. Moulson, A.J. and Herbert, J.M. (1990) Electroceramics, Chapman & Hall, London. A very good text on this topic. Owens, F.J. and Poole, C.P., Jr. (1996) The New Superconductors, Plenum Press, New York. A gentle intro- duction to ceramic superconductors includes a very readable account of the flux lattice. Purcell, E.M. (1985) Electricity and Magnetism, 2nd edition, McGraw-Hill, New York. An E&M reference. Purcell shared the 1952 Nobel Prize in physics with Bloch. Standley, K.J. (1972) Oxide Magnetic Materials, 2nd edition, Clarendon Press, Oxford. A very useful refer- ence on this topic. Described the structure of manganates before their commercial importance was realized. SPECIFIC REFERENCES Kato, Y. and Takei, T. (1932) Japanese patent 98,844. The first commercial applications of ferrites. Néel, L. (1948) “Proprietes magnetiques des ferrites—ferrimagnetisme et antiferromagnetisme,” Ann. Phys. 3, 137. The original description of ferrimagnetism. Néel won the 1970 Nobel Prize in physics for his work on antiferromagnetism and ferrimagnetism. Perez, J.M., Simeone, F.J., Saeki, Y., Josephson, L., and Weissleder, R. (2003) “Viral-induced self-assembly of magnetic nanoparticles allows the detection of viral particles in biological media,” J. Am. Chem. Soc. 125, 10192. Description of a viral nanosensor using iron oxide nanoparticles. This group is at Harvard Medical School. Roth, W.L. (1960) “Neutron and optical studies of domains in NiO,” J. Appl. Phys. 31, 2000. The first descrip- tion (and naming) of domain boundaries in antiferromagnets. Shull, C.G. and Smart, J.S. (1949) “Detection of antiferromagnetism by neutron diffraction,” Phys. Rev. 76, 1256. The original neutron diffraction studies on antiferromagnetic materials. Smit, J. and Wijn, H.P.J. (1959) Ferrites, Wiley, New York. More detailed description of magnetoplumbite ferrites. C h a p t e r S u m m a ry .......................................................................................................................................................... 617  Snoeck, J.L. (1947) New Developments in Ferromagnetic Materials, Elsevier, New York. The first major published study of ferrites. Weiss, P. (1906) “The variation of ferromagnetism with temperature,” Compt. Rend. 143, 1136. Weiss domains. Williams, D.B. and Carter, C.B. (1996) Transmission Electron Microscopy: A Textbook for Materials Science, Plenum, New York. The Lorentz technique is described on pp. 534–537. Zener, C (1951) “Interaction between the d-shells in the transition metals,” Phys. Rev. 81, 440 and “Interaction between the d-shells in the transition metals 2: Ferromagnetic compounds of manganese with perovskite structure,” Phys. Rev. 82, 403. These two papers have been cited collectively almost 4000 times and describe the double exchange mechanism. Clarence Zener spent a short time (1940–1942) as an instructor at Washington State University when it was still known as Washington State College. EXERCISES 33.1 Diamagnetism is present in all materials. Why do we not usually need to consider its contribution when we determine χ for a paramagnetic material using a Gouy balance? 33.2 You are given a sample of a ceramic powder that you believe to be paramagnetic. You have access to a Gouy balance. Explain how you would determine χ for your powder and what possible sources of error there might be. 33.3 In Section 33.4 we said that there are two general categories of magnetic behavior. Assign each of the five main types of magnetic response, diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, and ferrimagnetism, into one of the two categories. Explain briefly how you arrived at your assignments. 33.4 Al2O3, BeO, diamond, MgO, NaCl, and Si are all diamagnetic. Explain this observation. 33.5 You perform experiments using a Gouy balance using sintered rods of Al2O3, BeO, CeO2, and TiO2. What sign would you expect to obtain for χ for each material? Would you get a different result if you replaced the oxide with its corresponding metal? 33.6 How would the magnetic properties of magnetite change if it were a normal spinel? 33.7 Sketch the position of the atoms in the perovskite unit cell that you would expect for the CMR compound La0.5Ca0.5MnO3. 33.8 The compounds in the La1−xA xMnO3 system contain both Mn3+ and Mn4+ ions and are collectively called “manganites.” Is the use of this term correct scientific usage or not? Briefly explain your answer. 33.9 Liquid phase epitaxy (LPE) was used for forming thin garnet films for magnetic bubble memories. Describe the basic principles behind this technique. Would sputtering or evaporation be good alternative techniques for such films? Explain how you arrived at your answer. 33.10 Compare the energy and width of domain boundaries with values for grain boundaries. Based on the values you obtain discuss the relative ease of movement of the two types of boundary. 618 .............................................................................................................. U s i n g M ag n e t i c F i e l d s a n d S t o r i n g Data  34 Responding to Temperature Changes CHAPTER PREVIEW Heat is essentially the vibration of atoms in a material. Consequently thermal properties reflect the type and strength of interatomic bonding and the crystal structure. The important thermal properties of any material are  Heat capacity  Coefficient of thermal expansion  Thermal conductivity Thermal properties of ceramics differ from those of metals whenever free (conduction) electrons are involved, such as in thermal conductivity. However, heat transfer by phonon (lattice vibration) transport can in some cases be more effective than through the movement of electrons. We describe melting and vaporization of ceramics as the temperatures for these transformations tend to be high, which can be critical in certain applications, such as the tiles on the space shuttle, but present problems during processing. It should also be obvious by now that heat affects many of the properties of ceramics such as Young’s modulus, electrical con- ductivity, magnetic behavior, and dielectric constant. There are major applications that utilize the varied thermal properties of ceramics, from high thermal conductivity substrates for elec- tronic packaging to enormous mirror blanks for telescopes that have “zero” expansion. 34.1 SUMMARY OF TERMS AND UNITS equilibrium positions. This vibrational motion represents the thermal energy of the solid. There are other mecha- Table 34.1 lists the important parameters used in this nisms for heat absorption, but these are either negligible chapter and their units. The SI unit of temperature is or absent entirely. However, we will list them here and kelvin (K), but as you will have realized by now °C is very briefly describe them because they relate to some often used in presenting data in materials science. As concepts that have been described in earlier chapters such mentioned in Chapter 1, the numerical value of a tempera- as point defects. ture difference or temperature interval expressed in °C is equal to the numerical value of the same temperature dif-  Rotational: Rotational absorption is important in ference or interval when expressed in K. This point is liquids and gases where the molecules are free to worth remembering when coefficients of thermal expan- rotate, but this contribution is negligible in solids. sion or thermal conductivities are compared for different  Electronic: Absorption by conduction electrons is very materials. small, but it can be used to provide information about the electronic structure of a solid, so from that point of view it is useful. 34.2 ABSORPTION AND HEAT CAPACITY  Defect formation: The formation of Frenkel and Schottky defects can contribute, although usually only When a solid absorbs an amount of heat, dq, its internal at high temperatures. energy, E, rises by an amount dE where  Phase transformations: These involve absorption by structural, magnetic, and ferroelectric transformations dE = dq (34.1) in certain materials. The increase in internal energy is largely due to the Heat capacity is a measure of the amount of energy increased vibrational amplitude of the atoms about their required to raise the temperature of a material. At room 3 4 . 2 A b s o r p t i o n a n d H e at C a pa c i t y ....................................................................................................................... 619  TABLE 34.1 Summary of Terms Used to Describe the In the literature you will find that “heat capacity” is Thermal Properties of Materials often used to describe all these three terms. But it is Definition Units/value usually obvious from the units given what term is actually the correct one to use. The next term is really the confus- α Linear coefficient of thermal °C −1 or K−1 ing one. Fortunately it is not used now, but it does occur expansion from time to time in some of the older literature so Cv Heat capacity at constant volume J/K cv Molar heat capacity at constant J mol−1 K−1 beware: volume Cp Heat capacity at constant pressure J/K  Specific heat is the ratio of the heat capacity of a sub- cp Molar heat capacity at constant J mol−1 K−1 stance to the heat capacity of water. This term is a pressure unitless ratio and was used when the heat capacity of ΔS f Entropy of fusion J mol−1 K−1 or J g-atom−1 K−1 water was unity. In the SI system of units the heat ΔSv Entropy of vaporization J mol−1 K−1 or capacity of water is not unity. J g-atom−1 K−1 k Thermal conductivity W m−1 K−1 Heat capacities of solids are always functions of tem- Tb Boiling temperature °C or K perature, as illustrated for several ceramics in Figure 34.1. Tm Melting temperature °C or K RTS Thermal shock resistance Note the units are J g-atom−1 K−1. At absolute zero the W/m θD Debye temperature internal energy of a solid is a minimum and the heat °C or K R Gas constant capacity is zero. As the temperature rises the heat capacity 8.314 J mol−1 K−1 increases, which is indicative of the various mechanisms by which energy is absorbed. The heat capacity approaches a classical limit of 3R temperature the specific HEAT CAPACITY (∼25 J mol−1 K−1) at a suffi- heat capacity of many For most ceramics heat capacity reaches 3nR by 1000°C; ciently high temperature ceramics is between 0.75 n is the number of atoms per formula unit. that differs from one solid and 1.0 J g−1 K−1. For to another. This statement example, granite (an is essentially the Dulong– igneous silicate rock) has a specific heat capacity of Petit law. The crystal structure and composition of a mate- 0.79 J g−1 K−1 at 25°C, which means that it takes about 0.8 J rial do not appreciably affect heat capacity but n does: e.g., of energy to raise the temperature of 1 g of granite by 1 K. cP is 3R for Cu but 6R for MgO. Water has a specific heat capacity of 4.184 J g−1 K−1 at 25°C; The temperature at which the heat capacity becomes this value is more than five times greater than that of constant, or varies only slightly with temperature, is the granite. This difference is crucial in regulating the earth’s Debye temperature, θD. Values of θ are typically in the temperature. It takes five times more energy to increase range of Tm /5 to Tm /2 and depend on the temperature of water by 1 K than it does to increase the temperature of granite. If the earth’s surface were  Bond strength composed entirely of rock (i.e., there were no oceans) then  E daytime temperatures would be extremely high. The  T m oceans also help limit the temperature drop at night, because they have absorbed more energy during the day, For example, in diamond, where the covalent bonds are which is released at night. If the earth had no oceans very strong, θD is ∼2000 K. However, the value of θD for temperature swings between day and night would be very NaCl is 281 K. large. When referring to heat capacity, and in particular when various other sources are consulted, it is necessary Heat Capacity to be careful about terminology. Here are the definitions J (g-atom °C)-1 of all the terms you are likely to encounter: MgO SiC x x x 3R x  Heat capacity is the amount of heat required to change x x Al2O3 Mullite 20 the temperature of an object by 1 K. The units of heat x x capacity are J/K. x  Specific heat capacity is the amount of heat required x to change the temperature of 1 g of a substance by 1 K. x The units of specific heat capacity are J g−1 K−1. x 0  Molar heat capacity is the amount of heat required to 0 500 1000 T (°C) change the temperature of 1 mol of a substance by 1 K. FIGURE 34.1 Heat capacity of some ceramics as a function of The units of molar heat capacity are J mol−1 K−1. temperature. 620 ...................................................................................................................... R e s p o n d i n g t o Te m p e r at u r e C h a n g e s Heat Capacity where a, b, and c are “constants,” which have been tabu- CaO + SiO2 lated for a wide range of materials. (J (mole °C)-1) 120 CaSiO3 34.3 MELTING TEMPERATURES One of the very useful properties of many ceramics is their 80 SiO2 high Tm as shown in Table 34.2. This property makes ceramics without equal for application at high tempera- ture, such as refractories and thermal barrier coatings. CaO There is a direct correlation between Tm and bond strengths. 40 Also, ceramics with the highest values of Tm tend to have a significant fraction of covalent character to their bonding as shown in Table 34.3; this table is calculated using Eq. 4.24 and values of Pauling electronegativities given in Figure 3.4. However, Tm does not correlate directly with 0 the fraction of covalent character of the bond or ionic 0 1000 T (K) FIGURE 34.2 Heat capacity of SiO2 as a function of temperature. potential (φ) of the cation as shown for the oxides of the alkaline earth elements in Table 34.4, which is calculated in the same manner. (The values of ionic radii are given in Table 4.6.) Abrupt changes in heat capacity are observed over a Compounds with very high fractions of ionic character narrow temperature range when a material undergoes a to their bonds such as the alkali halides NaCl and LiF tend structural transformation or some other change in order. to have lower values of Tm than their corresponding oxides. The example shown in Figure 34.2 is for quartz (a poly- The reason is the greater ionic charges (e.g., O2− rather morph of SiO2), which undergoes a displacive α–β phase than Cl−) involved and hence the stronger electrostatic transformation at 573°C. Similar changes in heat capacity attraction. We can illustrate this point for the two com- occur in glasses at the glass transition temperature, pounds Li2O and LiF. Bond energies for ionic compounds Tg, because of the increase in configurational entropy can be obtained using Eq. 34.4 (this is simply the Born– in the liquid. Anomalous heat capacities are also associ- Landé equation given in Chapter 4 written for a single ated with the alignment of magnetic dipoles in ferromag- bond): netic materials and the alignment of electric dipoles in ferroelectrics. Z1 Z 2 e2 ⎛ 1− ⎞ 1 The heat capacity of a material can be calculated, Ebond = (34.4) depending on the temperature range of interest, using one 4πε 0 r0 ⎝ n⎠ of two equations. At very low (cryogenic) temperatures For Li2O we have r Li + = 0.068 nm and rO2− = 0.140 nm, so 3 r0 = 0.208 nm. Taking n = 10, and substituting into Eq. cP ≅ cV = K ⎛⎜ ⎞⎟ + γ T T ⎝ θD ⎠ (34.2) 34.4 we get a value of Ebond = 1.997 × 10−18 J. For LiF we have r Li + = 0.068 nm and r F − = 0.133 nm, so r0 = 0.201 nm. Taking n = 10 and substituting into where K is a constant equal to 1940 J mol−1 K−1 and γ is the Eq. 34.4 we get a value of Ebond = 1.033 × 10−18 J. electronic heat capacity coefficient. Values of θD and γ are So we would expect Li2O to have a higher Tm than LiF, tabulated in several lists of thermodynamic properties. and if you look at Table 34.2 you will see that for Li2O These values are generally widely available for metals and Tm = 1570°C while for LiF Tm = 848°C. somewhat more obscure for most ceramics. The overall contribution of Eq. 34.2 to the heat capacity of a material The entropy difference between the solid and the liquid is small and is really of importance only if you wish to at Tm is obtain a fundamental understanding of the nature of a material or if you are designing systems to operate at ΔH f cryogenic temperatures. ΔSf = (34.5) At high temperature Tm (usually above room tem- RICHARD’S RULE perature) heat capacities Values of ΔSf are shown in can be calculated using the ΔSf = 8.4 J g-atom−1 K−1 Table 34.2. They are posi- empirical relation tive because the liquid is always more disordered than the solid, but vary consider- cP = a + bT + cT −2 J mol−1 K−1 (34.3) ably from the empirical prediction known as Richard’s 3 4 . 3 M e lt i n g Te m p e r at u r e s ....................................................................................................................................... 621  TABLE 34.2 Tm and DSf for Selected Ceramics Compound Tm (°C) ΔSf (J mol−1 °C−1) Compound Tm (°C) ΔSf (J mol−1 °C−1) Oxides Al2O3 2054 ± 6 47.70 Mullite 1850 BaO 2013 25.80 Na 2O (α) 1132 33.90 BeO 2780 ± 100 30.54 Nb2O5 1512 ± 30 58.40 Bi2O3 825 Sc2O3 2375 ± 25 CaO 2927 ± 50 SrO 2665 ± 20 25.60 Cr 2O3 2330 ± 15 49.80 Ta 2O5 1875 ± 25 Eu2O3 2175 ± 25 ThO2 3275 ± 25 Fe2O3 Decomposes at 1735 K to TiO2 (rutile) 1857 ± 20 31.50 Fe3O4 and oxygen UO2 2825 ± 25 Fe3O4 1597 ± 2 73.80 V2O5 2067 ± 20 Li2O 1570 32.00 Y2O3 2403 ≈38.70 Li2ZrO3 1610 ZnO 1975 ± 25 Ln2O3 2325 ± 25 ZrO2 2677 29.50 MgO 2852 25.80 Halides AgBr 434 LiBr 550 AgCl 455 LiCl 610 22.60 CaF2 1423 LiF 848 CsCl 645 22.17 LiI 449 KBr 730 NaCl 800 25.90 KCl 776 25.20 NaF 997 KF 880 RbCl 722 23.85 Silicates and other glass-forming oxides B2O3 450 ± 2 33.20 Na 2Si2O5 874 31.00 CaSiO3 1544 31.00 Na 2SiO3 1088 38.50 GeO2 1116 P2O 5 569 MgSiO3 1577 40.70 SiO2 (high 1423 ± 50 4.6 Mg2SiO4 1898 32.76 quartz) Carbides, nitrides, borides, and silicides B 4C 2470 ± 20 38.00 ThN 2820 HfB2 2900 TiB2 2897 HfC 3900 TiC 3070 HfN 3390 TiN 2947 HfSi 2100 TiSi2 1540 MoSi2 2030 UC 2525 NbC 3615 UN 2830 NbN 2204 VB2 2450 SiC 2837 VC 2650 Si3N4 At 2151 K partial pressure of VN 2177 N2 over Si3N4 reaches 1 atm WC 2775 ZrB2 3038 TaB2 3150 ZrC 3420 TaC 3985 ZrN 2980 ± 50 TaSi2 2400 ZrSi2 1700 ThC 2625 TABLE 34.3 Predominantly Covalent Ceramics with Very TABLE 34.4 Melting Temperatures of Alkaline Earth Metal High Melting Temperatures Oxides Covalent character Covalent Ceramic Tm (°C) of bond (%) Oxide Tm (°C) character (%) φ (nm−1) = Z/r HfC 3890 70 BeO 2780 37 57 TiC 3100 78 MgO 2852 27 28 WC 2775 85 CaO 2927 21 20 B 4C 2425 94 SrO 2665 21 17 SiC 2300 88 BaO 2017 18 15 C (diamond) 3727 100 622 ...................................................................................................................... R e s p o n d i n g t o Te m p e r at u r e C h a n g e s rule. Richard’s rule holds fairly well for many elements The entropies associated with each of the melting reac- (e.g., Au, Ti, Pb, Na, K, B) but not for compounds. tions given above are related as follows: We can consolidate the values in Table 34.2 with Richard’s rule by considering the processes involved ΔS1 = ΔS2 + ΔS3 (34.11) when a compound, AB, melts. The overall melting reaction is We will now apply this approach to a real compound, MgO. 1 x y The entropy of fusion for MgO, given in Table 34.2, is Ax By ( s ) = A (l ) + B (l ) (34.6) ΔSf = 12.9 J g-atom−1 K−1, i.e., ΔS1 = 12.9 J g-atom−1 K−1. The x+y x+y x+y entropy of mixing, ΔS3, can be calculated from Eq. 34.7 ΔS1 = ΔSf as ΔS30 = −8.314 ⎡ ln ⎛ ⎞ + ln ⎛ ⎞ ⎤ 1 1 1 1 This reaction can be broken down into two steps. First, ⎣⎢ 2 ⎝ 2 ⎠ 2 ⎝ 2 ⎠ ⎦⎥ = −8.314 ln ⎛ ⎞ = 5.76 J g - atom −1K −1 (34.12) 1 1 1 ⎝ 2⎠ Ax By ( s ) = Ax By (l ) (34.7) x+y x+y Using Eq. 34.11 this gives the entropy for the hypothetical melting reaction of 7.14 J g-atom−1 K−1. This value, which which gives ΔS2 and corresponds to a hypothetical melting is closer to Richard’s rule, does not consider a mixing process in which the compound retains its ordered struc- contribution but only the vibrational change on melting ture in the liquid phase. This step is followed by such as occurs for an element. By assuming that we can apply Richard’s rule as shown above then it is possible to 1 x y determine ΔS1 (ΔSf ), where such values are not available Ax By (l ) = A (l ) + B (l ) (34.8) x+y x+y x+y in the literature, and hence obtain ΔHf. which gives ΔS3 = ΔSm and represents disordering of the compound in the liquid to form a random solution. For 34.4 VAPORIZATION this latter step the entropy change is given by the “entropy of mixing,” which is Most ceramics have very high Tb. Consequently their vapor pressures are negligible at room temperature and ΔSm = −R[XA ln XA + XB ln XB] (34.9) become appreciable only at high temperature. Also very few ceramics vaporize without a molecular change. The where XA and XB are the atom fractions of A and B, result is that the vapor composition is usually not the same respectively. For our particular example we can write the as that of the original liquid or solid. A practical conse- entropy of mixing as quence is that when we try to grow ceramic thin films by evaporation as described in Chapter 28 the film may have a stoichiometry different from that of the source. Some of ⎡ x ⎛ x ⎞ y ⎛ y ⎞⎤ ΔS30 = − R ⎢ ln ⎜ ⎟+ ln ⎜ ⎟ (34.10) the phenomena that can occur when compounds evaporate ⎣ x + y ⎝ x + y ⎠ x + y ⎝ x + y ⎠ ⎥⎦ are shown in Table 34.5. TABLE 34.5 Possible Reactions during the Evaporation of Compounds Chemical reaction Reaction type (M = metal, X = nonmetal) Examples Comments Evaporation without MX(s or l) → MX(g) SiO, B2O3, GeO, Compound stoichiometry maintained in deposit dissociation SnO, AlN, CaF2, MgF2 Decomposition MX(s) → M(s) + (1/2)X 2 (g) Ag2S, Ag2Se Separate sources are required to deposit these MX(s) → M(l) + (1/n)Xn (g) III–V semiconductors compounds Evaporation with MX(s) → M(g) + (1/2)X 2 (g) CdS, CdSe, CdTe Deposits are metal-rich; separate sources are dissociation required to deposit these compounds Chalcogenides (X = S, Se, Te) Oxides MO2 (s) → MO(g) + (1/2)O2 (g) SiO2, GeO2, TiO2, Metal-rich discolored deposits; dioxides are SnO2, ZrO2 best deposited in O2 partial pressure (reactive evaporation) 3 4 . 4 Va p o r i z at i o n ......................................................................................................................................................... 623  TABLE 34.6 Temperature at Which the Vapor Pressure Is ference phonons move from the high temperature end, 10 -4 torr (1.3 ¥ 10 -2 Pa) where their concentration is high, to the lower temperature Oxide Tm (°C) T (vapor pressure = 10−4 torr) end, where their concentration is lower. The driving force is the concentration gradient, just as it is in the diffusion of PbO 890 550°C matter. The rate of heat flow dq/dt is proportional to the TiO2 1640 ∼1300°C temperature gradient dT/dx, where the constant of propor- ZrO2 2700 ∼2200°C tionality is the thermal conductivity, k: dq dT In many multicomponent oxide ceramics the vapor = − kA (34.14) pressure of each component may be different. This effect dt dx is particularly noticeable in lead-containing compounds such as lead zirconium titanate (PZT), an important piezo- where A is the cross-sectional area normal to the direction electric ceramic. PZT contains PbO, ZrO2, and TiO2 in the of heat flow. form of a solid solution. PbO is significantly more volatile Thermal conductivity depends on three factors: than the other two oxides (Table 34.6). As a result if PZT films are heated during processing then significant Pb loss 1. Heat capacity C can occur, leading to a change in film stoichiometry and 2. Average particle velocity, v dramatically different properties. If Pb loss is to be avoided 3. Mean free path of a particle between collisions, l then special precautions must be taken. For example, we can compensate for Pb loss by making our starting films Pb rich. From the kinetic theory of gases the thermal conduc- tivity of an ideal gas is 34.5 THERMAL CONDUCTIVITY 1 k = Cvl (34.15) 3 At all temperatures the atoms in a solid are vibrat- Debye (in 1914) applied ing about their equilibrium v AND l FOR ELECTRONS AND PHONONS Eq, 34.15 to phonon con- positions with a set of For electrons in a metal at room temperature, v ∼ 106 m/s duction to describe thermal characteristic frequencies, and l ∼ 10 nm. conductivity in dielectric ν, with values as high as For phonons in a ceramic at room temperature, v ∼ solids. Then C is the heat 1012 Hz at room tempera- 103 m/s and l ∼ 1–4 nm. capacity of the phonons, v ture. The energies of the The phonon mean free path greatly increases with is the phonon velocity, and lattice vibrations are quan- decreasing temperature; it is ∼10 μm at 20 K.l is the phonon mean free tized and given by path. Phonon conduction in ceramics is very different from E = ⎛ n + ⎞ hν 1 that found in metals where the free electrons are the source (34.13) ⎝ 2⎠ of the thermal conductivity. The mobility of phonons is usually significantly lower where n is an integer, than that of electrons which is zero at 0 K, and h VIBRATIONAL AMPLITUDES because they are scattered is Planck’s constant. At In a solid these may be as large as 0.02–0.03 nm. by lattice vibrations (i.e., absolute zero the atoms other phonons). Conse- have E = hν/2: the zero point energy. If the solid is heated quently ceramics generally have low thermal conductivi- E will increase in integer steps of hν and similarly if the ties. However, the phonon mechanism can be very effective solid is cooled the vibrational energy will decrease in and it is often a surprise to realize that the thermal con- steps of hν. You can see immediately that there is a simi- ductivity of some ceramics is actually higher than that of larity between this process and the absorption or emission metals! At temperatures above ∼50 K, diamond has the of light (photons). And so the name phonon is used as the highest thermal conductivity of any known material. quantum unit of lattice vibrational energy. The thermal conductivity of a gem quality diamond is in Wave-particle duality applies equally to phonons as it the range of 2000–2500 W m−1 K−1 at room temperature does to photons. Thus, phonons possess the characteristics whereas that of copper is 400 W m−1 K−1. Values for the of both waves and particles. In ceramics the conduction of room temperature thermal conductivity of some selected heat is primarily due to the movement of phonons. When a ceramics are given in Table 34.7. ceramic is heated we can think in terms of an increase in Ceramics having high thermal conductivities generally the number of phonons. When there is a temperature dif- share the following characteristics: 624 ...................................................................................................................... R e s p o n d i n g t o Te m p e r at u r e C h a n g e s  TABLE 34.7 The Thermal Conductivity of Some Ceramics around with which to collide and more chances of a scattering event taking place. The interactions between Material k (W m−1 K−1) Material k (W m−1 K−1) phonons was first described by Rudolf Peierls (1929) who Al2O3 30.0–35.0 Spinel 12.0 identified two types of scattering processes: (MgAl2O4) AlN 200.0–280.0 Soda–lime– 1.7  Umklapp (from the German umklappen, which means silicate glass “flipping over”) BeO 63.0–216.0 TiB2 40.0  Normal MgO 37.0 PSZ 2.0 SiC 84.0–93.0 SiAlON 21.0 The normal process has no effect on the thermal resis- SiO2 1.4 Si3N4 25.0 tance. However, the umklapp process leads to an increase Cordierite (Mg- 4.0 Forsterite 3.0 aluminosilicate) in thermal resistance with temperature given by 1  Strong interatomic bonding l∝ (34.16) T  Simple crystal structure  Comprise light elements that are close together in the Eventually l decreases to a value close to the interplanar periodic table spacing and k due to phonon transport becomes tempera- From Table 34.7 you can see that BeO and AlN are exam- ture independent. The temperature variation of l for several ples of ceramics with high thermal conductivity and both ceramics is shown in Figure 34.4. these materials satisfy the conditions given above. At high temperatures part of the thermal energy may Figure 34.3 shows the thermal conductivity of single also be transferred by radiation. The radiant energy con- crystal alumina as a function of temperature. At very low ductivity, kr, is given by temperatures the mean free path, l, of the phonons becomes comparable to the size of the specimen and k depends 16 2 3 kr = σn T lr (34.17) mainly on the heat capacity, which increases with T 3. The 3 thermal conductivity reaches a maximum at some low temperature (∼ 40 K in this case). As the temperature where σ is the Stefan–Boltzmann constant, n is the refrac- increases k decreases because there are more phonons tive index, and lr is the mean free path of the photons responsible for radiant heat transfer. Some single crystals and glasses have good transpar- k ency in the visible and in frared (IR) parts of the electro- magnetic spectrum and lr can become large. In most 104 polycrystalline ceramics, lr is very short because of absorp- tion and scattering, mainly due to the presence of pores. Wm-1K-1 For opaque materials lr ∼ 0 and radiation transfer is neg- ligible except at very high temperatures. 103 At the other extreme when lr is very large there is no interaction with the material and radiation heat transfer 102 3.0 Al2O3 l −1 Fused SiO2 TiO2 (nm-1) 2.0 Mullite MgO 101 ThO2 BeO 1.0 SiC 0 400 800 1200 T (K) FIGURE 34.3 Thermal conductivity of single crystal aluminum 0 0 800 T (K) 1600 oxide over a wide temperature range. The variation in the data above 800 K is due to the differences in the experimental FIGURE 34.4 Inverse phonon mean free paths for several method used. crystalline oxides and for vitreous silica. 3 4 . 5 Th e r m a l C o n d u c t i v i t y ...................................................................................................................................... 625 becomes a surface effect. The contribution of kr to the k = ρcp Dth (34.19) overall thermal conductivity becomes significant only when lr is small compared with the sample size but large The measurements can be performed at room temperature compared with atomic dimensions. or at a range of higher temperatures by enclosing the In ceramics with mobile electrons or holes there is a sample in a furnace. third mechanism that can contribute to thermal conductiv- ity. The electronic thermal conductivity ke is 34.7 MICROSTRUCTURE AND ⎛ Eg ⎞ THERMAL CONDUCTIVITY ke ∝ exp ⎜ − ⎟ (34.18) ⎝ kT ⎠ As mentioned in Chapter 1, thermal conductivity depends where Eg is the band gap energy and k is Boltzmann’s on microstructure. Anything that changes the local atomic constant. arrangement or induces elastic strains in the lattice will In most ceramics the electronic contribution to the decrease l. overall thermal conductivity is negligible. However, it can be significant in electrically conducting and semiconduct-  Impurities. The presence of impurities disrupts the ing ceramics such as SiC, TiC, and graphite. normal lattice arrangement. As temperature increases the effect of the impurity becomes less because l approaches the dimensions of the unit cell. The effect 34.6 MEASURING THERMAL on k is illustrated for solid solutions in the isomor- CONDUCTIVITY phous system MgO–NiO in Figure 34.6.  Porosity. The thermal conductivity of air is only There are several methods 0.026 W m−1 K−1, signifi- available to measure k, but cantly less than most no single one is appropri- MgO crystalline ceramics. Con- ate for all ceramics because l ∼ 3 nm at 200°C. sequently ceramics con- of their wide range of l ∼ 0.6 nm at 1000°C. taining a high volume thermal conductivities. aMgO = 0.421 nm. fraction of porosity have The laser flash method illustrated in Figure 34.5 is one of the most popular. In this technique a laser pulse is 30 used to rapidly heat one face of the ceramic, which is in Thermal the form of a thin plate. A typical laser would be an Nd: Conductivity glass laser producing radiation with λ ∼1060 nm. The (Wm-1K-1) energy of each laser pulse is ∼15 J. An IR detector mea- 25 sures the temperature of the face remote from the laser. The time taken for the peak in the temperature profile to reach the remote face of the sample and the reduction in the peak temperature are measured. These measurements 20 provide us with the thermal diffusivity, Dth, and the heat capacity, cp. If the density, ρ, of the ceramic is known then k can be obtained using 15 Furnace 10 200°C Laser IR Laser beam 5 detector 1000°C Specimen 0 20 40 60 80 100 MgO NiO FIGURE 34.5 Schematic of the laser flash method used for FIGURE 34.6 The thermal conductivities of solid solutions in the measuring thermal conductivity of ceramics. MgO–NiO system. 626 ...................................................................................................................... R e s p o n d i n g t o Te m p e r at u r e C h a n g e s  low values of k. This property is used to good effect in designing materials for thermal insulation such as the tiles used on the outside of the space shuttle to protect it during reentry into the earth’s atmosphere. The tiles consist of a porous mat of SiO2 fibers as showed earlier in Figure 15.19. The SiO2 provides the high strength and high melting temperature requirements of the tile and the porous microstructure ensures a very low k.  Grain size. The mean free path of phonons at room (A) (B) (C) temperature is significantly smaller than typical grain FIGURE 34.8 Three models for the distribution of two phases in a sizes in ceramics. As a result phonon scattering at material. (a) Parallel slabs, (b) continuous matrix phase, discon- grain boundaries is not important in reducing k in most tinuous particulate dispersion, and (c) large isolated grains practical applications. Figure 34.7 shows the tempera- separated by a continuous minor phase. ture dependence of k for CaF2, TiO2, and Al2O3 in single crystalline and polycrystalline form. The devia- tion in the relative thermal conductivities at higher There are three idealized kinds of phase distributions temperatures is due to the contribution from photon for which equations have been derived to estimate k of the conductivity. bulk material and these are illustrated in Figure 34.8 with  Dislocations. A dislocation consists of a core in which examples summarized in Table 34.8. the structure and density of the material is altered. Around the core there is a long-range strain field. Both 1. For parallel slabs with heat flow parallel to the phase these regions can cause phonon scattering. The thermal boundary: resistance associated with dislocations is proportional to the dislocation density. There is no theory that so km = V1k1 + V2 k2 (34.20) far accounts entirely satisfactorily for the magnitude of phonon scattering by dislocations. If you want to where V1 and V2 are the volume fractions of the two delve into some of the theories that have been proposed phases. much of the original work has been discussed by 2. For parallel slabs with heat flow perpendicular to the Nabarro (1987). phase boundary: k1k2 Most practical ceramics are multiphase materials in km = (34.21) V1k2 + V2 k1 which each constituent will, in general, have a different k. The value of k for the heterogeneous material is dependent 3. For a continuous major phase: upon the amount and distribution of the different phases. ⎡ 1 + 2V ⎛ 1 − kc ⎞ ⎛ 2 kc + 1⎞ ⎤ ⎢ d ⎝ kd ⎠ ⎝ kd ⎠ ⎥ km = kc ⎢ ⎥ (34.22) Thermal Conductivity ⎢ 1 − Vd ⎛ 1 − kc ⎞ ⎛ kc + 1⎞ ⎥ (W m-1 °C-1) ⎢⎣ ⎝ kd ⎠ ⎝ kd ⎠ ⎥⎦ 16 where kc is the thermal conductivity of the continuous phase, kd is the thermal conductivity of the dis- persed phase, and Vd is the volume fraction of the dis- 12 persed phase. sc TiO2 ||c axis sc Al2O3 x TABLE 34.8 Examples of Models for Phase Distribution a 8 x Parallel slabs Continuous matrix Continuous minor x x x x x x Furnace linings Dispersed impurities Common x x x x microstructure x x x sc TiO2 to c axis pc Al2O3 Thermal barrier Common two-phase Grain-boundary 4 17μm 9μm coatings microstructure phase sc pc TiO2 Cutting tool Dispersed-particle Glass-bonded CaF2 pc 28μm coatings composites ceramic Enamels Immiscible phases Cermet such as 0 Co-bonded WC 0 200 400 600 800 1000 1200 Layered Reaction-sintered T (°C) composites SiC FIGURE 34.7 Comparison of the thermal conductivity of single a crystal (sc) and polycrystalline (pc) ceramics. See Figure 34.8. 3 4 .7 M i c r o s t ru c t u r e a n d Th e r m a l C o n d u c t i v i t y .............................................................................................. 627 34.8 USING HIGH THERMAL ΔM CONDUCTIVITY Γ∝ (34.24) M One of the most important applications of high-k ceramics Aluminum has an atomic weight of 27 and the vacancy is as substrates and packages for electronic devices as has zero weight. So for our example ΔM/M is 1. When an shown in Figure 34.9. Due to the complexity and density N atom is replaced by O on the anion sublattice ΔM/M = of modern electronic devices, efficient thermal manage- 0.1. As a result the scattering cross section is smaller. ment is important. Removal of heat from the semiconduc- We can reduce the oxygen content in polycrystalline tor is essential to prevent thermally induced damage. AlN by adding rare earth or alkaline metal oxides (such Alumina (96 wt% Al2O3) is the most commonly used as Y2O3 and CaO) to the initial powder. During sintering substrate material. It has a thermal conductivity in the the additive reacts with the oxide coating on the AlN range 15–20 W m−1 K−1. The higher k alternatives are AlN, grains forming a liquid. The liquid helps in densification SiC, and BeO. Aluminum nitride is the most promising (as described in Section 24.7) and also acts as an oxygen because it combines a high k and a high electrical resistiv- “getter,” removing Al2O3 from the bulk of the grains. ity (unlike SiC), it is nontoxic (unlike BeO), and it has a During cooling the liquid concentrates mainly at triple coefficient of thermal expansion closely matched to Si in points leaving mostly clean and sharp AlN–AlN grain the temperature range 25–400°C. Theoretically AlN has boundaries as shown in Figure 1.4. k = 320 W m−1 K−1. However, in polycrystalline AlN k is The record-high thermal conductivity of diamond typically in the range 50–200 W m−1 K−1. One of the reasons makes it an obvious choice for consideration as a substrate that commercially available materials show a wide range for high power electronic devices. One method that has in k and values lower than predicted by theory is because been successful in producing diamond films is chemical of the presence of impurities, mainly oxygen. When vapor deposition (CVD). The CVD diamond films are oxygen replaces nitrogen, an aluminum vacancy is formed. polycrystalline, but can still have k > 2000 W m−1 K−1. We can represent this process using Kröger–Vink notation The high cost of diamond films still precludes their wide- (we gave the details of this notation in Chapter 11): spread use. Al2O3 → 2AlAl x + 3O ·N + VAl′′′ (34.23) 34.9 THERMAL EXPANSION The aluminum vacancy leads to phonon scattering because its scattering cross section, Γ, for phonons is large: Γ is We know from our everyday experiences that when we proportional to the relative difference in mass between the heat most materials they expand and when we cool them original site occupant and the new site occupant. they contract. The linear coefficient of thermal expansion, α, indicates how much the dimensions of a solid change with temperature: Δl α= (34.25) ΔTl0 where Δl is the change in length of the sample, l0 is the original length, and ΔT is the temperature interval. Figure 34.10 shows a typical bond–energy curve. At 0 K the atoms are separated by the equilibrium spacing, r 0, which corresponds to the minimum in the bond–energy curve. The atoms will be in their lowest vibrational energy state, corresponding to the zero point energy hν/2 and posses the minimum amplitude of vibration, x0. When the solid is heated its energy increases as shown by the hori- zontal lines in Figure 34.10. The width of the trough in the bond–energy curve represents the average vibrational amplitude of the atoms for a specific energy (or T). The average distance between the atoms is represented by the mean position along this line. A solid expands when heated because the bond–energy curve is asymmetric. If the curve was symmetric (the dashed curve in Figure 34.10) the average vibrational amplitude would increase with FIGURE 34.9 A ceramic pin-grid-array package (96% pure Al2O3) increasing temperature, but there would be no increase in with multilayer Au metallization. the interatomic separation. 628 ...................................................................................................................... R e s p o n d i n g t o Te m p e r at u r e C h a n g e s  -6 15x10 E α MgFe2O4 SrTiO3 NiFe2O4 (°C ) -1 ZnAl2O4 LiTaO3 LiAlO2 BeAl2O4 0 Y3Al5O12 r1 r0 r2 r -6 Fe2O3 Cr2O3 10x10 FeTiO3 BaTiO3 CaTiO3 MgAl2O4 NaNbO3 Ga2O3 CaZrO3 YAlO3 ZnO Al2O3 BaAl2O4 -6 Higher T 5x10 1400 1600 1800 2000 2200 2400 T (°C) FIGURE 34.11 Plot of the average coefficient of thermal expansion versus melting temperature for many ceramics. Low T 0K FIGURE 34.10 A typical bond-energy curve. Values of α for various ceramics are given in Table 34.9. For most ceramics α lies between about 3 × 10−6 and 15 × 10−6 °C−1. As described in Chapter AN EXAMPLE—MgO Since α is a function of 4 the shape of the bond– temperature, usually energy curve depends on α = 13.5 × 10−6 °C−1 = 13.5 ppm/°C increasing with increasing the strength and type of α(°C −1) × 106 = 13.5; α(106 °C) −1 = 13.5 temperature as shown in the interatomic bonding: Figure 34.12, a mean value Heating MgO from 25°C to 50°C (ΔT = 25°C) increases  The greater the bond is often quoted for a par- a (0.421 nm at 25 °C) by only 0.14 pm. strength the deeper and ticular material over a narrower the trough in stated temperature range. the bond–energy curve and the smaller the value of α. The values in Table 34.8 are mean values and the tempera-  The more ionic the bonding the more asymmetric the ture range over which these values are applicable is given. curve. Ionically bonded materials will, in general, have Most values of α found in the literature are room tempera- higher values of α than covalently bonded ones. ture values and from a practical point of view it would be  As melting temperature increases α decreases as shown incorrect to use these values when considering an applica- in Figure 34.11. tion over a different temperature range. TABLE 34.9 Mean Thermal Expansion Coefficients of Various Ceramics Ceramic α (ppm/°C ) Ceramic α (ppm/°C ) Binary oxides α-Al2O3 7.2–8.8 ThO2 9.2 BaO 17.8 TiO2 8.5 BeO 8.5–9.0 (25–1000) UO2 10.0 Bi2O3 (α) 14.0 (RT–730°C) WO2 9.3 (25–1000) Bi2O3 (δ) 24.0 (650–825°C) Y2O3 8.0 (c axis) Dy2O3 8.5 ZnO 4.0 (a axis) Gd2O3 10.5 ZrO2 (monoclinic) 7.0 HfO2 9.4–12.5 ZrO2 (tetragonal) 12.0 MgO 13.5 Mixed oxides Al2O3 · TiO2 9.7 (average) Cordierite 2.1 Al2O3 · MgO 7.6 MgO · SiO2 10.8 (25–1000) 5Al2O3 · 3Y2O3 8.0 (25–1400) 2MgO · SiO2 11.0 (25–1000) BaO · ZrO2 8.5 (25–1000) MgO · TiO2 7.9 (25–1000) BeO · Al2O3 6.2–6.7 MgO · ZrO2 12.0 (25–1000) CaO · HfO2 3.3 (25–1000) 2SiO2 · 3Al2O3 (mullite) 5.1 (25–1000) CaO · SiO2 (β) 5.9 (25–700) SiO2 · ZrO2 (zircon) 4.5 (25–1000) CaO · SiO2 (α) 11.2 (25–700) SrO · TiO2 9.4 (25–1000) CaO · TiO2 14.1 SrO · ZrO2 9.6 CaO · ZrO2 10.5 TiO2 · ZrO2 7.9 (25–1000) 2CaO · SiO2 (β) 14.4 (25–1000) 3 4 . 9 Th e r m a l E x pa n s i o n ............................................................................................................................................. 629  TABLE 34.9 Continued Ceramic α (ppm/°C ) Ceramic α (ppm/°C ) Borides, nitrides, carbides, and silicides AlN 5.6 (25–1000) SiC 4.3–4.8 B 4C 5.5 TaC 6.3 BN 4.4 TiB2 7.8 Cr 3C2 10.3 TiC 7.7–9.5 HfB2 5.0 TiN 9.4 HfC 6.6 TiSi2 10.5 MoSi2 8.5 ZrB2 5.7–7.0 β-Mo2C 7.8 ZrC 6.9 (25–1000) NbC 6.6 ZrSi2 7.6 (25–2700) Si3N4 3.1–3.7 ZrN 7.2 Halides CaF2 24.0 LiCl 12.2 LiF 9.2 LiI 16.7 LiBr 14.0 MgF2 16.0 NaCl 11.0 Glasses Soda-lime glass 9.0 Fused silica 0.55 Pyrex 3.2 34.10 EFFECT OF CRYSTAL anisotropic and have different values of α along different STRUCTURE ON a crystallographic directions. Some examples are given in Table 34.10. In a polycrystalline sample of an anisotropic Cubic crystals like MgO are isotropic because they have material such as Al2O3, α would be intermediate between uniform thermal expansion along the three crystallo- the single crystal values for each of the different graphic axes. Single crystals of noncubic structures are orientations. Some silicate minerals such as quartz (SiO2) and cor- 14 dierite (Mg2Al4Si5O18) have very low coefficients of α MgO thermal expansion (for cordierite α is actually negative ( ppm °C-1) along the c axis!). This property is attributed to the very 12 open three-dimensional structure of many silicates. Cor- Al2O3 dierite is a ring silicate made up of [SiO4] 4− tetrahedral units as described in Chapter 7. During heating, thermal 10 energy can be absorbed by rearrangement of these tetra- hedral units by tilting or rotating. Structural changes that occur in a ceramic during 8 heating can also produce a change in α. An example is shown in Figure 34.13 for BaTiO3. Similar changes are 6 Mullite TABLE 34.10 Thermal Expansion Coefficients for Some Anisotropic Crystals (ppm/°C) 4 Crystal Normal to c axis Parallel to c axis Al2O3 8.3 9.0 2 Al2TiO5 −2.6 +11.5 3Al2O3 · 2SiO2 4.5 5.7 TiO2 6.8 8.3 ZrSiO4 3.7 6.2 0 CaCO3 −6 25 0 200 400 600 800 1000 1200 T (°C) SiO2 (quartz) 14 9 NaAlSi3O8 (albite) 4 13 FIGURE 34.12 Thermal expansion coefficients versus temperature C (graphite) 1 27 for some ceramic oxides. 630 ...................................................................................................................... R e s p o n d i n g t o Te m p e r at u r e C h a n g e s  MgO 20x10-3 Stabilized Δl α 10x10-6 ZrO2 l0 Δl 0 α l0 Typical Ni-base 1.6x10-3 -10x10 -6 superalloy Al2O3 -6 -20x10 16x10-3 Polyethylene Nylon 0.8x10-3 Rhombohedral Orthorhombic Tetragonal Cubic Δl l0 12x10-3 NaCl Al6Si2O13 (Mullite) Al alloys ZrSiO4 0 (Zircon) 8x10-3 SiC Si3N4 -0.8x10-3 -100 0 100 200 4x10-3 T (°C) FIGURE 34.13 The coefficient of thermal expansion of BaTiO3 as a function of temperature. Fused SiO2 0 LiAlSi2O6 seen in the crystalline forms of SiO2. Displacive phase (β-spodumene) transformations usually produce sudden changes in α. 200 400 600 800 1000 1200 1400 1600 T (°C) Reconstructive phase changes, which involve bond break- ing, usually occur more slowly and are often characterized FIGURE 34.15 Thermal expansion characteristics of several polycrystalline ceramics. by hysteresis. A typical plot of Δl/lo versus T for a commercial sili- 34.11 THERMAL EXPANSION cate glass is shown in Figure 34.16. The sudden increase MEASUREMENT in α in the temperature range 500–600°C is associated with the change from the glassy state into the supercooled The usual method of measuring α is to record mechani- liquid (i.e., Tg). The temperature range over which this cally the change in length of a test piece as it is heated in change occurs depends not only on the glass composition an instrument called a push-rod dilatometer, which is but also on the thermal history of the glass and the rate illustrated in Figure 34.14. The data that are obtained are of heating (remember Tg is not an absolute value). The plotted as Δl/lo versus T as shown in Figure 34.15. The decrease in length at about 700°C corresponds to the dila- slope of a line at any temperature is α. Accuracies of com- tometric softening temperature (Td), which is due to the mercial dilatometers can be as good as 0.5%. viscous flow of the sample under the stresses imposed by Thermocouple LVDT Sensor Furnace PR1 6x10-3 PR2 Δl l0 Specimen material 4x10-3 2x10-3 Transformation range Viscous flow Reference 0 standard 200 400 T (°C) 600 FIGURE 34.14 Schematic of a double pushrod differential FIGURE 34.16 Typical data for thermal expansion of a commercial dilatometer. silicate glass. 3 4 .11 Th e r m a l E x pa n s i o n M e a s u r e m e n t ................................................................................................................ 631  Material 1 Residual Tension T0 Material 2 Residual Compression α1 > α2 Material 1 Residual Compression T > T0 Material 2 Residual Tension FIGURE 34.17 Stresses generated in a layered structure due to differences in α. FIGURE 34.18 Artistic cracking in a glaze as a result of stresses generated due to differences in α. the dilatometer. Measurement of α for a glass should always be done on well-annealed samples. Ni, 17% Co, 54% Fe; α = 5.1 × 10−6 °C−1) were developed to have αs as close as possible to alumina. 34.12 IMPORTANCE OF MATCHING as  Glass to metal seals. In incandescent lamps the tung- sten wire coil is fused to the glass lamp bulb to form Thermal expansion plays a key role when two or more a vacuum tight seal. The best seal is achieved when materials are combined in situations in which they will be the glass and metal have similar values of α. Tungsten subjected to changes in temperature. Consider the situa- has α = 4.5 × 10−6 °C−1. A typical glass composition for tion illustrated in Figure 34.17. On heating, material 1 matching with tungsten is an alkali alumina borosili- (with the higher α) will experience a compressive stress cate (72.9 SiO2, 4.5 Al2O3, 14.5 B2O3, 3.5 Na2O, 2.4 during heating while material 2 (with the lower α) will K2O, 1.2 BaO) which has α20–300°C = 4.5 × 10−6 °C−1. experience tensile stresses. On cooling back down, mate-  Porcelain enameled metals. Porcelain enameling is an rial 1 will be in tension while material 2 will be in com- established technology for bonding a coating of glass pression. These stresses can lead to on to ferrous metal objects (e.g., stoves). The coeffi- cient of thermal expansion of the glass must be closely  Bowing matched to that of steel (α1025 steel = 16 × 10−6 °C−1).  Delamination  Thin films. Differences in α between a thin film and a  Cracking substrate can lead to film stress. In a thin film (where the Here are some important examples: thickness of the film is considerably less than that of the substrate), the thermal stress, σf, in the thin film is  Glazes on ceramics. Most types of pottery and white- ware are coated with a glaze for both aesthetic reasons (α − α f ) ΔTEf σf = s (34.26) and to make the body impermeable to liquids. The (1 − vf ) glaze (like most glasses) is strong in compression yet weak in tension. Typical compressive stresses in a where αf and αs are the coefficients of thermal expan- glaze are on the order of 70 MPa. If tensile stresses are sion of the film and substrate, respectively, Ef is the generated they can cause cracking of the glaze as illus- Young’s modulus of the film, and νf its Poisson ratio. trated in Figure 34.18.  Metal to ceramic bonding. In the packaging of semicon- ductor devices it is often necessary to join a ceramic (the 34.13 APPLICATIONS FOR LOW-a substrate on which the “chip” is mounted) to a metal (the lead frame that pro- Glass-ceramics, such as vides connections to the lithium-aluminosili- and from the outside EXAMPLE OF THERMAL STRESS cates (LAS), can be world). The most Determine the thermal stress in a TiC coating deposited designed to have very low, common substrate onto 1025 stainless steel by CVD at 1000°C: in fact near zero, αs over a −6 −1 −6 −1 material is a 96% wt% α1025 steel = 16 × 10 °C αTiC = 8 × 10 °C wide temperature range Al2O3 ceramic (α = 7.2 ETiC = 450 GPa νTiC = 0.19 making them particularly × 10−6 °C−1). The Kovar suitable as supports for metal alloys (e.g., 29% Substitution into Eq. 34.26 gives σf = 1.67 GPa at 0°C. telescope mirrors. Tele- 632 ...................................................................................................................... R e s p o n d i n g t o Te m p e r at u r e C h a n g e s  TABLE 34.11 Comparison of Thermal Shock Parameters for a Number of Ceramicsa Material MOR (MPa) E (GPa) α (ppm/K) k (W m−1 K−1) RTS (W/m) SiAlON 945 300 3.0 21 22,050 Hot-pressed Si3N4 890 310 3.2 15–25 13,458 Reaction-bonded Si3N4 240 220 3.2 8–12 2,727 SiC (sintered) 483 410 4.3 84 23,012 Hot-pressed Al2O3 380 400 9.0 6–8 633 Hot-pressed BeO 200 400 8.5 63 3,706 PSZ 610 200 10.6 2 575 a Poisson’s ratio was taken to be 0.25 for all materials. scopes are precise optical instruments and the resolution modulus. For high thermal shock resistance we want a is very sensitive to the alignment of the mirrors and other ceramic with optical components. Support materials with low αs mini- mize thermally induced strains. A commercial glass  High σf ceramic that is used for this application is known as Zero-  High k durTM. In addition to the very low α, Zerodur is stable up  Low E to 800°C and insensitive to thermal shock. The world’s  Low α largest optical mirror is located at the Parnal Observatory in the Atacama Desert in Chile. The mirror, which is Values to calculate RTS for several ceramics are given made of a polished Zerodur base coated with aluminum, in Table 34.11. As an example, the RTS of SiC is 2.3 × is 8.2 m in diameter with a surface area of more than 104 W/m, while that of Al2O3 is 740 W/m Ceramics 50 m2. such as SiC and Si3N4, which also have a high RTS, are the most useful for components that are loaded at high temperature. 34.14 THERMAL SHOCK Silica glass (SiO2) has an RTS of 5.27 × 103 W/m. Addition of other components to the glass lowers E and Thermal shock resistance is the ability of a material to increases α, hence decreasing RTS. Soda-lime–silicate withstand failure due to rapid changes in temperature. glasses such as those used for holding beverages are very Ceramics and glasses are much more likely to develop susceptible to thermal shock as you have probably found thermal stress than metals because out at one time or another because of their high α = 9.2 ×  They generally have lower k 10−6 °C−1. Modification of RTS can most easily be accom-  They are brittle plished by changing α. The other parameters in Eq. 34.23 do not vary significantly with glass composition. If the Rapid cooling of a ceramic or a glass is more likely to CaO and Na2O contents are reduced and B2O3 is added inflict thermal shock than heating, since the induced then a borosilicate glass is formed. This is known as surface stresses are tensile. And, as you know, crack for- PyrexTM glass (α = 3.3 × 10−6 °C−1), which is much more mation and propagation from surface flaws are more prob- resistant to thermal shock. Most cookware and the major- able when the imposed stress is tensile. ity of laboratory glassware are Pyrex. From a practical The thermal shock resistance (RTS) of a material can point of view a soda-lime–silicate glass will fail if the be estimated using temperature difference is ≥80°C (so pouring boiling water into a glass beaker will certainly crack it). Pyrex glass can RTS = σfk/(Eα) (34.27) withstand temperature differences of 270°C before failure. Glass-ceramics with their extremely low α have very high where σf is the fracture stress (which for ceramics is often thermal shock resistance and can withstand temperature taken as the flexural strength or MOR) and E is Young’s changes of >1000°C. CHAPTER SUMMARY The thermal properties of ceramics, like many of their other physical properties, vary over a very wide range. A good example is that of thermal conductivity. Diamond, a ceramic material, has the highest known thermal conductivity, whereas the thermal conductivity of a multiphase ceramic such as partially stabilized zirconia is three orders of magnitude lower. Thermal properties of ceramics are dominated primarily by the nature of the interatomic bonding (bond strength and ionicity). In practical ceramics we, of course, have to consider the presence of defects, impurities, and porosity as these all affect thermal properties. C h a p t e r S u m m a ry .......................................................................................................................................................... 633  PEOPLE IN HISTORY Debye, Petrus (Peter) Josephus Wilhelmus (1884–1966) was born in the Netherlands and became a natural- ized American citizen in 1946. In 1912 he proposed the idea of quantized elastic waves, called phonons. From 1940 to 1952 Debye was Professor of Chemistry at Cornell University. He won the Nobel Prize in Chemistry in 1936. Thomson, William (Lord Kelvin) (1824–1907), Scottish mathematician and physicist, was born in Belfast, Ireland. He proposed his absolute scale of temperature in 1848. During his life he published more than 600 papers and was elected to the Royal Society in 1851. He is buried in Westminster Abbey next to Isaac Newton. GENERAL REFERENCES Berman, R. (1979) in The Properties of Diamond, edited by J.E. Field, Academic Press, London, p. 3. Dis- cusses the thermal conductivity of diamond and the effect different impurities have on this property. Kingery, W.D., Bowen, H.K., and Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd edition, Wiley, New York, pp. 583–645. A very detailed chapter on thermal properties. The discussion of photon conductivity and the thermal properties of glasses are covered in more depth than we do. Lynch, C.T. (1975) Ed., CRC Handbook of Materials Science, Volume III: Nonmetallic Materials and Appli- cations, CRC Press, Cleveland. Relevant data for thin-film deposition are given on pp. 128–145. A useful resource for vapor pressures of various ceramics. Rosenberg, H.M. (1988) The Solid State, 3rd. edition, Oxford University Press, Oxford, p. 96. Has a clear discussion of phonon scattering mechanisms. SPECIFIC REFERENCES Debye, P. (1912) “The theory of specific warmth,” Ann. Phys. 39, 789. An English translation of this classic paper appears in The Collected Papers of P.J.W. Debye (1954), Interscience, New York, p. 650. Debye, P. (1914) Vortäge über die Kinetische Theorie, B.G. Teubner, Leipzig. The original source. In German. Hultgren, R., Orr, R.L., Anderson, P.D., and Kelley, K.K. (1963) Selected Values of Thermodynamic Proper- ties of Metals and Alloys, Wiley, New York. Useful lists of thermodynamics properties. Kubaschewski, O., and Alcock, C.B. (1979) Metallurgical Thermochemistry, 5th edition, Elsevier, Oxford. More thermodynamic properties. Nabarro, F.R.N. (1987) Theory of Crystal Dislocations, Dover, New York, p. 746. The Dover edition is essentially a republication of the work first published by the Clarendon Press, Oxford in 1967. Peierls, R. (1929) “The kinetic theory of thermal conduction in crystals,” Ann. Phys. 3, 1055. EXERCISES 34.1 Show that Eq. 34.4 gives energy in units of J. 34.2 The melting temperature of MgO is 3073 K while that of NaCl is 1074 K. Explain the reason for this difference. 34.3 Consider the structure of graphite. Would you expect the thermal conductivity to be the same parallel to the basal plane and perpendicular to the basal plane? If not, why not? 34.4 (a) Would you expect the thermal conductivity of crystalline quartz to be higher or lower than that of fused quartz? (b) Would you expect the differences in k to increase or decrease with increasing temperature? Explain the reasoning behind your answers. 34.5 Using the criteria given in Section 34.5 rank the following ceramics in order of increasing thermal conductiv- ity: B4C, UO2, TiO2, and Si3N4. Explain the reasoning for your ranking. 34.6 Why is thermal transfer by radiation important only at high temperatures? 34.7 An AlN ceramic substrate contains 0.05 vol% porosity. Calculate the thermal conductivity of the ceramic at room temperature. 34.8 Which has the greater effect on the thermal conductivity of an AlN ceramic, 0.05 vol% porosity or 0.5 vol% of an Y3Al5O12 second phase? 34.9 Would hot pressing or reaction bonding be the best method to produce Si3N4 components for applications in which sudden changes in temperature will occur? Explain how you arrived at your answer. 34.10 Would the alkali alumina borosilicate glass given in Section 34.12 be a good choice to glaze a mullite crucible? If not, would you be better off using a soda-lime–silicate glaze or a pure silica glaze? 634 ...................................................................................................................... R e s p o n d i n g t o Te m p e r at u r e C h a n g e s  35 Ceramics in Biology and Medicine CHAPTER PREVIEW Bioceramics are ceramics used for the repair and reconstruction of human body parts. There are many applications for bioceramics; currently the most important is in implants such as alumina hip prostheses. Alumina is classified as an inert bioceramic because it has very low reactivity in the body. However, bioactive materials have the ability to bond directly with bone. The advantages are  Earlier stabilization of the implant  Longer functional life Bioactive ceramics are relatively weak compared with common implant metals and high strength ceramics such as alumina and zirconia. As a result they are often used as coatings, relying on the mechanical strength and toughness of the substrate. An important bioactive ceramic is hydroxyapatite (HA). Natural bone is a composite in which an assembly of HA particles is reinforced by organic collagen fibers. Hydroxyapatite-reinforced polyethylene com- posites have been developed in an attempt to replicate the mechanical behavior of bone. A major problem with this topic stems from the realization that you cannot replace bone if you do not understand why bone has such incredible mechanical properties. So if you work in this field you must learn about biology. 35.1 WHAT ARE BIOCERAMICS? field of bioceramics is relatively new; it did not exist until the 1970s. However, many bioceramics are not new mate- A comprehensive definition of a biomaterial was provided rials. One of the most important is Al2O3, which we first at the National Institutes of Health (NIH) Consensus encountered as a constituent of many traditional ceramic Development Conference on the Clinical Applications of products. Bioceramics are typically classified into sub- Biomaterials in the United States: groups based upon their chemical reactivity in the body. The subgroups are listed A biomaterial is any sub- in Table 35.1 and their rel- stance, other than a drug, or PROSTHESIS ative reactivities are com- combination of substances, A prosthesis is an artificial replacement for a part of the pared in Figure 35.1. synthetic or natural in origin, body. If a nearly inert mate- which can be used for any rial is implanted into the period of time, as a whole or body it initiates a protective response that leads to en- as a part of a system which treats, augments, or replaces any tissue, organ, or function of the body. capsulation by a nonadherent fibrous coating about 1 μm thick. Over time this leads to complete isolation of This definition was significantly simplified in 1986 the implant. A similar response occurs when metals at the European Society for Biomaterials Consensus and polymers are implanted. In the case of bioactive Conference: ceramics a bond forms across the implant–tissue interface that mimics the bodies natural repair process. Bioactive Biomaterial—a non-viable material used in a medical device ceramics such as HA can be used in bulk form or as part intended to interact with biological systems. of a composite or as a coating. Resorbable bioceramics, such as tricalcium phosphate (TCP), actually dissolve A bioceramic is defined as a ceramic used as a bioma- in the body and are replaced by the surrounding tissue. terial (which is great if you know what a ceramic is). The It is an important requirement, of course, that the 3 5 .1 Wh at a r e B i o c e r a m i c s ? ...................................................................................................................................... 635  TABLE 35.1 Classification Scheme for Bioceramics Skull: repair Nearly inert bioceramics Eye: replace lens Middle ear: repair orbit Examples: Al2O3, low-temperature isotropic (LTI) carbon; ultra replace bones LTI carbon; vitreous carbon; ZrO2 Jawbone: repair Simulate Tissue attachment: Mechanical hearing Bioactive ceramics Preserve teeth Repair mastoid bone Examples: HA; bioactive glasses; bioctive glass-ceramics Replace teeth: implants Tissue attachment: Interfacial bonding Resorbable bioceramics Anchor tooth implants: expand jawbone Examples: Tricalcium phosphate (TCP); calcium sulfate; trisodium phosphate Tissue attachment: Replacement Long bones: Composites replace segments Examples: HA/autogenous bone; surface-active glass ceramics/ poly(methyl methacrylate) (PMMA); surface-active glass/ Heart valves: metal fibers; polylactic acid (PLA)/carbon fibers; PLA/HA; use artificial PLA/calcium/phosphorus-based glass fibers Tissue attachment: Depends on materials Vertebrae: replace & repair with spacers Iliac crest repair after bone removal dissolution products are not toxic. As in the case of HA, TCP is often used as a coating rather than in bulk form. Fill bone It is also used in powder form, e.g., for filling space in space bone. Knee Figure 35.2 shows a number of clinical uses of replace Finger bioceramics. The uses go from head to toe and include joints repairs to bones, joints, and teeth. These repairs become Hip necessary when the existing part becomes diseased, replace totally or damaged, or just simply wears out. There are many other Tendons use revision surgery & ligaments: applications of bioceramics including pyrolytic carbon replace coatings for heart valves and special radioactive glass formulations for the treatment of certain tumors. We will describe these latter two applications toward the end of Foot joints: this chapter. In the next section we will look at the advan- repair tages and disadvantages of ceramics as biomaterials as compared to the use of polymers and metals. We note that nanomaterials show interesting possibilities for such appli- cations, but may pose as many health problems in other situations. FIGURE 35.2 Illustration of the head-to-toe clinical uses for bioceramics. 35.2 ADVANTAGES AND Relative DISADVANTAGES OF CERAMICS Reactivity Resorbable (e.g., TCP) In the selection of a material for a particular application we always have a choice. Materials selection is a critical Surface Reactive part of any component design process and is especially (e.g., bioGlass) important for implants and other medical devices. Nearly inert The three main classes of material from which we can (e.g., alumina) select for a load-bearing application are metals, polymers, and ceramics. Table 35.2 is a comparative list of the sig- 10-1 1 10 102 103 104 105 nificant physical properties of different biomaterials from t (days) each of the three classical material classes. Table 35.3 com- FIGURE 35.1 Relative reactivity of the different classes of pares the behavior of these different classes relevant to bioceramic. TCP is tricalcium phosphate. their potential use as implants. 636 .......................................................................................................................... Cer am ics in Biology and M edicine  TABLE 35.2 Significant Physical Properties of Different Biomaterials Fracture Compressive surface Density UTS strength K1c Hardness α energy Poisson’s k Material (g cm−3) (MPa) (MPa) E (GPa) (MPa m1/2) (Knoop) (ppm/°C) (J/m 2) ratio (W m−1 K−1) HA 3.1 40–300 300–900 80–120 0.6–1.0 400–4,500 11 2.3–20 0.28 TCP 3.14 40–120 450–650 90–120 1.20 14–15 6.3–8.1 Bioglasses 1.8–2.9 20–350 800–1200 40–140 ∼2 4,000– 5,000 0–14 14–50 0.21–0.24 1.5–3.6 A-W glass 3.07 215 1080 118 2 ceramic SiO2 glass 2.2 70–120 ∼70 0.7–0.8 7,000– 7,500 0.6 3.5–4.6 0.17 1.5 Al2O3 3.85–3.99 270–500 3000–5000 380–410 3–6 15,000– 20,000 6–9 7.6–30 0.27 30 3 5 . 2 A dva n tag e s a n d D i s a dva n tag e s o f C e r a m i c s PSZ 5.6–5.89 500–650 1850 195–210 5–8 ∼17,000 9.8 160–350 0.27 4.11 Si3N4 3.18 600–850 500–2500 300–320 3.5–8.0 ∼22,000 3.2 20–100 0.27 10–25 SiC 3.10–3.21 250–600 ∼650 350–450 3–6 ∼27,000 4.3–5.5 22–40 0.24 100–150 Graphite 1.5–2.25 5.6–25 35–80 3.5–12 1.9–3.5 1–3 ∼500 0.3 120–180 LTI-ULTI 1.5–2.2 200–700 330–360 25–40 1–10 0.3 2.5–420 Carbon fiber 1.5–1.8 400–5000 330–360 200–700 Glassy carbon 1.4–1.6 150–250 ∼690 25–40 8,200 2.2–3.2 PE 0.9–1.0 0.5–65 0.1–1.0 0.4–4.0 170 11–22 500–8,000 0.4 0.3–0.5 PMMA 1.2 60–70 ∼80 3.5 1.5 160 5–8.1 300–400 0.20 Ti 4.52 345 250–600 117 60 1,800– 2,600 8.7–10.1 ∼15,000 0.31 Ti/Al/V alloys 4.4 780–1050 450–1850 110 40–70 3,200– 3,600 8.7–9.8 ∼10,000 0.34 Ti/Al/Nb/Ta 4.4–4.8 840–1010 105 50–80 ∼17,000 0.32 alloys Vitallium- 7.8–8.2 400–1030 480–600 230 120–160 3,000 15.6–17.0 ∼5,000 0.30 stellite alloys (Co–Cr–Mn) Low C steel 7.8–8.2 540–4000 1000– 4000 200 55–95 1,200– 9,000 16.0–19.0 ∼50,000 0.20–0.33 46 Fe–Cr–Ni alloys .............................................................................................. 637  TABLE 35.3 General Comparison of Materials for Implants Most bioceramic implants are in contact with bone. Bone is a living material composed of cells and a blood Material class Advantages Disadvantages supply encased in a strong composite structure. The com- Polymers Resiliant Weak posite consists of collagen, which is flexible and very Tough Low E tough, and crystals of an apatite of calcium and phosphate, Easy to fabricate Not usually bioactive resembling calcium hydroxyapatite; we will proceed as if Low density Not resorbable Metals Strong Can corrode in a it is HA. It is the HA component that gives bone its hard- Wear resistant physiological ness. The acicular apatite crystals are 20–40 nm in length Tough environment and 1.5–3 nm wide in the collagen fiber matrix. Two of the Easy to fabricate High E various types of bone that are of most concern in the use High density of bioceramics are Not usually bioactive Not resorbable Ceramics Biocompatible Low tensile strength  Cancellous (spongy bone) Wear resistant Difficult to fabricate  Cortical (compact bone) Certain compositions Low toughness lightweight Not resiliant Cancellous bone is less dense than cortical bone. Every bone of the skeleton has a dense outer layer of compact bone covering the spongy bone, which is in the form of a honeycomb of small needle-like or flat pieces called tra- beculae. Figure 35.3 is a schematic showing a longitudinal The main advantage of ceramics over other implant section of a long bone. The open spaces between the tra- materials is their biocompatibility: some are inert in the beculae are filled with red or yellow bone marrow in physiological environment while others have a controlled living bones. Because of its lower density, cancellous bone reaction in the body. The main disadvantages of most has a lower E and higher strain-to-failure ratio than corti- bioceramics are cal bone, as shown in Table 35.4. Both types of bone have higher E than soft connective tissues, such as tendons and  Low toughness (which can affect reliability) ligaments. The difference in E between the various types  High E (which can lead to stress shielding, see Section of connective tissues ensures a smooth gradient in mechan- 35.3) ical stress across a bone, between bones, and between muscles and bones. One of the main ways of increasing the toughness of ceramics is to form a composite. The ceramic may be the reinforcement phase, the matrix, or both. An example of a polymer–matrix composite (PMC) reinforced with a bio- ceramic is polyethylene (PE) reinforced with HA particles. The toughness of the composite is greater than that of HA and, as we will see in Section 35.8, E is more closely Compact matched to that of bone. Bioceramics are also used as bone coatings on metal substrates. An example is a bioactive glass coating on stainless steel, which utilizes the strength and toughness of steel and the surface-active properties of the glass. Compact bone 35.3 CERAMIC IMPLANTS AND THE STRUCTURE OF BONE Spongy bone The requirements for a ceramic implant depend on what its role in the body will be. For example, the requirements Spongy for a total hip prosthesis (THP) will be different from bone those for a middle ear implant. However, there are two basic criteria: 1. The ceramic should be compatible with the physiologi- cal environment. 2. Its mechanical properties should match those of the FIGURE 35.3 Longitudinal section showing the structure of tissue being replaced. long bone. 638 .......................................................................................................................... Cer am ics in Biology and M edicine  TABLE 35.4 Mechanical Properties of Skeletal Tissues Cortical Cancellous Articular Property bone bone cartilage Tendon Compressive 100–230 2–12 strength (MPa) Flexural 50–150 10–20 10–40 80–120 strength (MPa) Strain to 1–3% 5–7% 15–50% 10% failure E (GPa) 7–30 0.5–0.05 0.001–0.01 1 K1c (MPa m1/2) 2–12 Compressive 20–60 stiffness (N/mm) Compressive 4–15 FIGURE 35.5 Medical grade alumina used as femoral balls in creep THP. The schematic shows how the femoral ball fits into the modulus socket. (MPa) Tensile 50–225 stiffness (MPa) 35.4 ALUMINA AND ZIRCONIA The mechanical properties of the implant are clearly Al2O3 and ZrO2 are two nearly inert bioceramics. They very important. Figure 35.4 compares E of various implant undergo little or no chemical change during long-term materials to that of cortical and cancellous bone. exposure to body fluids. High-density, high-purity (>99.5%) alumina is used in a number of implants, par-  E of cortical bone is ticularly as load-bearing 10–50 times less than hip prostheses and dental STRESS SHIELDING implants. By 2006, >106 that of Al2O3. This occurs when a high-E implant material carries  E of cancellous bone is hip prostheses used an nearly all the applied load. alumina ball for the several hundred times less than that of Al2O3. femoral-head component. Figure 35.5 shows three femoral components of THP with If the implant has a much higher E than the bone it is alumina balls. The U.S. Food and Drug Administration replacing then a problem called stress shielding can occur. (FDA) approved the use of alumina in this type of applica- Stress shielding weakens bone in the region at which the tion in 1982. applied load is lowest or is in compression. (Bone must be Although some alumina dental implants are made loaded in tension to remain healthy.) Bone that is unloaded from single crystals, most alumina implants are very fine- or is loaded in compression will undergo a biological grained polycrystalline Al2O3. These are usually made change that leads to resorption. Eliminating stress shield- by pressing followed by sintering at temperatures in the ing, by reducing E, is one of the primary motivations for range of 1600–1800°C. A small amount of MgO (<0.5%) the development of bioceramic composites. is added, which acts as a grain growth inhibitor and allows a high-density product to be achieved by sintering without 400 Bioinert implants Bioactive implants Bone Bio- cement composites Bone E (GPa) Bioactive composites Al2O3 200 A/W Glass-Ceramic 45S5 Bioglass® Co-Cr Alloys Cortical bone Cancelous bone 316L Steel ZrO2 Ceravita® Ti Alloys PMMA HA 0 FIGURE 35.4 Young’s modulus (E) for various implants compared with bone. 35.4 A lu m i na a n d Z i rc on i a ....................................................................................................................................... 639  TABLE 35.5 Physical Characteristics of Al 2O3 Bioceramics A similar transformation has been observed to occur in aqueous environments. Commercially available high The wear resistance of zirconia is inferior to that of alumina ceramic alumina. In ceramic/ceramic combinations the wear Property implants ISO Standard 6474 rate of zirconia can be significantly higher than that of alumina. In combination with ultrahigh-molecular- Alumina content (wt%) >99.7 ≥99.51 SiO2 + Na 2O (wt%) <0.02 <0.01 weight polyethylene (UHMWPE) excessive wear of Density (g/cm3) 3.98 ≥3.94 the polymer occurs. Average grain size (μm) 3.6 <4.5 Zirconia may contain low concentrations of long half- Hardness (Vickers, HV) 2400 >2000 life radioactive elements such as Th and U, which are Bending strength (MPa, 595 >450 difficult and expensive to separate out. The main after testing in Ringer’s solution) concern is that they emit α-particles (He nuclei) that can destroy both soft and hard tissue. Although the activity is small, there are questions concerning the long-term effect of α radiation emission from zirconia pressure. Table 35.5 lists the physical characteristics ceramics. of Al2O3 bioceramics. The International Standards Orga- nization (ISO) requirements are also given. The most current ISO standard relating to alumina for implants is 35.5 BIOACTIVE GLASSES ISO 6474: 1994, Implants for Surgery—Ceramic Materi- als Based on High Purity Alumina. The ISO is the inter- Bioactive materials form an interfacial bond with sur- national agency specializing in standards at the highest rounding tissue. Hench and Andersson (1993) give the level. Individual countries also have their own standards following definition: organizations. An important require- A bioactive material is one ment for any implant mate- BLOMEDICAL APPLICATIONS OF Al2O3 that elicits a specific biologi- rial is that it should outlast There are many other applications of alumina as an cal response at the inter- the patient. Because of implant material including knee prostheses, ankle joints, face of the material, which the probabilistic nature of elbows, shoulders, wrists, and fingers. results in the formation of a bond between tissues and the failure in ceramics it is not material. possible to provide specific and definite lifetime predic- tions for each individual implant. This was the approach The first and most thoroughly studied bioactive glass that we discussed in Section 16.14. [See the discussion of is known as Bioglass® 45S5 and was developed at the Figure 16.27, a diagram showing applied stress versus University of Florida. Bioglass® 45S5 is a multicomponent probability of time to failure (SPT) for medical-grade oxide glass with the following composition (in wt%): 45% alumina.] It shows, as you might expect, that increased SiO2, 24.5% Na2O, 24.4% CaO, and 6% P2O5. loads and longer times increase the probability of failure. The majority of bioactive glasses are based on the Results from aging and fatigue studies show that it is same four components and all current bioactive glasses essential that Al2O3 implants be produced with the highest are silicates. However, the structure of Bioglass® 45S5 is possible standards of quality assurance, especially if different from that of the silicate glasses we described they are to be used as orthopedic prostheses in younger in Chapter 7. Bioactive glasses have a random, two- patients. dimensional sheet-like structure with a low density. This Although alumina ceramics combine excellent bio- is a result of the relatively low SiO2 content. (You can compatibility and outstanding wear resistance they have compare the bioglass composition with that of other sili- only moderate flexural strength and low toughness. This cates given in Table 21.6.) Bioglass is mechanically weak limits the diameter of most alumina femoral head pros- and has low fracture toughness. Both these properties are theses to 32 mm. Zirconia ceramics have higher fracture related to the glass structure. toughness, higher flexural strength, and lower E than Bioactive glasses can readily be made using the alumina ceramics as shown in Table 35.2. However, there processes developed for other silicate glasses. The con- are some concerns with ZrO2: stituent oxides, or compounds that can be decomposed to There is a slight decrease in flexural strength and tough- oxides, are mixed in the right proportions and melted at ness of zirconia ceramics exposed to bodily fluids. high temperatures to produce a homogeneous melt. On The reason is associ- cooling a glass is produced. ated with the martens- Because bioactive glasses itic transformation A MOIETY are going to be used inside from the tetragonal to A moiety is a group of atoms that forms a distinct part the body it is necessary to the monoclinic phase. of a large molecule. use high-purity starting 640 .......................................................................................................................... Cer am ics in Biology and M edicine materials and often the melting is performed in Pt or Pt tooth is removed. Bioactive glass implants have also been alloy crucibles to minimize contamination. used to repair the bone that supports the eye (the orbital Bioactive glasses have certain properties that are rele- socket). vant to their application in the body. In powder form, bioactive glasses have been used in the treatment of periodontal disease and for the treatment Advantages: There is a relatively rapid surface reaction that of patients with paralysis of one of the vocal cords. When leads to fast tissue bonding. There are five reaction mixed with autologous bone they have been used in maxil- stages on the glass side of the interface. The reaction lofacial reconstruction (i.e., mixed with natural bone to rates and mechanisms at each of the five stages have rebuild a jaw). been determined by Fourier transform infrared (FTIR) spectroscopy. Bonding to tissue requires a further series of reactions that are at present not as well defined. But 35.6 BIOACTIVE GLASS-CERAMICS the bonding process starts when biological moieties are adsorbed onto the SiO2–hydroxycarboapatite layer. In We know that glass-ceramics are produced by ceramming addition, E is in the range 30–35 GPa, close to that of a glass (see Chapter 26): converting it to a largely crystal- cortical bone (see Figure 35.4). line form by heat treatment. Several glass-ceramic com- Disadvantages: They are mechanically weak. Tensile positions are bioactive. Their behavior in the body is very bending strengths are typically 40–60 MPa. In addi- similar to that of the bioactive glasses, i.e., they form a tion, the fracture toughness is low. strong interfacial bond with tissue. As a result of this combination of properties bioactive  Cerabone® A-W is a glass-ceramic containing oxyfluo- glasses are not found in load-bearing applications, rather roapatite (A) and wollastonite (W). they are used as coatings on metals, in low-loaded or  Ceravital® is primarily now used in middle ear compressively loaded devices, in the form of powders, and operations. in composites. The first successful use of Bioglass® 45S5  Bioverit I® is a class of bioactive machinable glass. was as a replacement for the ossicles (tiny bones) in the middle ear. The position of these bones (the malleus, incus Cerabone® A-W glass-ceramic is produced by crystal- and stapes) is illustrated in Figure 35.6. lization of a glass of the following composition (in Cone-shaped plugs of bioactive glasses have been used wt%): 4.6 MgO, 44.7 CaO, 34.0 SiO2, 6.2 P2O5, and in oral surgery to fill the defect in the jaw created when a 0.5 CaF2. The crystalline phases are oxyfluoroapatite FIGURE 35.6 (a) The middle ear cavity and the auditory ossicles. (b) Ear implants. 3 5 . 6 B i oac t i v e G l a s s - C e r a m i c s ................................................................................................................................. 641  TABLE 35.6 Composition Range in wt% of Bioverit ® Glass lel to the c axis. Six of the 10 Ca2+ ions in the unit cell are Ceramics associated with the hydroxyls in these particular columns. Composition Composition Composition One group of three Ca2+ ions describing a triangle, sur- Constituent range 1 2 rounding the OH group, is located at z = 0.25 and the other set of three is located at z = 0.75. The six phosphate SiO2 29.5–50 30.5 38.7 (PO4)3− tetrahedra are in a helical arrangement from levels MgO 6–28 14.8 27.7 CaO 13–28 14.4 10.4 z = 0.25 to z = 0.75. The network of (PO4)3− groups pro- Na 2O/K 2O 5.5–9.5 2.3/5.8 0/6.8 vides the skeletal framework that gives the apatite struc- Al2O3 0–19.5 15.9 1.4 ture its stability. (It is complicated but certainly crystalline F 2.5–7 4.9 4.9 and very natural!) P2O 5 8–18 11.4 8.2 Substitutions in the HA structure are possible. Substi- TiO2 Additions — 1.9 tutions for Ca, PO4, and OH groups result in changes in the lattice parameter as well as changes in some of the properties of the crystal, such as solubility. If the OH− [Ca10 (PO4) 6 (O,F)2] as the A phase and β-wollastonite groups in HA are replaced by F− the anions are closer to (CaO·SiO2) as the W phase. These phases precipitate out the neighboring Ca2+ ions. This substitution helps to at 870°C and 900°C, respectively. The composition of the further stabilize the structure and is proposed as one of residual glassy phase is (in wt%) 16.6 MgO, 24.2 CaO, the reasons that fluoridation helps reduce tooth decay as and 59.2 SiO2. The properties of A-W glass-ceramic are shown by the study of the incorporation of F into HA and shown in Table 35.2. The applications include vertebral its effect on solubility. Biological apatites, which are the prostheses, vertebral spacers, and iliac crest prostheses. mineral phases of bone, enamel, and dentin, are usually Ceravital® refers to a number of different compositions referred to as HA. Actually, they differ from pure HA in of glasses and glass-ceramics that were developed in the stoichiometry, composition, and crystallinity, as well as 1970s in Germany for biomedical applications. The only in other physical and mechanical properties, as shown in field in which Ceravital® glass-ceramics are clinically Table 35.7. Biological apatites are usually Ca deficient and used is in the replacement of the ossicular chain in the are always carbonate substituted: (CO3) 2− for (PO4)3−. For middle ear. In this application the mechanical properties of the material are sufficient to support the minimal applied loads. Bioverit I® consists of two crystalline phases in a glass TABLE 35.7 Comparative Composition and Crystallo- matrix. The key crystalline component that makes this graphic and Mechanical Properties of Human Enamel, Bone, and HA Ceramic glass-ceramic machinable is mica. We have already described the idea behind machinable glass-ceramics in Cortical Section 18.10. For bioactivity, the other crystalline phase Enamel bone HA is apatite. The type and amounts of each phase depend on Constituents (wt%) the initial glass composition. Table 35.6 shows the typical Calcium, Ca 2+ 36.0 24.5 39.6 composition range of Bioverit I® glass-ceramics. Compo- Phosphorus, P 17.7 11.5 18.5 sition 1 produces fluorophlogopite mica and apatite. Com- (Ca/P) molar 1.62 1.65 1.67 Sodium, Na + 0.5 0.7 Trace position 2 produces tetrasilicic mica and apatite. There Potassium, K + 0.08 0.03 Trace are several clinical applications of bioactive machinable Magnesium, Mg2+ 0.44 0.55 Trace glass-ceramics, such as spacers in orthopedic surgery and Carbonate, CO32+ 3.2 5.8 — middle ear implants. Fluoride, F− 0.01 0.02 — Chloride, Cl− 0.30 0.10 — Total inorganic 97.0 65.0 100 Total organic 1.0 25.0 — 35.7 HYDROXYAPATITE Absorbed H2O 1.5 9.7 — Crystallographic properties The apatite family of minerals has the general formula Lattice parameters A10 (BO4) 6X2. In HA, or more specifically calcium hydroxy- (±0.03 nm) apatite, A = Ca, B = P, and X = OH. The mineral part of a 0.9441 0.9419 0.422 teeth and bones is made of an apatite of calcium and c 0.6882 0.6880 0.6880 Crystallinity index 70–75 33–37 100 phosphorus similar to HA crystals. Natural bone is ∼70% Crystallite size, nm 130 × 30 25 × 2.5–5.0 HA by weight and 50% HA by volume. Hydroxyapatite is hexagonal (space group is P63/m) Products after sintering >800°C HA + TCP HA + CaO HA with a = 0.9432 nm and c = 0.6881 nm. The hydroxyl ions lie on the corners of the projected basal plane and occur Mechanical properties E (GPa) 14 20 10 at equidistant intervals [one-half of the cell (0.344 nm)] Tensile strength (MPa) 70 150 100 along columns perpendicular to the basal plane and paral- 642 .......................................................................................................................... Cer am ics in Biology and M edicine this reason you will sometimes see biological apatites stromal component) of the bone. The ideal microstructure referred to as carbonate apatite and not as hydroxyapatite for regeneration of cortical bone is an interconnected or HA. porosity of 65% with pore sizes ranging from 190 to For use in biomedical applications, HA is prepared in 230 μm. The ideal graft substitute for cancellous bone one of two forms: either dense or porous. would consist of a thin framework of large (500–600 μm) We will now discuss interconnected pores. how these two forms are DENSE HA Several methods have produced and some of the Porosity <5 vol% been used to produce applications for each. Pore size <1 μm diameter porous HA ceramics. The methods used to Grain size >0.2 μm Remember that historically produce dense HA are much of ceramic process- ones that we have already ing was concerned with encountered in Chapter 23. The simplest is to dry press trying to produce components that were fully dense. So to HA powder. Mold pressures are typically 60–80 MPa. The produce porous components, particularly where we need powder may also be mixed with a small amount of a to control pore size, often requires ingenuity and a rethink. binder. Suitable binders are 1 wt% cornstarch and water, We discussed porous ceramics in Section 23.15, so will steric acid in alcohol, or low-molecular-weight hydrocar- just point out special features for producing porous HA bons. After pressing, the green ceramic is sintered in air. ceramics. Sintering temperatures are up to 1300°C with dwell times at peak temperature of several hours.  Sintering HA powders By using hot isostatic pressing (HIP) techniques, we  Make a cement can to achieve densification at much lower temperatures  Use a natural template (900°C vs. 1300°C). The use of lower sintering tempera- tures not only saves on energy costs but prevents the for- Sintering HA powders, or a mixture of suitable reac- mation of other calcium phosphate phases, such as TCP, tant powders, uses naphthalene particles that volatilize which usually form when HA is sintered at T > 900°C. during heating to create an interconnected porous network. HIPing has also been used to form HA ceramics. Similar approaches have been used to produce foam glass HIPing results in products with more uniform densities (Section 26.9) and in the fugitive electrode method of than those obtained by uniaxial pressing and higher com- producing multilayer chip capacitors (MLCCs) (Section pressive strength. 31.7). The disadvantage of both hot pressing and HIPing is By mixing water-setting HA cements with sucrose the equipment costs. granules, porosity can be There are many appli- created when the sucrose cations for dense HA in RESORPTION is dissolved prior to the both block form and as Resorption is the process of reabsorbing biological cement setting. One particles as listed in Table material. example of an HA cement 35.8. One important appli- is that obtained by the fol- cation is replacements for tooth roots following extraction. lowing reaction in an aqueous environment: The implants help minimize alveolar ridge resorption and maintain ridge shape following tooth loss, which affects Ca4 (PO4) 2 + CaHPO4 → Ca5(PO4)3OH (35.1) millions of people. The particular advantage of porous HA is that it The natural-template method was developed in 1974. permits ingrowth of tissue into the pores, providing bio- It can produce porous HA powders. A suitable template logical fixation of the implant. The minimum pore size was found to be the calcium carbonate (CaCO3) skeleton necessary is ∼100 μm. When used as a bone graft substi- of reef-building corals, such as those found in the South tute, the porous HA should mimic the framework (or Pacific. The reaction to produce HA involves a hydrother- mal exchange reaction of carbonate groups with phosph- ate groups, which can occur via the following chemical reaction: TABLE 35.8 Applications for Dense HA Ceramics Application Form 10CaCO3 + 6(NH4) 2HPO4 + 2H2O → Augmentation of alveolar ridge for better denture fit Blocks Ca10 (PO4) 6 (OH) 2 + 6(NH2)CO3 + 4H2CO3 (35.2) Orthopedic surgery Blocks Target materials for ion-sputtered coatings Blocks The HA structure produced by this exchange reaction Filler in bony defects in dental and orthopedic surgery Particles replicates the porous marine skeleton, including its inter- Plasma sprayed coatings on metal implants Particles connected porosity. Hydroxyapatite grown on Porites and Filler in composites and cements Particles Goniopora coral skeleton templates can be used to mimic 3 5 .7 H y d r ox ya pat i t e .................................................................................................................................................... 643 the stroma of cortical bone and cancellous bone, 25 respectively. Ductile Brittle εf E (%) (GPa) E (Cortical bone) 10 100 x 35.8 BIOCERAMICS IN COMPOSITES εf The main reason for forming composites is to improve the 8 80 x mechanical properties, most often toughness, above that of the stand-alone ceramic. For bioceramic composites we E often are trying to increase KIC and decrease E. 6 Bioactive 60 The first bioceramic composite was a stainless-steel fiber/bioactive glass composite made of Bioglass® 45S5 x and AISI 316L stainless steel. The composite was made 4 x 40 by first forming a preform of the discontinuous metal fibers, then impregnating it with molten glass, and finally x x heat treating the composite to develop the desired mechan- x ical properties. 2 εf 20 For effective stress transfer between the glass matrix E and the reinforcing metal fibers when the composite is x under load, there must be a strong glass–metal bond. This 0 0 requires that the glass wet the metal surface during 0 10 20 30 40 50 processing. Wetting is achieved by oxidizing the metal vol. % HA fibers before they are immersed in the glass. Chemical FIGURE 35.7 Effect of volume fraction of HA on E and strain to analysis across the glass–metal interface showed that failure of HA-reinforced PE composites, in comparison to cortical there is Fe diffusion from the oxide into the glass and Si bone. diffusion from the glass into the oxide. The composition gradient across the interface indicates chemical interac- tion between the two phases, which leads to improved Other current bioceramic composites of interest are adhesion. Assuming that the fibers are aligned in the direction  Ti-fiber-reinforced bioactive glass of the applied load, and that there is good adhesion with  ZrO2-reinforced A-W glass the matrix such that the elastic strains are equal in both  TCP-reinforced PE components, we can write  HA-reinforced PE Hydroxyapatite-reinforced PE is a good illustration σc = σfVf + σmVm (35.3) of a composite that can have properties that are not available in a single material. These composites were The subscripts c, f, and m refer to the composite, fiber, developed as a bone replacement that would have a matched and matrix, respectively, and V is the volume fraction of modulus, be ductile, and bioactive. Figure 35.7 shows each phase. If we assume 45 vol% of steel fibers and σf = how increasing the volume fraction of HA to 0.5 in a 530 MPa and σm = 42 MPa, then σc = 262 MPa. This value, composite can be achieved with E in the range of that of which is close to experimentally measured values, repre- cortical bone. When the volume fraction of HA in the sents a significant strengthening above that of the glass composite is increased above about 0.45 the fracture alone. mode changes from ductile to brittle. For clinical applica- One of the potential problems associated with forming tions a volume fraction of 0.4 has been found to composites is that of mis- be optimum. The HA- match in α between the two reinforced PE composite components, which is sig- AISI 316L is designated commer- nificant for glass and steel. −6 −1 cially as HAPEXTM and For reinforcing fibers for α = 20.0 × 10 °C (to 200°C) several thousand patients which the difference in α have received middle ear with the glass phase is even α = 21.8 × 10−6 °C−1 (to 400°C) implants made from this greater than that with steel, material. The technology e.g., Ti, it is necessary to BIOGLASS® 45S5 was granted regulatory change the composition of approval by the FDA in the the glass to lower its α. α = 18.0 × 10−6 °C−1 (to 450°C) United States in 1995. 644 .......................................................................................................................... Cer am ics in Biology and M edicine 35.9 BIOCERAMIC COATINGS the plasma temperature may exceed 10,000°C!) so the mechanical properties of the metal are not compromised. Applying a glass or ceramic coating onto the surface of a The coating thickness typically averages 40–60 μm with substrate allows us to have the best of both worlds. We a residual porosity <2%. have the bulk properties of the substrate and the surface Hydroxyapatite coatings prepared by plasma spraying properties of the coating. There are three main reasons for typically contain considerable amounts of amorphous applying a coating: calcium phosphate and small amounts of other crystalline phases. Heat treating the coating can increase crystallinity 1. Protect the substrate against corrosion and also improve the adhesion to the substrate. However, 2. Make the implant biocompatible this process is not usually done because of economic 3. Turn a nonbioactive surface into a bioactive one factors and concerns about the adverse effects it might have on the mechanical properties of the substrate. There are four substrate-coating combinations: In addition to plasma spraying other methods have been used to apply HA coatings: 1. Polycrystalline ceramic on ceramic 2. Glass on ceramic  Electrophoretic deposition when line-of-sight deposi- 3. Polycrystalline ceramic on metal tion is not possible 4. Glass on metal  Sputtering when very thin coatings are needed  HIPing when we need a very dense material Bioceramic coatings are often used on metallic sub- strates in which the fracture toughness of the metal is Electrophoretic deposition (see Section 27.6 for a combined with the ability of the coating to present a bioac- description of the technique) can be used to coat porous tive surface to the surrounding tissue. The use of a bio- surfaces that cannot be completely coated by line-of-sight ceramic coating on a metal implant can lead to earlier techniques such as plasma spraying. But the adhesion of stabilization of the implant in the surrounding bone and the HA particles to the substrate and each other is weak extend the functional life of the prosthesis. Under the and high-temperature sintering after deposition is usually proper conditions a cementless prosthesis should remain necessary. functional longer than a cemented device in which stabi- Sputtering has been used to produce thin (1 μm) HA lity is threatened by fracture of the bone cement. coatings. The deposited films are amorphous because The important ceramic coatings are HA and TCP. We the sputtered components do not possess enough kinetic described the structure and properties of HA, a bioactive energy to recombine in a crystalline form. Heat treatment ceramic, in some detail in Section 35.6. Tricalcium phos- at 500°C is enough to crystallize the amorphous film. phate is a resorbable bioceramic. It occurs in two poly- Durability of thin sputtered films in the body has not yet morphs, α-whitlockite and β-whitlockite. The β form is been demonstrated. the more stable. When TCP is implanted into the body it HIPing is a technique we encountered earlier, but not will eventually dissolve and be replaced by tissue. The role in the context of forming films. If a metal implant is of resorbable bioceramics is to serve as scaffolding, per- coated with HA particles then HIPing can be used to form mitting tissue infiltration and eventual replacement. Essen- a dense adherent coating. To achieve a uniform application tially, this is the same function as bone grafts. Tricalcium of pressure on the HA particles an encapsulation material phosphate has been clinically applied in many areas of (e.g., a noble metal foil) is necessary. As mentioned earlier, dentistry and orthopedics. Bulk material, available in HIPing allows the use of lower sintering temperatures dense and porous forms, is used for alveolar ridge aug- than pressureless techniques; as a result there is less mentation, immediate tooth root replacement, and maxil- chance of altering the microstructure or mechanical pro- lofacial reconstruction. However, because bulk TCP is perties of the metal substrate. mechanically weak, it cannot be used in load-bearing There are several requirements for HA coatings used applications. Therefore, TCP is often used as a coating on for prosthetic devices: metal substrates. The most widely used method for applying coatings of  Correct crystalline phase HA and TCP is plasma spraying. We already described  Stable composition this technique in Section 27.5; it is one of the methods  Dense used to produce thermal barrier layers. Plasma spraying  Good adhesion to the substrate uses a plasma, an ionized gas, that partially melts the HA  High purity particles and carries them to the surface of the substrate.  No change to the substrate For HA coatings the starting material is pure 100% crys- talline HA particles in the 20–40 μm range. One of the Plasma sprayed coatings often contain a mixture of advantages of plasma spraying is that the substrate remains crystalline and amorphous phases, which may be undesir- at a relatively low temperature (generally less than 300°C; able. The adhesion of plasma-sprayed HA coatings to 3 5 . 9 B i o c e r a m i c C oat i n g s ........................................................................................................................................... 645 metal substrates is principally mechanical, and so surface roughness of the substrate plays an important role. Bioactive glass coatings are also important for implant devices. These are usually applied by one of the following techniques:  Enameling  Flame spraying  Dip coating Flame spraying is similar to plasma spraying except that the carrier gases are not ionized and the temperatures are considerably lower than in plasma spraying. In dip coating, the metal implant is preoxidized to provide a suit- able surface for wetting of the molten glass. The heated metal is then dipped into the molten glass. Enameling is a traditional method of applying glass FIGURE 35.8 Lithium calcium borate glass microspheres produced by passing through a flame at 1400°C. coatings and uses a particulate form of the glass called a frit, which is formed when molten glass is quenched in water. The resulting coarse particles of the frit are ground etration ∼10 mm). For the radioactive material to reach the to a fine powder that is applied to the metal substrate by site of the tumors between 1 and 15 million microspheres painting, spraying, or dipping. The coated article is then are injected into the hepatic artery, which is the primary heated to soften the glass and form a uniform coating. In blood supply for the target tumors. Treatment time takes traditional enameling the adhesion between the glass and 2–4 hours. The size of the microspheres is 15–35 μm in metal is improved by using what enamellers call a “ground diameter, which allows the blood to carry them into the coat.” This is a mixture of metal oxides that reacts chemi- liver, but they are too large to pass completely through the cally with both the metal and the glass enabling the forma- liver and enter the circulatory system. The microspheres tion of a chemical bond. However, this approach has not concentrate in the tumor because it has a greater than proved to be successful with bioactive glasses and alterna- normal blood supply. And there they irradiate it with β- tive approaches are being used. particles. Since the half-life of 90Y is 64.1 hours, the radio- activity decays to a negligible level in about 3 weeks. 35.10 RADIOTHERAPY GLASSES Although the use of radiotherapy glass spheres in treating liver cancer is still at a relatively early stage the Radioactive yttrium aluminosilicate (YAS) glasses have results appear promising. The commercially available been used to provide in situ irradiation of malignant product called TheraSphereTM made by MDS Nordion is tumors in the liver. Although primary liver tumors are approved in the United States and Canada for treating relatively rare in the United States (about 3000–4000 patients with inoperable liver cancer. Other medical appli- deaths per year in the United States, 1.2 million world- cations for these glass spheres have been considered such wide) they are almost always lethal. And most of these as the treatment of cancers of the kidney and brain. tumors are inoperable due to various medical complica- Figure 35.8 shows lithium calcium borate (LCB) glass tions. Irradiating the tumors inside the body allows the microspheres that were spheroidized by passing them through use of large (>10,000 rads) localized doses of radiation a high-temperature flame. A similar process is used to make directly to the tumor while minimizing damage to sur- the smaller YAS microspheres. The LCB microspheres are rounding healthy tissue. And this procedure represents an subsequently converted into hollow hydroxyapatite micro- important tool in treating this disease. spheres that have potential application in drug delivery. YAS glasses are particularly suitable because they are 35.11 PYROLYTIC CARBON  Not toxic HEART VALVES  Easily made radioactive  Chemically insoluble while the glass is radioactive Carbon is an important bioceramic. It combines out- The sol-gel process has been used to produce high standing biocompatibility and chemical inertness. Carbon purity YAS glass spheres. The radioactive isotope pro- exists in many forms, some of which have been discussed duced when the YAS glass spheres are irradiated is 90Y, a in earlier chapters. The most important form of carbon β emitter with a half-life of for biomedical applications 64.1 hours. The average is a type of pyrolytic penetration of β-particles LTI graphite known as the low- (electrons) in human tissue Low T refers to the forming T < 1500°C. For ceramics temperature isotropic form is 2.5 mm (maximum pen- 1500°C is not a high T. (LTI carbon). 646 .......................................................................................................................... Cer am ics in Biology and M edicine  Low-temperature isotropic carbon is an example of what are referred to as turbostratic carbons. These have a disor- dered structure based on graphite (and thus are also called turbostratic graphite). In turbostratic carbon the ABABA stacking sequence is disrupted through random rotations or displacement of the layers relative to each other. The indi- vidual LTI carbon crystallites are only ∼10 nm in size and are arranged randomly in the bulk material. This microstructure leads to the material having isotropic mechanical and physical properties, unlike graphite in which the properties are highly anisotropic. The density and mechanical properties of LTI are influenced by the number of carbon vacancies in each of the layers and distortions FIGURE 35.9 LTI pyrolytic carbon-coated heart valve. within each plane. The densities range from 1400 kg/m3 up to a theoretical maximum of 2200 kg/m3. High-density LTI carbons are the strongest bulk form materials. The first use of LTI carbon in humans for pros- of turbostratic carbon; we can increase their strengths thetic heart valve was in 1969. The majority of artificial further by adding Si. The material then consists of discrete heart valves currently use Si-alloyed LTI pyrolytic submicrometer β-SiC particles randomly dispersed in a carbon. matrix of roughly spherical micrometer-sized subgrains of pyrolytic carbon; the carbon itself has a “subcrystalline” turbostratic structure, with a crystallite size typically 35.12 NANOBIOCERAMICS <10 nm. This is analogous to the microstructure produced during precipitation hardening of metals. By 20.12, there will be books on the uses of nanoparticles A chemical vapor deposition (CVD) process (see and there are already hundreds of research papers. There Section 28.4) involving the codeposition of carbon and may also be books discussing the toxicity of these mater- SiC is typically used to produce the LTI–Si alloys. Two ials. The asbestos fibers linked to respiratory illness have possible reactions are widths <250 nm; amphibole (red or blue asbestos) fibers are ∼75–∼240 nm wide, therefore definitely counting as 1. Decomposition of propane: nanoparticles. Examples of a microbarcode made by Corning are C3H8 → 3C + 4H2 (35.4) shown in Figure 35.10. The information is coded into the small glass bars so that they fluoresce. The pattern can 2. Decomposition of methyltrichlorosilane then be read by illuminating the glass with UV; otherwise it is not only too small to see but the information could CH3Cl3Si → SiC + 3HCl (35.5) not be detected. The magnetite nanocrystals we discussed in Chapter The articles to be coated are suspended within a flui- 33 are used by nature in ways we do not fully understand, dized bed of granular particles, usually ZrO2. The reactions but they appear to allow certain species to detect the take place in the range of 1000–1500°C and the products earth’s magnetic field and use it to navigate. coat the components as well as the ZrO2 particles. TiO2 nanoparticles are used in sunscreen to protect the One of the major applications for LTI carbon is in skin from UV radiation. The particles used for this appli- making prosthetic heart valves as shown in Figure 35.9. cation are typically 10–100 nm in diameter and block both This is one of the most demanding applications for bio- UVA (320–400 nm) and UVB (290–320 nm) irradiation. FIGURE 35.10 Microbar codes from Corning. The cyllindrical bars are typically 100 μm long and 20 μm in diameter. 3 5 .1 2 N a n o b i o c e r a m i c s ................................................................................................................................................ 647  Veneer Veneer Bulk ceramic Dentine Pulp Dentine FIGURE 35.11 Tooth restoration. There is some concern that these nanoparticles (and those of ZnO) are so active that they might catalyze the break- down of DNA, but they do not appear to penetrate the outer layers of the skin. The positive aspect of this is the potential for using these same TiO2 nanoparticles for photo-killing of malignant cells—known as photody- namic therapy. TiO2 and ZnO particles are actually being coated with silica so that the particle surface is more inert. (A use for core-shell nanoparticles.) FIGURE 35.12 (a) Schematic of the abalone shell. (b) Abalone 35.13 DENTAL CERAMICS slabs. The felspathic porcelains (porcelain’s based on feld- Biomimetics can poten- DENTAL RESTORATIONS spar) are used as the veneer tially lead to an enormous Feldspathic veneers to “cap” the front of a tooth subset of ceramics. Not Porcelain jacket crowns (PJCs) for cosmetic reasons; these only are the materials Metal-ceramic crowns veneers are ∼500 μm thick. important but their topo- Inlays and onlays Today, this material is logy and microstructure Implants mainly replaced by glass, are also special. The aim is although the name may not to mimic natural materials have changed. Leucite is added to modify the thermal that have special behaviors, but to do it with “better” (i.e., expansion coefficient. Dicor is the glass-ceramic devel- ceramic) materials. oped by Corning for construction of replacement teeth. The tooth is cast as a glass using a lost-wax mold and then Shells (especially the abalone shell). Biological organisms cerammed. Alumina has also been used to form the tooth, can deposit inorganic layers. The abalone shell consists although porosity causes failure during “use.” One way of layers of aragonite with ∼5 wt% organic material to improve this is to infiltrate the alumina with a lantha- (protein, etc.) between the layers to toughen it. A sche- num-containing glass (known commercially as In-Ceram). matic cross section and a scanning electron micro- The different restorations are shown schematically in scopic (SEM) image of the aragonite layers are shown Figure 35.11. in Figure 35.12. Coral. Coral is used “as harvested” or after processing in the manufacture of bone grafts. It is a natural porous 35.14 BIOMIMETICS ceramic and can be converted to porous HA (see Section 35.7). Surgeons in the United States perform The topic of biomimetics was actually mentioned earlier ∼500,000 bone grafts each year. but not using the new name. The principle underlying the Petrified wood. A natural material is infiltrated by a development of biomimetics is “learning from nature.” ceramic. 648 .......................................................................................................................... Cer am ics in Biology and M edicine  FIGURE 35.13 Wood converted into ceramics by a reactive melt-infiltration process. Petrified wood provides a good illustration of the sur- the wood used. Beech, pine, and rattan produce very dif- prising potential of biomimetics in a way that is analogous ferent microstructures which are of course different in to the conversion of coral. Wood can be intentionally cross section and longitudinally. In this example, the infil- converted into biomorphic, microcellular SiC-based trating liquid was a molten Si-M alloy (Mo, Ta, Ti, and Fe ceramics using a reactive melt-infiltration process, or more were explored as the metal, M). For Mo, this produces an specifically liquid-Si infiltration (LSI). The images shown MoSi2 /Si composite. The LSI technique has been used in Figure 35.13 illustrate the possibility: the microstruc- previously to produce SiC and Si3N4; the special feature ture of the resulting composite depends on the nature of here is the biomimetic structure produced by the wood. CHAPTER SUMMARY Bioceramics is a relatively new field and an increasingly important one. Bioceramics are implanted into the human body to replace existing parts that have become diseased, damaged, or worn out. More than 1 million hip prostheses using alumina components have been performed. Alumina is a very important bioceramic because it is biocompatible—it does not produce any adverse reactions in the body. One of the disadvantages of alumina is that it is also an example of what is termed a nearly inert bioceramic: it does not allow interfacial bonding with tissue. When bioactive ceramics and glasses are implanted into the body they undergo chemical reactions on their surface leading to strong bond formation. The most important bioactive ceramic is hydroxyapatite, which is very similar to the mineral part of teeth and bones. Hydroxyapatite is brittle and mechanically weak, but if it is combined with a polymer a composite can be produced that is ductile and has E close to that of bone. Hydroxyapatite and other bioactive ceramics and glasses are often used as coatings on metal supports. This allows the excellent mechanical properties of the metal to be combined with the biocompatibility of ceramics. Another ceramic material that is used in the form of a coating is pyrolytic carbon. The application here is artificial heart valves, which is a very demanding materials application: reliability is critical. We concluded the chapter with a brief discussion of biomimetics (which is related to bionics, etc.) and emphasize that this will become a large field in itself but the materials must be understood to take full advantage of this potential. GENERAL REFERENCES Hench, L.L. and Wilson, J.K. (Eds.) (1993) An Introduction to Bioceramics, World Scientific, Singapore. A collection of chapters on different aspects of bioceramics written by experts in the field. This is an excellent resource. C h a p t e r S u m m a ry .......................................................................................................................................................... 649  LeGeros, R.Z. and LeGeros, J.P. (Eds.) (1998) Bioceramics, Volume 11, Proceedings of the 11th International Symposium on Ceramics in Medicine, World Scientific, Singapore. The most recently published proceed- ings in this annual conference series. Covers the latest developments in all aspects of the field of bioceramics. Marieb, E.N. (1998) Human Anatomy and Physiology, 4th edition, Benjamin Cummings, Menlo Park, CA. For a more detailed description of bone. Park, J.B. (1984) Biomaterials Science and Engineering, Plenum, New York. A textbook covering all aspects of biomaterials. The section covering ceramic implant materials is quite brief, but there is information about polymers and metals and a general background about the field. Ravaglioli, A. and Krajewski, A. (1992) Bioceramics: Materials, Properties, and Application, Chapman & Hall, London. Covers the history of bioceramics, scientific background to the field, and state of the art as of 1991. Shackelford, J.F. (Ed.) (1999) Bioceramics: Applications of Ceramics and Glass Materials in Medicine Mater. Sci. Forum, 293. A recent monograph on bioceramics. Williams, D.F. (1999) The Williams Dictionary of Biomaterials, Liverpool University Press, Liverpool. The latest collection of definitions used in the field of biomaterials. Yamamuro, T., Hench, L.L., and Wilson, J. (Eds.) (1990) Handbook of Bioactive Ceramics, Volume I: Bioactive Glasses and Glass Ceramics, Volume II: Calcium Phosphate and Hydroxylapatite Ceramics, CRC Press, Boca Raton, FL. A collection of articles on bioactive and resorbable bioceramics. JOURNALS AND CONFERENCE PROCEEDINGS The following journals and conference proceedings contain reports of advances in bioceramics. Bioceramics. This is the title of the Proceedings of the International Symposium on Ceramics in Medicine. The symposium has been held annually since 1988. Biomaterials. 1980–present (volume 27) Biomedical Materials and Engineering. Covers all aspects of biomaterials and includes details of clinical studies. Usually found with medical journals rather than physical science or engineering publications. Journal of Biomedical Materials Research. (Now volume 80; 4 volumes in both ‘A’ and ‘B’.) Journal of Materials Science Materials in Medicine. Emphasising the materials science aspects. Journal of the American Ceramic Society. Covers the entire ceramics field including bioceramics. Nature. A journal with a wide readership. Publishes important news articles having a significant impact on the field. SPECIFIC REFERENCES Annual Book of ASTM Standards, 13.01, Medical Implants, ASTM, Philadelphia. The American Society for Testing and Materials (ASTM) has developed several standards related to bioceramics for surgical implants: the Annual Book of ASTM Standards. Bokros, J.C., LaGrange, L.D., Fadali, A.M., Vos, K.D., and Ramos, M.D. (1969) J. Biomed. Mater. Res. 3, 497. First use of carbon heart valves in humans. Bonfield, W., Grynpas, M.D., Tully, A.E., Bowman, J., and Abram, J. (1981) “Hydroxyapatite reinforced polyethylene—a mechanically compatible implant,” Biomaterials 2, 185. Brömer, H., Pfeil, E., and Käs, H.H. (1973) German Patent 2,326,100. Patent for Ceravital. Chakrabarti, O., Weisensel, L., and Sieber, H. (2005) “Reactive melt infiltration processing of biomorphic Si–Mo–C ceramics from wood,” J. Am. Ceram. Soc. 88(7), 1792. DiB: Defi nitions in Biomaterials (1987) D.F. Williams (Ed.), Elsevier, Amsterdam, 6. Includes a discussion of biocompatibility. Ducheyne, P. and Hench, L.L. (1982) “The processing and static mechanical properties of metal fibre rein- forced bioglass®,” J. Mater. Sci. 17, 595. Diffusion across a bioglass-metal interface. Galletti, P.M. and Boretos, J.W. (1983) “Report on the Consensus Development Conference on Clinical Appli- cations of Biomaterials” J. Biomed. Mat. Res. 17, 539. Defined “biomaterial.” Hench, L.L. (1991) “Bioceramics: From concept to clinic,” J. Am. Ceram. Soc. 74, 1487. An excellent review on this topic. Hench, L.L. and Andersson, O. (1993) “Bioactive glasses,” in An Introduction to Bioceramics, edited by L.L. Hench and J.K. Wilson, World Scientific, Singapore, 41. Klawitter, J.J. and Hulbert, S.F. (1971) “Application of porous ceramics for the attachment of load bearing orthopedic applications,” J. Biomed. Mater. Res. 2, 161. Determined that a minimum pore size of 100 μm is necessary for bone ingrowth. Mehmel, M. (1930) Z. Kristallogr. 75, 323. One of two original determinations of the structure of hydroxy- apatite. The structure was originally taken to be the same as that of fluorapatite, Ca10 (PO4) 6F2, which had already been resolved. 650 .......................................................................................................................... Cer am ics in Biology and M edicine  Merwin, G.E., Wilson, J., and Hench, L.L. (1984) in Biomaterials in Otology, edited by J.J. Grote, Nijhoff, The Hague, pp. 220–229. Description of bioglass. Náray-Szabó, S. (1930) Z. Kristallogr. 75, 387. The other paper on the structure of hydroxyapatite. Posner, A.S., Perloff, A., and Diorio, A.F. (1958) “Refinement of the hydroxyapatite structure,” Acta Cryst. 11, 308. Determined atom positions, bond lengths, and lattice parameters for the HA crystal structure. Roy, D.M. and Linnehan, S.K. (1974) “Hydroxyapatite formed from coral skeletal carbonate by hydrothermal exchange,” Nature 247, 220. Developed the natural-template method for making porous HA. Sarakiya, M. (1994) “An introduction to biomimetics: A structural viewpoint,” Microsc. Res. Techn. 27, 360. A very useful introduction. Sato, T. and Shimada, M. (1985) “Transformation of yttria-doped tetragonal ZrO2 polycrystals by annealing in water,” J. Am. Ceram. Soc. 68, 356. Described the martensitic transformation in ZrO2 in aqueous environments. Wang, Q., Huang, W., Wang D., Darvell, B.W., Day, D.E., and Rahaman, M.N. (2006) “Preparation of hollow hydroxyapatite microspheres,” J. Mater. Sci: Mater. Med. 17, 641. WWW www.mds.nordion.com/therasphere/ The TheraSphere® web site. EXERCISES 35.1 Briefly compare and contrast the suitability of metals, ceramics, and polymers for use in biomedical applica- tions. In your answer consider the following factors: biocompatibility, mechanical properties, and ease of processing. 35.2 Alumina (Al2O3) ceramic implants are required to have a small grain size (<4.5 μm). (a) Why do you think a small grain size is important? (b) How does the addition of MgO to the powder mixture help to keep the grain size small? (c) Are there any other ways that could be used to limit the extent of grain growth? 35.3 Explain why tetragonal zirconia polycrystal (TZP) and Mg-partially stabilized zirconia (PSZ) ceramics have higher toughness than alumina ceramics. 35.4 The Weibull modulus of an alumina bioceramic is given as 8.4. (a) What does a value of m = 8.4 imply? (b) For an implant made out of a metal the value of m ∼ 100. What implications would this have for lifetime predictions for the metal component compared to the alumina component? (c) How does the value of m affect the design of a component for a load-bearing application? 35.5 The composition of Bioglass® 45S5 is 45% SiO2, 24.5% Na2O, 24.4% CaO, and 6% P2O5. (a) Classify each of the oxide constituents of 45S5 as either network formers, modifiers, or intermediates. (b) What would the composition of Bioglass® 45S5 be in mol%? (c) Explain briefly how the structure of 45S5 differs from the silicate glasses described in Chapter 7 and what implications this difference has on the properties of 45S5. 35.6 The substitution of ions in the HA structure can change the lattice parameters of the unit cell. Explain how you think the substitution of Ca2+ for the following ions would change both the a and c lattice parameters: Sr2+ , Ba2+ , Pb2+ , Mg2+ , Mn2+ , and Cd2+ . 35.7 According to ASTM Standards [American Society for Testing and Materials (1990) Annual Book of ASTM Standards, Section 13, F 1185–1188] the acceptable composition for commercial HA is a minimum of 95% HA, as established by X-ray diffraction (XRD) analysis. Describe how XRD can be used to determine phase proportions in a mixture. 35.8 We mentioned that in steel fibers/bioactive glass composites it was important that there was chemical interac- tion between the two components to ensure stress transfer during loading. We have just formed a bioceramics company and want to hire you as a consultant. We want you to determine whether such interactions have occurred in a composite we have just made. What analytical technique or techniques would you use for your evaluation? Explain the reasoning behind your answer and some of the pros and cons of the technique or techniques you chose. 35.9 One of the advantages of plasma spraying for producing HA coatings on metallic implants is that the substrate temperature can be kept relatively low. What possible mechanisms can lead to a loss in the mechanical strength of a metal if it is exposed to high temperatures? (You can limit your discussion to the cases of Ti alloys and stainless steel.) 35.10 Explain why the mechanical properties of turbostratic carbons such as LTI are different from those of gra- phite. Both are forms of carbon and are chemically identical. C h a p t e r S u m m a ry .......................................................................................................................................................... 651  36 Minerals and Gems CHAPTER PREVIEW We begin this chapter by explaining why we are including gems in a text on ceramics. Gems have been intimately linked with many developments in the use of ceramics or have been the motivation for what has become a leap forward in ceramic processing or application. We saw earlier how the efforts by August Verneuil in the early 1900s to produce synthetic ruby led to an industry that produces 2 × 105 kg of single-crystal Verneuil sapphire each year. Similarly, flux-growth techniques and hydrothermal quartz owe much to the desire to create gems. Gem- stones use some special properties of ceramics: they can be transparent but with a range of colors, they scatter light (the sparkle), and the valuable ones are generally very stable (the less valuable ones have often been treated); actually most gemstones have been processed in some way. We will discuss the well-known gems and a few of the lesser known gems (for their special features). The most important gems are diamond, ruby, sapphire, and emerald. However, many other gems that are less well known may often be more valuable. Incidentally, the weight of a gemstone is usually given in carats (5 ct = 1 g). We will also use this chapter to summarize the links between some preceding topics, including history. If a friend hands you a blue (or red, yellow, green, or colorless) faceted sparkling stone and asks you to identify it (because you studied ceramics) what do you do or say? So when you read this chapter, keep asking your- self—what ceramic science is involved here. 36.1 MINERALS Crush lapis lazuli like the Persians did to make ultramarine Mining and mineral engineering are not always popular Grind azurite like the ancient Egyptians to produce the topics today. Many gemstones and mineral specimens blue pigment azure are found during mining operations. Most minerals are Grind tin oxide like the Romans to make a white cosmetic then processed by physical or chemical means. Ceramists paste should have some knowledge of mineral processing Be cautious about using ground talc on your body because this can be the clue to understanding why certain impurities are present in powders used to produce high- Of course, grinding is also the principle of the abrasives tech ceramics (hence our discussion of raw materials in industry. Powders may be made by grinding or used for Chapter 19), but minerals and gemstones have many com- grinding/polishing as discussed in Section 18.12. mercial in addition to decorative (ornamental) uses. A crystal of galena was used in the cat’s whisker radio Grinding is a particularly simple example of physical (in the “point-contact” diode); Cu wire was slowly moved processing. It has been used to make pigments, early cos- across the galena crystal to tune the device. Thin slices of metics, and the ingredients for the potter’s slip. It is a key tourmaline crystals were used in making the pressure step in modern ore processing (Chapter 19), but it has been gauges that measured the power dissipated by the first used for centuries to make powders. atom bomb explosions (tourmaline is piezoelectric). Chalcedony is “non- Grind hematite to pro- crystalline” quartz. Exam- duce the red pigment NATURAL GLASS THREAD ples of chalcedony are ochre Pele’s hair (the Hawaiian goddess of volcanoes, not the agate, jaspar, and carne- Grind cinnabar to produce soccer player) consists of natural threads of basalt glass lian; they form by hydro- the major component often containing crystals of olivine. Like obsidian and thermal growth—hence of vermillion pumice it forms in volcanic eruptions. the banding you see on 652 ....................................................................................................................................................... Minerals and Gems stones in museum shops. The color depends on the impuri- TABLE 36.1 Gemstones ties and not much impurity is needed (it can easily be Hard and resistant Chrysoberyl, BeAl2O4 changed/dyed). We will discuss flint and opal separately, to chemicals Corundum, Al2O3 although they are closely related. Flint tools, like obsidian Quartz and chalcedony, SiO2 tools, were used thousands of years ago. Flint consists of Spinel, MgO · Al2O3 fine-grain silica (the black color is caused by trapped Gem carbonates Calcite, CaCO3 carbon) and fractures like obsidian, producing sharp edges (not so hard) Malachite, Cu2 (OH) 2CO3 Rhodochrosite, MnCO3 that are ideal for cutting. Gem phosphates Apatite, Ca5 (F2Cl)(PO4) 3 Alabaster, gypsum (CaSO4 ·2H2O), and Plaster of Paris (not so hard) Turquoise, a complex hydrated phosphate (2CaSO4 ·H2O) are all calcium sulfate (the last of these has of copper and aluminum been treated to produce the hemihydrate). Fine-grain Gem silicates Beryl, Be3Al2 (SiO3) 6 gypsum is easily carved: fractures do not propagate far. (hard and Feldspar group gems: aluminum silicates durable) in combination with calcium, potassium, Alabaster ornaments were made in Assyria (Iraq) before or sodium 2000 bce and Plaster of Paris was used by the Egyptians Garnet group gems: silicates of various in ∼3000 bce in making mortar. combinations of magnesium, manganese, iron, calcium, aluminum, and chromium Jadeite, NaAl(SiO3) 2 Nephrite, complex calcium, magnesium, or iron silicate 36.2 WHAT IS A GEM? Peridot, (Mg,Fe) 2SiO4 Rhodonsite, MnSiO3 Gems are often characterized as expensive sparkling Topaz, Al2 (F2OH) 2SiO4 stones. The value is not necessarily as obvious as we might Tourmaline, a complex borosilicate of aluminum and iron hope. Even so, you will probably spend significant money Zircon, ZrSiO4 on gems. A gem can be real (natural), synthetic (grown in the laboratory or factory), or a simulant (one material made to look like another). Gems can provide a link between ceramics, geology, crystallography, mechanical testing, solid-state, physical, and inorganic chemistry, and electrical engineering. They  Are there defects in my emerald? (Yes.) provide the ceramist with many challenges, such as iden-  Is natural emerald better than synthetic emerald? tify this ceramic (gem) without removing it from the gold (Synthetic emerald is usually more perfect.) band in which it is set. Table 36.1 lists some of the best-  Should I wash my opal with water or with alcohol? known gemstones with some of their special features. (No.) One challenge is to identify a particular gemstone. The questions emphasize the need for techniques to aid The scientist’s way is to use X-ray diffraction (XRD), X- the eye in examining these materials, or the need to under- ray energy-dispersive spectrometry (XEDS), wave- stand the structure and chemistry of gemstones when han- length-dispersive spectroscopy (WDS), or comparable dling them. techniques for chemical analysis. The gemologist’s way is to use the refractive index or the thermal and/or electrical conductivity. 36.3 IN THE ROUGH The difference, of course, is that the gemologist must The traditional mining of gemstones is illustrated in often identify the gemstone in the field (in the home, in Figure 36.1. Since many mines are in less developed coun- the mine, or really in the field) without taking the sample tries and very small stones can be very valuable, the to the laboratory. With experience, you can, for example, mining tends to rely on manual labor. Open mines like the “feel” if a stone is a good thermal conductor. one shown in Figure 36.1 are inexpensive to establish and Some examples of questions you might be asked: in many cases have not changed in centuries. Miners then and now often have to endure brutal conditions. The fol-  Is this stone really diamond not cubic zirconia (CZ), lowing quotation, which is believed to be dated about 1830 white sapphire, or even moissonite? bce, describes the conditions suffered by Egyptian tur-  Why is the Black Prince’s Ruby so dark? (It is in the quoise miners in the Sinai: English Crown Jewels and it is not a ruby.)  Is this stone peridot or green glass? (If you cannot tell [The Pharaoh] dispatched the Seal-Bearer of the God, the Over- need you care?) seer of the Cabinet, and Director of Lances, Hor-ur-Re, to this  Is this natural turquoise? (Probably, but the better mining area. This land was reached in the 3rd month of the question is: has it been treated?) second season [June, an almost unbearably hot season in Sinai], 36.3 I n th e Rough ........................................................................................................................................................ 653  (A) (B) (C) FIGURE 36.2 As-collected samples of rough (a) sapphire, (A) (b) peridot, and (c) diamond. 250 km India Examples of gemstones in the rough are shown in Figure 36.2; many of these natural stones have shapes that China are determined by their crystallography. Sources of sap- phire, ruby, emerald, and diamond are given in Table 36.2. Sapphire tends to grow with a hexagonal shape as seen in these images; the best quality natural sapphire is shaped Magok like a double hexagonal pyramid. Many of the harder gemstones (especially diamonds, sapphires, and garnets) are found in rivers where they have been deposited after removal from their native (natural) softer matrix. Myanmar Some specimens of natural gemstones are much larger Burma than you might think. Just to remind you: amethyst cathe- (B) drals and wheels are the result of natural hydrothermal FIGURE 36.1 Open cast mining in the Magok region of Myanmar growth. The cathedrals can be >2 m tall. (Burma). 36.4 CUTTING AND POLISHING although it was not at all the season for coming to the mining Agates started to be polished in Idar-Oberstein in the area. The Seal-Bearer of the God says to the officials who may come to this mining area at this season: 1800s and the city is now a center for polishing gemstones. Let not your faces flag because of it. Behold ye, Hat-Hor Antwerp and Amsterdam have been the centers for [Egyptian goddess of the Sinai mines] turns it to good. I have seen (it so) with regard to myself. I came from Egypt with my face flagging. It was difficult, in my experience, to find the TABLE 36.2 Gemstone Locations (proper) skin for it, when the land was burning hot, the highland was in summer, and the mountains branded an (already) blis- Ruby Myanmar (formerly Burma) tered skin. When the day broke for my leading to the camp, I Sapphire India kept on addressing the craftsmen about it: “How fortunate is he Emerald Colombia who is in this mining area!” But they said: “Turquoise is always Madagascar in the mountain, but it is the (proper) skin which has to be Diamonds Russia South Africa (the Kimberley pipe) sought at this season. We used to hear the like, that ore is forth- Tanzanite Tanzania coming at this season, but, really, it is the skin that is lacking Amethyst Brazil (Minas Gerais) for it in this difficult season of summer!” 654 ....................................................................................................................................................... Minerals and Gems  (A) (C) (B) (D) FIGURE 36.3 Equipment used for polishing gemstones. diamond cutting for many years, although much of this trade is now carried out in Asia. The basic tools are the saw and the polishing wheel. The saw will be tipped with G SiC, alumina, or diamond for precision work. Originally, the polishing pads used jeweler’s rouge, but they now use various compounds including sytonTM, alumina, zirconia, T and ceria. For most polishing, the process actually used has both a chemical and mechanical component and is Plan thus known as chemical/mechanical polishing (CMP). views The professional polisher uses a dop stick and wheel. In the diamond trade this has been partly automated using a T Crown (bezel, top) tripod device [not unlike the tripod used for polishing transmission electron microscopy (TEM) samples] to replace, or to help steady the hand of the polisher; these are illustrated in Figure 36.3. G There are numerous books describing the shapes pro- duced by polishers of gemstones. Figure 36.4 shows the Pavilion main parts of a faceted stone to illustrate the terminology. (base, back) For faceted stones the upper part is called the crown and Cross-section views consists of the table and the bezel. The girdle separates C the crown from the pavilion, which is also called the base or the back. If a face is polished on the pavilion parallel to the table, it is called the culet. If you can see straight through the stone from the table through the culet, then Cabochons the stone has a window. The shape of a brilliant-cut diamond is designed so that the light will all be reflected FIGURE 36.4 Different regions of polished (cut, faceted) stones back to the source place directly in front of it—the and two cross sections of cabochons. T, table; C, culet; G, girdle. 3 6 . 4 C u t t i n g a n d P o l i s h i n g ...................................................................................................................................... 655 pavilion facets act as mirrors. The term en cabochon 36.5 LIGHT AND OPTICS IN GEMOLOGY refers to the shape (a cabochon—like a skull) shown in the lower part of Figure 36.4, which is essentially a non- The gemologist judges diamonds by the four Cs: color, faceted stone. clarity, cut, and carat (weight). Here cut may actually The {111} plane of diamond is the hardest plane to mean cleave followed by polish. You would rather avoid polish, which is why diamonds were initially left with cutting a stone since that wastes material. Remember, 1 {111} surfaces and just the tip polished off. Small natu- carat is 0.2 g (about the weight of a carat—the small seed rally occurring octahedral crystals of diamond are quite used in ancient Egypt as a unit of weight). Since diamonds common. can be expensive you may also encounter points (there are Carving minerals and gemstones is an old art. An 100 points in 1 carat). example of a rock crystal bowl is shown in Figure 36.5. The following important optical properties contribute Old jade statues, fluorite bowls, and alabaster figures are to the attractiveness associated with precious gems: museum pieces, but new ones are still being produced. The challenge in carving the harder minerals and gem- Color. Color is one of the main features we consider when stones is simply that they are hard and you reduce the choosing a gemstone. There are many different reasons weight of the stone as you carve it. for these colors: Cr makes emerald green and rubies red. Refractive index. The higher the value of the refractive index (n or RI) of a properly cut gem, within limits, the more light will return to the eye of the viewer, resulting in brilliance, sometimes also termed life or liveliness. Diamond has a particularly high value of n = 2.417. Dispersion. The dispersion is usually given as the differ- ence in n for the b and g Fraunhofer solar spectrum lines. The Fraunhofer lines serve as reference markers across the spectrum. The b line is in the green part of the spectrum and the g line is in the violet part. The dispersion is 0.044 for diamond, one of the highest values for a natural gemstone. Dispersion causes rays of light to be split into their colored components that then emerge in slightly different directions to produce what the trade calls fire. We discuss the causes of color in gemstones separately, but the point to remember here is that color is deter- (A) mined by the wavelength of the light, λ, and the n of a crystal depends on λ (dispersion). Table 36.3 gives exam- ples of n of minerals and related materials, which are determined by measuring the critical angle on a hand-held refractometer (Figure 36.6) or a bench-top goniometer- style refractometer (Figure 36.7). Not all materials are transparent to visible light when they are too thick (i.e., we think of them as being opaque). Sphalerite, for example, is a gray crystal, but it is an orange gemstone with an n of 2.36. Absorption. The other factor that is particular to dif- ferent materials is the optical absorption. The absorption spectrum can easily distinguish different gems. Although laboratory instruments are best, gemologists can use a hand-held spectrometer. Hematite is gray unless the light (B) passes through it, in which case it appears red (hence its FIGURE 36.5 Examples of natural mineral specimens that have name). A streak of hematite will appear red for the same been shaped: (a) Buddha in garnet; 45 mm tall (b) rock-crystal reason; hematite with powder on the surface appears red. bowl (∼150 mm diameter). The reason for the red color is that hematite absorbs blue 656 ....................................................................................................................................................... Minerals and Gems  TABLE 36.3 Refractive Index of Gemstones and Related Crystals Al2O3, α-alumina 1.761, 1.769 KCl (sylvite) 1.49 AlSb 3.2, 3.2 MgAl2O4 1.723 CaF2 (fluorite) 1.434 MgF2 (sellaite) 1.378, 1.39, 1.378 CaS (oldhamite) 2.137 MgO (periclase) 1.735 CdS, cubic 2.506, 2.529 Mn3O4 (hausmannite) 2.15, 2.46 CdS, hexagonal (greenockide) 2.32 Mullite, 3Al2O3 –2SiO2 1.64 CdTe, cubic 2.5 PbO (litharge) 2.535, 2.665 Cordierite 1.54 PbS (galena) 3.91 Diamond, natural 2.419 Sb2O3 (senarmontite) 2.087 Fe2O3 (hematite) 2.91, 3.19 Sb2O3 (valentinite) 2.18, 2.35, 2.35 Fe2O3 (maghemite) 2.63 SiC (moissanite) 2.648, 2.691 Fe3O4 (magnetite) 2.42 SiC (wurtzite structure) 2.654 GaAs 3.309 Silica Aerogel 1 1.05 GaP 3.2 SiO2 (alpha quartz) 1.544, 1.553 GaSb 3.8 SiO2 (cristobalite) 1.484, 1.487 Ge mullite, 3Al2O3 –2GeO2 1.664 SiO2 (tridymite) 1.475, 1.476, 1.479 Glass (fused quartz) 1.46 SnO2 (cassiterite) 2.006, 2.097 Glass 96% silica 1.458 ThO2 (thorianite) 2.2 Glass borosilicate 1.474 TiO2 (anatase) 2.488, 2.561 Glass Corning Pyrex ® 7740 1.474 TiO2 (brookite) 2.583, 2.584, 2.7 Glass Corning Vycor ® 7907 1.458 TiO2 (rutile) 2.9, 2.609 Glass GE 214 fused-quartz 1.4585 ZnO (zincite) 2.013, 2.029 HgO (montroydite) 2.37, 2.5, 2.65 ZnS (sphalerite) 2.356 Ice 1.31 ZnS (wurtzite) 2.356, 2.378 InAs 3.5 ZnSe 2.89 InP 3.1 ZnTe, cubic 3.56 InSb 3.96 ZrO2 (baddeleyite) 2.13, 2.19, 2.2 light. Two types of absorption spectrometer are used: one illustrated in Figure 36.9, where you can clearly see stones based on prisms and the other using a diffraction grating; with the same color clearly differentiated. both are shown in Figure 36.8. The wavelengths that are Facets. The faceted gemstone is ideally shaped to opti- absorbed are well defined and are characteristic of both mize its sparkle, which is simply saying we want to max- the doping (if it colors the stone) and the matrix itself as imize the amount of light that is reflected back to the Laser beam Gem pivot axis Test plate Mirror Translucent screen Laser beam traverse Hematite Fluorspar = 71° = 55° Rutile = 70° N (B) FIGURE 36.6 (a) Portable jeweler’s refractometer for measuring the critical angle; (b) the optics of determining the critical angle using (A) the refractometer. 3 6 . 5 L i g h t a n d O p t i c s i n G e m o l o g y ........................................................................................................................ 657  650nm 450nm Diamond Diamond Ruby Spinel Emerald Garnet Zircon Apatite Spinel FIGURE 36.9 Spectra from different minerals. FIGURE 36.7 Goniometer-style refractometer. observer as shown schematically in Figure 36.10. The object of faceting then is to make the most of internal reflection. Note that the facets that you see on most gem- stones are not crystallographic planes; the gemologist essentially never uses XRD to orient the sample! Immersion. A simple method for estimating the refrac- tive index is to use liquid immersion. The stone is immersed in a series of liquids of known refractive index (values of the n for different liquids are given in Table 36.4). The idea is that the gemstone will “disappear” when placed in a liquid that has the same n (Figure 36.11). The principle is that there is no longer a change in refractive index at the surface of the stone so that even if it is faceted, it will not reflect light internally. Of course, the technique is not (A) good if the solvent can penetrate the stone or dissolve any filler. Calibration screw λ scale Reflection. A more accurate method for determining the n of a gemstone is to measure the critical angle (the Slit Brewster angle, θB) for reflection using a reflectometer. The principle is that the refractive index of a material is given by n = (sin θI)/(sin θE) (36.1) Here the angle is defined as the angle to the normal (θI = Eyepiece Prisms Converging lens Slit adjustment incident angle; θE = exit angle). In the reflectometer, we (B) place the gemstone in contact with the prism, the n of which is chosen to be large. We then adjust the incident Slit Diffraction grating Prism angle until it is θB and deduce the n of the stone from Eq. 36.2: Incident light ngemstone = nprism × sin θB (36.2) Figure 36.6b illustrates the optics of the reflectometer. Collimating Spectrum lens Pleochroism. When n of a crystal varies with the (C) direction in which light travels through it, the absorption FIGURE 36.8 (a) Photograph of a spectrometer. (b) The prism can be different in different directions. The crystal then spectrometer and (c) the absorption spectrometer. shows a different color when viewed in different direc- 658 ....................................................................................................................................................... Minerals and Gems  Low % Extinction Extinction transmission Brilliance Window Brilliance 34° 48° 70° 41° High % reflection Cone 25° critical-angle = 34.5° High % return High % transmission 34° 41° 34° 25° High % reflection FIGURE 36.10 The origin of the sparkle in gemstones: total internal reflection (TIR). tions and this gives another method for identifying the crystal. If there are two distinct directions, the crystal is said to be dichroic (tetragonal, trigonal, and hexagonal crystals). Iolite (cordierite, Mg2Al4Si5O18) and tanzanite [the purple form of zoisite, Ca2Al3 (SiO4)3 (OH)] are two of the best-known examples. Crystals can show three colors: orthorhombic, monoclinic and triclinic crystals are trichroic. Pleochroic means either dichroic or trichroic. The dichroscope (Figure 36.12) is a simple hand-held device that is used to estimate the dichroism of a gem- nstone < nliquid nstone > nliquid stone. It uses a crystal of calcite to separate the polarized Card under liquid rays and then compare them side by side to see how the color differs. Calcite has a strong double refraction. You (A) have to rotate the stone since dichroism will not be present when viewing along the optic axis. In the laboratory you TABLE 36.4 Refractive Index of Liquids Liquid n Water 1.33 Ethyl alcohol 1.36 Acetone 1.36 Amyl alcohol 1.41 Glycerine 1.46 (B) Olive oil 1.48 Toluene 1.49 Xylene 1.49 Benzol 1.50 Clove oil 1.53 Ethyl dibromide 1.54 Diamond Strontium CZ GGG YAG Monobromobenzene 1.56 titanate Bromoform 1.60 (C) Monoiodobenzene 1.62 α-Monobromonaphthalene 1.66 FIGURE 36.11 Determining the shadow patterns when stones are Methylene iodide 1.74 immersed in methyl iodide or liquid of other n. Different liquids are given in Table 36.4. 3 6 . 5 L i g h t a n d O p t i c s i n G e m o l o g y ........................................................................................................................ 659  Aperture Calcite rhomb  The arrangement of defects (as in labradorite feldspar) Glass prism or of grains (as in opal) can cause diffraction of the light.  The mineral may be a semiconductor as in the case of sphalerite. Blue. The common blue stones are sapphire, lapis, and End view Glass prism Eyepiece irradiated topaz. Less common gemstones include blue (A) diamond, although such stones could be common if irradiated more often. Green. The green stones include emerald, malachite, and both uvarovite and tsavorite garnets. Red. The red stones include ruby and both pyrope and almandite garnet (almandine). Yellow. Yellow stones are less common but include citrine, yellow sapphire, and yellow diamond. The color of ruby red and emerald green is the result of a transition metal in a ligand field (Section 32.5). In both cases the coloring ion is Cr3+ substituting for an Al3+ ion. Ruby is red corundum (Al2O3) containing about 1% Cr2O3. The Cr3+ ion, which is only a little larger than Al3+ , is easily accommodated into the corundum structure. The five 3 d orbitals in the Cr3+ ion split in the distorted octa- hedral ligand field. This is a slightly more complicated (B) case than for the simple octahedral ligand field we FIGURE 36.12 A dichroscope for estimating the dichroism of a described in Section 32.5 and involves further splitting of stone and the optics on which it is based. the 3 d levels (see Figure 32.9). Nevertheless absorption of selected values of λ in the visible spectrum is due to electron transitions. Absorption is strongest in the green and violet and least in the red and blue regions; this gives might use the polarizing visible light microscope (VLM) ruby its red color with a slight purple overtone. In emerald instead of the hand-held device. 36.6 COLOR IN GEMS AND MINERALS TABLE 36.5 Transition Element Dopants and Color We will treat color separately for the different minerals Titanium Blue sapphire (with iron), blue zoisite (tanzanite) and just add a few notes here; the importance of dopants Vanadium Grossular garnet (tsavorite), green vanadium beryl, is clear from Table 36.5. There are several different causes synthetic corundum (alexandrite simulant), some of color in gemstones. Most are associated with local synthetic emeralds, blue/violet sapphire Chromium Ruby, emerald,a red spinel, pyrope garnet, chrome trapped charges. grossular garnet, demantoid garnet, uvarovite garnet,b chrome diopside, green jadeite, pink  Metal ions can give up an electron that may remain topaz, alexandrite, hiddenite trapped locally; tsavorite is green because of the V3+ , Manganese Rhodochrosite,b rhodonite,b spessartite garnet,b but the same ion causes tanzanite to be purple. rose quartz, morganite variety of beryl, andalusite Iron Sapphire, sinhalite,b peridot,b aquamarine, blue and  When we have two metal ions in different oxidation green tourmaline, enstatite, amethyst, almandine states, we can have intervalence charge transfer. The garnetb interplay between Fe2+ and Ti4+ causes the blue in blue Cobalt Synthetic blue and green spinel, synthetic blue sapphire and blue kyanite but also makes dravite quartz (except for a rare blue spinel, cobalt is not brown; Mn2+ and Ti4+ combine to cause elbaite to be found in any natural transparent gemstone); cobalt glass yellow. Nickel Chrysoprase, synthetic green and yellow sapphires  Instead of using a reactor or other source of radiation, Copper Diopside, malachite,b turquoise,b synthetic green natural ionizing radiation can excite electrons in the sapphire crystal. Fluorite can be red, green, or purple due to a In UK and Europe only beryl colored by chromium may be described as natural irradiation. The same irradiation can cause emerald. topaz to be brown (see below). b Idiochromatic gemstones. 660 ....................................................................................................................................................... Minerals and Gems  c-axis shown in Eq. 36.3. The blue color can be produced by doping with Ni or Co but the mechanism is different. O 36.7 OPTICAL EFFECTS 3.0 E Chatoyancy. The scattering of light by aligned fibers or Fe2+ (eV) Fe 3+ 3+ + Ti channels within a matrix gives the optical effect seen in 2.0 the minerals cat’s eye and tiger-eye; the effect is termed chatoyancy. The crystals are cut en cabochon with the 0.265 nm long axis parallel to the fibers, because you do not need hν the internal reflection from the surfaces. Tiger-eye (or 1.0 absorption tiger’s eye) is quartz that contains oriented fibers of cro- Ti4+ cidolite; the mineral started as crocidolite (a form of Fe2+ + Ti4+ 0 asbestos) and was partly replaced by silica, which then o-ray becomes the matrix to the crocidolite fibers. This effect is shown together with others caused by interference in Figure 36.14. Precious, or oriental, cat’s eye is the rarest and most highly prized form of chrysoberyl; it is a green mineral called cymophane; the chatoyant effect is due to parallel (A) (B) arrays of pores. FIGURE 36.13 (a) Illustration of the combined effect of incorpora- tion of Ti and Fe in sapphire. The distance between the dopant cations is 0.265 nm. (b) The corresponding energy band diagram for the excitation showing how a gemstone with blue coloration is obtained by absorption. the color is again due to the Cr3+ ion replacing Al3+ in a distorted octahedral arrangement very similar to that in corundum. Emerald without the chromium impurity is beryl, which has the chemical formula 3BeO·Al2O3 ·6SiO2 or Be3Al2Si6O18. Because of the presence of the other con- stituents (it is a ring silicate) the overall bonding is a little weaker and the ligand field is less strong. As a result the splitting of the energy levels is different with strong absorption occurring in the yellow-red and violet and strong transmission in the blue-green regions. For sapphire blue, the color results from a charge (A) transfer mechanism. Sapphire shares the corundum struc- Precipitates ture with ruby, but the impurities are now small amounts or fibers of both iron and titanium oxides. Both Fe2+ and Ti4+ take the place of Al3+ in the corundum structure. If they are present on adjacent sites, as shown in Figure 36.13, then an interaction between them becomes possible. In this configuration there is enough overlap of the dz2 orbitals of the two ions that it is possible for an electron to transfer from the Fe2+ ion to the Ti4+ ion as follows: Fe2+ + Ti4+ → Fe3+ + Ti3+ (36.3) The energy of the combination on the right side of Eq. 36.3 is 2.11 eV higher than that on the left side, as shown (B) in Figure 36.13. If light of this energy falls on blue sap- FIGURE 36.14 Chatoyancy: the scattering of light by aligned fibers phire, it is absorbed while producing the charge transfer or precipitates. 3 6 .7 O p t i c a l E f f e c t s ................................................................................................................................................... 661  Large λ Red Orange Yellow Green Blue Short λ (A) FIGURE 36.16 The origin of opalescence: Bragg scattering of light from a surface of ordered spheres. Best known in opals. +a3 -a1 just the right dimensions to diffract light as illustrated in Figure 32.16. Labradorescence and adularescence (shiller). These are two forms of iridescence caused by planar interference in a transparent mineral. Labradorite is a plagioclase feld- -a2 +a2 spar named after the Labrador Peninsular in Canada; spectrolite is a special feldspar found in Finland. Labra- dorescence results from the presence of lamellar inter- growths inside the crystal; two phases of slightly different composition separated out as the mineral cooled. The +a1 -a3 interference occurs when light is reflected from the different interfaces. The color we see (illustrated in Figure 36.17) depends on the effective thickness of the (B) layers and thus on the viewing angle. Moonstone is trans- FIGURE 36.15 Asterism: the effect of precipitates oriented along parent feldspar that shows this effect. The planar defects several different directions giving rise to the star in star sapphire. in these feldspars are actually lamellar twin boundaries arising from chemical twinning. Asterism. This term refers to the star effect that can occur in sapphires, rubies, and garnets. The effect is illus- trated for sapphire, where it is often the strongest, in Figure 36.15. In this case, aligned precipitates in the single crystal cause the optical effect. Since sapphire has a 3-fold axis, the precipitates reproduce this symmetry by aligning along particular directions giving the 6-fold star. In black sapphire, the needles are hematite; in essentially all other sapphires they are rutile. Some star sapphires from Thai- land contain both hematite and rutile (sometimes called silk because they are so fine) and show 12-fold stars. In star garnets and diopside, the star shows 4-fold symmetry. In garnet the crystals lie at 90° along [001] directions; in diopside they lie at 73° to one another. Iridescence. The best known form of iridescence is opalescence. The reason opals show different colors when FIGURE 36.17 Laboradite causes an iridescence due to scattering viewed in different directions is that the silica spheres are by twin planes in the feldspar crystal. 662 ....................................................................................................................................................... Minerals and Gems  TABLE 36.6 The Classical Mohs’ Hardness Scale for Gems Mohs Abs Classic number number mineral Other materials 1 1 Talc Pencil lead (graphite) 2 3 Gypsum Your fingernail (2.2) 3 9 Calcite Chalk (3), gold (2.5–3.0), dolomite (3.5–4.0), ZnS (3) 4 21 Fluorite Copper penny (3.2) 5 48 Apatite Knife blade (5.0), window glass (5.5), strontium titanate (5.5), sodalite (5.5–6.0), hematite (5.5–6.5) 6 72 Orthoclase Steel file, other feldspars, pumice (6), pyrite (6.5), magnetite (6), porcelin (6–7), anatase (5.5–6) 7 100 Quartz Streak plate (7.0), zircon (6.5–7.5), olivine (6.5), garnet (6.5–7.5), rutile (6.5) 8 200 Topaz Spinel (8), YAG (8), ZrO2 (8), chrysoberyl (8.5) 9 400 Sapphire WC (9) 10 1600 Diamond Scratches everything! B 4C3 (9–10), SiC (9–10) 36.8 IDENTIFYING MINERALS AND GEMS An additional problem in using mechanical tests for minerals is that many tend to cleave. Wear (or abrasion) Since many gemstones appear quite similar, which is why might be a better test but it is more difficult for the they can be simulated, it is important to be able to distin- gemologist. guish the real from the synthetic or from the simulant. If you have a scanning electron microscope (SEM) with Thermal Conductivity XEDS available, the latter task is not a problem, but this is usually not the case in the field (or the shop). The basic The thermal conductivity of gemstones provides a useful tests are thermal conductivity, optical properties, and way of identifying the mineral in the field. Table 36.7 lists mechanical properties. Using a mechanical test to charac- values used for gemstones. The common assumption is terize a material that you do not want to damage is clearly that gemstones are poor conductors of heat. Diamond is tricky, so the use of hardness measurements is directed actually a much better thermal conductor than Cu. The more toward minerals than gemstones. measurement of thermal conduction of gemstones is par- ticularly attractive as a test because it can be applied to stones that are already mounted, e.g., in a ring. The instru- Hardness (Toughness) ment supplies the heat, and the sink is either the ring or Indentation has been discussed in Section 16.3. Although another part of the device. The device shown in these tests could be used for gemstones, they are not, Figure 36.18 measures the change in temperature of the except as a calibration. The Mohs scratch hardness scale tip when it is placed in contact with the gemstone. When is much more popular since the principle is to test what testing the poorer thermal conductors, the temperature of the stone will scratch, not what will scratch the stone. the tip is allowed to fall until it reaches a first set value The Mohs’ hardness test (the word scratch is assumed) is almost a nondestructive test. The hardness of a gem- stone is usually referred to as its Mohs’ hardness. Since this hardness value is determined by a scratch test, it is TABLE 36.7 Thermal Conductivity not actually a hardness. The scale has many drawbacks Mineral Thermal conductivity (W m−1 °C−1) including the fact that it is not linear, it does not necessar- ily relate to wear resistance, and it damages the specimen Diamond 1000–2600 Synthetic moissanite 200–500 so it is not ideal for polished stones. Silver 430 Table 36.6 gives Mohs’ hardness values for the Gem Copper 390 Scale and for some other materials as a comparison. (Note Gold 320 that in Chapter 16 we consider the extended version as Platinum 70 defined by Ridgeway, but it is not nearly so widely used Corundum 40a Zircon (high) 30a in the Gem industry.) Table 36.6 also includes a “relative” YAG 15 hardness scale. Remember that minerals are anisotropic, GGG 8 so the Mohs’ hardness of kyanite is ∼4.5 when scratched Rutile 8a parallel to the long axis and ∼6.5 when scratched perpen- Quartz 8a dicular to the long axis. Incidentally, this material will not CZ 5 Glass 1 be confused with kaolinite using this test since the latter has a Mohs’ hardness of 2–2.5. a Mean value between c axis and z axis directions. 3 6 . 8 I d e n t i f y i n g M i n e r a l s a n d G e m s ..................................................................................................................... 663  irradiated diamond is still an insulator. A concentration of 10−6 B in diamond gives it a deep blue color as seen in the Hope diamond. A B-doped diamond fluoresces under UV and continues to glow for minutes afterward. Diamonds are actually mined in large quantities in South Africa and Russia with newer sources in Sierra FIGURE 36.18 Pocket-sized instrument for measuring thermal Leone and northeast of Yellowknife in Canada’s North- conductivity. west Territories. Natural diamonds are created 150 km beneath the earth’s surface and are transported to the surface by volcanic when the subsequent DIAVIK DIAMOND MINE activity. The Kimberley decrease to the next set Production began in 2003 in Lac de Gras 300 km north- Pipe is the remains of such value is timed; it is much east of Yellowknife; it may be the richest diamond lode volcanic activity. A pipe is like taking a blood pres- in the world. It has estimated reserves of 30 million tons a carrot-shaped volcanic sure reading. and yields over 3 ct per metric ton of ore (more than neck; there is a cluster of three times the world average), In 2005, 8 million ct 11 pipes at Kimberley— were extracted valued at over US$400 million. they are about 1.2 billion 36.9 CHEMICAL years old. The largest kim- STABILITY berlite pipe is now the (DURABILITY) Premier Mine at Cullinan, which produces 1.6 million ct annually. The original location of kimberlite is now known Gemstones are usually thought of as being chemically as Kimberley’s “Big Hole.” stable. Some are; some are certainly not. Opal contains a Nitrogen causes both synthetic and natural (like the significant amount of water; if this water is removed, then Tiffany Yellow) diamonds to be yellow. A Florida company the opal will fracture and degrade. Emeralds are slightly has up to 200 diamond-making growth chambers, each different in that they usually already contain many frac- weighing about 4000 lb (cost ∼$50,000 each). Each tures that have been filled with oil or polymer. If this filler chamber can produce eight 3-ct rough stones per month. is removed, for example by cleaning with a solvent, the A little history: a team of five Russian scientists in fracture may extend. Even though the diamond in an Novosibirsk, Siberia, managed to create gem-quality dia- engagement ring is durable, the 18 k gold setting holding monds at the relatively low pressure of 60,000 atmospheres it in place may not be, especially if it is exposed to in 1989; this avoids the high pressure of the so-called GE chlorine-containing liquids such as in a swimming pool process used to make industrial diamond. Carter Clarke, and hot tub. an American entrepreneur, paid $57,000 in 1996 for a “diamond-growth chamber” during a business trip to Russia; the chamber was the size of a washing machine. 36.10 DIAMONDS, SAPPHIRES, RUBIES, He then founded Gemesis. AND EMERALDS For some time, mixtures of H2 and natural gas have been used for chemical vapor deposition (CVD) growth Why diamond? Yes, it is hard, but it is its optical qualities of diamond-like carbon (DLC) films. It is now possible to (and great advertising) that have made it so popular. The use this technique to grow diamond seed crystals to refractive index of diamond is 2.42 while rutile (once produce clear, perfect colorless diamonds. Diamonds proposed as a diamond simulant) and moissanite (now grown by the high-pressure methods are invariably doped being used as such) have refractive indices of 2.6/2.9 and and thus colored. One company, Apollo, has used the 2.65/2.69, respectively; so it does not have the best optical CVD technique to grow 1-ct diamonds. properties (for internal reflection). Examples of famous diamonds are listed in Table 36.8. Diamonds can now be synthesized to weigh more than One obvious feature is that these gemstone were all cut 0.6 g [3 carats (ct)]. This is an art: for the color and clarity. from much larger rough stones. When first extracted from The production of gem quality synthetic diamonds (Section the Premier mine near Pretoria, the Cullinan diamond 29.14) results in a deep yellow color. Colored diamonds weighed 0.621 kg. It was later cut into nine major gem- tend to be more valuable than colorless ones simply stones (the largest two being in the list and shown in Figure because they are more rare. The Dresden Green diamond 36.19) and 96 other stones. The Hope diamond, thought to weighs 40.70 ct and is the largest known green diamond be from the Kollur mine in Golconda, India, was first cut in the world. Natural red, pink, and yellow diamonds can –3 -ct stone. In 1673, it was recut to give into a triangular 112 16 1 also command prices of near $1 M per ct. The danger is a 67 –8 -ct stone and then presumably cut again to give the that diamonds can also be artificially colored by irradiat- current 45.52 ct stone. We say “presumably” because the ing them; diamond was perhaps the first irradiated gem. diamond disappeared for 20 years following looting after Blue B-doped diamond is a semiconductor while blue the French Revolution in 1792 (the current Hope diamond 664 ....................................................................................................................................................... Minerals and Gems  TABLE 36.8 Famous Diamonds C C+O C+O O +C O Name Weight Notes Hope 45.52 ct Blue due to B doping L = 25.60 mm, W = 21.78 mm, D = 12.00 mm In the Smithsonian Koh-I-Noor 105.60 ct Originally 186 ct (Mountain of In the Tower of London Light) Cullinan I 530.20 ct Original rough Cullinan (Great Star diamonds 3106 ct C+D O +D D +O D of Africa) In the Tower of London FIGURE 36.20 Different diamond shapes produced by diamonds (10 cm by 6 cm by 5 cm) faceting on three different crystallographic planes while keeping Cullinan II 317.40 ct In the British Imperial crown the same symmetry. (Lesser Star In the Tower of London of Africa) The Regent 140.50 ct In the Louvre The Centenary 273.85 ct Found in 1986 (de Beers sapphire or fancy sapphire. There are many ways to Centenary) produce the color as summarized in Section 36.6. Ruby is Rough weight 599 ct Cr doped while the blue gemstones contain the Fe–Ti In the Tower of London complex (see Section 36.7). The Tiffany Yellow 128.51 ct Found in De Beers mine, Sapphires can be colored by diffusing in dopants. Co Kimberly 1887 Rough weight 287.42 ct gives blue and Be gives yellow. Doping with Be is quite Still at Tiffany’s New York new; the Be diffuses much more quickly that Co and can penetrate the whole crystal so there are no tell-tale effects at the facets. The process involves surrounding the sap- phire with chrysoberyl (BeAl2O3) powder and heating to could indeed fit inside the old Hope diamond). The Presi- ∼1300°C. dente Vargas was found in the Rio Santo Antonio in Minas Gerais and weighed 726.6 metric ct (56.2 by 51.0 by 24.4 mm) but was cut into 29 separate stones. Emerald and Beryls Figure 36.20 shows the different facets found on The mineral is generally referred to as beryl and is found natural diamonds; all these shapes just involve {001} and in several forms as summarized in Tables 36.9. Commer- {111} surfaces. Modern diamond faceting does not need cially, the mineral beryl is the principal source of Be. to take account of the crystallography because, as an face- Beryl occurs in three forms: emerald, aquamarine, and centered cubic (fcc) crystal, diamond is structurally quite precious beryl (everything else); this is somewhat analo- isotropic. gous to the naming of sapphires. Some precious beryls do have their own names in the gem trade. In the field, gem- Sapphire and Ruby ologists use the Chelsea filter specifically to identify emer- alds. The Chelsea filter is a dyed gelatin film designed to These gemstones are both mainly Al2O3. If the stone is transmit the red but absorb the green; through it emeralds red it is called ruby; if it is any other color it is called appear red. The filter became less useful when synthetic emeralds became common. The formula is Be3Al2Si6O18 (with up to 1 H2O); it has n = 1.595. The crystal structure is hexagonal and is com- posed of 6-fold rings of SiO4 tetrahedra, which make up the Si6O18 unit. It cleaves along both {101̄0} and (0001) faces; fractures on these planes do not need to break Si–O TABLE 36.9 Beryl (Be 3Al2Si 6O18 ) Name Color Dopant (B) Beryl Blue Cr Emerald Green Cr or V Aquamarine Blue/light green Fe (A) Morganite (rose beryl) Pink Mn (also in red beryl) Heliodor Gold-yellow Fe FIGURE 36.19 Two examples of blue diamonds: both were cut Goshenite None from the same Cullinan rough diamond. 3 6 .10 D i a m o n d s , Sa p p h i r e s , R u b i e s , a n d E m e r a l d s ............................................................................................. 665  FIGURE 36.22 Natural opal in a vein. other examples are common opal or fire opal. A key com- FIGURE 36.21 An emerald cut in the classical style that minimizes ponent of opal is the included water, which is typically the likelihood of fracture. present in 3–9 wt% but may be as much as 20 wt%. It is a little tricky to polish opal (a fine example is shown in Figure 36.24), partly because you must not remove the bonds. Actually, cleavage is so easy that essentially all water and partly because it is quite soft. Opal thus has natural emeralds contain fractures. The so-called emerald much in common with chalcedony, another form of fine- cut shown in Figure 36.21 has the corners removed; it was grain quartz. developed to minimize the likelihood of fracture (while Opals are synthesized commercially by allowing maximizing the size of the stone). monosized SiO2 spheres to slowly settle from a dispersion Synthetic emerald can be grown by the flux method or in the lab. Since the structure is quite open, it is easy to hydrothermally (like synthetic quartz and natural emer- diffuse a dye into the matrix to change the overall color. alds) as shown in Figure 29.15, and is much more perfect. We can produce inverse opals in a similar way using latex The largest natural single crystal of gem-quality aquama- spheres instead of SiO2 and then various sols such as TiO2 rine was found in Minas Gerais and weighed 110.5 kg. In instead of the dye. When the impregnated polymer is one form of aquamarine known as Maxixe, the blue is burned out, the inverse opal has potential as a photonic enhanced by irradiation, but the color is not permanent. The coloring of morganite can often be improved by heating the gem above 400°C. The same treatment can change green beryl into blue aquamarine. The likely effect is that the process reduces Fe3+ to Fe2+ . Not included in Table 36.9 are Co and Ni doping, which produce pink/ violet and pale green, respectively. 36.11 OPAL Natural opal was deposited in fissures in rocks or fossil- ized (silicified) wood from water-based solutions at rela- tively low temperatures as illustrated in Figure 36.22. Precious opal consists of perfect arrays of identical spheres of SiO2 as shown in the SEM image in Figure 36.23. The spheres have a radius of ∼300 nm so arrays of the spheres look like crystals (3D diffraction gratings) to incident visible light. Thus the light is diffracted (in the actual “reflection” Bragg geometry), which is why we see different colors when viewing the opal from different directions. The spheres can be amorphous or partially crystalline. Not all opal shows these colors since the term opal refers to any material made up of such SiO2 spheres; FIGURE 36.23 SEM image of a Gilson opal. 666 ....................................................................................................................................................... Minerals and Gems  Topaz is a silicate with the general formula of Al2SiO4 (F2OH)3. It is the hardest silicate, testing at 8 on the Mohs scale. The crystal structure is unusual. It is orthorhombic consisting of chains of AO6 octahedra linked together with SiO4 tetrahedra. Cleavage is parallel to the basal plane since there are no Si–O bonds crossing this plane. It is found in a variety of shades of blue and the Imperial Yellow. Figure 36.26 shows several natural single crystals. Color is produced either by high-energy neutron irradiation in a nuclear reactor or in a gamma cell (in Brazil they use 60Co to produce γ-rays) or with a linear accelerator (linac: producing a high-energy electron FIGURE 36.24 Polished precious opal. band-gap material. The last point reminds us that opal was the first photonic material; we are now exploring how we can exploit this natural phenomenon using synthetic materials. 36.12 OTHER GEMS Quartz crystals are known by several different names. The colorless form is known as rock crystal (see Figure 36.5). Amethyst is single-crystal quartz. The crystals grew natu- rally by a hydrothermal process and are found as cathe- drals or wheels as shown in Figure 36.25. The purple color can be caused by Fe that is in the excited 4+ state due to (A) (B) natural (or artificial) irradiation or by Mn. The Fe concen- tration is probably in the range of 20–40 ppm. Smoky quartz is gray also due to irradiation, but the dopant is probably Al3+ . When heat treated, the stones become yellow-orange-brown and are known as citrine. Rhine- stones were originally quartz pebbles collected from the River Rhine. The lesson is that each of these forms of quartz grew by natural hydrothermal processes and were then “treated” by nature (or humans). (C) FIGURE 36.25 Amethyst crystals from a section of a cathedral: FIGURE 36.26 Topaz. Examples of irradiated rough, natural The crystals were inially inside the geode. imperial topaz and a huge natural single crystal. 3 6 .1 2 O t h e r G e m s .......................................................................................................................................................... 667  TABLE 36.10 Tourmalines Species X Y3 Z6 T6O18 V3 W Color Elbaite Na Li1.5Al1.5 Al6 Si6O18 (OH) 3 (OH) Dravite Na Mg3 Al6 Si6O18 (OH) 3 (OH) Chromdravite Na Mg3 Al6 Si6O18 (OH) 3 (OH) Schorl Na Fe(II) 3 Al6 Si6O18 (OH) 3 (OH) Black Olenite Na Al3 Al6 Si6O18 O3 F Buergerite Na Fe(III) 3 Al6 Si6O18 O3 F Uvite Ca Mg3 MgAl5 Si 6O18 O3 F Rossmanite Ca LiAl2 Al 6 Si6O18 (OH) 3 (OH) Foitite vac Fe(II) 2Al Al6 Si6O18 (OH) 3 (OH) beam). The stones may be radioactive for some time after symmetry; the space group is R3m with a = 1.594 nm and processing (a few weeks for the Sky Blue produced by the c = 0.7138 nm, but the actual values of a and c depend on linac and several months for the London Blue produced which cations are present. Commercially, this mineral is with neutrons). One story concerns a gem dealer who was a principal source of boron. We mentioned the piezoelec- surprised to find that the gems in his pocket were still hot. tric property earlier; it is strongest along the c axis, but Gamma radiation can produce both yellow and blue color quartz is now used more often except in special pressure centers giving a brown color; the yellow can be annealed sensor applications. out by annealing at ∼450°C leaving the blue, which lasts Spinels are less common gemstones, but sometimes a lifetime (but may not be an heirloom). they are quite famous, even if known by another name; Tourmaline is another mineral that can show many the Black Prince’s Ruby (5 cm long) and the Timur Ruby colors because it can contain different cations, some of (polished but not faceted, 361 ct) in the English imperial which are listed in Table 36.10. This table is quite new and state crown are both spinels. The largest known natural is still being developed. For example, the Y ion in dravite spinel crystal weighed 104 g (520 ct). Although the spinel can be replaced by Mn(II) or V(II); Mn doping can be as structure can accommodate wide variations in chemistry, high as 9 wt% and makes tourmaline pink. Some cations most spinel gemstones are actually naturally doped tend to share the Y site, compensating charge. Color varia- MgAl2O4. One variation is gahnite, the zinc aluminate tion is especially known for the variant watermelon tour- spinel, ZnAl2O4. The best known spinel, magnetite maline, which is naturally pink in the interior and green (FeFe2O4), is not very attractive as a gemstone. Synthetic on the outside as illustrated in Figure 36.27. As always, spinels can be doped in many colors and have the advan- we have to be careful since electron irradiation can change tage over synthetic sapphire in that they are more nearly yellow-brown tourmaline into pink tourmaline. The terms isotropic. red tourmaline and blue tourmaline have now replaced the Garnet crystals are one of the older popular gemstones names rubellite and indocolite since these are not distinct and a special class of mineral (much like spinel). The minerals. Natural crystals of schorl can be >15 cm long. crystal structure is able to accommodate many different Tourmaline is an unusual crystal in that it has true 3-fold cations, which then produce different colors. All those shown in the box (on the next page) are natural silicates, although several synthetic garnets are now available; syn- thetic garnets produced for gemstones are usually doped YAG. FIGURE 36.27 Watermelon tourmaline. FIGURE 36.28 As grown crystal of RE-doped CZ. 668 ....................................................................................................................................................... Minerals and Gems  All natural garnets have the general formula Island) in the Red Sea near Aswan, Egypt. The largest cut R3M2 (SiO4)3, where R is Ca, Mg, Fe(II), or Mn and M is peridot (319 ct) was found on this island. Al, Fe(III), or Cr. They form two groups: Alexandrite is a variety of chrysoberyl. It is special because absorption is so different in two directions. When  Pyralspites viewed along the different crystallographic axes, its color  Ugrandites changes from red to orange-yellow to emerald-green. In daylight the color is green; Natural garnets are in artificial light it is red. rarely pure. Natural alman- SILICATE GARNETS Tanzanite is a purple dines usually contain Pyralspites are named according to the dominant R variety of zoisite. Most Ca, Mg, and Fe3+ , so these cation present: stones are green when denote the end-member mined and become purple Mg2+: Pyrope [Mg3Al2 (SiO4)3] garnets. We then use when heat treated. The Fe2+: Almandine [Fe3Al2 (SiO4)3] whichever name most stone is particularly inter- Mn2+: Spessartine [Mn3Al2 (SiO4)3] closely matches the com- esting (valuable) because position we have. There is The M cation in these garnets is Al, usually with it is found in only one then a whole extra array of Fe3+ . place, it is quite hard names. Rhodolite lies (Mohs 6.5–7), it can be Ugrandites (calcic garnets with R = Ca) are named after between pyrope and essentially perfect, and it the dominant M cation: almandite; tsavorite is a is pleochroic. green variation of Cr3+: Uvarovite [Ca3Cr2 (SiO4)3] grossular; demantoid, the Al3+: Grossular [Ca3Al2 (SiO4)3] most valuable garnet, and Fe3+: Andradite [Ca3Fe2 (SiO4)3] the black melanite are 36.13 MINERALS andradite garnets. Pyrope WITH INCLUSIONS is also known as Bohemian garnet and was the favorite red stone in the 1700s and 1800s, but it can look very Inclusions in gemstones are quite common and are often similar to almandite. Almandite is Dana’s name for alman- used as an indication that the stone is natural. The best- dine, which is also known as precious garnet and was known gems with inclusions are the star stones in which probably called alabandine (after the ancient Turkish city the stone can be sapphire, garnet, etc. Perfect star sap- of Alabanda) by Pliny, so the two names are used phires can now be synthesized. interchangeably. Quartz crystals containing a hematite seed and Cubic zirconia is a special case in that it is ubiquitous the rutile needles are particularly interesting. You will as a synthetic gemstone as shown in Figures 36.28 and also see hematite needles in quartz. When considering 36.29. Naturally occurring zirconia is rare and then only the origin of such structures you should know that the as the monoclinic baddeleyite. same arrangement of seed and needles occurs without Peridot is better known as the mineral olivine. the quartz matrix as shown in Figure 36.30. The name The gemstones usually have a composition close to cat’s eye originally referred to chrysoberyl, which con- (Mg0.9,Fe0.1) 2SiO4 and have a unique green color. It was tains inclusions, but the effect is seen in many other mined for 3500 years on the island of Zabargad (St. John’s gemstones. FIGURE 36.29 A single-crystal of RE-doped as-grown synthetic FIGURE 36.30 Rutile growing in hematite. This combination often CZ. (Diameter = 2.5 cm). causes patterns in quartz crystals. 3 6 .13 M i n e r a l s w i t h I n c l u s i o n s .............................................................................................................................. 669  TABLE 36.11 “Treatment” of Gems, Its Effectiveness, and “Publicity” Treatment Stable? Detectable? Disclosure? Aquamarine turned from green to blue by heat Yes No No Zircon heated to turn colorless or blue Almost all No, but these colors are No very rare in nature Sapphire or ruby heated to remove silk Yes Usually Yes Sapphire heated to modify or develop a blue color Yes Usually Yes Topaz turned blue by irradiation Yes No Explained Topaz or sapphire irradiated to a yellow or brown color No No, only fact of fading Explained Beryl irradiated: Maxixe-type blue color No Yes Yes Turquoise or opal impregnated with a colorless stabilizer Usually Usually Yes Emerald or ruby impregnated with a colorless substance Variable Yes Yes Beryl or emerald impregnated or coated with color No Yes Yes Sapphire impurity diffused to produce a surface color Yes/No Yes Yes or surface asterism Fracture-filled diamond Yes/No Yes Yes 36.14 TREATMENT OF GEMS afterward filling the hole with glass having a similar n. This is a variation on the technique used to create 3D Two methods that are widely used to enhance the color of images inside glass blocks for use as decorations. In gemstones are irradiation and heating, usually in that either process, a pulsed laser is focused to a small area at sequence. Table 36.11 summarizes some of the heat and the required location in the crystal and pulsed to create irradiation treatments that have been used. The reason for an internal fracture (in the glass model) or ablating mate- treating (processing) gemstones is invariably to enhance rial (in the gemstone). This process is illustrated in their appearance and thus increase their value. We will Figure 36.33. review the general features of the different treatments and How effective diffusion is depends on the rate of dif- the science behind them, but refer discussion of the details fusion. If the intention is to improve the color of a gem- to the sections on particular materials. All irradiated stone, then the color must be uniform throughout the samples will be heated. stone. Hence, after diffusion the stone should be equili- brated for a long period to remove the concentration gradi- Heating sapphires: Overheating can cause good stones to ent. This equilibration would take too long for the gem become so dark that they are not transparent. Most trade so the dopant will have a concentration profile citrine is produced by heating amethyst. This process peaking at the surface. Dopant is diffused into the cut can also occur naturally. stone because otherwise the surface region will have a Irradiation: Topaz is sold as Swiss blue, London blue, etc. different color when faceted. In the case of Co, which In all cases, the material has been irradiated and produces a blue color in sapphire, diffusion is slow so that heated. the facets will have a different color from the bulk. The color difference will be particularly obvious at the facet Composite stones can be constructed by joining dif- junctions as shown in Figure 36.34. ferent stones as illustrated in Figure 36.31. One of these methods is essentially equivalent to making a bicrystal with an amorphous (polymer) intergranular layer. 36.15 THE MINERAL AND GEM TRADE Filling cracks with oil, polymer, or glass is common- place. The different procedures produce a similar result, There are many interesting international aspects to the the difference being mainly how long it takes until the history of gems. Economies of countries have been based result degrades. The extreme example of this is the trans- on gem production. Though not usually as bad as pre- formation of turquoise chalk shown in Figure 36.32 to cious-metal mines, the effect of gem mines on the envi- something that looks like the real thing. In 2004, some ronment can be very negative. The Kimberley mine highly priced rubies were is always associated with found to have had internal “Big Hole,” which by 1914, fractures filled with Pb- BLOOD DIAMONDS IN POP CULTURE when work on it stopped, containing glass (chosen Diamonds from Sierra Leone by Kanye West won a was the largest man- to match the n). 2006 Grammy for Best Rap Song. created excavation in the Lasers are used to drill Blood Diamond starring Leonardo DiCaprio and Jen- world, having a depth of channels into diamonds to nifer Connelly was released by Warner Brothers in late 215 m, a surface area of remove internal blemishes, 2006. ∼17 hectares, and a 670 ....................................................................................................................................................... Minerals and Gems  Natural green sapphire Natural ruby with obvious natural inclusions Glue layer (colorless) Colorless glass Verneuil blue sapphire or glue used as adhesive Verneuil ruby Natural green sapphire Glue layer (colorless) Red plastic coating Verneuil ruby Natural white or gray star sapphire Natural green sapphire Transparent Verneuil ruby (hollowed out) Glue layer (colorless) Natural white or Verneuil yellow sapphire gray star sapphire Opaque natural ruby or sapphire Verneuil blue sapphire Glue layer (colorless) Transparent natural or synthetic ruby or sapphire Verneuil blue spinel Engraved lines in 3 directions produce a star-like reflection Natural ruby Metal mirror Glue layer (colorless) or foil backing Natural ruby Top Assembled rough view Natural blue sapphire Verneuil ruby crystal faces simulate the appearance Side of a natural crystal Glue layer (colorless) view Natural blue sapphire Glue layer (colorless) Natural Natural ruby colorless with obvious sapphire natural inclusions Red glue Natural Transparent natural colorless ruby or sapphire: sapphire pale color Drill hole filled with Natural ruby red dye or red cement Glue layer (colorless) Natural or assembled matrix hides drill hole Faux-grown synthetic ruby FIGURE 36.31 Different methods of simulating (faking) gemstones by forming composites (bicrystals, etc.). perimeter of ∼1.6 km; 22.5 million tons of earth were producing region. Many gemstones are exported through excavated to produce 2722 kg of diamonds. In the 1990s Thailand, which is a worldwide center for processing and later, the diamond trade in Sierra Leone became asso- (cutting and polishing) gemstones. ciated with raising funds to fund ongoing wars. The stones In Brazil, the most important production area for gems were referred to as “blood diamonds” and international and minerals is Minas Gerais. It is a more remote region organizations tried to minimize the trade in these stones. of Brazil but with a growing industrial presence. Now these diamonds account for 0.2% of diamonds sold, In India, the major source of talc is located in the Dagota down from a peak of 4%. district. The talc is prepared by crushing boulders that have It is often very difficult to reach the mines in Myanmar been produced in the soapstone mines. Mining is threaten- (Burma), but historically, Magok is the center of the ruby- ing the existence of the Indian tiger (see Section 37.6). 3 6 .1 5 Th e M i n e r a l a n d G e m Tr a d e .......................................................................................................................... 671  (A) FIGURE 36.33 Laser etching to remove inclusions in a gemstone. Untreated Surface-diffusion treated Top View (A) (B) Side View High RI (B) liquid FIGURE 36.32 Examples of turquoise before and after processing. (C) (D) Both samples are real turquoise. An old method of infiltration to modify the properties of a material is common for turquoise. FIGURE 36.34 Diffusion to modify the color of a gemstone. The history of De Beers and the diamond trade lasers). The diamonds from Canada’s Northwest Territo- has been covered in several books, so we will not ries have a laser-inscribed polar bear and are known as examine it here except to say that it makes for a fascinat- “Polar Bear Diamonds”. ing story; it surprises some to hear that diamonds are There are, of course, many other uses of gemstones not rare. One aspect of the diamond business is that including jewel bearings for watches and other precision the stones are very portable and can easily be made machinery, but here we have concentrated on their use in unrecognizable. The company De Beers is now based decoration and the science behind the preparation of the in Amsterdam and Antwerp. A new development is to gemstone from the rough. There is also a worldwide trade use a laser to inscribe each diamond with a code number in mineral specimens such as you will see in museums; after it has been faceted (another “modification” using these specimens can be priced in excess of $100 k. CHAPTER SUMMARY The topic of this chapter is unusual in a ceramics textbook. It is an example of real world ceramics where mineralogy, chemistry, physics, materials science, art, and commerce meet. 672 ....................................................................................................................................................... Minerals and Gems  PEOPLE IN HISTORY Cullinan, Sir Thomas, owned the mine where, in 1905, the world’s largest diamond was found. De Beer, Johannes Nicholas and Diederik Arnoldus, were brothers who owned the farm that became the Kimberley “Big Hole.” Mohs, Fredrich (1773–1839) introduced the term scratch hardness in 1826. He was born in Gernrode/Harz Germany and studied at the University of Halle and at Freiberg; he later worked in Austria. Moissan, Ferdinand Frederic Henri (1852–1907) discovered naturally occurring SiC in 1905 in a meteorite from the Diablo Canyon in Arizona. He developed the electric furnace, which he used to make carbides and to prepare pure metals. He received the Nobel Prize in 1906 for successfully isolating fluorine (1886). Winston, Harry (1896–1978) was a key figure in the diamond trade. He opened his business in New York City in 1932 and in 1958 donated the Hope diamond to the Smithsonian. GENERAL REFERENCES Hughes, R.W. (1997) Ruby and Sapphire, RWH Publishing, Boulder, CO. A great book by the sapphire guru; beautiful illustrations. Hurlbut, C.S. and Kammerling, R.C. (1991) Gemmology, 2nd edition, John Wiley, New York. The 1991 edition has trigons on the cover. Johnsen, O. (2002) Photographic Guide to the Minerals of the World, Oxford University Press, Oxford. Another excellent pocket guide. Nassau, K. (Ed.) (1998) Color for Science, Art and Technology, Elsevier, Amsterdam. A collection of articles describing the origins of color in gemstones. Nassau, K. (2001) The Physics and Chemistry of Color, 2nd edition, Wiley-Interscience, New York. Nassau, K. (1994) Gemstone Enhancement, 2nd edition, Butterworth-Heinemann, Oxford. The book on the topic. Easy reading and fascinating details (see also his books on crystal growth). Read, P.G. (1999) Gemmology, 2nd edition, Butterworth-Heinemann, Oxford. This is a classic manageable text at a similar level to this one on ceramics, though aimed at the practicing gemologist. Schumann, W. (2006) Gemstones of the World, 3rd edition, Sterling Publishing Co., New York. This is the pocket book. Smith, G.F.H. (1972) Gemstones, 14th edition, Chapman & Hall, London. Worth a trip to the library. Ward, F. (2003) Rubies & Sapphires (also Emeralds, Opals, Pearls, Jade, Diamond), 4th edition, Gem Book Pub. SPECIFIC REFERENCES Guinel, M.J.-F. and Norton, M.G. (2006) “The origin of asterism in almandine-pyrope garnets from Idaho,” J. Mater. Sci. 41, 719. Microscopy study showing origin of the “star” in star garnets and why both 4- and 6-ray stars are possible. Published in the 40th Anniversary issue of Journal of Materials Science. Muller, H. (1987) Jet, Butterworth-Heinemann, Oxford. Pritchard, J.B., Ed. (1955) Ancient Near Eastern Texts Relating to the Old Testament, Princeton University Press, Princeton, p. 229. Describes the conditions endured by miners during Egyptian times. Themelis, T. (1992) The Heat-Treatment of Ruby and Sapphire, Gemlab Inc USA. Yavuz, F., Gültekin, A.H., and Karakaya, M.Ç. (2002) “CLASTOUR: A computer program for the classifica- tion of the minerals of the tourmaline group,” Computers Geosci. 28, 1017. WWW http://atol.ucsd.edu/%7Epflatau/refrtab/index.htm www.Krüss.com Makers of gemologist equipment. www.diavik.ca The Diavik diamond mine in Canada. www.debeersgroup.com Website for De Beers includes a history of the company. www.debeers.com Where to buy their diamonds. WHERE TO SEE GEMSTONES Musée du Louvre, Paris. www.louvre.fr The Smithsonian Institution, Washington, D.C. www.minerals.si.edu The Tower of London. www.toweroflondontour.com/crnjewel.html C h a p t e r S u m m a ry .......................................................................................................................................................... 673  EXERCISES 36.1 What are the lines in Figure 36.9? 36.2 In Figure 36.11 the stones are immersed in a liquid. Why is this liquid chosen? Show that the observations are what you would expect. 36.3 What can you deduce regarding the size, shape, and alignment of the particles causing the stars in Figure 36.15? 36.4 Explain the phenomenon of labradorescence seen in Figure 36.17. 36.5 What is the common flaw found in natural emeralds? Explain your answer from a crystallographic point of view. 36.6 If you had a good means for measuring thermal conductivity, would you prefer such a test to Mohs’ scratch test? How sensitive would your apparatus need to be? We can use a hand-held tester to distinguish diamond and moissanite. How is this fact connected to the electronics industry? 36.7 Why must you be particularly careful when polishing opal? How is opal related to today’s electronics industry? 36.8 What do the stabilization of turquoise, the treatment of emerald, and ZnO varistors have in common? 36.9 Diamond has a high n and is also a very hard material. (a) Are these two features linked? (b) If so, explain why SrTiO3 has a higher n but is not as hard. 36.10 Explain using your knowledge of ceramic processing how you might take turquoise powder and turn it into a gemstone. 674 ....................................................................................................................................................... Minerals and Gems  37 Industry and the Environment CHAPTER PREVIEW Throughout this book we have highlighted the engineering applications for ceramics. In the final analysis the importance of any material is based on the applications for which it can be used. For example, at the present time high-temperature superconductors (HTSC) are of research interest but are not commercially so important. Because of the unparalleled range of properties shown by ceramics they find application in a vast number of areas. This last chapter looks at the field from an industrial perspective. Because it is impossible to cover every aspect of the multibillion-dollar ceramic industry in one chapter we have chosen to focus on a few topics, mainly through examining case studies. One of the exciting prospects for the industry over the next decade is in nanotechnology. Ceramic nanopowders already represent the largest segment of the nanopowders market and are used for polishing and sunscreens, etc. With the demonstration of the successful growth of ceramic nanowires, nanosprings, and nanotubes, the potential exists for even more applications in critical areas such as hydrogen storage. As we have often done we begin with some history. 37.1 THE BEGINNING OF THE MODERN was, and still is, a source of clay. The proximity of raw CERAMICS INDUSTRY materials provided an economic advantage over other rural potteries that were still In Chapter 2 we described using a diminishing supply some of the early history SÈVRES of timber. Staffordshire of ceramics and their pro- Royal Commission: The factory at Sèvres was commis- is a long way from the duction. The transition to a sioned to make an 800-piece dinner service for Cathe- major metropolitan areas large-scale manufacturing rine II of Russia. It took 3 years to complete. of London, Bristol, and industry occurred in Norwich. Early pictures of Western Europe during the eighteenth century as part of Tunstall, one of the six towns that formed the Potteries and the period that became known as the Industrial Revolu- in 1910 became absorbed into the city of Stoke-on-Trent, tion. The great porcelain factories established, and subsi- show a town surrounded by hilly countryside. By the mid- dized, by royal patronage at Mießen in Germany and eighteenth century there were many separate potteries Sèvres in France began to give way to purely commercial employing a large number of workers. A petition presented products being made in Staffordshire in the north of before the British Parliament in 1763 read: England. Later the factories at Mießen and Sèvres began to imitate English designs. They were certainly helped in In Burslem [another of the six towns that made up the Potteries] this area by immigrant workers. Emigration was a concern and its neighborhoods (sic) are nearly 150 separate potteries for for the ceramics industry more than many others, such as making various kinds of stone and earthenware, which, together, iron production, because it relied on secret processes, such find constant employment and support for nearly 7,000 people. as specific body and glaze compositions. Once these became known a worker would become valuable to a In the early days of the pottery industry in England, competitor. transport of raw materials in and product out was ineffi- The development of the Staffordshire area as the prom- cient. The costs of transportation had to be included in the inent pottery center in selling price of every England was in large part article produced. Clearly, due to the use of coal as a SIX TOWNS: THE POTTERIES quantity production could fuel for the kilns. Coal was Tunstall, Burslem, Hanley, Stoke-upon-Trent, Fenton, not be achieved without abundant in this area as and Longton better transportation. 3 7.1 Th e B e g i n n i n g o f t h e M o d e r n C e r a m i c s I n d u s t ry .................................................................................... 675  Master potter and entrepreneur Josiah Wedgwood was tableware. Wedgwood merged in 1986 with Waterford instrumental in organizing a potters’ association to push Crystal forming Waterford Wedgwood plc to become the for the development of improved roads and a canal system. world’s largest tableware company with sales in excess of Wedgwood realized that cheaper and more regular trans- $1 billion. As with other industries the ceramic industry port meant an even flow of production, fewer breakages, has seen much consolidation and acquisition in recent lower prices, wider markets, and greater sales. Stafford- years. shire potters lobbied successfully for the development of a canal that would link the rivers Trent and Mersey, which was authorized by an Act of Parliament in May 1766. The 37.2 GROWTH AND GLOBALIZATION project was completed in 1772 at a total cost of Although the UK was a CERAMIC IC PACKAGES £300,000. The completion traditional leader in the Together with substrates, ceramic packages compete of the Trent-Mersey Canal development of ceramics, with polymers but are superior in terms of thermal con- ensured that Staffordshire there were major changes ductivity and hermeticity and are used in high-reliability would remain the center of during the latter half of the applications. English pottery production. twentieth century when A complex web of railway Japan became the major routes followed and these developments transformed an producer of ceramics. Rapid transportation routes meant isolated rural area into a major industrial center. that manufacturing sites no longer needed to be near Wedgwood made contributions in several areas that mineral resources. For example, Japan has no significant helped transform the production of pottery into a major domestic energy supplies but is a major industrialized industry. He changed the manufacturing process and manufacturing nation. One of the significant changes that adopted mechanization that would enable him to increase led to the growth and dominance of Japan was a shift in production while lowering prices; the increased productiv- its business from traditional low value-added basic ceram- ity helped to maintain a stable wage for his employees. ics to one that has a large component of high value added. He had many ideas about sales and marketing of his prod- Table 37.1 shows the market for high technology ceramics ucts and was the first manufacturer to introduce the as it was in 1980. Japanese companies satisfied about half “satisfaction-guaranteed-or-your-money-back” policy, which of the $4.25 billion demand. In some areas they were is now an extensively used tool for selling. dominant, producing over 60% of the worldwide market Wedgwood was an advocate of free trade and a com- for integrated circuit (IC) packages and almost 80% of the mercial treaty with France was welcomed by many of the ferrites. The market for IC packages, which is based on ceramic manufacturers as a means of stimulating imports. alumina, was established largely by U.S. companies, but Industries that had not adapted to new technology, such as there are few remaining that sell on the open market. the use of steam, feared the competition of imports. Wedg- The rapid growth in the Japanese production of ferrites wood wrote on this issue of the treaty with France: in the 1970s and 1980s coincided with a decline in this area in the United States and in Europe. The only serious An exchange of the produce of one nation for the manufactures constraint on the expanded production of ferrites in Japan of another are happy circumstances, and bid fair to make the during this period was a shortage of raw material (second- intercourse lasting; but sensible as I am to the interests of trade, ary iron oxide) caused by weak steel production. manufacturers and commerce, they all give place to a consider- ation much superior in my mind to them all. I mean the proba- bility that a friendly intercourse with so near and valuable a neighbour (sic), may keep us in peace with her—may help to TABLE 37.1 The 1980 Market for High Technology do away with prejudices as foolish as they are deeply rooted, Ceramics a and may totally eradicate that most sottish and wicked idea of Product Japan World our being natural enemies . . . . Ceramic powders $130 $250 Electronic IC packages/substrates 540 880 The production of ceramics became an important and Capacitors 325 750 growing export industry. Vast quantities of ceramic ware Piezoelectrics 295 325 produced in the Potteries were exported from the major Thermistor/varistors 125 200 Ferrites 380 480 seaports of London, Bristol, Liverpool, and Hull to Gas/humidity sensors 5 45 America, the West Indies, and all over Europe. Translucent ceramics 20 45 Today many of the most famous names associated with Cutting tools: carbide, cermet, coated 120 1000 the Staffordshire Potteries are still thriving companies, noncarbide such as Royal Doulton and Spode. A visit to any depart- Structural ceramics (heat and wear resistant) 120 250 Totals $2065 $4250 ment store will demonstrate that these companies are still regarded as producing some of the highest quality ceramic a In millions of dollars; excluding fi bers, nuclear fuels, and spark plugs. 676 ................................................................................................................................. I n d u s t ry a n d t h e E n v i r o n m e n t  TABLE 37.2 Challenges Facing the Ceramic Industry categories as listed, with examples, in Table 37.3. In this According to Percentage of Survey Respondants section we describe in more detail one example of each Environmental standards 39% activity and some current industrial trends. Changing markets 33% Cost of labor 32% Imports 27% Silicon Nitride Powder Health and safety standards 26% Silicon nitride, Si3N4, is not a naturally occurring mineral. Cost of materials 25% Quality of labor 20% All the Si3N4 that we use must be synthesized, usually by Capital for expansion 20% one of the following methods (more details are given in Quality control 19% Chapter 19): Cost of fuel 19%  Direct nitridation of Si  Carbothermal reduction of silica in N2  Vapor phase reaction of SiCl4 or silane (SiH4) with Table 37.2 shows some of the challenges that face ammonia ceramics companies worldwide. This information was gathered from a survey of over 250 ceramics companies. The following characteristics of the resulting powder The major challenges are meeting environmental stan- are important to end-users: dards, adapting to changing markets, and labor costs. The ceramics industry, like many others, can establish  Particle size and distribution. Powder compacts con- production facilities in which labor costs are lower. For taining a few coarse particles produce components example, KEMET Corporation based in Greenville, SC, a with significantly reduced strength and toughness (two manufacturer of tantalum electrolytic and multilayer of the properties we are often trying to maximize). ceramic chip capacitors, is relocating all manufacturing to Milling can be used to reduce particle size but often lower-cost facilities in Mexico and China. leads to significantly increased costs and the introduc- tion of unwanted contamination.  Surface area. This affects how easily the powder can 37.3 TYPES OF MARKET be densified during sintering and the final grain size in the sintered component. As we described in Chapter 1, the ceramics industry is  Purity. Purity depends on the processing route and generally divided into six distinct markets: wide variations are possible. Oxygen on the surface of the powders can affect densification, however, we need  Glass enough to form the liquid phase during sintering.  Advanced ceramics  Structure. A high α-Si3N4 content is desirable because  Whiteware this favors the conversion to rodlike interlocking β-  Porcelain enamel Si3N4 during subsequent processing into bulk compo-  Refractories nents as illustrated in Figure 37.1.  Structural clay The cost of Si3N4 powders can vary from $30/kg up to It is in advanced ceramics that many of the exciting $150/kg depending on particle size and purity. The high developments are occurring. The average annual growth costs of raw material and the subsequent shaping and rate of the U. S. advanced ceramics market during the past 5 years was about 8% (now currently $12 billion). The largest growth segments are electronic ceramics, which TABLE 37.3 Types of Ceramic Industry includes capacitors, piezoelectrics, and ferrites. In chemi- cal processing and environmental-related applications Activity Examples ceramics are used for automotive catalyst supports and Ceramic powders SiC for abrasives filters that are being increasingly employed to reduce pol- Nanosized TiO2 for sunscreen lutants in response to regulations on both automobile and Bioactive glasses for bone reconstruction industrial emissions. Bayer process Al2O3 for the production of Al using Hall–Héroult cells Forming powders Slip casting of toilet bowls into bulk forms CZ growth of Nd:YAG single crystals 37.4 CASE STUDIES AlN sheets by tape casting Glass melting Again following Chapter 1, the ceramics industry covers Fabricating ceramic Ceramic chip capacitors components Packages for integrated circuits a wide range of materials and products. We can generally SiC pressure sensors divide the activities of this industry into three distinct 3 7. 4 C a s e S t u d i e s .......................................................................................................................................................... 677  SiO2 include cutting tool inserts, bearings and rollers, refrac- Liquid α m tory parts, cam followers in engines blades, vanes in heat α engines, and turbocharger rotors. The advantage of using α Heat Si3N4 for cutting tool inserts should be clear from Figure α-Si3N4 m α 37.2. The units are given as SFM, surface feet per minute, m which is a measure of the distance covered by a rotating m α tool (traditionally a saw or lathe now used in wear); the α oxide surface foot is a linear foot (3.28 SF = 1 m). additive There are several powder manufacturers, primarily Heat Liquid in Germany and Japan, producing hundreds of tons of β Si3N4. There are currently no U.S. suppliers of Si3N4 β β β powder. GTE, Dow Chemical, and Ford Motor Company Cool β α developed high-quality Si3N4 powders between about 1973 β and 1995, but none of these companies is a supplier β α today. β α β Glass Ceramic Chip Capacitors FIGURE 37.1 Schematic showing processing steps in forming We described the structure of a multiplayer chip capacitor Si3N4 by liquid phase sintering (LPS). The metal oxide additive (m) (MLCC) in Chapter 31. They are used in a large number would be something like Y2O3 and the liquid an oxynitride/silicate. of products, in particular, personal computers and cell phones. A typical cell phone may contain 400 MLCCs. The goal is to make smaller components with larger TABLE 37.4 Summary of Costs for Direct-Nitrided Si3N4 capacitances at a lower cost. Powder Capacitors are extremely price competitive because of their relatively simple structure (see Figure 31.18). The Cost distribution $/kg % of total following costs are involved: By cost element Silicon powder 7.49 25.4  The ceramic dielectric. The ceramic capacitor industry Silicon nitride seed powder 1.71 5.8 uses more than 10,000 tons of BaTiO3-based dielec- Capital equipment 0.49 1.7 Direct labor 1.18 4.0 trics (about 90% of the total produced). Energy 1.88 6.4  The metal electrodes are usually precious metal Process materials 16.74 56.8 based. Total 29.48 100.0  Labor costs are particularly important in this industry By process step because of the low value-added costs. Silicon powder 7.49 25.4 Silicon nitride seed powder 1.71 5.8 Figure 37.3 shows the trend in the size of MLCCs since Direct nitriding 3.30 11.2 1981. The designations used follow the Electronic Indus- Crushing 6.62 29.3 Fine grinding 8.36 tries Association (EIA) guidelines. In the 1980s most 28.4 Total 29.48 MLCCs produced were either 1206 or 0805 (the two 100.0 largest sizes). By 2000, the 1206 accounted for less than 10% of the market, while 30% of the market was for the 0402: a component with a fraction of the area and using much less material. Since 2000, the very small 0201 has forming processes have restricted the use of Si3N4. Table captured an increasingly larger market share. 37.4 shows a summary of a cost analysis performed for The use of lower operating voltages in handheld direct-nitrided Si3N4 powder. Most of the cost of the devices and microprocessors has allowed dielectric layer powder is due to the raw materials and the process materi- thickness to be reduced; consequently higher layer als—namely the milling counts are possible within media. Si3N4 milling media the same overall device is very expensive; it costs EIA CAPACITOR CODE dimensions, as shown in about $150/kg, as com- The size of MLCCs is “llww”: ll is the length of the Figure 37.4. pared with alumina or steel capacitor and ww is the width, both in thousandths of You may recall from media at $16/kg and $4/ an inch (a case where Imperial and U.S. units are still Chapter 31 that capaci- kg, respectively. widely used in industry!) Example: 0805 means a capac- tance, C, is given by Some of the present itor of length 0.080 in. (∼2 mm) and width 0.050 in. applications for Si3N4 parts (∼1.25 mm). C = κε0 A/d (31.13) 678 ................................................................................................................................. I n d u s t ry a n d t h e E n v i r o n m e n t C tool High-speed Cast Sintered Al2O3 Al2O3-TiC Si3N4 C (μF) steel steel non-Fe carbide ceramic composite ceramic 1.0 2.2 4.7 10 22 47 100 220 330 470 Δ 1200 vcut (μm) N 100 1000 1500 N 900 800 300 150 10 600 Δ 400 30 5 15 200 N Δ 1970 1 0 1994 1996 1998 2000 2002 1800 1850 1900 1950 1982 FIGURE 37.4 Trends in number (N) of dielectric layers and FIGURE 37.2 Improvements in the rate of metal cutting for various thickness (Δ) of the dielectric layer. cutting-tool inserts. By reducing d and increasing the number of layers (effec- worldwide. The Czochralski process, which we described tively increasing A) it has been possible to expand the in Chapter 29, is used to grow singles crystals of YAG. capacitance of MLCCs into the tantalum and aluminum Typical growth conditions are pull rates of 0.4 mm/h at electrolytic capacitor range. temperatures nearing 1900°C. The ability to cast thin One of the most layers (×3 μm) requires YAG LASERS common dopants is Nd3+ , highly disperse, uniform, The first application for Nd-doped YAG lasers was in which substitutes for fine-grained ceramic pow- laser range finding. Nonmilitary applications include yttrium in the crystal ders (100–300 nm particle cutting, welding, and drilling of metals for the automo- lattice. Commercial Nd- diameter). To achieve these bile industry and in medical and dental procedures. doped YAG is regularly particles sizes extensive produced with Nd concen- milling may be used or the trations ranging between 0 powder can be made by solution methods such as using and 1.5 substitutional percent (sub%) of yttrium sites; metal alkoxides as described in Chapter 22. from the chemical formula Y3−x (Ndx)Al5O12, the substitu- A major challenge in the MLCC industry has been to tional percent Nd is given by x/3. For instance, 1.02 sub% replace the precious metal electrodes (usually a Pd–Ag Nd = 0.153 at% Nd. Few crystals beyond 1.5 sub% Nd are alloy) with base metals such as Ni. The MLCC industry available commercially. accounts for about 75% of the electronic industries use of The goal for commercial suppliers is to grow highly palladium. doped, large-diameter crystals. Increasing the dopant con- centration results in a higher absorption coefficient, lower fluorescence lifetime, and greater overall laser efficiency. Nd-Doped YAG Laser Crystals However, raising the Nd concentration increases the fre- Yttrium aluminum garnet (YAG) single crystals are the quency of cracking during growth as we showed in Figure most widely used laser host, with over 100,000 YAG lasers 16.1. If fracture occurs during growth then the process must be halted, which results in significant loss of time as a single boule can take 2 months to grow. One of the causes of fracture has been shown to be 80 small regions of inhomogeneity in the crystal as shown in Constituent 0805 (%) the transmission electron micrograph (TEM) image in 60 Figure 37.5. The widely spaced fringes in the image are 0603 x x x moiré fringes caused by interference of the electron beam x x x x 0402 as it passes through two lattices that have different lattice 40 x x parameters. The particle shown in Figure 37.5 actually has x x x a larger lattice parameter corresponding to a local Nd x 20 x concentration of 2.768% compared to the matrix, which Others 0201 x x has an Nd concentration of 1.02% Nd. (There is also a x x x x x x very small misorientation between the particle and the 0 1985 1990 1995 2000 matrix, which also affects the spacing of the moiré FIGURE 37.3 Multilayer ceramic capacitor-sized trends. fringes.) 3 7. 4 C a s e S t u d i e s .......................................................................................................................................................... 679  global nanoparticle market, which is dominated by ceram- ics, is now around $1 billion. Current applications for ceramic nanoparticles are summarized in Table 37.5.  Electronic, magnetic, and optoelectronic applications account for 70%. The largest single use is slurries of abrasive silica particles (50–70 nm) for chemical/ mechanical polishing (CMP).  Biomedical, pharmaceutical, and cosmetic applica- tions account for 18%. Sunscreens use nanosized powders of TiO2 or ZnO.  Energy, catalytic, and structural applications account for the remaining 12%. Uses include catalyst supports (e.g., for low-temperature H2 production), ceramic membranes, fuel cells, and scratch-resistant coatings. A recent example of the potential of nanosized ceramic powders in medicine is the demonstration that 5-nm cerium oxide (CeO2) nanoparticles can prolong the life of brain cells. Usually these cells live for around 25 days in the laboratory, but after a low dose of the nanoparticles they have been shown to survive and function normally FIGURE 37.5 Moiré fringes spacing ~3 nm observed in a high- for 6 months. The hope is that this approach might one resolution TEM image of an Nd-rich particle in single-crystal YAG. day be used to treat age-related disorders such as Alzheim- er’s disease. It was also More recently there has found that the treated cells PRECIOUS METAL been interest in using had increased protection In January 2001 Pd prices reached a staggering $1000 nanopowders to make against damage from ultra- per troy oz. Currently Pd trades for $330 per troy oz in polycrystalline laser hosts. violet (UV) radiation, as January 2007. These would avoid the shown in Figure 37.6. The need to use slow single implication is that the crystal growth methods. The problem is keeping the grain nanoparticles mop up free radicals—reactive molecules size small enough during sintering to maintain that damage cells and are known to be involved in aging transparency. and inflammation. An energy-related application undergoing extensive testing is the use of 10-nm CeO2 particles as additives to 37.5 EMERGING AREAS diesel fuel. The CeO2 nanoparticles catalyze the combus- tion of the fuel. The claim is that they release oxygen to The topic of advanced ceramics is exciting as technologies oxidize carbon monoxide and hydrocarbon gases to carbon developed in research laboratories and universities become dioxide, and also reduce quantities of harmful nitrogen adopted by industry. This market segment shows contin- oxides. The result is a cleaner burning fuel that converts ued growth offering good employment opportunities for more fuel to carbon dioxide, produces less noxious exhaust, MS&E graduates. and deposits less carbon on the engine walls. In this section we will describe three emerging areas: The market for nanosized powders is much smaller than ceramic nanopowders, high-temperature superconductors, for conventional ceramic powders, but the cost per kilogram and ceramic–matrix composites. is much higher. Despite progress in scaling up production and reducing costs, nanosized powders remain relatively Ceramic Nanopowders expensive (often 100 times more than conventional ceramic Nanotechnology is a “hot” research topic. The field is powders). trendy, popular, and high-tech. Although silica and iron There are growing concerns about the impact of oxide nanoparticles have a commercial history spanning nanoparticles on human health and the environment. half a century or more it is Inhaling fine quartz parti- really only within the plast cles is known to cause sili- 15–20 years that technolo- NANO POWDERS cosis, a potentially fatal gies have been developed Nanosized ceramic powders have grain sizes on the scarring of delicate lung for producing ultrapure order of tens of nanometers or less; conventional ceramic tissue. Fine particles shed nanosized powders of a particles typically have grain sizes of several microme- from hip and knee replace- range of ceramics. The ters or more. ments as they wear cause 680 ................................................................................................................................. I n d u s t ry a n d t h e E n v i r o n m e n t  TABLE 37.5 Current and Emerging Applications for Nanosized Powders Electronic, optoelectronic, Biomedical, pharmaceutical, Energy, catalytic, magnetic applications cosmetic applications structural applications Chemical-mechanical Antimicrobials Automotive catalyst polishing (CMR) supports Biodetection and labeling Ceramic membranes Electroconductive coatings Biomagnetic separations Fuel cells Magnetic fluid seals Drug delivery Photocatalysts Magnetic-recording media MRI contrast agents Propellants Multilayer ceramic capacitors Orthopedics Scratch-resistant coatings Sunscreens Structural ceramics Optical fibers Thermal spray coatings Phosphors Quantum optical devices Solar cells inflammation of the surrounding tissues and may result in tion and power transmission. The applications to date have the implant having to be replaced. Studies in which carbon been a little more modest. Magnetic levitation (maglev) nanotubes were placed directly into the lungs of mice for highspeed transportation has not been achieved with showed that there was significant damage to the lung HTSC, but continues to a limited extent with the use of tissue. Because many of the potential applications for low-temperature materials. The other major application nanoparticles are in the human body it is important to proposed for HTSC was in power transmission. However, determine their safety. It is also necessary to evaluate their due to the high cost and impracticality of cooling miles environmental impact. of superconducting wire, this has happened only with short “test runs.” In May 2001 about 150,000 residents of High-Temperature Superconductors Copenhagen, Denmark began receiving their electricity through superconducting cables. The superconductor One of the benefits of increasing Tc above 77 K is that chosen for this application was BSCCO (see Section 7.16) liquid nitrogen rather than liquid helium can be used as in the form of a tape wrapped around a flexible duct that the coolant. Liquid nitrogen is both cheaper and more carries the liquid N2. The remainder of the cable consists readily available than liquid helium. You will find the cost of thermal and electrical insulation. In November 2001 of liquid nitrogen described as either less than milk or less commercial power was delivered to about 30,000 homes than cheap beer! The cost of liquid helium is often likened in Detroit, Michigan using a similar approach. to fine champagne. One area in which HTSC is poised to make a signifi- Soon after the discovery of high-temperature super- cant impact is in filters that improve network performance conductors (HTSC) and, in particular, the YBCO com- between wireless (cellular) devices and cell sites. Super- pound there were grand predictions that these materials conductivity avoids a typical trade-off by filtering out would revolutionize areas such as a high-speed transporta- interference from adjacent signal bands without hindering the base station’s ability to pick up weak signals. This Number market could be a $10 billion business by 2011. of No UV exposure According to estimates by the European Conectus con- injured sortium the worldwide market for HTSC products is pro- cells Exposed to UV jected to grow to about $5 billion by 2010 and to almost $40 billion by 2020. Ceramic–Matrix Composites Ceramic–matrix composites (CMCs) are being developed to provide an alternative to single-phase ceramic compo- nents because of the possibility of designing with higher toughness. The most important CMCs will probably be those with continuous fiber reinforcement. We described some of the processing routes in Chapter 20. Ceramic– matrix composites are at a relatively early stage of devel- 20-day-old 20-day-old 68-day-old opment compared to polymer–matrix composites (PMCs) untreated treated treated cells cells cells and metal–matrix composites (MMCs) and significant FIGURE 37.6 Effect of nanosized cerium oxide particles on the life research is needed if they are to meet their full potential. of rat neurons. Table 37.6 lists some of the priorities. 3 7. 5 E m e r g i n g A r e a s .................................................................................................................................................... 681  TABLE 37.6 Priority Needs in CMCs to Address Key situation is opposite to that in PMCs where we often Challenges Faced by Ceramic Manufacturers and End want a strong interface so that the load is transferred Users to the stronger fibers. Key Challenges for  Increase Temperature Stability: Fiber-reinforced CMCs Priority needs to address the challenge CMCs have been demonstrated to survive in the severe environment of a gas turbine engine for 2500 hours at Reduce the cost of Scale-up/cost reduction of fiber precursors manufacturing temperatures up to 1200°C. The use of environmental Lower-cost interface materials and barrier coatings (EBCs) such as oxide layers on SiC deposition processes appears to help extend durability, but more research is Improve understanding Basic understanding of interactions needed to determine whether they present a long-term of failure modes between CMC constituents and solution. application environments Micro- and macromechanics  Scale-up: The high price of finished components made understanding of interactions of from fiber-reinforced CMCs is a major limitation. CMC with an applied stress or strain Reducing materials costs and increasing production Increase temperature Higher-temperature fibers, matrix volume would reduce costs substantially. One of the stability to 1200– materials, and interface coatings requirements for large-scale manufacturing of CMCs 1500°C Environmental barrier coatings (EBCs) Active cooling designs is the development of quick and inexpensive quality Manufacturing scale-up Larger furnace design and construction control procedures that can be used during production. and cost reduction Automation/semiautomation of preform The main processing defects are voids, density varia- fabrication tions, and cracks. X-ray computed tomography (CT) is Low-cost tooling a powerful technique for this type of investigation and Near-net-shape fabrication Low-cost in-process and postprocess high-resolution detectors can detect defects and resolve quality assurance features as small as 5 μm (see Chapter 10). But the technique remains expensive and slow and is not suit- able at the present time for in-line process control.  Cost: Nonoxide fibers cost thousands of dollars per kilogram. Oxide fibers, even those that have been com- Ceramics as the Enabling Materials mercially available for years, sell for hundreds of As you have realized from the discussion of capacitors, dollars per kilogram. The main reason is that produc- glass, data storage, etc., ceramic materials are often the tion volumes are small. Most fiber-reinforced CMCs critical part of a program or product even if the consumer utilize a layer between the fiber and matrix to optimize never sees them. mechanical properties. The methods used for deposit- Sapphire single crystals are grown for use in sub- ing this layer tend to be expensive and difficult to scale strates, as windows, as IR-transparent domes, in jewel up for production. bearings, and as the “glass” on your best watch, but there  Understanding Failure Modes: We generally want a are other applications of these and other single crystals weak fiber–matrix interface in CMCs. A propagating that most of us never see. Large sapphire crystals are crack is deflected around the fibers as shown in Figure being tested for use in the LIGO Fabry-Perot interferom- 37.7 and does not propagate through the fibers. This eter. The aim of LIGO (laser interferometer gravitational- wave observatory) is to study astrophysical gravitational waves. There are two LIGO sites, one in eastern Washing- ton and one in Louisiana. Sapphire should reduce the thermal noise compared to the fused silica that was ini- tially used. The LIGO requires the crystals to be 35 cm in diameter and 12 cm long and uses 5N-pure alumina powder. The factors studied in assessing the sapphire mirrors for future generations of LIGO include all aspects of the influence of temperature on mechanical properties and the results are compared with the current fused-silica mirrors. In either case, the ceramic is the enabling mate- rial and is the topic of very focused research. 37.6 MINING From the ugliness of an open cast mine, to the health FIGURE 37.7 Crack propagation through a fiber-reinforced problems of mine workers, to the bitter civil wars fought composite: SiC fiber in calcium aluminosilicate glass. over mineral resources in Africa, the impact of mining 682 ................................................................................................................................. I n d u s t ry a n d t h e E n v i r o n m e n t and our search for raw Ta IN CAPACITORS wide operating tempera- materials are frequent The major use for Ta is in electrolytic capacitors; it ture range (−55°C to topics in the news media. accounts for about 60% of this market. The annual value 125°C), and are very Many of the ceramic prod- of all Ta consumed is ∼$200 M. reliable. ucts we use are produced Controversy has arisen from natural resources. recently concerning the For example, the main component of most glasses is SiO2, source of tantalum: the mineral tantalite, which is found which comes from sand. The main component of tradi- in association with niobium as the ore columbite-tantalite tional ceramic products like tableware and bricks is clay, or col-tan. A major supply of col-tan is found in the which is available in different grades and is usually Kahuzi-Biéga Park in the Democratic Republic of Congo. extracted by opencast mining. These raw materials are The park is home to the eastern lowland gorilla, one of abundant and widespread. the rarest animals in the world. As a result of col-tan mining the gorilla population is being decimated and the billion-dollar export has funded the Congo’s civil war. Talc A mineral that has caught the attention of environmental- ists and conservationists is talc. Talc is used in the produc- 37.7 RECYCLING tion of paper and tiles, and as coatings in the motor industry for dashboards and fenders (bumpers). However, There are three basic reasons given for recycling: its main use is in beauty products such as eye shadow, lipstick, body lotions, deodorants, and soaps. Talc is pro- 1. Preserve finite resources duced from soapstone, which occurs in the form of large 2. Protect the environment subsurface boulders. The concern is that some of the finest 3. Save energy powder is obtained from soapstone that is the result of illegal mining in India’s The raw materials used Jamwa Ramgarh Wildlife GLASS RECYCLING IN THE UK for glass production are Sanctuary and the neigh- Bottle banks first appeared in the UK in August 1977. abundant and unlike many boring Sariska Tiger There are now over 22,000 bottle bank sites and more metal ores are not in any Reserve 250 km southwest than 570,000 tons of glass are recycled annually. imminent danger of being of Delhi. These sites are depleted. But producing considered essential to the glass does involve con- revival of the Indian tiger. The current population of sumption of large amounts of energy as shown in Table Indian tigers is about 3000, but they are threatened with 37.7. (Glass is the lowest on this list because high-purity extinction because of the loss of habitat and prey caused sources of SiO2 are readily available.) Table 37.8 shows by the mining activities. the total energy involved in producing a 12-oz beverage bottle including factors such as mining and transportation. Tantalite The dielectric in tantalum electrolytic capacitors is tanta- TABLE 37.7 Energy Consumption to Extract 1 ton of Raw lum pentoxide (Ta2O5), which forms as a thin layer on Material from Its Ore or Source tantalum as illustrated in Figure 37.8. The benefits of Material Energy (GJ) using tantalum capacitors are that they are small, have a Aluminum 238 Plastics 100 Zinc 70 Steel 50 Ag paint Epoxy Ta2O5 Glass 20 Ta Graphite Ta MnO2 Ag paint TABLE 37.8 Energy Consumption per Use for a 12-oz Beverage Container + _ Container Energy (MJ) _ + Aluminum can used once Glass bottle used once 7.4 3.9 Leads Recycled aluminum can 2.7 Recycled glass bottle 2.7 FIGURE 37.8 Schematic diagram of the structure of a solid Refillable glass bottle used 10 times 0.6 electrolyte Ta capacitor. 3 7.7 R e c yc l i n g ............................................................................................................................................................... 683 The energy savings by GLASS RECYCLING: FACTS AND FIGURES It is important that con- recycling and reusing glass More than 40 billion glass containers are produced each tainer glass is not mixed containers are also shown year in the United States. with other types of glass in Table 37.8. All glass food and beverage containers can be product such as windows, Glass recycling has recycled. light bulbs, mirrors, and been going on for thou- Recycling a glass jar saves enough energy to light a tableware. These glasses sands of years; broken glass 100-W light bulb for 4 hours. have different composi- was reused in antiquity to Glass constitutes about 6% of U.S. municipal solid tions as we showed in make new glass objects. waste. Chapter 26. Because of This ancient recycling Approximately 12 million tons of waste glass food problems associated with system makes it difficult and beverage containers are generated each year in the contamination of recycled for archeologists to deter- United States. glass the use of returnable/ mine the provenance of a About 25% of all glass food and beverage containers refillable glass bottles and glass object from its chemi- are recycled in the United States. containers is increasing. cal composition alone. A The average glass bottle contains over 25% recycled Switching to refillable con- structured recycling pro- glass. tainers can save up to 56% gram for domestic glass of the energy consumed, waste started in 1975 and reduce water consumption was initiated by the glassmaking companies. by up to 82%, and decrease materials consumption over In Chapter 26 we described the glass-forming process. 10 times for 35 refills. The initial step is that the batch, which consists primarily Currently the cost of recycling far outweighs the value of sand, is melted. The temperature required varies with of the recyclables. It may take up to five times the amount the composition of the batch, but is typically in the range of money a recyclable product is worth to collect, process, of 1300–1600°C. Adding crushed recycled glass, called and transport it to a buyer. As a result, the recycling indus- cullet, to the melt promotes melting of the sand permitting try is currently driven by consumer demand, not by profit. the use of reduced furnace temperatures with considerable Many environmental economists point out that in a “sus- savings in both raw materials and energy. For example, tainable” economic system (one based on the real costs to if a glass batch for beverage container glass contains the environment resulting from the transportation and pro- 25% cullet it requires 5% less energy to melt. Although duction of goods and materials), recycling is financially cullet has been used in ratios ranging from 0 to 100% cost effective. In such a system, the prices of products of the glass, 30–60% cullet is the most effective range. made from virgin materials would be prohibitive, encour- For colored bottles cullet comprises about 50% of the aging manufacturers to use recycled materials instead. batch. However, under such a system, the concept of curbside One difficulty associated with using recycled glass, recycling would become even less cost effective than it is particularly from consumer recycling, is the necessity to now, due to increasing transportation and energy costs. sort the discarded bottles according to color. In the United Some of the issues that drive the need for recycling in States over 65% of container glass is clear, 25% is brown Europe are quite different from those in the United States. or “amber,” and 10% comes in different shades of green One significant difference is population density. Recycling and occasional blue and other colors. These percentages in the Netherlands, which recycles more than 80% of its do not correspond exactly to the glass contents in domestic glass waste, is much more important than in the United waste because of the consumption of imported beverages States. The population densities are about 372 inhabit- that come in mostly brown and green bottles. In France, ants/km2 and 27 inhabitants/km2, respectively. As the 80% of the glass containers are green. Wine is usually population density increases, the landfilling of waste, par- packed in green bottles because it provides better UV ticularly industrial waste, becomes more difficult and protection, but the original reason is that when the wine unacceptable for the nearby population. Landfill space has bottle was invented in England during the seventeenth to compete with the land requirements for expanding sub- century it was made of green glass. urban developments and in many cases agricultural land Clear glass is the most valuable glass for recycling. as well. Both clear and brown glasses are very sensitive to impuri- One recycling issue that is important throughout the ties so they cannot be mixed with each other or with other developed world is what to do with the approximately 300 types of glass. Green glass, however, can accept other million TVs and computer monitors that are thrown out glass types without noticeable influence on the color. each year. The European Union Waste Electrical and However, green glass is often the most difficult for the Electronic Equipment Directive have banned them from glass manufacturers to use simply because the supply of being dumped in landfills because the screens contain recycled green glass often exceeds the demand. One appli- PbO added to shield against the X-ray radiation released cation for recycled green glass that is not influenced by by the high anode voltage. Table 37.9 shows typical com- color is for fiberglass insulation. positions of cathode ray tube (CRT) glasses. 684 ................................................................................................................................. I n d u s t ry a n d t h e E n v i r o n m e n t  TABLE 37.9 Some Typical Chemical Compositions of CRT  Reprocessing (adopted by UK, France, Germany, Glasses (wt%) Japan, China, and India) Color TV Color PC Color TV  Storage (adopted by the United States, Canada, and Oxide panel panel funnel PC funnel Sweden) Na 2O 8.0–8.6 6.6 6.3–6.8 5.45 In Europe, spent fuel is frequently reprocessed, which K 2O 7.0–7.5 7.3 7.8–9.7 8.05 MgO 0.2–1.3 0.33 1.0–1.8 1.5 involves dissolving the fuel elements in nitric acid. Since CaO 0.5–2.5 1.15 1.4–3.8 3.5 plutonium is created in the fission process, reprocessed SrO 1.5–8.5 8.65 0.15–0.5 0.5 fuel contains both radioactive U and Pu, and is referred BaO 10–12 1.15 1.0–1.95 3.5 to as a mixed oxide (MOX) fuel. Al2O3 2.2–3.2 2.05 3.0–4.0 3.6 The remaining liquid after Pu and U are removed is ZrO2 0.2–1.5 0.95 0.08 0.1 PbO 0.0–0.1 0.05 14.7–22.7 20.25 high-level waste (HLW), containing about 3% of the spent SiO2 60–62 59 52–59 53 fuel. It is highly radioactive and continues to generate a CeO2 0.25 — — — lot of heat. This waste must be immobilized and because TiO2 0.4 0.6 0.05 0.07 of the presence of radioisotopes with long half-lives it Sb2O3 0.25 0.5 0.05 — must be immobilized for tens of thousands of years. As2O3 0.02 0.02 0.01 — Fe2O3 0.07 0.12 0.06 — Ceramics are key materials in this process. ZnO — 0.6 — 0.06 The following are major requirements for waste immobilization:  The radioactive elements must become immobilized in To prevent a growing mountain of TVs one of the plans the crystal or glass structure. is to melt down the tubes in a sealed furnace under condi-  The leaching rate of radioactive elements must be tions that would reduce the PbO to Pb. The heavy molten low. metal would run out of fissures at the base of the furnace,  The cost must be acceptable. but the molten glass will be retained. The purified glass could then be used for other applications, such as bottles. The main method of solidifying HLW, not already The use of recycled glass as an ingredient in concrete contained in spent fuel rods, is to “vitrify” it into a boro- is being explored in several locations worldwide. silicate glass and cast it into stainless steel cans for ulti- mate burial. Vitrification of civil HLW first took place on 37.8 IN THE NUCLEAR INDUSTRY an industrial scale in France in 1978. A year’s worth of HLW from a 1000-MW reactor can be stored in about Uranium dioxide (UO2) has been important as a nuclear 26 m3. fuel since the mid-1950s and is obtained from its major A second-generation immobilization material, ore, uraninite. After leaching the ore, U3O8 is precipitated “synroc,” is in development. This synthetic rock, based on out. The average price for U3O8 is about $25/kg and the mixed titanate phases such as zirconolite, hollandite, or United States used about 24 million kg of U3O8 last year. perovskite, incorporates the HLW elements into its crystal Before use in a nuclear reactor U3O8 is converted into UF6 structure, yielding excellent chemical stability. Synroc gas. Then using either diffusion or centrifugal processing, features leach rates more than an order of magnitude lower U235F6 is separated from U238F6. The U235-enriched gas is than borosilicate glass. reacted to form UO2 powder, which is pressed into pellets. Whether the final HLW is vitrified material from These pellets are loaded into zirconium alloy tubes making reprocessing or entire spent fuel assemblies, it eventually the fuel rods. A 1000-MW reactor will “burn” 25 t of UO2 needs to be disposed of safely. This means that it should per year, and 1 kg of fuel costs about $900. Thus, a 1000- not require any ongoing management after disposal. While MW reactor will consume about $22.5 million of UO2 final disposal of HLW will not take place for some years, annually. preparations are being made for sites for long-term dis- In the United States there are presently about 100 oper- posal. One of these is Yucca Mountain in Nevada. able nuclear reactors (over 400 worldwide) producing 21% of the country’s electrical power. The number of operable reactors has decreased since it reached its peak in 1990, but there is some interest in reviving the nuclear industry 37.9 PRODUCING AND because it is a zero “greenhouse emission” technology and STORING HYDROGEN because it does not consume limited resources of fossil Thermochemical Processing fuels. One of the major problems with increasing nuclear We know it is completely feasible to produce hydrogen reactor capacity is what to do with the spent fuel. There using solar energy from the point of view of thermody- are two current approaches: namics. The idea is to use thermochemical processing. 3 7. 9 P r o d u c i n g a n d S t o r i n g H y d r o g e n .................................................................................................................. 685 The goal is to convert water (in the form of steam) into TABLE 37.10 Catalytic Properties of Mo Carbide for Fuel its components, hydrogen and oxygen, and then to collect Reforming Applications the hydrogen for use as a fuel. It is simple! The process is Other important catalytic particularly exciting because efficiencies of up to 76% Reactivity properties should be achievable, which makes it both commercially and environmentally very attractive. Similar reactivity to Pt in High resistance to coking even alcohol synthesis, methane under stoichiometric fuel The principle behind the process is to use solar energy dehydrogenation, and reforming conditions to drive a highly endothermic reaction and then produce hydrocarbon isomerization hydrogen by a subsequent exothermic reaction. This is Excellent hydrodesulfurization Shows the potential of being known as a two-step water-splitting cycle. Solar energy in activity sulfur-tolerant the form of heat is used to reduce the ceramic (a metal Promotes the water gas shift High selectivity for hydrocarbon (WGS) reaction at low conversions oxide); this reduced metal oxide is then reoxidized by temperatures removing the oxygen from water, thus producing hydrogen gas. The reduced (lower valence) metal oxide in step I (thermal reduction) could alternatively be a metal carbide, a metal nitride, or even a metal. The second step (oxida- tion by water) is known as hydrolysis. The limit for step I source of energy for hydrogen production but is more chal- would be lenging because it is dirty. Abraham Darby I realized the problems with coal in the early eighteenth century, which Step I: metal oxide → reduced metal oxide + O2 led to his use of coke (a high purity form of carbon) for Step II: reduced metal oxide + H2O → metal oxide + smelting iron. This process allowed the expansion of the 2H2 iron trade. y Catalysts required for reforming of coal into hydrogen Μ x Ο y → xΜ + Ο 2 must be resistant to poisoning by contaminants. Current 2 catalysts are based on expensive precious metals, mainly If we use FeO in step I, then the temperature must be platinum. A possible low-cost alternative is molybdenum >1600 K. However, step II is then spontaneous at a tem- carbide. Molybdenum carbide is one of the more widely perature of ∼1200 K. studied carbide systems and has shown useful catalytic Several systems are being explored for this purpose. properties for fuel reforming applications, which are sum- These include the reduction of ZnO (in some cases marized in Table 37.10. enhanced by the presence of C), the reduction of ceria, The stable phase is β-Mo2C and there are several non- and the reduction of oxides containing Fe3+ (both iron stoichiometric high-temperature phases MoC1−x, with both oxide and a range of ferrites). hexagonal and cubic structures. Nanoparticles of molyb- All that we need to do is to optimize the ceramics and, denum carbide seem to be most effective for catalysis perhaps the more challenging step, optimize the geometry because of their large surface areas (up to 200 m2 /g). of the sample to allow repeated cycling (1) without degra- Catalyst nanoparticles about 10 nm in diameter are formed dation and (2) while allowing easy extraction of the hydro- on various supports such as Al2O3, ZrO2, and even carbon gen. So the usual process is to improve the design (tailor) nanotubes. It is important to prevent the particles from of both the material (e.g., powder versus multilayer films oxidizing because MoO2 is inactive for fuel reforming. or foams) and of the reactor itself. This whole process should remind you of our discus- Hydrogen Storage sion of phase boundaries (PBs) in Chapter 15 and reac- tions in Chapter 25. The solar part of this has many Of all the limitations preventing the achievement of the similarities to processes that are now being explored for hydrogen economy the most significant is hydrogen producing lime (the endothermic calcinations of CaCO3) storage. For transportation applications storage require- and other ceramics. Currently we use fossil fuels to ments are particularly stringent and none of the current produce cement and lime, which account for 5% and 1%, approaches comes close to meeting targets. Indeed some respectively, of the global human-made CO2 emissions— of the approaches are actually dangerous. Storing hydro- up to 40% of this is from burning the fossil fuels. gen on the surface of nanomaterials is an exciting possibil- ity. The idea is again to use the very large surface areas Proton Exchange Membrane Fuel Cells available at the nanoscale. The hydrogen attaches nondis- sociatively (i.e., as H2) through weak molecular-surface High purity hydrogen is needed for use in proton exchange interactions such as van der Waals forces. Studies have membrane (PEM) fuel cells. Hydrogen is currently pro- shown that hydrogen will attach to the surface of carbon duced industrially (9 Mt per year in the United States) nanotubes, but the temperatures do not seem to be ideal through steam reforming of natural gas. Alternative fossil for transportation needs. Recently, using glasses for fuel hydrogen technologies are needed. Coal is a potential hydrogen storage has been proposed and experimentally 686 ................................................................................................................................. I n d u s t ry a n d t h e E n v i r o n m e n t FIGURE 37.9 TEM image of silica nanoropes for hydrogen storage (on a lacy C film). hydrogen has been shown to attach to the surface of two-dimensional silica glass nanostructures (e.g., wires, ropes, and springs) at room temperature and be released FIGURE 37.10 Looking through two ceramic extruded cordierite at ∼100°C. Figure 37.9 shows a TEM image of silica nano- honeycomb substrates for catalytic converters. ropes. The only difference, apart from size, between these nanostructures and “bulk” glass fibers appears to be that the surface is more ionic, which may be important for hydrogen attachment. The nanoropes grow by the vapor– shock resistance a ceramic with a near-zero coefficient of liguid–solid (VLS) mechanism described in Chapter 29. thermal expansion is required. One such material is cor- The Au catalyst is the dark particle. The deposition process dierite. Figure 37.10 shows an example of a ceramic hon- occurs at temperatures as low as 300°C allowing them to eycomb substrate for a catalytic converter. Substrates have be formed on polymer substrates. been produced with up to 900 cells per square inch and walls of thickness of 50 μm. These complex shapes are produced by extrusion, a process we described in Chapter 37.10 AS GREEN MATERIALS 23. The ceramic powder is mixed with a hydraulic-setting polyurethane resin. The mix is extruded into a water bath Catalytic Converters at a rate of about 2 mm/s. The extrusion rate matches the Catalytic converters are used in the exhaust system of rate at which the resin cures. automobiles and can reduce emissions of carbon monox- Other requirements for the catalyst substrate are ide and hydrocarbons by up to 90%. Carbon monoxide can be transformed into carbon dioxide, and unburned hydrocarbons from the fuel get burned on the metal sur-  Low cost faces. Nitric oxide, one of the main contributors to urban  Thermal-mechanical durability smog, will react with carbon monoxide to form carbon  Lightweight dioxide and nitrogen gas. These processes are conducted in catalytic converters. The first catalytic converters used mainly platinum, Photoelectrochemical Solar Cells but palladium is now the predominant catalyst metal. Sixty percent of the palladium manufactured worldwide Photoelectrochemical (PEC) solar cells use a hybrid struc- is used in catalytic converters. Other uses are as the elec- ture consisting of inorganic semiconductors and organic trodes in MLCCs and other electronic components, and a molecules. There are several different geometries. The small amount is used in jewelry (for example, an alloying one shown in Figure 37.11 uses a film of sintered TiO2 element in white gold). nanoparticles (10–30 nm) on a conducting glass substrate. The metal is dispersed Dye molecules that absorb as tiny particles on a sup- sunlight are coated onto porting framework of a CATALYTIC CONVERTERS the TiO2 particles. The porous ceramic. Because These have reduced automobile pollution by more than TiO2 itself does not absorb of the need for thermal 1.5 billion tons since 1974. a significant amount of 3 7.10 A s G r e e n M at e r i a l s .......................................................................................................................................... 687  Conducting Liquid sunlight; it is a wide-band-gap semiconductor (Eg = 3.0 eV). glass electrolyte The dye molecules absorb by electrons moving into excited support states. These excited electrons are injected into the TiO2, TiO2 particles which creates positively charged dye molecules. The inci- (10 - 30 nm) dent solar energy has created electron–hole pairs. If these pairs are separated then we have a photovoltaic (or solar) Adsorbed cell. The circuit is completed by a liquid electrolyte and dye transparent electrode. Despite the high efficiencies of PEC Sunlight molecules solar cells, the lifetime of the photoelectrode and the high cost have restricted commercialization. Transparent counter electrode (TCO) nano-TiO2 film 10 μm FIGURE 37.11 Schematic of a dye-sensitized nanocrystalline solar cell. CHAPTER SUMMARY In this chapter we described some of the industrial aspects of ceramics. Ceramics make money. Unfortunately obtaining the raw materials can have some undesirable environmental and soci- etal impacts. The environmental impact of nanomaterials is an issue that has not yet signifi- cantly concerned the ceramics industry because no one knows exactly what that impact is. But as the market for ceramic nanopowders and other nanostructures (such as wires and tubes) increases the environmental concerns will have to be addressed. Many of the “grand chal- lenges” we face as a society, such as energy, the environment, and health care, will require innovative technological solutions. Ceramics can play an important role in these areas, e.g., nuclear waste immobilization, catalytic conversion, and viral nanosensors. It is important to realize that industry is constantly in a state of flux so numbers reported here can change from year to year. Also this chapter reflects a snapshot of an industry at the beginning of the twenty-first century. In a decade, the relative importance of some of the topics we described may have increased, decreased, or disappeared altogether. PEOPLE IN HISTORY Darby, Abraham I (1678–1717) was born in Staffordshire; he patented sand casting in 1708 and invented coke smelting in 1709. Feynman, Richard (1918–1988). The beginning of research in nanotechnology can be traced back to a vision- ary talk given by Feynman in 1959 titled “There’s Plenty of Room at the Bottom.” Since then nanotech- nology has captured the minds and imaginations of many scientists and engineers. A transcript of his nanotechnology talk can be found at http://www.zyvex.com/nanotech/feynman.html. Feynman won the 1965 Nobel Prize in Physics. Wollaston, William Hyde (1766–1828) was an English scientist who discovered Pd in 1803 and named it after the asteroid Pallas, found in 1802. The mineral wollastonite is named after him. GENERAL REFERENCES Tames, R. (1984) Josiah Wedgwood, An Illustrated Life of Josiah Wedgwood 1730–1795, Shire Publications Ltd., Aylesbury, Bucks, UK. A brief biography of the man described by British Prime Minister William Gladstone (1868–1874) as “the greatest man who ever, in any age or country, applied himself to the important work of uniting art with industry.” SPECIFIC REFERENCES DOE. Basic Research Needs for Solar Energy, Report of the Basic Energy Sciences Workshop on Solar Energy Utilization, April 18–21, 2005. Defining the direction for U.S. solar energy research. Eakins, D.E., Held, M., Norton, M.G., and Bahr, D.F. (2003) “A study of fracture and defects in single crystal YAG,” J. Cryst. Growth 267, 502. This research was funded by a U.S. crystal growth company to help solve a processing problem. Fletcher, E.A. and Moen, R.L. (1977) “Hydrogen and oxygen from water,” Science 197, 1050. Fletcher, E.A. (2001) “Solarthermal processing: A review,” J. Solar Energy Engin. 123, 63. Kenney, G.B. and Bowen, H.K. (1983) “High tech ceramics in Japan: Current and future markets,” Am. Ceram. Soc. Bull., 62, 590. Describes the ceramics market in Japan in the 1980s. 688 ................................................................................................................................. I n d u s t ry a n d t h e E n v i r o n m e n t  WWW Advanced Ceramics Technology Roadmap—Charting Our Course, December 2000. Sponsored by United States Advanced Ceramic Association and the U.S. Department of Energy. Available on the web at www. ceramics.org/cic/marketresources.asp. www.kitco.com Precious metal prices and historical trends. www.nulifeglass.com NuLife Glass of Wilmslow in Cheshire. A company that plans to recycle the glass used in TV and computer screens. www.kemet.com KEMET Corporation in Greenville, South Carolina is the largest manufacturer of solid tantalum capacitors and the fourth largest manufacturer of MLCCs in the world. www.conectus.org The European superconductivity consortium. Company sites that make some of the products we mention in this chapter: www.oxonica.com Oxonica website. You can find out about the status of the nanoparticle fuel efficiency trials. www.utilities.dteenergy.com Detroit Edison website. www.ceramicindustry.com Ceramic Industry magazine. Also find out about the Giants of Ceramics. NWT Diamond Industry www.iti.gov.nt.ca/diamond/production.htm for details on the Diavikmine. EXERCISES 37.1 In addition to oxygen what other impurities might you expect in Si3N4 powder? 37.2 Why is the extent of Nd substitution in YAG so small? 37.3 What companies make the Pd–Ag metallization used for MLCCs? 37.4 Do TiO2 and ZnO play different roles in sunscreen? Which is the better material for this purpose? 37.5 Describe one process used to make CeO2 nanoparticles. 37.6 In the form of a table compare the cost of conventional (micrometer-sized) ceramic powders with the nano- sized equivalents. 37.7 How much glass is recycled in your community (or state)? 37.8 Compare the costs of recycling to landfilling for various materials. 37.9 Why is the BSCCO superconductor the material of choice for superconducting wires? 37.10 What is the current world capacity for reprocessing nuclear waste? C h a p t e r S u m m a ry .......................................................................................................................................................... 689  Index A Arrhenius, Svante August, 48 beryl, 107, 661, 665 Abbe, Ernst, 382, 479 arsenic oxide (As2O3), 468 beryllia, (BeO), 90, 290, 489, 548 absorption, 576, 656 Aspdin, Joseph, 22, 30 Bessemer converter, 25 Acheson process, 354, 365 associated centers, 182 binary phase diagram, 121, 122, 126 Acheson, Edward Goodrich, 357 asterism, 662 binder burnout, 421 adamite, 585 atomic orbitals, 58, 59, 60, 62, 69 binder, 412, 413, 482, 489 adularescence, 662 atomic packing factor (APF), 79, 80 Binnig, Gerd, 176, 243 agate, 652 atomic structure, 35, 36 bioactive materials, 635, 640 AgBr, 182, 186, 200 atomic-force microscopy (AFM), 154, 161, bioceramic composites, 6, 44 agglomerates, 364 162, 176, 177, 219, 236, 237, 240, 263, bioceramics, 6, 7, 28, 296, 305, 635–42, aggregates, 360 278, 301, 435, 436, 571, 610 646 Al2SiO5, 77, 84 attrition mill, 362 biomaterials, 635 alabaster, 653 Auger electron spectroscopy (AES), 174 biomimetics, 648 AlAs, 183 augite, 109 biotite mica, 353 alexandrite, 669 Avogadro number, 226 birefringence, 577 alkoxides, 401–6 azurite, 652 bismuth ruthenate (Bi2Ru2O7), 5, 490 allotropes, 96 bismuthates, 113 alloys, 3 B Bitter technique, 610 almandine, 660, 669 backscattered electrons (BSE), 158 Bitter, Francis, 616 almandite garnet, 660 Bacon, Roger, 397 Blaschka, Leopold, 477 alumina (Al2O3), 5, 7, 9, 10, 20, 22, 28, 47, baddeleyite, 353 Blaschka, Rudolph, 477 52, 55, 64, 66, 71, 77, 79, 81, 82, 84, 86, ball milling, 360–1 Bloch walls, 609 87, 94, 95, 106, 110, 118, 122, 124, 146, band gap, 66, 68, 69, 90, 531 Bloch, Felix, 616 159, 160, 184, 190, 193, 197, 200, 207, band-gap energy, 197, 385 Blue John, 91 208, 210, 216, 218, 219, 226, 232, 239, Bardeen, John, 554 body-centered cubic (bcc), 72, 211 269, 270, 271, 273, 276, 278, 284, 290, Bardeen–Cooper–Schrieffer (BCS) theory, boehmite, 445 291, 295, 298, 305, 307, 312, 313, 319, 550–1, 554 Bohr model, 36, 37, 49 320, 338, 351, 391, 415, 428, 435–7, 445, barium hexaferrite (BaO.6Fe2O3), 5, 438, Bohr, Neils, 48 446, 449, 450, 454, 456–8, 463, 466, 608 Bollmann, Walter, 267 543, 548, 585, 589, 596, 628, 635, 639, barium magnetoplumbite, 110 Boltzmann, Ludwig Eduard, 48, 199 640, 649, 651, 655, 665, 686 barium titanate (BaTiO3), 7, 35, 77, 93, 102, Boltzmann’s constant, 185, 626 aluminosilicates, 19, 100, 114, 301 121, 133, 136, 448, 495, 508, 519, 558, bond strength, 88, 101 aluminum nitride (AlN), 5, 7, 9, 62, 77, 87, 562–65, 567, 571, 573, 597, 631, 678 bonding, 35, 51, 154, 224, 228, 248 90, 168, 182, 209, 218, 260, 266, 332, Barkla, Charles Glover, 36, 37, 48 bonding, anodic, 284 354, 439, 458, 501, 548, 628 barrier layer, 453 bonding, covalent, 3, 4, 53, 58, 64, 66, 100, amethyst, 654, 667, 670 barriers, 452 208, 283 anatase, 93, 353 basalt, 358 bonding, hydrogen, 66 andalusite, 100, 351 basis, 72 bonding, ionic, 53, 64 anhydrite, 347 batteries, 544 bonding, metallic, 63, 64 anorthite, 264 bauxite, 350, 351, 352, 357, 548 bonding, mixed, 64, 83 antiferromagnetism, 606 Bayer process, 351, 357 bonding, van der Wals, 64, 65 antiphase boundaries (APB), 168 Bayer, Karl Joseph, 357 bonds, primary, 51, 63 antireflection coatings (ARC), 577, 580 Be3Al2 (SiO3) 6, 519, 652–4, 660, 661, 664, bonds, secondary, 51, 64, 100 antisite defect, 182 665 bone china, 20, 422 aquamarine, 665 BeAl2O4, 127 Born, Max, 69 aragonite, 257, 462 beam bending, 383 Born-Haber cycle, 51, 56 arc-image growth, 511 Bednorz, Johannes Georg, 28, 30, 31 Born-Landé equation, 55, 56, 71, Arrhenius equation, 47, 321, 543 Beer-Lambert law, 367, 577 621 Arrhenius plot, 47, 48, 195 bend test, 297 Born-Mayer equation, 56 Arrhenius relationships, 198, 396 beneficiation, 345, 347, 348, 349, 351, 352 boron carbide (B4C), 7, 14, 64, 71, 325 I n d e x ................................................................................................................................................................................. 691 boron nitride (BN), 4, 62, 64, 65, 68, 69, calcium zirconate (CaZrO3), 100 chemical vapor deposition (CVD), 371, 96 cancellous bone, 638, 644 494, 495–500, 549, 572, 586, 587, 594, boron oxide (B2O3), 134, 193, 492 capacitance, 565 597, 628, 664 borosilicate glass, 474 capacitors, 566–7 chemical vapor infiltration (CVI), 375, 496 Böttger, Johann Friedrich, 20, 30 capillarity, 230, 231 chert, 15, 347 Bowen’s reaction series, 346 carbides, 3, 120 chrome ore, 26 Bragg diffraction, 162 carbon nanotubes, 340, 523, 681 chrome oxide (Cr2O3), 94, 387, 392 Bragg, W.H., 98, 162 carbon, 26, 46 chromium dioxide (CrO2), 93, 605, 615 Bragg, W.L., 98 carnelian, 652 chrysoberyl, 127, 661, 669 Bravais lattice, 72, 73, 88, 101 Carnot efficiency, 546 cinnabar, 652 Bravais, Auguste, 85 Cassius, Andreas, 397 citrine, 660, 670 brazing, 284 Ca-stabilized cubic zirconia (CSZ), 189 Clark, William, 382 Brewster angle, 658 casting, 412, 423 Clausius-Clapeyron equation, 122 brick, 4, 5, 6, 7, 142, 146 catalysis, 225, 242, 284 clay, 4, 6, 7, 15, 19, 20, 22, 109, 120, 349, Bridgman, Percy Williams, 508, 524 catalytic converters, 233, 687 357, 365, 413, 419, 438, 548, 677 Bridgman-Stockbarger method, 508, 509, cathodoluminescence, 585 clay, hard-porcelain, 422 515 cavitation, 319 climb dissociation, 211 brittle fracture, 326 cement, 22, 23, 111, 459 climb, 213, 216, 217, 317 brittleness index (BI), 294 center of symmetry, 72 close-packed lattices, 84 brittleness, 4, 294, 309, 325–27 ceramic glass, 393 close-packed structure, 79 brookite, 93 ceramic implant, 638 coatings, 7, 407, 481, 485, 486 Brouwer diagrams, 188, 189 ceramic, green, 413, 482 coatings, bioceramic, 645 Brown, Robert, 424 ceramic, single-phase, 429 cobalt oxide (CoO), 188, 195 Brunauer, Stephen, 369, 376 ceramic-matrix composites (CMC), 4, 5, 7, cobaltosic oxide, (Co3O4), 21, 392 Brunauer–Emmett–Teller (BET) method, 22, 111, 297, 335, 341, 359, 373, 374, 375, Coble creep, 318, 442 369, 376 376, 378, 446, 496, 508, 681 Coble, Robert (Bob) L, 27, 442, 596 bubble memory, 614 ceramics, 3–14, 120, 181, 197, 232 coefficient of thermal expansion, 619, 628 buckyballs, 279, 523 ceramics, advanced, 5, 6, 7, 12, 14, 359, Coes, Loring, 98 buffer layer, 456 360, 366, 376, 677 coincidence-site lattice (CSL) theory, 247, bulk diffusion, 457 ceramics, biomimetic, 233 248, 267 bulk modulus, 292 ceramics, cellular, 232 Colburn-Libbey-Owens process, 469 Buerger, M.J., 310 ceramics, color in, 580–83 cold isostatic pressing (CIP), 415 Burgers vector, 111, 201, 202, 205, 206, ceramics, diamagnetic, 601, 616 colloids, 360, 413 208, 209, 211, 219, 221, 222, 268, 271, ceramics, engineering, 6, 13, 14 color centers, 190, 581 313 ceramics, macroporous, 232 colossal magnetoresistance (CMR), 605, Burgers, Johannes (Jan) Martinus, 202, ceramics, magnetic, 598 606, 615, 616, 617 221 ceramics, microporous, 232 compliance curves, 301 Burgers, W.G., 221 ceramics, monolithic, 409 composites, 3, 4, 5, 7, 376, 496 Burne-Jones, Sir Edward Coley, 479 ceramics, nitrogen, 27 compression, 297 ceramics, optical, 575 compressive strength, 5 C ceramics, paramagnetic, 603 computed tomography (CT), 157 cadmium iodide (CdI2), 87, 95 ceramics, polycrystalline, 8, 9, 248, 265 computer modeling, 199 cadmium selenide (CdSe), 582 ceramics, porous, 2, 79, 422, 439, 440 concentric cylinder (or Couette) viscometer, cadmium sulfide (CdS), 241, 387, 582 ceramics, structural, 291 405 calcination, 351 ceramics, thermal properties, 619 concrete, 297 calcining, 352 ceramics, tough, 28 conduction band, 532 calcite, 72, 74, 85, 86, 103, 347, 462, 578, ceramics, traditional, 4, 5, 6 conductivity, 385, 537 585, 596 ceramics, transparent, 5, 8 controlled fracture, 339 calcium aluminate cements (CAC), 111 ceramming, 474 convergent beam electron diffraction calcium aluminates, 22, 110–111, 176 ceria (cerium oxide) (CeO2), 173, 184, 339, (CBED), 162, 168 calcium carbonate (CaCO3), 72, 86 433, 655, 680 Cooper pairs, 530, 551, 553, 554, 603 calcium chloride (CaCl2), 193, 194, 265 cesium bromide (CsBr), 88 Cooper, Leon Neil, 554 calcium fluoride (CaF2), 87, 91, 98, 313, cesium choride (CsCl), 55, 56, 71, 77, 78, coordination number (CN), 72, 76–80, 86, 315 81, 87, 88 88–90, 95, 99, 100, 101, 107, 112, 115, calcium magnesium silicate, (CaMgSiO4), cesium iodide (CsI), 88 116, 184, 200, 226, 562 210 chalcedony, 652 copper (II) oxide (cupric oxide, CuO), 32, calcium oxide (CaO), 9, 22, 185, 194, 435 chalcogenides, 92, 95 87, 93, 145, 196, 390, 392 calcium phosphate, 20 Champion, Albert, 424 copper carbonate (CuCO3), 390 calcium silicate (CaSiO4), 22, 119 charge distribution, 224 cordierite (Mg2Al4Si5O18), 107, 630, 659 calcium sulphate, 653 chatoyancy, 661 core, structure, 208 calcium titanate (CaTiO3), 79, 81, 102 chemical mechanical polishing (CMP), corrosion resistance, 338 calcium tungstate (CaWO4), 508 339, 655, 680 corrosion, 392 692 .................................................................................................................................................................................. Index cortical bone, 638, 644 dewetting, 231, 243, 247, 260, 261, 266, 453 electroceramics, 27 corundum structure, 605 diamagnetism, 618 electron affinity, 42, 44 corundum, 52, 94, 312, 351, 581 diamond, 3–5, 7, 35, 47, 58–62, 66, 69, 71, electron backscattered diffraction (EBSD), Couette flow, 405 96, 125, 136, 325, 354, 521, 652–4, 660, 162, 168, 436 Couette, Maurice Frédéric Alfred, 410 663–4 electron energy-loss spectroscopy (EELS), Coulter counter, 368, 376 diamond-cubic (dc) structure, 90, 209 168, 172, 173, 249 Coulter, Wallace H., 376 diatoms, 395 electron holes, 196 crack resistance, 330 dielectric constant, 103, 558, 619 electron paramagnetic resonance (EPR), creep deformation map, 320, 321 dielectric strength, 559 279 creep resistance, 415 dielectrics, 491, 556–60, 577 electronegativity, 58, 64, 71 creep, 291, 309, 317–9 dielectrics, relaxor, 565 electronic defects, 183 cristobalite, 100, 105, 106, 351 differential interference contrast, 156 electronic thermal conductivity, 626 critical cracks, 331 differential scanning calorimetry (DSC), electro-optic (EO) materials, 590 critical resolved shear stress, 313 122 electro-optics, 592 critical stress intensity factor, 294 differential thermal analysis (DTA), 122, electrophoresis, 486 crocidolite, 661 176, 177 electrophoretic deposition, 486, 645 crystal chemistry, 87 diffraction, 162, 168 Ellingham diagrams, 120, 121, 283 crystal growth, 139, 157 diffraction, X-ray, 154, 162 emerald (Be3Al2 (SiO3) 6), 519, 652–4, 660, crystal growth, hydrothermal, 507 diffusion, 192, 193, 195, 196, 198, 431 661, 664, 665 crystal lattice, 71, 83 diffusion couples, 457 Emmett, Paul, 369, 376 crystal point groups, 75 diffusion-controlled reaction, 458 enamel, 390, 392, 474, 580 crystal structure, 81, 88, 98, 102–3, 106–11, diffusion-induced grain-boundary enameling, 646 505 migration (DIGM), 436 energy bands, 51, 66, 69 crystal systems, 72, 75 diopside, 109, 662 enstatite, 109 crystal templating, 276 dip coating, 484, 646 enthalpy of sublimation, 226 crystallization, primary, 437 dipoles, 218 entropy charge, 235 cubic zirconia (CZ, ZrO2), 91, 181, 189, dislocation creep, 317 environmental SEMs, 159, 241 194, 198, 325, 507, 514, 543, 653, 669 dislocation glide, 310 Eötvos rule, 250 Cullinan, Sir Thomas, 673 dislocation velocity, 315 epitaxy, 233, 494 cuprite (Cu2O), 87, 93, 540 dislocation, screw, 253 equilibrium, 120 Curie law, 604 dislocations, 201–21, 246, 289, 551, 627 ErAs, 208 Curie, Jacques, 573, 617 dislocations, core, 207, 209, 220, 221 etch pits, 208, 253, 228, 316 Curie, Pierre, 573, 617 dislocations, edge, 201–5, 208, 210, 214–7, etching, 226 Curie-Weiss law, 605 219, 222, 223 etch-pit method, 207, 268, 316 Curl, Robert F. Jr, 118 dislocations, misfit, 451, 454 ettringite, 23 curved interfaces, 461 dislocations, mixed, 202, 205 eutectic temperature, 121, 122, 128 cyclic fatigue, 332 dislocations, observation of, 206 eutectics, 121, 128, 281 cymophane, 661 dislocations, partial, 205, 206, 211 evaporation, 500 Czochralski process, 191, 296, 508–9, dislocations, screw, 202–5, 215 exaggerated grain growth, 437–38 511–14, 516, 597, 679 dispersion, 656 extrusion, 418 Czochralski, Jan, 508, 524 displacement field, 204 displacement-shift-complete lattice F D (DSCL), 247, 271 F centers, 190 Dana, James Dwight, 357 dodecacalcium hepta-aluminate, 111 face-centered cubic (fcc) lattice, 72, 79, 86, Danner, Edward, 382 dolomite (CaCO3.MgCO3), 25, 26, 146, 347, 87–9, 206, 211, 227, 255, 256 Darken equation, 453 352 facets, 227 Davisson, C.J., 37, 48, 49 dopants, 387 Faraday effect, 610 Davy, Sir Humphrey, 199 doping, 190 Faraday rotation, 614 de Beer, Diederik Arnoldus, 673 drawing process, 469 fatigue, 325 de Beer, Johannes Nicholas, 673 Drude, Paul Karl Ludwig, 554 fayalite, (Fe2SiO4), 105, 106, 210 de Broglie, Louis, 49 dry pressing, 414 Fe2O3, 5, 82, 94, 102, 130, 187, 200, 236, de Mortillet, Gabriel, 17 Dulong-Petit law, 620 255, 271, 390 Debye frequency, 194 Fe3C, 3 Debye temperature, 620 E Fe3O4, 82, 200 Debye, Petrus Josephus Wilhelmus, 624, earthenware, 20, 22 feldspar, 19, 20, 47, 105, 114, 346, 348, 353, 634 Edison, Thomas, 382 357 defects, 155, 157 elastic modulus, 289, 294, 301 FeO, 82, 84, 86, 130, 187, 195, 390, 472, deflocculents, 413, 417 elasticity, 203 686 densification, 427, 439 electrical conduction, 3, 4, 6, 8, 9 FeRAMs, 569 density of states, 67 electrical conductivity, 529, 619, 653 Fermi function, 67 desintering, 429 electrical insulators, 546 Fermi-Dirac function, 532 devitrite, 281 electrical resistivity, 385 ferrimagnetism, 598, 606 I n d e x ................................................................................................................................................................................. 693 ferrites, 101, 266, 362, 598, 612–14 Fuller, Richard Buckminster, 118 glass, lead-crystal, 25 ferroelectric effect, 556 fullerenes, 113, 114, 356 glass, mechanical properties of, 385 ferroelectric titanates, 27 furnaces, 139–51 glass, metallic, 380 ferroelectricity, 103, 560 fused deposition modeling (FDM), 420 glass, natural, 394 ferromagnetism, 604, 606 fused silica, 394 glass, optical properties of, 385 FeS2, 74, 79, 81, 87, 92 fusing, 350 glass, phosphate, 394 Feynman, Richard, 688 glass, polymer, 380 fiber elongation, 383, 384 G glass, safety, 297 fibers, 359, 363, 370, 372, 373, 375, 376, gadolinium gallium garnet (GGG), 614 glass, silicate, 384, 393 400, 407, 408 gahnite, 668 glass, structure of, 379, 380, 397 Fick, Adolf Eugen, 199 galena, 652 glass, thermal properties of, 385 Fick’s laws, 47, 193, 461 Gallé, Émile, 479 glass-ceramics, 25, 27, 32, 458, 474, 475, film growth, 233–35, 242 gallium arsenide (GaAs), 77, 87, 89, 90, 641 films, 407 183, 211, 236, 269, 502, 508 glassmaking, 29 fining, 467 gallium nitride (GaN), 3, 4, 64, 68, 71, 168, glaze, lead, 20, 22, 32 flame emission spectroscopy (FES), 370 209, 220, 269, 588 glaze, tin, 18, 20, 21 flame spraying, 646 gallium oxide (Ga2O3), 94 glazes, 20, 390, 459, 413, 439, 580, 632 flame-fusion process, 508, 509 garnet (Ca3Al2 (SiO4)3), 607, 614 glide bands, 311 flash glass, 478 garnets, 84, 107, 252, 347, 519, 654, 660, glide dissociation, 211 flash goggles, 593 662, 668, 669 glide plane, 202, 206, 208, 215–7, 312 flat glass, 468, 472 Gay, D.H., 200 glide, 216, 317 flaws, 327 Generalized Utility Lattice Program Glow Discharge Ion Source, 172 flint glass, 382 (GULP), 84, 85 goethite, 615 flint, 15, 22, 325, 347, 380, 653 GeO2, 579 Goldschmidt, Victor Moritz, 85 float glass, 26 germanium, 67 Gouy method, 604 float-glass process, 463, 468, 469, 470, 479 Germer, Lester Halbert, 37, 48 grain boundaries (GBs), 197, 246, 268, floating-zone (FZ) method, 508, 510 giant magnetoresistance (GMR), 606, 615, 277, 289, 314, 315, 318, 319, 338, 427, flocs, 360 617 444, 448, 455, 458, 495, 551, 566, 583, fluorescence, 585, 588 Gibbs adsorption, 251 593 fluorides, 92 Gibbs free energy, 45–7, 81, 82, 121, 123, grain boundaries, low-angle, 275, 515, fluorite, 91, 585, 660 134, 184, 185, 194, 234, 277, 406, 431, 561 fluorspar, 91 445, 497 grain boundary, mixed, 246 flux growth, 507, 519 Gibbs phase rule, 121, 124 grain boundary, properties, 265 foam glass, 473 Gibbs triangle, 128, 130 grain boundary, sliding, 318 foams, 232, 233 Gibbs, Josiah Willard, 134 grain boundary, tilt, 246 focused ion-beam (FIB), 207 Gibbs-Thompson effect, 461 grain boundary, twin, 246 formation, 224 Gilchrist Percy, 25 grain boundary, twist, 246 forsterite (Mg2SiO4), 77, 105, 106, 210 Gillinder, William, 25 grain growth, 431, 435–37 Fourcault process, 469 glass blowing, 24, 463, 470 grain morphology, 246 Fourcault, Emile, 382 glass ionomer cements (GIC), 460 grain size, 427, 437 Fourier-transform IR (FTIR), 162, 163, glass laser, 388 grain-boundary diffusion, 457 164, 176, 641 glass microspheres, 479 grain-boundary energy, 249 fractography, 332 glass processing, 463–74 grain-boundary films, 259 fracture strength, 309, 315 glass, 4–8, 12–14, 24, 25, 48, 82, 100, 116, grain-boundary grooves, 262, 263, 267 fracture toughness, 294, 300, 307, 330, 335 117, 120, 133, 139, 181, 325, 408, 433, grain-boundary low-angle tilt, 252 fracture, 325 259, 264, 270, 278, 677 grain-boundary low-energy, 251 fracture, conchoidal, 333, 325 glass, borate, 394 grain-boundary migration, 432 fragility, 380 glass, calcium phosphate (Ca3(PO4) 2), 476 grain-boundary pinning, 434 FRAMs, 569 glass, ceramic, 380 grain-boundary, high-angle, 254, 603 Frank, Sir Charles, 221 glass, chalcogenide, 394 grain-growth inhibitor, 459 Frank’s rule, 203 glass, coating, 472 granite, 346, 353 Frank-Read source, 216, 217, 219, 315 glass, coloring, 386 granules, 360 Frenkel defects, 182–4, 186, 187, 200, 619 glass, crown, 394 graphite, 1, 3, 30, 47, 61, 62, 65, 66, 69, 95, Frenkel pairs, 191 glass, crystallization, 458 96, 114, 136, 145, 211, 212, 296, 313, Frenkel, Jacov Il’ich, 199 glass, defects in, 386 354–8, 415, 426, 439, 495, 521, 523 Fresnel’s equation, 577 glass, definition of, 379 graphite, pyrolytic, 646 Friedel, G., 267 glass, electrical properties of, 385 green body, 428, 429, 439, 440 Friedel, J., 267 glass, flint, 393 green machining, 420 frit bonding, 490 glass, halide, 394 Griffith equation, 327 fuel cells, 28, 544 glass, heterogeneous, 386 Griffith, Alan Arnold, 325, 327, 339, 340 Fulcher equation, 318 glass, history of, 380 grinding, 339, 652 fulgarites, 394 glass, lead, 393 grossular, 119 694 .................................................................................................................................................................................. Index Grove, Sir William Robert, 28, 554 Huygens, Christian, 294 kaolinite (Al2O3.2SiO2.2H2O), 19, 66, 109, gypsum (CaSO4.2H2O), 32, 347, 350, 450, hybrid orbitals, 60, 61, 62, 63 120, 146, 548 653 hybridization, 51, 60–3, 69, 71 Kawai, Kanjiro, 424 hydrogen storage, 686 KBr, 309, 310 H hydrothermal method, 517 KCl, 52, 56, 71, 160, 193, 194, 315 Haber, Fritz, 69 hydroxyapatite (HA), 7, 635, 642–44 Keck, Donald, 27 halides, 88 keramos, 4 halite, 88, 585 I Kerr effect, 590, 592, 610 Hall–Heroult cells, 356 illite, 109 kinetics, 35, 47, 48, 181 Hall–Petch equation, 266, 315 ilmenite (FeTiO3), 94, 102, 345, 353, 565 Kingery, W. David, 30, 442 halophytes, 381 image, bright-field, 159, 160 kink, 206, 214, 215, 216, 227, 239 Hamada, Shoji, 424 image, BSE, 158 Kirchhoff, Gustav Robert, 151 Hamaker constant, 65, 66 image, CT scans, 157 Kirchhoff’s law, 141 Hankel, W.G., 573 image, dark-field, 156, 159, 160, 273, 310 Kirkendall effect, 449 hardening, 316 image, infra-red (IR), 156 KNbO3, 102 hardness tests, 299, 300 image, IR, 217 KNO3, 487 hardness, 292, 294, 299, 301, 307, 338 image, ultraviolet (UV), 156 Kröger, Ferdinand Anne, 199 Hashin and Shtrikman (HS) bounds, 295 image, X-ray, 157 Kröger-Vink notation, 183, 187, 200, 540, Hashin-Shtrikman model, 308 imaging, 154, 155 547, 628 Haüy, René-Just, 85 immiscibility, 386 Kroto, Sir Harold W., 118 heat capacity, 619–21 impurities, 270 kyanite (Al2OSiO4), 72, 77, 100, 350, 663 heat transfer, 148 indentation test, 299 heat-exchange method (HEM), 516 indium oxide (In2O3), 94, 158, 453 L Heisenberg uncertainty principle, 37 indium phosphide (InP), 502 La Farge, John, 397 Heisenberg, Werner, 49 induction skull melting (ISM), 514 labradorescence, 662 Helmholtz-Smuluchowski equation, 487 Inglis equation, 329 labradorite feldspar, 660, 662 hematite (Fe2O3), 82, 94, 276, 339, 345, Inglis, Sir Charles Edward, 340 Lalique, René, 479 361, 446, 615, 652, 656 injection molding, 419 Lambert’s law, 577 Hermann-Mauguin notation, 74 integrated circuits (IC), 548 LaMer diagram, 364 Herring, W. Conyers, 323 interfaces, 87, 155, 224–6, 444, 558 laminated glass, 473 Hess’s law, 56 interfacial energies, 231, 232, 270 lanthanum phosphate (LaPO4), 112 heterojunctions, 271, 289 interferometer, 163 Lanxide process, 375, 376 hexagonal close-packing (hcp), 79, 87, 94, intergranular film (IGF), 270, 280, 318, lapis lazuli, 652, 660 95, 209 319, 323, 541, 583 laser Raman microprobe, 165 hibonite, 111 International Union of Crystallography, 98 lattice energy, 51, 55 high-alumina cement (HAC), 11, 460 interstitials, 182, 183 lattice misfit, 272, 282, 454 highest occupied molecular orbital inverse spinel, 184 lattice mismatch, 505, 594 (HOMO), 66 inversion axis, 72 lattice parameter, 71, 87, 101, 122, 192, 211, high-resolution STEM, 192 invisibility criterion, 207 323 high-resolution transmission electron iolite, 659 lattice points, 71, 72, 75 microscopy (HRTEM), 90, 160, 201, ion-beam-assisted deposition (IBAD), 504 lattice spacing, 327 207, 213, 229, 238, 250, 254, 259, 264, ionic conductivity, 197 Laue technique, 171 266, 272, 282, 319, 409 ionic radius, 57 Le Chatelier, Henry, 134 high-temperature ceramic superconductors, ionization energy, 36, 42, 44, 53 Leach, Bernard Howell, 424 6 iridescence, 662 lead iron niobate (PFN), 565 high-temperature superconductors (HTSC), iron oxide (Fe2O3), 22, 351 lead iron tungstate (PFW), 565 4, 7, 12, 27, 112, 113, 269, 495, 529, iron, 25, 598 lead magnesium niobate (PbMg1/3Nb2/3O3 or 551–54, 598, 602, 675, 681 isoelectric point (IEP), 488 PMN), 565 Hockman, George A., 27 lead oxide (PbO), 20, 25 holosymmetric point group, 74 J lead ruthenate (Pb2Ru2O6), 490 Hooke, Robert, 85, 221 jadeite, 109 lead titanate (PbTiO3), 570 Hooke’s law, 203, 206, 327 jasper, 15, 652 lead zirconate (PbZrO3), 570 Hoover Dam, 23 jeweler’s rouge, 339, 655 lead zirconate titanate (PZT), 7, 27, 400, hot forging, 434 jog, 206, 214, 215, 216, 223, 239 570, 572, 624 hot isostatic pressing (HIP), 416, 643, 645 Jomon, 17 lead, 22 hot pressing, 414, 429, 433 Josephson junction, 266, 554, 603 lead-crystal glass, 382 hot-pressed silicon nitride (HPSN), 27 Josephson, Brian David, 617 Lennard-Jones potential, 64 hot-stage XRD, 171 Joule, James Prescott, 151 Lenz, Heinrich Friedrich Emil, 617 Houghton Sr, Amory, 382 Libbey-Owens process, 469 Hume-Rothery rules, 187 K Libyan desert glass, 394, 399 Hume-Rothery, William, 134 Kao, Charles K., 27 ligand field, 580, 660 Hund’s rule, 39, 603 kaolin, 19, 20, 348, 349, 350, 357 lime, 22 I n d e x ................................................................................................................................................................................. 695 line defects, 202 magnetic moment, 599 Mohs scratch hardness scale, 294, 663, Lipperhey, Hans, 397 magnetism, 598 667 liquid-crystal templating (LCT), 440 magnetite (Fe3O4), 35, 82, 130, 446, 598, Mohs scratch test, 674 liquid-phase sintering (LPS), 139, 146, 319, 606, 615, 668 Mohs, Fredrich, 306, 673 678 magnetoencephalography (MEG), 603 Moissan, Ferdinand Frédéric-Henri, 98, liquidus, 121, 122, 123, 128 magnetoplumbite structure, 607 357, 673 litharge (PbO), 370 magnetoplumbite, 110, 608 moissanite, 71, 91, 653, 664 lithium fluoride (LiF), 53, 57, 58, 310, 311, malachite, 660 molar heat capacity, 620 316 manganates, 120, 598, 616 moldavite, 394 lithium niobate (LiNbO3), 516, 565 markers, 452 molding, 423 lithium, 39 MARVIN, 200, 242 molecular dynamic (MD), 82, 84 lithium-alumino-silicates (LAS), 632 mass spectrometry, 172 molecular orbitals, 58, 59, 66 Littleton, Harvey K, 479 Matthews, John, 267 molecular-beam epitaxy (MBE), 481, 494, load-displacement curve, 301 Maurer, Robert, 27 502 lodestone, 598 Maxwell, James Clark. 177, 596 molten carbonate fuel cell (MCFC), 545 Lomer-Cottrell dislocation, 218 Maxwell’s equations, 576, 586 molybdenite, 95 London, Fritz, 617 mayenite, 111 molybdenum carbide (Mo2C), 63, 686 London, Heinz, 617 Megaw, Helen Dick, 118 molybdenum dioxide (MoO2), 686 long-range order (LRO) , 83, 100, 379, 380, Meissner effect, 602, 603, 617 molybdenum disilicide (MoSi2), 145, 439 387 Meissner, Walter, 617 molybdenum sulfide (MoS2), 62, 65, 87, 95, Lord Rayleigh. See Strutt, John William melaconite, 93 96, 211, 296 Lorentz force, 611 Mergules viscometer, 383, 406 molybdenum trioxide (MoO3), 146 Lorentz-Lorentz equation, 578 metal oxide semiconductor field effect molybdenum, 146 low-energy electron diffraction (LEED), transistor (MOSFET), 499, 549 monazite, 71, 72, 111, 446 174, 236, 238 metal oxides, 9, 146 monticellite, (Ca(Mg,Fe)SiO4), 106, 210, low-energy electron microscopy (LEEM), metal-matrix composites (MMC), 359, 374, 458 240 375, 376, 681 montmorillonite, 109, 439 lowest unoccupied molecular orbital metal-oxide-semiconductor (MOS), 549 moonstone, 662 (LUMO), 66 metals, 3–5, 56, 57, 63, 64, 67, 68, 71, 83, Morse, Samuel, 152 low-temperature isotropic (LTI) carbon, 84, 120 Mossbauer analysis, 177 646–7 metasilicates, 107 Mössbauer spectrum, 167 low-temperature superconductors (LTSC), Mg2SiO4, 77, 210 Mössbauer, Rudolf, 176 551–54 MgAl2O4, 101, 252, 265, 268, 315 muffle glass, 470 Lubbers, John, 382 MgCO3, 26 Müller, Karl Alexander, 28, 30, 31 Lubbock, John, 17 MgF2, 93 Mullins, William W., 267 Lucalox, 27 MgFe2O4, 511 mullite, 111, 348, 350, 357, 375, 462, luminescence, 588 MgIn2O4, 158, 453 466 MgO smoke experiment, 250, 267 multilayer chip capacitor (MLCC), 566, M MgSiO3, 103 568, 643, 678, 687 machinable glass-ceramics (MGC), 338 mica, KAl3Si3O10 (OH) 2, 19, 100, 108, 348, muscovite mica, 346, 349, 357 Madelung constant, 54, 55, 66, 84, 242 349, 365, 439, 475, 567, 585 Mynon, pit of, 24 Madelung, Erwin, 69 microdiffractometer, 171 maghemite, 102, 615, 616 microelectromechanical systems (MEMS), N magnesite (MgCO3), 26, 352 7, 27, 407, 410, 411, 485, 556, 572 Na2O, 117, 134 magnesium fluoride (MgF2), 580 microprobe, 449 Na2SO4, 468 magnesium hydroxide (Mg(OH) 2), 352 microstructure, 3, 5, 8, 154 Nabarro, Frank Reginald Nunes, 323 magnesium oxide (MgO, magnesia), 8, 26, Miller indices, 75, 76 Nabarro-Herring creep, 318, 323 27, 52, 55, 56, 64, 72, 74, 77, 84, 86–8, Miller, William Hallowes, 85 Nabarro-Herring source, 217 123, 158, 208, 215, 218, 226, 232, 239, Miller–Bravais indices, 75, 76, 94, 95 NaCl, 52, 53, 54, 55, 56, 57, 58, 71, 74, 77, 250, 255, 261, 262, 265, 268, 271, milling, 360–1 78, 81, 87, 88, 89, 183, 190, 197, 198, 307–10, 313, 314, 316, 319, 323, 326, 330, mineral formation, 345 208, 209, 214, 215, 226, 265, 310, 313, 340, 352, 432, 435, 436, 446, 452, 504, mirror plane, 72 468 547, 585, 630 miscibility gap, 133, 386 nanobioceramics, 647 magnetic behavior, 619 misfit dislocation, 282 nanoceramics, 7, 8, 12 magnetic dipole, 599 misplaced atoms, 182 nanoindentation test, 301 magnetic domains, 610 Mn0.4Zn0.6Fe2O4, 5 nanomaterials, 441, 636 magnetic ferrites, 27 MnO, 195 nanoparticles, 228, 241, 242, 250, 273, 360, magnetic flux density, 601 MnO2, 25, 93, 392 365, 376, 409, 441, 616 magnetic force microscopy (MFM), 610, mobility, particle, 487 nanotubes, 113, 114, 160 611 modified chemical-vapor deposition NbN, 63 magnetic levitation (maglev), 603, 681 (MCVD) process, 587 Nd2O3, 191 magnetic materials, 598 modulus of rupture (MOR), 298, 307 Nd-YAG laser, 589 696 .................................................................................................................................................................................. Index near-field scanning optical microscopy Pascal, Blaise, 397, 505 planar defect, 205, 206 (NSOM), 156, 157, 236, 244, 478 paté de verre, 434, 477 Planck’s constant, 624 Néel, Louis, 27, 598 Pauli exclusion principle, 39, 604 plasma spraying, 485, 645 Neri, Antonio, 382 Pauli paramagnetism, 603 plaster of Paris (2CaSO4.H2O), 24, 653 Nernst-Einstein equations, 198 Pauli, Wolfgang, 49 plastic deformation, 296, 309, 313, 314, 325 neutron activation analysis (NAA), 175 Pauling, Linus Carl, 49, 71, 76, 77, 79, 85, plastic forming, 412 neutron scattering, 172 86 plasticity, 299, 309–23, 413 NiAl, 88, 185 Pauling’s classification, 45 plasticizer, 413 NiFe2O4, 184, 271, 275, 511 Pauling’s rules, 71, 76, 82–4, 87, 88, 94, platelets, 359, 365 NiO, 47, 123, 159, 160, 195, 236, 251, 252, 98, 104, 119, 126, 562 pleochroism, 658 254, 257, 265, 271, 273, 277, 456 Pb(ZrxTi1-x)O3, 7 Pliny the Elder, 24 nitrides, 63, 113, 120 PbO, 25, 391, 492, 684 PLZT, 5, 8, 591–94, 597 nitrum, 381 PbS, 208, 310 pneumoconiosis, 22 nodes, 218 PbTe, 310 Pockels effect, 590, 592 Nomarski, 156 PbTiO3, 391, 565 point defects, 87, 181, 183, 185, 187, 189, Norton, Frederick Harwood, 152 Pearson, 81 191, 194, 199, 200, 202, 323, 387 nuclear energy, 26 Pechini method, 364, 377 point groups, 75 nuclear magnetic resonance (NMR), 165, pegmatites, 353 Poiseuille, Jean Louis Marie, 397 166, 177, 279, 370 Peierls barrier, 216 Poisson, Siméon Denis, 306 nucleation, 233, 276 Peierls valley, 216, 217, 222 Poisson’s ratio, 203, 292, 301 Peierls, Sir Rudolf Ernst, 222, 625 polarizability, 578 O Peierls-Nabarro force, 222, 323 polaron, 533 obsidian, 15, 358, 379, 380, 394, 653 Peirels-Nabarro stress, 313, 315 pole figure, 171 Ochsenfeld, Robert, 617 periclase (MgO), 26, 88, 352 polishing, 339 Oersted, Hans Christian, 599, 617 peridot, 653, 669 polymer-matrix composites (PMC), 374, Ohm’s law, 141 peridote, (Mg0.9Fe0.1) 2SiO4, 106 359, 376, 681 olivine, 106, 209, 268, 346, 669 perovskite structure, 565 polymers, 3, 5 Onnes, Heike Kamerlingh, 554 perovskite, 100, 102, 103, 112, 118, 119, polymorphs, 48, 81, 82, 84, 96, 105, 111, opal, 428, 585, 653, 660, 666 448 154 optical fibers, 25, 27, 586–88 Perrot, Bernard, 382, 397 polytope, 118 optical transparency, 593 P-glass, 499 polytypes, 96, 97 orbital hybridization, 63 phase boundaries (PB), 269–70, 277, 440, polytypoids, 96 orbital motion, 599 444, 448, 449, 451, 454, 455 porcelain enamel, 6, 7, 632, 677 ores, 277–80 phase diagrams, 120, 121, 386, 570, 516 porcelain, 18–20, 47, 548 orientation, 313 phase rule, 47 porcelains, felspathic, 648 Orowan equation, 326, 327 phase transformations, 71, 139, 148, 276, pores, 269, 270, 285, 319 Orowan, Egon, 340 444–45, 447, 459, 619 porosity, 319, 278, 295, 583, 613, 626, 643 orthoclase (KAlSi3O8), 548 phlogopite mica, 109, 357, 475 porous coating, 536 Orton cones, 150 phonon (lattice transport), 619 positive temperature coefficient (PTC), 534 Orton Jr., Edward J., 30, 152 phonon, 624 potassium dihydrogen phosphate Ostwald ripening, 231, 272, 409, 427, 438 phosphor, 588 (KH2PO4), (KDP), 27, 157 Ostwald viscometer, 405 phosphorescence, 585, 588 pottery, 19–21, 439, 459, 632 Ostwald, Wilhelm, 410 phosphorus, 25 powder compaction, 412 outside vapor-phase oxidation (OVPO), 586 phosphorus-doped glass, 499 Powder Diffraction File (PDF), 170 Owens, Michael, 382, 479 photochromic glass, 474 powders, 359–65, 400, 407 oxides, 87, 88, 92, 93, 120, 228, 236 photoelectrochemical (PEC) solar cells, pozzolana, 22 oxygen partial pressure (pO2), 120, 121, 687, 688 precipitate-free zones (PFZ), 274 126, 130, 131, 188, 191, 195, 196 photoelectron spectroscopy (PES), 174 precipitation, 363, 448 oxynitrides, 120 photosensitive glass, 474 presuure enhanced CVD, 572 phyllosilicates, 349 primitive cell, 71, 72 P physical vapor deposition (PVD), 494, 572, primitive lattice, 72 paper clay, 422 580 proportional limit, 309 paraelectric, 562, 563 Piccolpasso, Cipriano, 150, 391 proton exchange membrane (PEM) fuel parallel electron energy-loss spectra piezoelectric effect, 103, 556 cells, 686 (PEELS), 172 piezoelectric materials, 507 pseudo-potential, 84 Paris-Erdogan equation, 332 piezoelectricity, 71, 84, 569 pulsed laser deposition (PLD), 453, 503 partial dislocations, 252 pigments, 581 pumice, 232, 279, 395 partially stabilized zirconia (PSZ), 28 Pilkington, Sir Alastair, 26, 30, 382 pyralspites, 669 particle growth, 276, 454 pillared interlayered clays (PILC), 439 pyrite, 92 particle-induced X-ray emission (PIXE), pinning, 315 pyrochlore (CaNaNb2O6F), 565 169 Pittsburgh process, 469 pyroelectric effect, 556 particles, 269, 270, 272, 276, 360 plagioclase feldspar, 662 pyroelectricity, 572 I n d e x ................................................................................................................................................................................. 697 pyrolusite, 25 Ringer’s solution, 296 self-energy, 253 pyrolytic carbon, 649 Rochelle salt, 573 semiconductor devices, 498 pyrometers, 149 rocks, igneous, 346, 349, 353 semiconductors, 3, 4, 12, 67, 68, 83, 89, 90, pyrometric cones, 150 rocks, metamorphic, 346, 349 91, 92, 93, 183, 192, 208, 226, 255, 270, pyrope garnet, 660 rocks, sedimentary, 347 537, 632 pyrope, 669 rocksalt structure, 310, 605 shaping, 412, 422, 438, 463 pyrophanite (MnTiO3), 345 rocksalt, 88, 126, 183, 265 shear modulus, 203, 292, 301 pyrophyllite, 65, 521 Rohl, A.L., 200 shear stress, 313 pyroxene, 109, 110 Rohrer, Heinrich, 176, 243 Shockley partial dislocations, 206 PZT, see lead zirconate titanate 407, 410, rotation axis, 72 short-range order (SRO), 83, 380 411, 445, 570, 572 ruby laser, 589 SiAlONs, 113, 118 ruby, 507, 510, 575, 652, 653, 654, 660, Siegbahn, Kai, 98 Q 662, 665 Siegbahn, Karl Manne, 98 quadruple junctions (QJ), 246, 261–263, Rupert, Prince of Bavaria, 397 Siemens, C.W., 382 280, 433 ruthenium dioxide (RuO2), 490 Siemens, F., 382 quantum numbers, 35–9, 50 Rutherford backscattering spectrometry sieving, 366, 376 quartz, (SiO2), 19, 20, 48, 66, 105, 177, (RBS), 162, 168, 169, 450 silane (SiH4), 677 220, 221, 255, 346–9, 353, 358, 361, 475, Rutherford, Ernest, 177 silica (SiO2), 4, 6, 96, 100, 105, 116, 125, 507, 548, 571, 621, 630, 652, 661, 667, rutile (TiO2, titania), 93, 94, 239, 274, 347, 301, 348, 351, 466 669 353, 664 silica glass, 379 quartz, cryptocrystalline, 15 silicates, 100, 101, 104, 105, 107 quaternary diagrams, 132 S silicon carbide (SiC), 4, 5, 7, 62, 64, 66, safety glass, 473 68, 71, 89, 96–7, 144–5, 151, 182–3, 211, R sand, 24, 683 220, 269, 282, 296, 308, 322, 327, 354, Rakuyaki, Chojiro, 397 sapphire, 94, 95, 209, 210, 215, 235, 249, 364–5, 415, 427, 428, 522 Raman spectra, 164 264, 268, 270, 301, 327, 450, 458, 507, silicon dioxide (SiO2), 5, 15, 20, 22, 48, Raman spectroscopy, 164, 165, 176 509, 513, 516, 652, 653, 654, 660, 661, 100, 122, 125, 134, 136, 177, 269, 391, Raman, Sir Chandrasekhara Venkata, 176 662, 665, 669, 670 396, 498, 549, 568, 572, 579, 666, 683 Ramsdell notation, 96, 132 scanned probe microscopy (SPM), 161, 235 silicon nitride, (Si3N4), 5, 7, 27, 113, 259, Raoult’s law, 122 scanning Auger microscopy (SAM), 174 260, 262, 266, 296, 303, 304, 354, 355, rapid prototyping (RP), 420 scanning electron microscopy (SEM) 364, 376, 415, 498, 568, 572, 677, 678 Ravenscroft, George, 30, 382 image, 389, 395, 595, 666 silicon oxynitride (Si2N2O), 119 Rayleigh scattering, 164, 588 scanning electron microscopy (SEM), 23, silicon, 157 reaction-barrier layer, 456 235, 237, 239, 241, 262, 278, 279, 366, sillimanite, 100, 351 reaction-bonded silicon nitride (RBSN), 27 449, 455, 501 silver bromide (AgBr), 182, 186, 200 reactive bonding, 490 scanning tunneling microscopy (STM), simple-cubic (sc) lattice, 87, 88 reactive evaporation (RE), 501 161, 236, 240, 263, 571, 610 Simpson, Edward, 30 reactive sputtering, 501 scapolite, 585 single-edged notched beam (SENB), 298–9 Read-Shockley formula, 250 scattering, 162, 171 single-walled nanotube (SWNT), 114 recrystallization, secondary, 437 scheelite, 585 sintering, 139, 225, 248, 270, 350, 360, 413, recycling, 683 Scherrer equation, 369 427–29 red lead (Pb3O4), 370 Schmalzried, Hermann, 461 SiO4, 104, 113 reflection electron microscopy (REM), 239, Schmid-Viechnicki method, 516 skull melting process, 514, 515 240 Schott, Otto, 382, 479 Slater-Bethe curve, 604 reflection high-energy electron diffraction Schottky defects, 265, 268, 619 slip, 310, 314, 413 (RHEED), 162, 176, 236, 238 Schottky formation energy, 194 slip bands, 311 reflection, 577 Schottky, Walter, 199 slip casting, 417, 450 reflectivity, 579 Schrieffer, John Robert, 554 slip planes, 209 refraction, 577, 578 Schrödinger wave equation, 37 slip systems, 310, 312, 314 refractive index, 577, 578, 656 Schrödinger, Erwin, 49 slurry, 412, 413, 482, 492 refractories, 4, 6, 7, 14, 25, 120, 358, 466, Schultz, Peter, 27 Smalley, Robert E., 118 467, 621, 677 screen-printing, 488 smectite, 109 Reid, A., 37 Seabright, C.A., 596 Snell’s law, 586 ReO3, 4 secondary electrons (SEs), 158 SnO2, 5, 93, 391 residual stress measurement, 165 secondary ion mass spectroscopy (SIMS), Snoeck, J.J., 598 Reuss model, 295, 308, 310 172 soda-lime silicate glass, 464 Reynolds number, 367, 377 sedimentation, 367 sodalite, 115 Reynolds, Osborne, 377 Seebeck, Thomas Johann, 149, 152 sodium carbonate (Na2CO3), 463 rhinestones, 667 seeding, 438 sodium vapor lamp, 584 rhodolite, 669 Seger, Hermann A., 30 sol-gel process, 363, 359, 364, 371, 377, Richard’s rule, 621, 623 Seignette, Pierre, 573 400–401, 403–6, 474, 484, 594, 646 Ringer, Sidney, 306 selected area diffraction (SAD), 162, 168 solid casting, 418 698 .................................................................................................................................................................................. Index solid freeform fabrication (SFF), 420 stress-probability-time diagrams (SPT), thermal etching, 219 solid solutions, 187 305 thermal shock resistance, 633 solid-oxide fuel cell (SOFC), 28, 32, 181, stress-strain curves, 290, 296, 310, 314, 335 thermally grown oxide (TGO), 446 545 structure, 154, 181, 211 thermistors, 541 solid-state laser, 575, 589, 597 structure, antifuorite, 92 thermochemical processing, 685 solid-state reactions, 444, 445, 449 Strukturbericht, 81, 85 thermocouples, 149 solid-state sintering, 428 Strutt, John William (Lord Rayleigh), 177 thermodynamic equilibrium, 248 solidus, 123 sublattice, 88 thermodynamics, 35, 45, 47, 48 solubility, 363 substitutional defects, 183 thermogravimetric analysis (TGA), 176, solvus lines, 121 substrate, 504 177 space group, 81 superconducting quantum interference thermoluminescence, 585 spark source mass spectrometry (SSMS), devices (SQUIDs), 603 thick-film circuits, 488–92 172 superconductivity, 63, 113, 551, 681 thin films, 264, 481, 494 specific heat, 620 superconductors, 113, 120, 197, 242, 255, thin-film diffractometer, 170 spectroscopy, 154, 163 265, 601 ThO2, 112, 184, 435 spectroscopy, IR, 163, 164 superconductors, non-metallic, 552 Thomas Sidney Gilchrist, 25 spectroscopy, Mössbauer, 155, 163–7, 172 superplasticity, 322 Thompson-Freundich equation, 461 spectroscopy, NMR, 165 surface charge, 242 Thomsen, Christian, 17 spectroscopy, Raman, 163, 164 surface diffusion, 228 Thomson, George Paget, 37, 49, 98 sphalerite (ZnS), 353, 585, 656, 660 surface energy, 224, 225, 226, 327, 328 Thomson, Joseph John, 48, 49, 98 spherulites, 281 Surface Evolver, 242 Thomson, William (Lord Kelvin), 634 spin coating, 484 surface stress, 225 TiC, 63, 208, 315, 354 spin, 599 surface structure, 227 tiger-eye, 661 spinel, 101, 102, 106, 110, 118, 127, 161, surface tension, 225, 230, 284 tilt boundary, 247, 253, 261, 268, 436 162, 182, 211, 213, 218, 227, 228, 239, surface-enhanced Raman scattering tilt, 254, 268 253, 254, 255, 256, 258, 268, 274, 311, (SERS), 165 tin oxide (SnO2), 145, 652 450, 454, 456 surfaces, 224–25 TiN, 5, 63, 219 spinels, 668 surfactants, 231, 284 TiO, 534 splat quenching, 380 symmetry, 71, 72, 74, 75, 82, 84, 85, 86 titanates, 93, 362 Spode, Josiah, 20, 424 Synge, E.H., 244 titania (TiO2), 87, 93, 95, 161, 315, 353, spodumene, 109, 110 Système International d’Unités (SI), 10, 11, 351, 391, 487, 687 spray drying, 362 12, 124, 347, 383, 600, 619 TlBr, 88 spraying, 485 TlCl, 88 sputtering, 501, 594, 645 T tobermorite, 23 SrO, 242 talc, 211, 212, 296, 683 Tomimoto, Kenkichi, 424 SrTiO3, 102, 160, 364, 552, 565 tantalite, 683 topaz, 660, 667, 670 stacking fault (SF), 205, 253 tantalum nitride (TaN), 490 Torricelli, Evangelista, 505 stacking-fault energy (SFE), 206, 211, 212, tantalum pentoxide (Ta2O5), 683 total internal reflection (TIR), 586 218, 253 tanzanite, 659, 660, 669 toughened glass, 473 standard test method, 383 tape casting, 481–84, 482, 483, 492, 568 toughening, 325, 335 static fatigue, 331 tektites, 394 tourmaline, 107, 108, 652, 668 steel, 3, 7, 14, 25 Teller, Edward, 369, 376 Trancrede de Dolomieu, Guy S, 479 Stefan-Boltzmann constant, 150, 625 temperature coefficient of resistivity (TCR), transgranular (or cleavage) fracture, 333 Stefan-Boltzmann law, 149 491, 534, 536, 541 transition metal borides, 63 stereolithography (SLA), 420 temperature stability, 536 transition metal carbides, 63, 89 steric hindrance, 482 tempered glass, 473 transition metal nitrides, 89 Stirling’s approximation, 185 tenorite, 93 transmission electron microscopy (TEM) stishovite, 93 tensile strength, 297, 328 image, 390, 430, 680, 687 Stokes law of fluorescence, 585 tensile stress, 579 transmission electron microscopy (TEM), Stokes scattering, 164 tensile test, 296 121, 146, 191, 207, 221, 235, 237, 238, Stokes, Sir George Gabriel, 177, 377 tension, 297 240, 251, 257, 259, 262–4, 274, 278, 366, Stokes’ law, 367–8, 467, 487 tephroite (Mn2SiO4), 106 369, 370, 380, 436, 449, 454, 455, 457, Stookey, S. Donald, 27, 382, 479 ternary systems, 128 501, 537, 611, 655 strain, 289, 330 tetragonal zirconia polycrystals (TZP), 28 transparency, 577 strain energy, 204, 206 thallates, 113 triboluminescence, 585 strain fields, 157, 204 theoretical strength, 327 tricalcium phosphate (TCP), 7, 636, 643, stress birefringence, 579 thermal analysis, 154, 175 645 stress corrosion cracking (SCC), 331 thermal barrier coatings (TBC), 269, 446, tridymite, 48, 105, 111 stress intensity factor, 293, 329 461, 621 trinitite, 395 stress rupture, 331 thermal conduction, 4, 9, 91, 147, 260, 266, triple junctions (TJ), 246, 261–264, 267, stress shielding, 639 415, 619, 624–28, 653, 663 268, 270, 275, 280, 433, 435 stress, 289, 313, 315, 330 thermal conduction module (TCM), 438 triple points, 439 I n d e x ................................................................................................................................................................................. 699 tsavorite, 660 Voight model, 294, 308 Y tungsten carbide (W6C), 3, 356 volatiles, 429 Y2O3, 9, 189, 319, 332, 439, 678 tungsten oxide (WO3), 258 Volterra, Vito, 222 Y3Al5O12, 5, 589 tungsten, 146 von Fraunhofer, Joseph, 382 Y3Fe2 (FeO4)3, 607 turbostratic carbons, 647 Von Hippel, Arthur Robert, 573 Yanagi, Soetsu, 425 turquoise, 653 von Mises criterion, 314 YBa2Cu3O7 (YBCO), 4, 5, 28, 32, 93, 100, twin boundaries, 247, 255–8, 268, 447, 561 von Mises, Richard, 323 112, 118–20, 197, 266, 377, 445, 446, twist boundary, 223, 247–8, 253, 261 von Tschirnhaus, Count Ehrenfried 495, 553, 681 Walther, 20, 30 yield strength, 309, 315 U Vycor process, 386 yield stress, 315 ugrandites, 669 Young, Thomas, 69, 232, 243, 306 ultrasonic testing, 301 W Young’s equation, 231 ultra-violet photoelectron spectroscopy Wagner, Carl, 461 Young’s modulus, 51–3, 71, 244, 289–95, (UPS), 174 Warren, Bertram Eugene, 397 297, 301, 307, 373, 619, 633, 639 unit cell, 71, 76, 83, 112 wavelength dispersive spectrometer (WDS), Young-Dupré equation, 232 uraninite, 685 172, 173, 653 yttrium aluminosilicate (YAS) glasses, 646 uranium dioxide (urania, UO2), 26, 87, 92, wear resistance, 338 yttrium aluminum garnet (YAG), 36, 107, 184, 194, 227, 277, 279, 685 Wedgwood, Josiah, 20, 21, 24, 31, 424, 676 191, 205, 207, 208, 266, 290, 439, 457, uvarovite, 660 Wedgwood, Thomas, 199 507, 514, 668, 679, 680 Weibull distribution function, 302 yttrium iron garnet (Y3Fe5O12 or YIG), 107, V Weibull modulus, 291, 308 519, 607, 608, 610 vacancy, 182–3, 185–6, 196, 215, 265, 318 Weibull statistics, 302–5 yttrium stabilized zirconia (YSZ), 173, 189, vacancy pairs, 190 Weibull, E.H. Waloddi, 306 446, 447 Valasek, Joseph, 573 Weiss, Pierre Ernest, 609, 617 yttrium vanadate, (YVO4), 157 valence, 116, 121 wetting, 231, 243, 247, 284 yttrium–aluminum (YA) glass, 386 van der Waals bonding, 96, 108, 109 whiskers, 359, 370, 372, 374, 376, 378 van der Waals forces, 100, 114, 211, 283, whiteware, 6, 7, 142, 148, 417, 582, 632, Z 686 677 Zachariasen, William Houlder, 31, 115, 118 van der Waals, Johannes Diderik, 69 wide-band-gap semiconductors, 542 Zachariasen’s model, 117 van Leeuwenhoek, Anton, 397 willemite (Zn2SiO4), 281, 391, 585 Zachariasen’s rules, 115 van Royen, Willebrod Snell, 596 Winston, Harry, 673 Zeiss, Carl Friedrich, 382, 479 vapor pressure, 231 Wollaston, William Hyde, 688 Zeiss, Roderick, 382 vaporization, 231 wollastonite; CaSiO3, 391 zeolite, 227, 233 vapor-liquid-solid (VLS) mechanism, 372, Wulff plot, 227, 249 zeolites, 84, 114, 115, 118, 279, 440 508, 521, 522 Wulff shapes, 242 zinc aluminate spinel (ZnAl2O4), 668 varistor, 540 Wulff, Georgii (Yurii) Viktorovich, 85 zinc blende (ZnS), 55, 77–8, 81, 90, 96–8, Venus Flower Basket (Euplectella), 395 Wulffman (NIST), 242 105, 211 vermiculite, 109, 439 wurtzite structure, 209 zinc oxide (ZnO), 7, 64, 90, 188, 191, 195, Verneuil process, 508, 509, 510 wurtzite, 55, 77, 90, 91, 98, 105, 239 196, 200, 254, 266, 353, 519, 539, 541, Verneuil, August Victor Louis, 508, 524, wüstite, 82, 130, 187, 188, 446 686 652 Wyckoff, Ralph Walter Graystone, 85 zincite, 353 viscometer, 384, 405 zircon, (ZrSiO4, zirconium dioxide), 100, viscosity, 284, 383, 384, 405, 406, 489 X 146, 281, 347, 353, 358, 392, 507, 582 viscous flow, 321 X-ray backscattering, 483 zirconia (ZrO2), 7, 28, 122, 144, 145, 189, visible light microscopy (VLM), 154, 156, X-ray computed tomography (CT), 682 194, 198, 276, 295, 336, 446, 507, 447, 172, 176, 177, 274, 278, 366, 388, 389, X-ray diffraction (XRD), 102, 113, 115, 501, 635, 639, 640, 655, 686 391, 449, 610 121, 122, 135, 162, 169, 170–1, 369, 370, zirconia-toughened alumina (ZTA), 336, visible light microscopy (VLM), polarized, 380, 653 337 156 X-ray energy dispersive spectroscopy zirconia-toughened ceramics (ZTC), 28 VO2, 93 (XEDS), 168, 172, 173, 249, 653 zirconium diboride (ZrB2), 354, 356 Vogel-Fulcher-Tammann (VFT) equation, X-ray photoelectron spectroscopy (XPS), zoisite (Ca2Al3(SiO4)3(OH)), 659, 669 318, 321 37, 174 zone axis, 75 voids, 227, 242, 278 X-ray topography, 157 zone refining, 508 700 .................................................................................................................................................................................. Index  Details for Figures and Tables This list summarizes the sources used for images and the Figure 2.7 From Henderson, J. (2000) The Science and origin of data used in tables and diagrams. Where pos- Archeology of Materials. Routledge, London, p. 199. sible, the original source for each figure is given, but on Reproduced by permission of Taylor and Francis. many occasions the figures have been so widely used in Figure 2.8 Courtesy of Paul E. Stutzman. the literature that the original source is not known to us; Figure 2.9 Data from Ashby, M.F. and Jones, D.R.H. in theses cases, when new diagrams have been created, no (1986) Engineering Materials 2, Pergamon Press, Oxford, citation is given in this list. We will add information p. 192. regarding original citations to the web site as it becomes Figure 2.10 Data from Ashby, M.F. and Jones, D.R.H. available. Images obtained by our students, postdocs or (1986) Engineering Materials 2, Pergamon Press, Oxford, colleagues in collaborative research with the authors but p. 192. not published elsewhere are denoted here by the author’s Figure 2.11 From the Travels of Sir John Mandeville, initials; those obtained by the authors are not attributed ink and tempera on parchment, Bohemia, circa 1410. The further. British Library (ms Add. 24189, f.16), London. Repro- duced by permission of the British Library. Chapter 1 Table 2.1 Data from Fergusson, J.E. (1982) Inorganic Chemistry and the Earth, Pergamon, Oxford, p. 47. Figure 1.2 Data from Evans, A.G. and Davidge, R.W. Table 2.2 Data from Wood, N. (1999) Chinese Glazes, (1969) “Strength and fracture of fully-dense polycrystalline A&C Black, London. MgO”, Phil. Mag. 20, 373. http://www.tandf.co.uk/journals Table 2.4 Data from Lechtman, H.N. and Hobbs, L.W. Figure 1.3 Courtesy of Sandia National Laboratory. (1986) “Roman concrete and the Roman architectural Figure 1.4 McKernan, S., MGN & CBC. revolution”, in: Ceramics and Civilization III: High- Figure 1.5 Data from Kingery, W.D., Bowen, H.K., and Technology Ceramics—Past, Present, and Future, edited Uhlmann, D.R. (1976) Introduction to Ceramics 2nd Ed., by W.D. Kingery, The American Ceramics Society, p. 1008. Westerville, OH, p. 95. Figure 1.6 Data from Moulson, A.J. and Herbert, J.M. (1990) Electroceramics, Chapman and Hall, London, p. 215. Chapter 3 Table 1.3 From the NIST Reference on Constants, Units, and Uncertainty (www.physics.nist.gov). Figure 3.7 Data from Lupis, C.H.P. (1983) Chemical Table 1.4 From S.I. and Related Units: Quick-Refer- Thermodynamics of Materials, Elsevier Science Publish- ence Conversion Factors (1968), compiled by Dryden, ing, New York, p. 35. I.G.C, BCURA, Leatherhead, Surrey, UK. Figure 3.8 Data from Schmalzried, H. (1974) Solid State Reactions, Academic Press, New York, p. 109. Table 3.5 Data from Moore, C.E. (1970), Ionization Chapter 2 Potentials and Ionization Limits Derived from the Analy- Figure 2.2 Adapted from Price, T.D. and Feinman, sis of Optical Spectra, NSRDS-NBS 34, National Bureau G.M. (2001) Images of the Past 3rd Ed., Mayfield, Moun- of Standards, Washington, D.C. Data on the actinides is tain View, CA. from Seaborg, G.T. (1968) Ann. Rev. Nucl. Sci. 18, 53 and Figure 2.3 From Hummel, R.E. (1998) Understanding references therein. Materials Science, Springer, New York, p. 283. Repro- Table 3.6 Data from Berry, R.S. (1969) Chem. Rev. 69, duced with permission from Springer. (The figurine is in 533 except: a Edlen, B. (1960) J. Chem. Phys. 33, 98; b the Moravske Museum, Brno, Czech Republic.) Baughan, E.C. (1961) Trans. Faraday Soc. 57, 1863; c Figure 2.4 Adapted from Kingery, W.D. and Vandiver, Ginsberg, A.P. and Miller, J.M. (1958) J. Inorg. Nucl. P.B. (1986) Ceramic Masterpieces, The Free Press, New Chem. 7, 351; d Politzer, P. (1968) Trans. Faraday Soc. 64, York, p. 19. 2241. D e ta i l s f o r F i g u r e s a n d Ta b l e s ............................................................................................................................... 701 Chapter 4 Figure 6.5 From Tillman, K., Thust, A., and Urban, K. (2004) “Spherical aberration correction in tandem with Figure 4.1a Data from Sproull, R. (1956) Modern exit-plane wave reconstruction: Interlocking tools for the Physics: A Textbook for Engineers, Wiley, New York, atomic scale imaging of lattice defects in GaAs” Microsc. Figure 7-2 on p. 192. Microanal. 10. 185, with permission from Cambridge Figure 4.2 Data from Wachtman, Jr., J.B., Tefft, W.E., University Press. Lam, Jr., D.G., and Apstein, C.S. (1961) “Exponential Figure 6.9 Adapted from Galasso, F.S. (1970) Structure Temperature Dependence of Young’s modulus for several and Properties of Inorganic Solids, Pergamon, Oxford, oxides,” Phys. Rev., 122, 1754. p. 69. Figure 4.3 Data from Wachtman, Jr. J.B. and Lam, Jr. Figure 6.17 Adapted from Parthé, E. (1964) Crystal D.G. (1959) “Young’s modulus of refractory materials as Chemistry of Tetrahedral Structures, Gordon and Breach, function of temperature”, J. Am. Ceram. Soc. 42, 254. New York, p. 16. Figure 4.7 Data from Schoknecht, V.G. (1957) Z. Table 6.1 Data from Toth, L.E. (1971) Transition Metal Naturf., 12A, 983. Carbides and Nitrides, Academic Press, New York, Figure 4.19 Data from Bader, R.F.W., Keaveny, I., and p. 33. Cade, P.E. (1967) “Molecular charge distributions and chemical binding: II. First-row diatomic hydrides, AH”, J. Chem. Phys. 47, 3381. Chapter 7 Figure 4.21 Data from Slater, J.C. (1934) Phys. Rev. 45, Figure 7.16c Reprinted from Iijima, S. (1993) “Growth 794. of carbon nanotubes,” Mater. Sci. Eng. B 19, 172, Copy- Table 4.2 Modified from Van Vlack, L.H. (1964) Physi- right 1993, with permission from Elsevier. cal Ceramics for Engineers, Addison Wesley Reading MA Figure 7.19 Adapted from Zachariasen, W.H. (1932) (1964) p. 118. “The atomic arrangement in glass”, J. Am. Chem. Soc. 54, Table 4.3 Data compiled by Huheey, J.E. (1975) Inor- 3841. ganic Chemistry: Principles of Structure and Reactivity, Figure 7.21 Adapted from Hobbs, L.W. (1995) “Network Harper & Row, London, p. 62. topology in aperiodic networks” J. Non-Cryst. Solids 192 Table 4.4 Data compiled by Huheey, J.E. (1975) Inor- & 193, 79. Copyright 1995, with permission from ganic Chemistry: Principles of Structure and Reactivity, Elsevier. Harper & Row, London, p. 61. Table 7.5 Data compiled by Wenk, H.-R. and Bulakh, Table 4.5 Data from (B-H): Johnson, D.A. (1982) Some A. (2004) Minerals, Cambridge University Press, p. 314. Thermodynamic Aspects of Inorganic Chemistry, Cam- bridge; (B-L): Morris, D.F.C. (1957) J. Inorg. Nucl. Chem. 4, 8. Chapter 8 Table 4.6 Data from Shannon, R.D. (1976) “Revised Figure 8.3 Data from Bergeron, C.G. and Risbud, S.H. effective crystal radii and systematic studies of interatomic (1984) Introduction to Phase Equilibria in Ceramics, The distances in halides and chalcogenides,” Acta. Cryst. A32, American Ceramic Society, Columbus, OH, p. 59. 751. Figure 8.4 Data from von Wartenberg, H. and Prophet, Table 4.8 Data compiled by Israelachvili, J.N. (1992) E. (1932) Z. Anorg. Allg. Chem. 208, 379. Intermolecular and Surface Forces, 2nd Ed., Academic Figure 8.5a Data from Lin, P.L., Pelton, A.D., Bale, C. Press, London, p. 186. W., and Thomson, W.T. (1980) CALPHAD: Computer Table 4.9 Data compiled by Israelachvili, J.N. (1992) Coupling of Phase Diagrams and Thermochemistry, Vol. Intermolecular and Surface Forces, 2nd Ed., Academic 4, Pergamon New York, p. 47. Press, London, p. 190. Figure 8.5b Data from Dorner, P., Gauckler, L.J., Kreig, Table 4.10 Data from van Vechten, J.A. (1973) Phys. H., Lukas, H.L., Petzow, G., and Weiss, J. (1979) Rev. B 7, 1479. CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry, Vol. 3, Pergamon, New York, p. 241. Chapter 5 Figure 8.11 Data from Doman, R.C., Barr, J.B., McNally, Figure 5.11 Data from McHale, J.M., Navrotsky, A., and R.N., and Alper, A.M. (1963) J. Am. Ceram. Soc. 46, 313. Perrotta, A.J. (1997) “Effects of increased surface area and Figure 8.16 Data from Osborn E.F. and Muan, A. (1960) chemisorbed H2O on the relative stability of nanocrystal- No.3 in Phase Equilibrium Diagrams of Oxide Systems, line γ-Al2O3 and α-Al2O3,” J. Phys. Chem. B 101, 603. American Ceramic Society, Columbus OH. Figure 8.18 Data from Morey, G.W. and Bowen, N.L. (1925) J. Soc. Glass. Technol. 9, 232, 233. Chapter 6 Figure 8.21 Data from Jack, K.H. (1976) “Sialons and Figure 6.2 Data from Galasso, F.S. (1970) Structure related nitrogen ceramics” J. Mater. Sci. 11, 1135. and Properties of Inorganic Solids, Pergamon, Oxford, Figure 8.24 Reprinted from Torres, F.C. and Alarcón, p. 113. J. (2004) J. Non-Cryst. Sol. 347, “Mechanism of crystal- 702 ................................................................................................................................ D e ta i l s f o r F i g u r e s a n d Ta b l e s lization of pyroxene-based glass-ceramic glazes” 45, imaging of oxygen in perovskite ceramics”, Science 299, Copyright 2004, with permission from Elsevier. 870. Copyright 2003 AAAS. Figure 10.12 Reprinted with permission from Han, W. Q., Chang, C.W., and Zettl, A. (2004) “HRTEM image of Chapter 9 a BN nanotube partly loaded with a crystal of KI” Nano Figure 9.4 Courtesy of Swindell Dressler. Letters 4, 1355. Copyright 2004 American Chemical Figure 9.5 Courtesy of Swindell Dressler. Society. Figure 9.6 Courtesy of David Demaray and Mike Figure 10.14 Reprinted from Diebold, U. (2003) Vinton, University of Washington. “The surface science of titanium dioxide” Surf. Sci. Figure 9.7 Courtesy of Kanthal Corporation. Reports 48, 53. Copyright 2003, with permission from Figure 9.8 Reprinted from Susnitzky D.W. and Carter, Elsevier. C.B. (1992) “Surface morphology of heat-treated ceramic Figure 10.18 Reprinted from Richardson, T.J. and Ross, thin films,” J. Am. Ceram. Soc. 75, 2471, with permission Jr., P.N. (1996) “FTIR spectroscopy of metal oxide inser- from Blackwell Publishing and the American Ceramic tion electrodes: thermally induced phase transitions in Society. LixMn2O4 spinels,” Mater. Res. Bull. 31, 935, Copyright Figure 9.11 Courtesy of Ferro Corporation. 1996, with permission from Elsevier. Table 9.1 Data compiled by Atkins, P.W. (1978) Physi- Figure 10.20 Courtesy of Yahia Djaoued. cal Chemistry, Oxford University Press, Oxford, p. 107. Figure 10.21 Data from Simmons, C.J. and El-Bayoumi, Table 9.2 Data compiled by Atkins, P.W. (1978) Physi- O.H., eds (1993) Experimental Techniques in Glass cal Chemistry, Oxford University Press, Oxford, p. 108. Science, The American Ceramic, Society, Westerville, Table 9.3 Data from Brown, R.L., Everest, D.A., Lewis, OH, p. 88. J.D., and Williams, A. (1968) “High-temperature pro- Figure 10.22 Data from Simmons, C.J. and El-Bayoumi, cesses with special reference to flames and plasmas,” J. O.H., eds (1993) Experimental Techniques in Glass Inst. Fuel. 41, 433. Science, The American Ceramic, Society, Westerville, Table 9.4 Data compiled by Nassau, K. (1994) Gem- OH, p. 91. stone Enhancement, 2nd Ed., Butterworth-Heinemann, Figure 10.24 Source. Data from Simmons, C.J. and El- Oxford, p. 207. Bayoumi, O.H., eds (1993) Experimental Techniques in Table 9.5 Data compiled by Nassau, K. (1994) Gem- Glass Science, The American Ceramic, Society, Wester- stone Enhancement, 2nd Ed., Butterworth-Heinemann, ville, OH, pp. 107 and 110. Oxford, p. 206. Figure 10.25 Data from Simmons, C.J. and El-Bayoumi, Table 9.6 Data compiled by Nassau, K. (1994) Gem- O.H., eds (1993) Experimental Techniques in Glass stone Enhancement, 2nd Ed., Butterworth-Heinemann, Science, The American Ceramic, Society, Westerville, Oxford, p. 205. OH, p. 111. Table 9.7 Data compiled by Nassau, K. (1994) Gemstone Figure 10.26 Reprinted from Williams, D.B. and Carter, Enhancement, 2nd Ed., Butterworth-Heinemann, Oxford, C.B. (1996) Transmission Electron Microscopy, Plenum, p. 220, modified with applications from the American Iso- New York, with permission from Springer. static Presses, Inc. data sheet. ANSI (American National Figure 10.27 Reprinted from Farrer, J.K., Carter, C.B., Standards Institute) symbols, except for G, C, and D. and Ravishankar, N. (2006) “The Effects of Crystallogra- Table 9.8 The pyrometric cone equivalent test is phy on Grain Boundary Migration in Alumina” J. Mater. described in ASTM Standard C24-56. Sci., 41(3), 661–674. Reproduced by permission of Springer. Figure 10.29 Reprinted from Simpson, Y.K., Colgan, Chapter 10 E.G., and Carter, C.B. (1987) “Kinetics of the growth of Figure 10.1 LeBret, J.B. & MGN. spinel on alumina using Rutherford backscattering spec- Figure 10.3 Reprinted from Smolsky, I.L., Voloshin, troscopy,” J. Am. Ceram. Soc. 70, C149. With permission A.E., Zaitseva, N.P., Rudneva, E.B., and Klapper, H. from Blackwell Publishing and the American Ceramic (1999) “X-ray topographic study of striation formation in Society. layer growth of crystals from solutions,” Phil. Trans R. Figure 10.30 Altay, A. & CBC. Soc. Lond. A. 357, 2631, with permission from the Royal Figure 10.33 Altay, A. & CBC. Society. Figure 10.34 Gilliss, S.R. & CBC. Figure 10.4 Reprinted from LeBret, J.B., Norton, M.G. Figure 10.35 Data from Haas, T.W., Grant, J.T., and and Bahr, D.F. (2005) “Examination of crystal defects Dooley III, G.J. (1972) “Chemical effects in Auger elec- with high-kV X-ray computed tomography,” Mater. Lett. tron spectroscopy,” J. Appl. Phys. 43, 1853. 59, 1113. Copyright 2005, with permission from Figure 10.37 Altay, A. & CBC. Elsevier. Table 10.5 Data from Raman Spectroscopic Library, Figure 10.11 Reprinted with permission from Jia, C.L., Dept. Chemistry, University College London (www.chem. Lentzen, M., and Urban, K. (2003) “Atomic resolution ucl.ac.uk/resources/raman/index.html). D e ta i l s f o r F i g u r e s a n d Ta b l e s ............................................................................................................................... 703 Table 10.6 Data compiled by Banwell, C.N. (1972) Fun- Figure 12.14 Reprinted from Delavignette, P. and damentals of Molecular Spectroscopy, 2nd Ed., McGraw- Amelinckx, S. (1962) “Dislocation patterns in graphite,” Hill, London p. 328. J. Nucl. Mater. 5, 17. Copyright 1962, with permission Table 10.7 From Smith, D.K. (1986) “Diffraction from Elsevier. methods: Introduction,” in: ASM Handbook Volume 10 Figure 12.18 Reprinted from Bontinck, W. and Materials Characterization, ASM International (1986) Amelinckx, S. (1957) “Observation of helicoidal dislocation p. 325. lines in fluorite crystals,” Phil. Mag. 2, 1. With permission Table 10.10 Modified after: Bowen, D.K. and Hall, C. from Taylor and Francis. http://www.tandf.co.uk/journals R. (1975) Microscopy of Materials: Modern Imaging Figure 12.19 Reprinted from Phillips, D.S., Plekta, B.J., Methods Using Electron, X ray and Ion Beams, Macmil- Heuer, A.H., and Mitchell, T.E. (1982) “An improved lan, London p. 86. model of break-up of dislocation dipoles into loops: appli- cation to sapphire (α-Al2O3),” Acta Metall. 30, 491. Copy- right 1982, with permission Elsevier. Chapter 11 Figure 12.21 Reprinted from Amelinckx, S. (1964) “The Figure 11.9 With permission from Voyles, P.M., Chadi, direct observation of dislocations Solid State Physics, Sup- D.J., Citrin, P.H., Muller, D.A., Grazul, J.L., Northrup, plement 6, Academic Press, New York pp. 1–487, figure P.A., and Gossmann, H.-J.L. (2003) “Evidence for a New 48, Copyright 1964, with permission from Elsevier. Class of Defects in Highly n-Doped Si: Donor-Pair- Figure 12.22 Reprinted from Amelinckx, S. (1964) Vacancy-Interstitial Complexes”, Phys. Rev. Lett. 91, “The direct observation of dislocations” Solid State 125505. Copyright 2003 American Physical Society. Physics, Supplement 6, Academic Press, New York pp. Figure 11.11 Data from Kingery, W.D., Bowen, H.K., 1–487, figure 49, Copyright 1964, with permission from and Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd Elsevier. Ed., Wiley, New York, p. 237. Figure 12.23a Reprinted from Amelinckx, S. (1964) Figure 11.12 Data from Kingery, W.D., Bowen, H.K., “The direct observation of dislocations” Solid State and Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd Physics, Supplement 6, Academic Press, New York pp. Ed., Wiley, New York, p. 240. 1–487, figure 149a, Copyright 1964, with permission from Figure 11.13 Data from Baumbach, H.H. and Wagner, Elsevier. C. (1933) Z. Phys. Chem. B 22, 199. Figure 12.24 Reprinted by permission from Macmillan Figure 11.14 Data from Kingery, W.D., Bowen, H.K., Publishers Ltd: Kodambaka, S., Khare, S.V., Swiech, W., and Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd Ohmori, K., Petrov. I., and Greene, J.E. (2004) “Disloca- Ed., Wiley, New York, p. 245. tion-driven surface dynamics on solids” Nature 429, 49. Figure 11.16 Data from Kirk R. and PL Pratt, P.L. Copyright 2004. (1967) Proc. Brit. Ceram. Soc. 9, 215. Figure 12.25 Reprinted from Tanaka, M. and Higashida, Table 11.7 Data from Jeffe, E.R. and Foote, F. (1933) J. K. (2004) “HVEM characterization of crack tip disloca- Chem. Phys., 1, 29. tions in silicon crystals,” J. Electron Microsc. 53, 353. Table 11.8 Data compiled by Hayes, W. and Stoneham, With permission from Oxford University Press. A.M. (1985) Defects and Defect Processes in Nonmetallic Figure 12.27a Reprinted with permission from Gutkin, Solids, Wiley, New York, p. 146. M.Y., Sheinerman, A.G., Argunova, T.S., Mokhov, E.N., Je, J.H., Hwu, Y., Tsai, W-L., and Margaritondo (2003) “Micropipe evolution in silicon carbide”, Appl. Phys. Lett. Chapter 12 83, 2157. Copyright 2003, American Institute of Physics. Figure 12.7 Courtesy of Y. Ikuhara. Figure 12.27b Reprinted with permission from Qian, Figure 12.9a Reprinted from Dash W.C. (1957) “The W., Rohrer, G., Skowronski, M., Doverspike, K., Rowland, observation of dislocations in silicon,” in Dislocations L., and Gaskill, D. (1995) “Open-core screw dislocations and Mechanical Properties of Crystals, Eds Fisher, J.C., in GaN epilayers observed by scanning force microscopy Johnston, W.G., Thomson, R. and Vreeland, T. Wiley, New and high-resolution transmission electron microscopy” York, pp. 57–68. Appl. Phys. Lett. 67, 2284. Copyright 1995, American Figure 12.9b Eakins, D.E. & MGN. Institute of Physics. Figure 12.11c Reprinted from Ray, I.L.F. and Cock- Figure 12.28 Reprinted from Carter, C.B. and Kohlst- ayne, D.J.H. (1971) “The dissociation of dislocations in edt, D.L. (1981) “Electron irradiation damage in natural silicon,” Proc. R. Soc. Lond. A. 325, 543. With permission quartz grains,” Phys. Chem. Minerals 7, 110, with permis- from the Royal Society. sion from Springer. Figure 12.13 Reprinted from Nakamura, A., Lagerlöf, K.P.D., Matsunaga, K., Tohma, J., Yamamoto, T. and Chapter 13 Ikuhara, Y. (2005) “Control of dislocation configuration in sapphire,” Acta Mater. 53, 455. Copyright 2005, with Figure 13.2 Reprinted with permission from Castell, permission from Elsevier. M.R. (2003) “Wulff shape of microscopic voids in UO2 704 ................................................................................................................................ D e ta i l s f o r F i g u r e s a n d Ta b l e s crystals” Phys. Rev. B 68, 235411. Copyright 2003 by the reflection electron microscopy of III–V compound epilay- American Physical Society. ers,” J. Electron Microsc. Techn. 2, 533. With permission Figure 13.4 Reprinted from Yanina, S.V. and Carter, from Wiley-VCH Verlag. C.B. (2002) “Dislocations at spinel surfaces,” Surf. Sci., Figure 13.24 Reprinted from McCarty, K.F. and Bartelt, 511, 133. Copyright 2002, with permission from N.C., “Spatially resolved dynamics of the TiO2 (110) Elsevier. surface reconstruction,” Surf. Sci. 540, 157. Copyright Figure 13.5 Reprinted from Heffelfinger, J.R., Bench, 2003, With permission from Elsevier. M.W., and Carter, C.B. (1995) “On the faceting of ceramic Figure 13.25 Ramachandran, D., Basu, J. & CBC. surfaces,” Surf. Sci. 343, L1161. Copyright 1995, with per- Figure 13.26(a) Reprinted from Chem. Phys. Lett. 394, mission from Elsevier. See also Heffelfinger, J.R. and Wang, Y, Teitel, S., and Dellago, C. “Melting and equilib- Carter, C.B. (1997) “Mechanisms of surface faceting and rium shape of icosahedral gold nanoparticles,” 257, Copy- coarsening.” Surf. Sci. 389, 188. right (2004), with permission from Elsevier. Figure 13.6(a–c) Reprinted with permission from Figure 13.26(b) From Goldstein, A.N., Echer, C.M., Frenkel, A.I., Hills, C.W., and Nuzzo, R.G. (2001) “A and Alivisatos, A.P. (1992) “Melting in semiconductor View from the Inside: Complexity in the Atomic Ordering nanocrystals,” Science, 256, 1425. Reprinted with permis- of Supported Metal Nanoparticles” J. Phys. Chem. B 105, sion from AAAS. 12689. Copyright 2001 American Chemical Society. Figure 13.27 Reprinted in part with permission from Figure 13.6d Ramachandran, D., Basu, J. & CBC. Sayle, D.C. and Watson, G.W. (2002) “Atomistic struc- Figure 13.9 Reprinted from Li, Y., Bando, Y., and tures of 25 000-atom oxide nanoparticles supported on an Golberg, D. (2004) “Indium-assisted growth of aligned oxide substrate” J. Phys. Chem. B, 106, 10793. Copyright ultra-long silica nanotubes,” Adv. Mater. 16, 37. With per- 2002 American Chemical Society. mission from Wiley-VCH Verlag. Figure 13.28 Reprinted from Ravishankar, N., Shenoy, Figure 13.11 Kotula, P.G., Michael, J.R., Gilliss, S.R. & V.B., and Carter C.B. (2004) “Electric field singularity CBC. assisted nanopatterning,” Adv. Mater., 16 76, with permis- Figure 13.12 Reprinted from Tuck, C. and Evans, J.R.G. sion from Wiley-VCH Verlag. (1999) “Porous ceramics prepared from aqueous foams,” Table 13.3 Data from Kingery, W.D., Bowen, H.K., and J. Mater. Sci. Lett. 18, 1003. With permission from Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd Ed., Springer. Wiley, New York, p. 210. Figure 13.15 Reprinted from Vaughan, D.J. and Pattrick, R.A.D., Eds. (1995) Mineral Surfaces, Chapman Chapter 14 and Hall, London p. 27. With permission from Springer. Figure 13.16 Reprinted from Heffelfinger, J.R., Bench, Figure 14.2(a) Data from Chiang, Y-M., Kingery, W.D., M.W., and Carter, C.B. (1997) “Steps and the structure and Levinson, L.M. (1982) “Compositional changes adja- of the (0001) α-alumina surface,” Surf. Sci. 370, L168, cent to grain boundaries during electrical degradation of Copyright 1997 with permission from Elsevier. a ZnO varistor,” J. Appl. Phys. 53, 1765. Figure 13.16 Yanina, S.V. & CBC. See also Yanina, S. Figure 14.2(b) Reprinted from Bouchet, D., Lartigue- V. and Carter, C.B. (2002) “Terraces and ledges on (001) Korinek, S., Molins, R., and Thibault, J. (2006) “Yttrium spinel surfaces,” Surf. Sci. Lett., 513, L402. segregation and intergranular defects in alumina” Phil. Figure 13.17 Gilliss, S.R. & CBC. Mag. 86, 1401. With permission from Taylor and Francis. Figure 13.18 Reprinted from Starke, U., Sloboshanin, http://www.tandf.co.uk/journals S., Tautz, F.S., Seubert, A., and Schaefer, J.A. (2000) Figure 14.3a Data from Chaudhari, P. and Matthews, “Polarity, morphology and reactivity of epitaxial GaN J.W. (1971) “Coincidence twist boundaries between crys- films on Al2O3 (0001)” Phys. Stat. Sol. (a) 177, 5. With talline smoke particles,” J. Appl. Phys. 42, 3063. permission from Wiley-VCH Verlag. Figure 14.3b Nowak, J. & CBC. Figure 13.19 Reprinted from Gao, W., Klieb, R., and Figure 14.4 Data from Morawiec, A. (1999) “Calcula- Altmana, E.I. (2005) “Growth of anatase films on vicinal tion of distribution of grain boundary energy over grain and flat LaAlO3 (110) substrates by oxygen plasma assisted misorientations,” Scripta Mater. 41, 13. molecular beam epitaxy,” Thin Solid Films 485, 115, Figure 14.7 Reprinted from Carter, C.B., Föll, H., Ast, Copyright 2005. With permission from Elsevier. D.G., and Sass, S.L. (1981) “Electron diffraction and Figure 13.20a Reprinted from Susnitzky D.W. and microscopy studies of the structure of grain boundaries in Carter, C.B. (1992) “Surface morphology of heat-treated silicon,” Phil. Mag. A 43, 441. With permission from ceramic thin films” J. Am. Ceram. Soc. 75, 2463. With Taylor and Francis. http://www.tandf.co.uk/journals permission from Blackwell Publishing and the American Figure 14.8 Reprinted from Sass, S.L. and Rühle, Ceramic Society. M. (1984) “The detection of the change in mean Figure 13.20b Morrissey, K.J. & CBC. inner potential at dislocations in grain-boundaries in NiO,” Figure 13.22 Reprinted from De Cooman, B.C., Phil. Mag. 49, 759, with permission from Taylor and Kuesters, K.-H., and Carter, C.B. (1985) “Cross-sectional Francis. http://www.tandf.co.uk/journals D e ta i l s f o r F i g u r e s a n d Ta b l e s ............................................................................................................................... 705 Figure 14.9(a) Reprinted from Amelinckx, S. (1958) sic and extrinsic stacking-fault energies of silicon,” Phil. “Dislocation patterns in potassium chloride,” Acta Metall. Mag. A40, 497. And Carter, C.B., Föll, H., Ast, D.G., and 6, 34, Copyright 1958. With permission from Elsevier. Sass, S.L. (1981) “Electron diffraction and microscopy Figure 14.9(b) Reprinted with permission from Gilman, studies of the structure of grain boundaries in silicon,” J.J., Johnston, W.G., and Sears, G.W. (1958) “Dislocation Phil. Mag. A43, 441. http://www.tandf.co.uk/journals etch pit formation in lithium fluoride,” J. Appl. Phys. 29, Figure 14.32a Courtesy of David Clarke. 747. Copyright 1958, American Institute of Physics. Figure 14.34 Ramamurthy, S. & CBC. Figure 14.16 Reprinted with permission from Oba, F., Figure 14.35 See: Simpson, Y.K., Carter, C.B., Mor- Ohta, H., Sato, Y., Hosono, H., Yamamoto, T., and Ikuhara, rissey, K.J., Angelini, P., and Bentley, J. (1986) “The iden- Y. (2004) “Atomic structure of [0001]-tilt grain boundar- tification of thin amorphous films at grain-boundaries in ies in ZnO: A high-resolution TEM study of fiber-textured Al2O3,” J. Mater. Sci. 21, 2689. thin films,” Phys. Rev. B 70, 125415. Copyright 2004 by Figure 14.36 Reprinted from Mallamaci, M.P., Bentley, the American Physical Society. J., and Carter, C.B. (1997) “In-Situ TEM crystallization Figure 14.19 Morrissey, K.J. & CBC. See also Mor- of silicate-glass films on Al2O3,” Acta Mater. 46, 283. rissey, K.J. and Carter, C.B. (1984) “Faceted grain bound- Copyright 1997, with permission from Elsevier. See also aries in Al2O3,” J. Am. Ceram. Soc. 67, 292. Mallamaci, M.P. and Carter, C.B. (1999) “Crystallization Figure 14.20 Morrissey, K.J. & CBC (as 14.19). of pseudo-orthorhombic anorthite on basal sapphire,” J. Figure 14.21 Reprinted from Carter, C.B., Elgat, Z., and Am. Ceram. Soc. 82, 33. Shaw, T.M. (1987) “Twin boundaries parallel to the common- Figure 14.37 Reprinted from McKernan, S., Norton, {111} plane in spinel,” Phil. Mag. A55, 1. With permission M.G., and Carter, C.B. (1992) “The 45° grain boundaries from Taylor and Francis See also Carter, C.B., Elgat, Z. and in YBa2Cu3O7-δ,” J. Mater. Res. 7, 1052. With permission Shaw, T.M. (1987) “Lateral twin boundaries in spinel,” Phil. from the Materials Research Society. Mag. A55, 21. http://www.tandf.co.uk/journals Figure 14.22 Kotula, P.G. & CBC. Chapter 15 Figure 14.24 From Moore, M.D., Tilley, R.J.D., and Williams, R.P. (1996) “The systematics of block-structure Figure 15.2 Rasmussen, Y.K. & CBC. shift lattices,” Proc. R. Soc. Lond. A 452, 841. With per- Figure 15.3 Summerfelt, S.R. & CBC. mission from the Royal Society. Figure 15.4 Anderson, I.M. & CBC. Figure 14.25 Reprinted from Sloan, S., Hutchison, J.L., Figure 15.5 Reprinted from Summerfelt, S.R. and Tenne, R., Yishay, T.T., and Homyonferà, M. (1999) Carter, C.B. (1989) “The movement of the spinel–NiO “Defect and ordered tungsten oxides encapsulated (X 5S interface in thin films,” Ultramicroscopy 30, 150. Copy- and Se) fullerene-related structures,” J. Sol. St. Chem. right 1989, with permission from Elsevier. 144, 100, Copyright 1999, with permission from Figure 15.6b Guinel, M. & MGN. Elsevier. Figure 15.7 Reprinted from: Simpson, Y.K. and Carter, Figure 14.27a Courtesy of Hans-Joachim Kleebe. C.B. (1990) “Faceting Behavior of Alumina in the Pres- Figure 14.27b Reprinted with permission from Shibata, ence of a Glass.” J. Am. Ceram. Soc. 73 (8), 2391. N., Painter, G.S., Satet, R.L., Hoffmann, M.J., Pennycook, Figure 15.8 Summerfelt, S.R. & CBC. S.J., and Becher, P.F. (2005) “Rare-earth adsorption at Figure 15.9 Reprinted from Suvaci, E., Oh, K.-S., and intergranular interfaces in silicon nitride ceramics: Sub- Messing, G.L. (2001) “Kinetics of template growth in nanometer observations and theory,” Phys. Rev. B 72, alumina during the process of templated grain growth 149191R. Copyright 2005 by the American Physical (TGG),” Acta Mater. 49, 2075. Copyright 2001, with per- Society. mission from Elsevier. Figure 14.28 Reprinted from Susnitzky D.W. and Carter, Figure 15.11 Reprinted with permission from Castell. C.B. (1990) “Structure of alumina grain boundaries pre- M.R. (2003) “Wulff shape of microscopic voids in UO2 pared with and without a thin amorphous intergranular crystals,” Phys. Rev. B 68, 235411. Copyright 2003 by the film,” J. Am. Ceram. Soc. 73, 2485. With permission from American Physical Society. Blackwell Publishing and the American Ceramic Figure 15.12 Reprinted from Santala, M.K. and Glaeser, Society. A.M. (2006) “Surface-energy-anisotropy-induced orienta- Figure 14.29 Reprinted from Ramamurthy, S., Malla- tion effects on Rayleigh instabilities in sapphire,” Surf. maci, M.P., Zimmerman, C.M., Carter, C.B., Duncombe, Sci., 600, 782. Copyright 2006, with permission from P.R., and Shaw, T.M. (1996) “Microstructure of polycrys- Elsevier. talline MgO penetrated by a silicate liquid,” JMSA 2, 113 Figure 15.13 Courtesy of Quantachrome Instruments. (reprinted in Microsc. Microanal., 3 suppl. 3). With per- Figure 15.14 Blanford, C.F., Stein, A. & CBC. mission from Cambridge University Press. Figure 15.15 Reprinted with permission from Dhara, S., Figure 14.30 Mallamaci, M.P. & CBC. Pradhan, M., Ghosh, D., and Bhargava, P. (2005) “Nature Figure 14.31 Föll, H. & CBC. See also Föll, H., and inspired novel processing routes for ceramic foams,” Adv. Carter, C.B. (1979) “Direct TEM determination of intrin- Appl. Ceram. 104, 9. Copyright 2005 Maney Publishing. 706 ................................................................................................................................ D e ta i l s f o r F i g u r e s a n d Ta b l e s Figure 15.14 Riesterer, J.L., Gilliss, S.R. & CBC. Table 16.2 Data compiled by Green D.J. (1998) An Figure 15.17 Courtesy of Andrew M. Kraynik, from Introduction to the Mechanical Properties of Ceramics, Kraynik, A.M. (2003) “Foam structure: From soap froth CUP, Cambridge, UK, p. 25. to solid foams”, MRS Bulletin April 275. By permission Table 16.3 Data coompiled by Wachtman, J.B. (1996) of the Materials Research Society. (Redrawn) Mechanical Properties of Ceramics, Wiley, New York, p. Figure 15.18 McKernan, S., Bentley, J. & CBC. See 25. also Bentley, J., McKernan, S., Carter, C.B., and Rev- Table 16.4 Data compiled by C.A. Harper, Editor-in- colevschi, A. (1993) “Microanalysis of directionally solid- Chief (2001) Handbook of Ceramics, Glasses, and Dia- ified cobalt oxide-zirconia eutectic,” Microbeam Analysis monds, McGraw-Hill, New York, p. 1.7. 2, S286. Table 16.5 Modified after Munz, D. and Fett, T. (1999) Figure 15.21 Data from Campbell, I.E. and Sherwood, Ceramics: Mechanical Properties, Failure Behavior, E.M., eds. (1967) High-Temperature Materials and Tech- Materials Selection, Springer, Berlin, p. 17. nology, Wiley, New York, p. 380. Table 16.6 Data compiled by Rice, R.W. (1970) “The Figure 15.22b From van Helvoort, A.T.J., Knowles, compressive strength of ceramics,” in: Ceramics in Several K.M., and Fernie, J.A. (2003) “Characterization of cation Environments, Vol. 5, Plenum Press, New York, pp. depletion in Pyrex during electrostatic bonding,” J. Elec- 195–229. trochem. Soc., 150, G624. By permission of ECS—The Table 16.10 Data from Ashby, M.F. and Jones, D.R.H. Electrochemical Society. And from van Helvoort, A.T.J., (1986) Engineering Materials 2: An Introduction to Knowles, K.M., and Fernie, J.A. (2003) “Nanostructure at Microstructures, Processing, and Design, Pergamon electronic bond interfaces,” J. Am. Ceram. Soc. 86, 1773. Press, Oxford, p. 169. By permission from Blackwell Publishing and the Ameri- Table 16.11 Data from Hulbert, S.F. (1993) “The use of can Ceramic Society. alumina and zirconia in surgical implants,” in: An Intro- Figure 15.23 McIlroy, D.N., Nowak, J., MGN and CBC. duction to Bioceramics, edited by L.L. Hench and J. See also LaLonde, A.D., Norton, M.G., Zhang, D., Wilson, World Scientific, Singapore, p. 30. Gangadean, D., Alkhateeb, A., Padmanabhan, R., and McIlroy, D.N. (2005) “Controlled growth of gold nanopar- Chapter 17 ticles on silica nanowires,” J. Mater. Res. 20, 3021. Figure 17.1 Data from Gorum, A.E., Parker, E.R., and Pask, J.A. (1958) “Effect of surface conditions on room- Chapter 16 temperature ductility of ionic crystals”, J. Am. Ceram. Figure 16.1 Eakins, D.E. & MGN. Soc. 41, 161. Figure 16.4a Data from Coble, R.L. (1958) “Effect of Figure 17.2 Data from Gilman, J.J. and Johnston, W.G. microstructure on mechanical properties,” Ceramic Fab- (1957) in: Dislocations and Mechanical Properties of rication Processes, Wiley, New York, p. 223. Crystals, Fischer, J.C., Johnston, W.G., Thomson, R., and Figure 16.4b Data from Coble, R.L. (1958) “Effect of Vreeland, T., Eds., Wiley, New York. microstructure on mechanical properties,” Ceramic Fab- Figure 17.4a Reprinted with permission from Gilman, rication Processes, Wiley, New York, p. 217. J.J. and Johnston, W.G. (1956) “Observations of disloca- Figure 16.5 Data from Wachtman, J.B. (1996) Mechani- tion glide and climb in lithium fluoride crystals”, J. Appl. cal Properties of Ceramics, Wiley, New York, p. 358. Phys. 27, 1018. Copyright 1956, American Institute of Figure 16.9 Data from Zeng, J., Tanaka, I., Miyamoto, Physics. Y., Yamada, O., and Niihara, K. (1992) “High-temperature Figure 17.4b Veyssière, P. and CBC. See also Veyssière, strength and cavitation threshold of silicon nitride-silica P. and Carter, C.B. (1988) “Dissociation of dislocations in ceramics,” J. Am. Ceram. Soc. 75, 195. MgAl2O4 spinel deformed at low temperatures,” Phil. Figure 16.12 Data from Wachtman, J.B. (1996) Mechan- Mag. Lett. 57, 211. http://www.tandf.co.uk/journals ical Properties of Ceramics, Wiley, New York, p. 362. Figure 17.10 Data from Kingery, W.D., Bowen, H.K., Figure 16.17c Courtesy of Dylan Morris. and Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd Figure 16.18 Zagrebelny, A., Lilleodden, E., Gerberich, Ed., Wiley, New York p. 740. W.W. and CBC. Figure 17.11 Data from Jiang, B. and Weng, G.J. (2004) Figure 16.23 Data from Sato, S., Taguchi, K., Adachi, “A theory of compressive yield strength of nano-grained R., and Nakatani, M. (1996) “A study of strength charac- ceramics”, Int. J. Plasticity, 20, 2007. teristics of Si3N4 coil springs,” Fat. Fract. Engng. Mater. Figure 17.12 Data from Evans, A.G. and Pratt, P.L. Struct. 19, 529. (1969) “Dislocations in fluorite structure”, Phil. Mag. 20, Figure 16.25 Data from Barsoum, M.W. (2003) Funda- 1213. http://www.tandf.co.uk/journals mentals of Ceramics, Institute of Physics, Bristol, UK, Figure 17.13 From Gilman, J.J. and Johnston, W.G. p. 388. (1957) in Fisher, J.G., Johnston, W.G., Thomson, R., and Table 16.1 Data from ASTM International (www.astm. Vreeland, T., Eds. Dislocations and Mechanical Proper- org). ties of Crystals Wiley, New York. D e ta i l s f o r F i g u r e s a n d Ta b l e s ............................................................................................................................... 707 Figure 17.14 Data from Liu, T.S., Stokes, R.J., and Li, and defects in single crystal YAG”, J. Cryst. Growth, 267, C.H. (1964) “Fabrication and plastic behavior of single 502. Copyright 2004, with permission from Elsevier. crystal MgO-NiO and MgO-MnO solid solution alloys”, Figure 18.18 Reprinted from Bao, Y. and Nicholson, P. J. Am. Ceram. Soc. 47, 276. S. (2006) “AlPO4 coating on alumina/mullite fibers as a Figure 17.18 Data from Wachtman, J.B. (1996) Mechan- weak interface in fiber-reinforced oxide composites”, J. ical Properties of Ceramics, Wiley, New York, pp. Am. Ceram. Soc. 89, 465. With permission from Blackwell 329–330. Publishing and the American Ceramic Society. Figure 17.19 Data from Ashby, M.F. (1972) “First report Figure 18.20 Data from Becher, P. (1991) “Microstruc- on deformation-mechanism maps,” Acta Metall. 20, 887 tural design of toughnened ceramics,” J. Am. Ceram. Soc. and Frost, H.J. and Ashby, M.F. (1982) Deformation- 74, 255. Mechanism Maps: The Plasticity and Creep of Metals Figure 18.21 McKernan, S. and CBC. and Ceramics, Pergamon, Oxford. Figure 18.23 Guinel, M. and MGN. Figure 17.22 Guinel, M. and MGN. See also Guinel, Figure 18.25 Riesterer, J.L., Gilliss, S.R. & CBC. M.J-F. and Norton, M.G. (2005) “Blowing of silica Table 18.2 Data compiled by Kelly, A. and MacMillan, microforms on silicon carbide,” J. Non-Cryst. Solids 351, N.M. (1986) Strong Solids, 3rd Ed., Oxford University 251. Press, Oxford. Table 17.1 Data compiled by Green D.J. (1998) An Table 18.3 Data from (Al2O3): Stokes, R.J. (1972) The Introduction to the Mechanical Properties of Ceramics, Science of Ceramic Machining and Surface Finishing, CUP, Cambridge, UK, p. 177. NBS Special Publication 348, U.S. Government Printing Table 17.2 Data from Gilman, J.J. and Buerger, J.M. Office, Washington, D.C., p. 347. (SiC): Richerson, D.W. (1930) “Translation-gliding in crystals,” Amer. Mineral. (1992) Modern Ceramic Engineering, 2nd Ed., Marcel 15, 45 and 174. Dekker, New York, p. 170. Table 17.4 Modified from from Kingery, W.D., Bowen, Table 18.4 Data compiled by Barsoum, M.W. (2003) H.K., and Uhlmann, D.R. (1976) Introduction to Ceram- Fundamentals of Ceramics, Institute of Physics, Bristol, ics, 2nd Ed., Wiley, New York, p. 714. UK, p. 364–365. Table 17.5 Data compiled by Barrett, C.R., Nix, W.D., Table 18.7 Data compiled by Ziegler, G. and Hüttner, and Tetelman, A.S. (1973) The Principles of Engineering W. (1991) “Engineering properties of carbon-carbon and Materials, Prentice-Hall, Englewood Cliffs, New Jersey, ceramic-matrix composites, in: Engineered Materials p. 255. Handbook, Volume 4 Ceramics and Glasses, ASM Inter- Table 17.6 Data compiled by Green D.J. (1998) An national, p. 838. Introduction to the Mechanical Properties of Ceramics, Table 18.8 Data from Corning Incorporated (www. CUP, Cambridge, UK, p. 200. corning.com). Table 18.9 Data compiled by Richerson, D.W. (2006) Modern Ceramic Engineering 3rd Ed., Taylor and Francis Chapter 18 Boca Raton p. 274. Figure 18.3 Data from Griffith, A.A. (1920) “The phe- Table 18.10 Data compiled by Indge, J.H. (1991) in: nomenon of rupture and flow in solids,” Phil. Trans. R. ASM Engineered Materials Handbook, Volume 4: Ceram- Soc. Lond., A221, 163. ics and Glasses, ASM International p. 351. Figure 18.6 Data from Griffith, A.A. (1920) “The phe- nomenon of rupture and flow in solids,” Phil. Trans. R. Chapter 19 Soc. Lond., A221, 163. Figure 18.9 Data from Wiederhorn, S. (1967) “Influ- Figure 19.4 Data from Ernst, W.G. (1969) Earth Mate- ence of water vapor on crack propagation in soda-lime rials, Prentice-Hall, Englewood Cliffs. p. 38. glass,” J. Am. Ceram. Soc. 50, 407. Figure 19.5 The reproduction of this image is through Figure 18.11b Data from Gilbert, C.J., Bloyer, D.R., the courtesy of Alcoa Inc. Barsoum, M.W., El-Raghy, T., Tomsia, A.P., and Ritchie, Figure 19.8 Courtesy of Exolon, a Washington Mills R.O. (2000) “Fatigue-crack growth and fracture properties Company. of coarse and fine-grained Ti3SiC2”, Scripta Mater. 42, 761. Table 19.1 Data compiled by Mason, B. (1966) Princi- Figure 18.13a Guinel, M. and MGN. ples of Geochemistry, Table 3.4, John Wiley and Sons, Figure 18.13b Guinel, M. and MGN. New York. Figure 18.15 Reprinted from Johnson, J.W. and Hollo- Table 19.2 Data from Gribble, C.D. (1988) Rutley’s Ele- way, D.G. (1966) “On the shape and size of the fracture ments of Mineralogy, 27th Ed., Unwin Hyman, London. zones on glass fracture surfaces,” Phil. Mag. 14, 731. With p. 119. permission from Taylor and Francis. http://www.tandf. Table 19.3 Data compiled by Ernst, W.G. (1969) Earth co.uk/journals Materials, Prentice-Hall, Englewood Cliffs. p. 10. Figure 18.16 Reprinted from Eakins, D.E., Held, M., Table 19.4 Data from Mineral Commodity Summaries Norton, M.G., and Bahr, D.F. (2004) “A study of fracture (2006) U.S. Department of the Interior, U.S. Geological 708 ................................................................................................................................ D e ta i l s f o r F i g u r e s a n d Ta b l e s Survey, United States Government Printing Office, Figure 21.4b Data from Doremus, R.H. (1994) Glass Washington D.C. Science, 2nd Ed., Wiley, New York, p. 103. Table 19.5 Data from Annual Minerals Review (1996) Figure 21.5 Redrawn after schematics on the Edward J. Am. Ceram. Soc. Bull. 75, 138. Orton Jr. Ceramic Foundation site (ANS-800 and RSV- Table 19.7 Data compiled by Lee, W.E. and Rainforth, 1600); see www.ortonceramic.com/instruments (and don’t W.M. (1994) Ceramic Microstructures: Property Control miss the Orton cones video). by Processing, Chapman and Hall, London. p. 261. Figure 21.6 Data from Moriya, Y., Warrington, D.H., Table 19.8 Data compiled by Lee, W.E. and Rainforth, and Douglas, R.W. (1967) Phys. Chem. Glasses, 1, 19. W.M. (1994) Ceramic Microstructures: Property Control Figure 21.8 Courtesy of Schott Glass. by Processing, Chapman and Hall, London. p. 261. Figure 21.9 Ravishankar, N. and CBC. Figure 21.10 Reprinted from Guinel, M. J-F. and Norton, M.G. (2006) “Oxidation of silicon carbide and the forma- Chapter 20 tion of silica polymorphs,” J. Mater. Res. 21, 2550. With Figure 20.5 Data from Silberberg, M. (1996) Chemis- permission from the Materials Research Society. try: The Molecular Nature of Matter and Change, Mosby, Figure 21.11 Reprinted from Vogel, W. (1971) Structure Boston, p. 477. and Crystallization of Glasses The Leipzig Ed., Pergamon Figure 20.9 Thompson, S., Perrey, C.R., Kortshagen, U. Press, Oxford. p. 150. & CBC. Also see: Thompson, S., Perrey, C.R., Carter, Figure 21.12 Reprinted from Vogel, W. (1971) Structure C.B., Belich, T.J., Kakalios, J., and Kortshagen, U. (2005) and Crystallization of Glasses The Leipzig Ed., Pergamon “Experimental investigations into the formation of Press, Oxford. p. 176. nanoparticles in a/nc-Si:H thin films,” J. Appl. Phys. 97, Figure 21.13 Reprinted from Vogel, W. (1971) Structure 034310-1. and Crystallization of Glasses The Leipzig Ed., Pergamon Figure 20.14 Data from Rahaman, M.N. (1995) Ceramic Press, Oxford. p. 35. Processing and Sintering, Marcel Dekker, Inc., New York, Figure 21.14 Reprinted from Riello, P., Canton, P., p. 112. Comelato, N., Polizzi, S., Verita, M., Fagherazzi, G, Hof- Figure 20.16 Data from Lowder, R.A. (1993) “Fiber meister, H., and Hopfe, S. (2001) “Nucleation and crystal- coatings and the mechanical properties of a continuous lization behavior of glass-ceramic materials in the fiber reinforced SiC matrix composite”, in: Designing Li2O-Al2O3-SiO2 system of interest for their transparent Ceramic Interfaces II. S.D. Peteves (ed.) Comm. of Europ. properties”, J. Non-Cryst. Sol. 288, 127. Copyright 2001, Communities: Luxembourg pp. 157–72. with permission from Elsevier. Table 20.1 From Rahaman, M.N. (1995) Ceramic Pro- Figure 21.16 From the ERSF-NL38 newsletter. This cessing and Sintering, Marcel Dekker, Inc., NY, p. 40. plate can be seen in the Museo Regionale della Ceramica Table 20.3 Data compiled by Richerson, D.W. (1992) di Deruta in Italy. Deruta is a beautiful city, overlooking Modern Ceramic Engineering, 2nd Ed., Marcel Dekker, the Tiber valley, renowned for its ceramic art dating back NY, p. 395. to the Middle Ages. See: www.museoceramicaderuta.it Table 20.4 Data compiled by McColm, I.J. and Clark, and www.deruta.net. N.J. (1988) Forming, Shaping and Working of High-Per- Figure 21.19 Riesterer, J.L. & CBC. formance Ceramics, Blackie, Glasgow, p. 81. Figure 21.20 From Aizenberg, J., Weaver, J.C., Thana- Table 20.5 Data compiled by Reed, J.S. (1988) Intro- wala, M.S., Sundar, V.C., Morse, D.E., and Fratzl, P. duction to the Principles of Ceramic Processing, John (2005) “Skeleton of euplectella sp.: Structural hierarchy Wiley & Sons, NY, p. 92. from the nanoscale to the macroscale,” Science 309, 275. Table 20.8 From Reed, J.S. (1988) Introduction to the Reprinted with permission from AAAS. Principles of Ceramic Processing, John Wiley and Sons, Figure 21.21 Data from Zhu, D., Chandra, S., Ray, C.S., New York, p. 71. Zhou, W., Delbert, E., and Day, D.E. (2003) “Glass transi- Table 20.9 Data compiled by Chawla, K.K. (1993) tion and fragility of Na2O–TeO2 glasses,” J. Non-Cryst. Ceramic Matrix Composites, Chapman and Hall, London, Sol. 319, 247. p. 51. Table 21.6 Data compiled by Tooley, F.V. (1960) Hand- book of Glass Manufacture, Ogden Publishing Co., New York, NY. Chapter 21 Figure 21.2 Copyright the Trustees of The British Museum. Chapter 22 Figure 21.3 Copyright the Trustees of The British Museum. Figure 22.10 Reprinted from Giuliano Gregori, G., Figure 21.4a Data from Pfaender, H.G. (1996) The Kleebe. H.-J., Readey, D.W., and Sorarù, G.D. (2006) Schott Guide to Glass. Chapman & Hall, London, UK, “Energy-filtered TEM study of Ostwald ripening of Si p. 21. nanocrystals in a SiOC glass”.) J. Am. Ceram. Soc. 89, D e ta i l s f o r F i g u r e s a n d Ta b l e s ............................................................................................................................... 709 1699. With permission from Blackwell Publishing and the N.E., Gilliss, S.R. and Carter, C.B. (2004) “Remnant American Ceramic Society. grooves on alumina surfaces,” Surf. Sci. 573, 391. Table 22.2 Data compiled from Bradley, D.C., Mehro- Figure 24.19 Ravishankar, N. & CBC. tra, R.C., and Gaur, D.P. (1978) Metal Alkoxides, Aca- Figure 24.20 Farrer, J. & CBC. See also Farrer, J.K., demic Press, London and Rahaman, M.N. (1995) Ceramic Carter, C.B., and Ravishankar, N. (2006) “The effects of Processing and Sintering, Marcel Dekker, New York, crystallography on grain boundary migration in alumina,” p. 211. J. Mater. Sci., 41, 661. Table 22.3 Data from: Gossink, R.G., Coenen, H.A.M., Figure 24.21 Altay, A. & CBC. Engelfriet, A.R.C., Verheijke, M.L., and Verplane, J.C. Figure 24.22 Reprinted from Kaysser, W.A., Sprissler, (1975) “Ultrapure SiO2 and Al2O3 for the preparation of M., Handwerker, C.A., and Blendell, J.E. (1987) “Effect low-loss compounds glass,” Mater. Res. Bull. 10, 35. of a liquid phase on the morphology of grain growth in Table 22.4 Data from Klein, L.C. (1991) “Sol-gel alumina,” J. Am. Ceram. Soc. 70 339. With permission process,” in: Engineered Materials Handbook Volume 4: from Blackwell Publishing and the American Ceramic Ceramics and Glass, ASM International. Society. See also R. D. Monahan, R.D. and Halloran, J.W. Table 22.8 Data compiled by Brinker, C.J. and Scherer, (1979) “Single-crystal boundary migration in hot-pressed G.W. (1990) Sol-Gel Science: The Physics and Chemistry aluminum oxide,” J. Am. Ceram. Soc. 62, 564. of Sol-Gel Processing, Academic Press, Boston, p. 864. Figure 24.24 Altay, A. & CBC. Figure 24.25 Courtesy of Paolo Colombo. Figure 24.27 Courtesy of Marc Anglada. Chapter 23 Figure 24.28 From Wakai, F. and Aldinger, F. (2003) Figure 23.11a Courtesy of Jim Robison. “Sintering through surface motion by the difference in Figure 23.11b Courtesy of Michael Sherrill. mean curvature”, Acta Mater. 51, 4013. Copyright 2003, Figure 23.15 Data from Mutsuddy, B.C. (1991) “Injec- with permission from Elsevier. tion Molding,” in: Engineered Materials Handbook, Volume 4 Ceramics and Glasses, ASM International, Chapter 25 p. 178. Figure 23.17 Courtesy of Rosette Gault. Figure 25.1 Reprinted from Hwang, T.J., Hendrick, M. Figure 23.18 From Bliss, G. (2001) Practical Solutions R., Shao, H., Hornis, H.G., and Hunt, A.T. (1998) “Com- for Potters. Sterling Pub Co. Inc. New York, p. 103. bustion chemical vapor deposition (CCVD) of LaPO4 Table 23.3 Data compiled by Reed, J.S. (1988) Intro- monazite and beta-alumina on alumina fibers for ceramic duction to the Principles of Ceramic Processing, John matrix composites,” Mater. Sci. Eng. A, 244, 91. Copy- Wiley, New York, p. 359. right 1998, with permission from Elsevier. Table 23.4 Data compiled by Richerson D.W. (1992) Figure 25.2 Moore, L.A. & CBC. See also Tietz, L.A., Modern Ceramic Engineering, Marcel Dekker, New York, Carter, C.B, Lathrop, D.K., Russek, S.E., Buhrman, R.A., p. 493. and Michael, J.R. (1989) “Crystallography of YBa2Cu3O6+x Table 23.5 Data compiled by Larson, D. (1991) “Green thin film-substrate interfaces,” J. Mater. Res. 4, 1072. Tietz, machining,” in: Engineered Materials Handbook, Ceram- L.A., De Cooman, B.C., Carter, C.B., Lathrop, D.K., Russek, ics and Glasses 4, ASM International, p. 184. S.E., and Buhrman, R.A. (1988) “Structure of supercon- ducting thin films of YBa2Cu3O7−x grown on SrTiO3 and cubic zirconia,” J. Electron Microsc. Tech. 8, 263. Chapter 24 Figure 25.3 Courtesy of David Clarke. Figure 24.2 Courtesy of Saint-Gobain. Figure 25.4 Susnitzky D.W. & CBC. See also Susnitzky, Figure 24.3 From Suzuki, K. and Sasaki, M. (2005) D.W., Hertl, W., and Carter, C.B. (1989) “Vanadia-induced “Effects of sintering atmosphere on grain morphology of transformations in yttria-stabilized zirconia,” Ultrami- liquid-phase-sintered SiC with Al2O3 additions,” J. Eur. croscopy 30, 223. Ceram. Soc. 25, 1611. Copyright 2005, with permission Figure 25.5 Reprinted from Lee, W.E. and Rainforth, from Elsevier. W.M. (1994) Ceramic Microstructures: Property Control Figure 24.7 Perrey, C.R. & CBC. by Processing, Chapman & Hall, London, p. 912. With Figure 24.10 Data from Kang, S.-J.L. and Jung, Y.-I. permission from Springer. (2004) “Sintering kinetics at the final stage of sintering: Figure 25.6 Moore, L.A. & CBC. Model calculation and map construction,” Acta Mater. 52, Figure 25.7 Ostyn, K.M., Schmalzried, S. & CBC. See 4373. also Ostyn, K.M., Carter, C.B., Koehne, M., Falke, H., and Figure 24.16 After Burke, J.E. Schmalzried, H. (1984) “Internal reactions in oxide solid Figure 24.17 Munoz, N., Gilliss, S.R. & CBC. See also solutions,” J. Am. Ceram. Soc. 67, 679. Munoz, N.E., Gilliss, S.R., and Carter, C.B. (2004) “The Figure 25.8 Data from Holt, J.B., Cutler, I.B., and monitoring of grain-boundary grooves in alumina,” Phil. Wadsworth, M.E. (1962) “Rate of thermal dehydration of Mag. Lett., 84, 21, http://www.tandf.co.uk/journals Munoz, kaolinite in vacuum.” J. Am. Ceram. Soc. 45, 133. 710 ................................................................................................................................ D e ta i l s f o r F i g u r e s a n d Ta b l e s Figure 25.9 Rasmussen, Y.K. & CBC. See also Simpson, growth of β-alumina on α-alumina,” J. Am. Ceram. Soc. Y.K. and Carter, C.B. (1986) “A new approach to the study 69, C25. of solid-state reactions,” Phil. Mag. A53, L1. http://www. Figure 25.23 Johnson, M.L. & CBC. See also Johnson, tandf.co.uk/journals M.T., Schmalzried, H., and Carter, C.B. (1997) “The effect Figure 25.10 Data from Simpson, Y.K., Colgan, E.G., of an applied electric field on a heterogeneous solid-state and Carter, C.B. (1987) “Kinetics of the growth of spinel reaction,” Solid State Ionics 101–103, 1327. Johnson M.T. on alumina using Rutherford backscattering spectros- and Carter, C.B. (1998) “Thin-film reaction between copy.” J. Am. Ceram. Soc. 70, C149. α-Fe2O3 and (001) MgO,” Microsc. Microanal. 4, 141. Figure 25.12 After Schmalzried, H. (1981) Solid State Johnson, M.T., Kotula, P.G., and Carter, C.B. (1999) Reactions p. 106. “Growth of nickel ferrite thin films using pulsed-laser Figure 25.13 Data from Pettit, F.S., Randklev, E.H., and deposition,” J. Cryst. Growth 206, 299. Felten, E.J. (1966) “Formation of NiAl2O4 by solid state Figure 25.24 See (i) Cooper, A.R. and Kingery, W.D. reaction,” J. Am. Ceram. Soc. 49, 199. (1964) “Dissolution in ceramic systems: I. Molecular diffu- Figure 25.14 Johnson, M.L. & CBC. See also Kotula, sion, natural convection, and forced convection studies of P.G., Johnson, M.T., and Carter, C.B. (1998) “Thin-film sapphire dissolution in calcium aluminum silicate,” J. Am. reactions,” Z. Phys. Chemie 206 S, 73. Johnson, M.T. and Ceram. Soc. 47, 37. (ii) Samaddar, B.N., Kingery, W.D., and Carter, C.B. (1999) “Movement of Pt markers in MgO Cooper, A.R. (1964) “Dissolution in ceramic systems: II. during a solid-state reaction,” Phil. Mag. Lett. 79, 609. Dissolution of alumina, mullite, anorthite, and silica in a http://www.tandf.co.uk/journals calcium-aluminum-silicate slag,” J. Am. Ceram. Soc. 47, Figure 25.15a Data from Chen, W.K. and Peterson, N. 249. (iii) Oishi, Y., Cooper, A.R., and Kingery, W.D. (1964) L. (1973) “Cation diffusion, semiconductivity and non- “Dissolution in ceramic systems: III. Boundary layer con- stoichiometry in (Co,Ni)O crystals,” J. Phys. Chem. centration gradients,” J. Am. Ceram. Soc. 48, 88. (A classic Solids. 34, 1093. series of papers: all on-line for ACerS members.) Figure 25.15b Data from Blank, S.L. and Pask, J.A. Figure 25.25 After Kingery, W.D., Bowen, H.K., (1969) “Diffusion of iron and nickel in magnesium oxide Uhlman, D.R., Kingery, W.D., Bowen, H.K., and Uhlmann, single crystals,” J. Am. Ceram. Soc. 52, 669. D.R. (1976) Introduction to Ceramics 2nd Ed., Wiley, New Figure 25.16 Data from Kingery, W.D., Bowen, H.K., York, p. 416. and Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd Ed., Wiley, New York, p. 240. Chapter 26 Figure 25.17b,c From Veblin, D.R. and Buseck, P.R. Figure 26.1 Data from Ceramic Industry, August 1993. (1981) “Hydrous pyriboles and sheet silicates in pyroxenes Figure 26.2 From Pfaender, H.G. (1996) Schott Guide and uralites; intergrowth microstructures and reaction to Glass 2nd Ed., Chapman and Hall, London. p. 39. By mechanisms,” Amer. Mineral. 66, 1107. With permission permission from Springer. from the Mineralogical Society of America. Figure 26.3 Redrawn after Pfaender, H.G. (1996) Schott Figure 25.18 Kotula, P.G. & CBC. See also Kotula, P. Guide to Glass 2nd Ed., Chapman and Hall, London. p. 37. G. and Carter, C.B. (1995) “Volume expansion and lattice By permission from Springer. rotations in solid-state reactions between oxides,” Scripta Figure 26.4 From Pfaender, H.G. (1996) Schott Guide Met. 32, 863. Kotula, P.G. and Carter, C.B. (1995) “Nucle- to Glass 2nd Ed., Chapman and Hall, London. p. 38. By ation of solid-state reactions between nickel oxide and permission from Springer. aluminum oxide,” J. Am. Ceram. Soc. 78, 248. Figure 26.12 Redraw after Prindle, W.R. (1999) in Figure 25.19 Kotula, P.G. & CBC. See also Kotula, P. Ceramic Innovations Ed. Wachtman, J.B., Am. Ceram. G. and Carter, C.B. (1998) “Kinetics of thin-film reactions Soc., Westerville, OH. p. 82. of NiO with Al2O3 I: (0001) and {112̄0} reaction couples,” Table 26.2 Data from Tooley, F.V. (1983) The Handbook J. Am. Ceram. Soc. 81, 2869 Kotula, P.G. and Carter, C.B. of Glass Manufacture 3rd. Ed. Volumes I, Ashlee Publish- (1998) “Kinetics of thin-film reactions of NiO with Al2O3 ing Co., New York. pp. 28–29. II: {11̄00} and {11̄02} reaction couples,” J. Am. Ceram. Table 26.4 Data compiled by Pinckney, L.R. (1991) Soc. 81, 2877. Ceramics and Glasses, Engineered Materials Handbook, Figure 25.20 Data from Kotula, P.G. and Carter, C.B. Volume 4, ASM International. p. 434. (1998) “Kinetics of thin-film reactions of NiO with Al2O3 I: (0001) and {112̄0} reaction couples,” J. Am. Ceram. Chapter 27 Soc. 81, 2869. Figure 25.21 Heffelfinger and CBC. See also Heffelfin- Figure 27.3 Courtesy of Richard E. Mistler, Inc., ger, J.R. and Carter, C.B. (1994) “Evolution of yttrium Yardley, PA, USA. aluminum garnet films by solid-state reaction,” Mater. Figure 27.4 Courtesy of Keko Equipment (Slovenia) Res. Soc. Symp. Proc. 317, 553. and Haiku Tech, Inc. (USA). Figure 25.22 Susnitzky, D.W. & CBC. See also Figure 27.13 Data from Jang, H.M. and Fuerstenau, Susnitzky, D.W. and Carter, C.B. (1986) “The topotactic D.W. (1986) “The specific adsorption of alkaline- D e ta i l s f o r F i g u r e s a n d Ta b l e s ............................................................................................................................... 711 earth cations at the rutile water interface,” Coll. Surf. 21, “Crystallization and high-temperature structural stability 238. of titanium oxide nanotube arrays,” J. Mater. Res. 18, 156. Figure 27.18 Data from Hammer, R.B., Powell, D.O., With permission from the Materials Research Society and Mukherjee, S., Tummala, R., and Raj, R. (1989) in: Prin- Beth Dickey. ciples of Electronic Packaging, Seraphim, D.P., Lasky, R., Figure 29.19c,d Reprinted from Chen, R.S., Chang, and Li, C-Y, Eds., McGraw-Hill, New York, p. 296. H.M., Huang, Y.S., Tsai, D.S., Chattopadhyay, S., and Table 27.1 Data from Mistler, R.E., Shanefield, D.J., and Chen, K.H. (2004) “Growth and characterization of verti- Runk, R.B. (1978) in: Ceramic Processing Before Firing, cally aligned self-assembled IrO2 nanotubes on oxide sub- Eds. G.Y. Onoda, Jr. and L.L. Hench, Wiley, New York, strates,” J. Cryst. Growth 271 105. Copyright 2004, with pp. 411–448. permission from Elsevier. Table 27.3 Data compiled by Atkins, P.W. (1978) Physi- Table 29.1 Data compiled by Brice, J.C. (1986) Crystal cal Chemistry, Oxford University Press, Oxford, p. 317. Growth Processes, p. 8. Table 27.4 Data compiled by Patton, T.C. (1979) Paint Table 29.2 Data compiled by Nassau, K. and Nassau, J. Flow and Pigment Dispersion, Wiley, New York, and (1980) in: Crystals: Growth, Properties, and Applica- Kelly, E.G. and Spottiswood, D.J. (1982) Introduction to tions, H.C. Freyhardt, Ed., Springer-Verlag, New York, Mineral Processing, Wiley, New York. p. 9. Table 27.6 Data compiled by Walton, B. (1984) in: Table 29.3 Data compiled by Laudise, R.A. (1970) The Hybrid Microelectronic Technology (Ed: P.L. Moran) Growth of Single Crystals, Prentice-Hall, Inc, Englewood Gordon and Breach, New York. p. 45. Cliffs, p. 215. Table 29.4 Data compiled by Brice, J.C. (1986) Crystal Growth Processes, Blackie, Glasgow, p 130. Chapter 28 Table 29.5 Data compiled by Brice, J.C. (1986) Crystal Figure 28.6 Kotula, P.G. & CBC. Growth Processes, Blackie, Glasgow, p. 108. Figure 28.8 Moore, L.A. & CBC. See also Tietz, L.A. Table 29.6 Data compiled by Hirano, S.-I. (1985) in: and Carter, C.B. (1993) “Structure of the Fe2O3-Al2O3 Fine Ceramics, S. Saito, Ed., Elsevier, New York, pp. (0001) interface,” Phil. Mag. A 67, 699. Tietz, L.A. and 20–23. Carter, C.B. (1993) “Structure of the Fe2O3-Al2O3 (1012) Table 29.7 Data compiled by Brice, J.C. (1986) Crystal interface,” Phil. Mag. A67, 729. Tietz, L.A. and Carter, Growth Processes, Blackie, Glasgow, p. 180. C.B. (1992) “Imaging and diffraction study of continuous α-Fe2O3 films on (0001)Al2O3,” J. Am. Ceram. Soc. 75, 1097. Tietz, L.A., Summerfelt, S.R., and Carter, C.B. Chapter 30 (1992) “The effect of substrate orientation on the chemical vapour deposition growth of α-Fe2O3 on α-Al2O3,” Phil. Figure 30.8 Data from Kingery, W.D., Bowen, H.K., Mag. A 65, 439. http://www.tandf.co.uk/journals and Uhlmann, D.R. (1976) Introduction to Ceramics 2nd Table 28.2 Data compiled by Ohring, M. (1992) The Ed., Wiley, New York, p. 867. Materials Science of Thin Films, Academic Press, Boston, Figure 30.9 Data from Moulson, A.J. and Herbert, J.M. p. 154. (1990) Electroceramics, Chapman and Hall, London, Table 28.3 Data from Veprek, S. (1985) “Plasma- p. 129. induced and plasma-assisted chemical vapour deposition,” Figure 30.10 Data from Kulwicki, B.M. (1991) “Therm- Thin Solid Films 130, 135. istors and related sensors,” in: Ceramics and Glasses, Table 28.4 Data compiled by Ohring, M. (1992) The Engineered Materials Handbook Vol. 4, ASM Interna- Materials Science of Thin Films, Academic Press, Boston, tional, p. 1148. p. 189. Figure 30.13 Data from Baumbach, H.H.V. and Wagner, Table 28.5 Data compiled by Ohring, M. (1992) The C. (1933) Z. Phys. Chem. B22, 199. Materials Science of Thin Films, Academic Press, Boston, Figure 30.16 Data from Barsoum, M.W. (1996) Funda- p. 119. mentals of Ceramics, Institute of Physics, Bristol, p. 208. Figure 30.17 Data from Gupta, T.K. (1991) “Varistors”, in: Ceramics and Glasses, Engineered Materials Hand- Chapter 29 book Vol. 4, ASM International, p. 1151. Figure 29.9 Redrawn after www.crystalsystems.com/ Figure 30.19 Data from Moulson, A.J. and Herbert, J. hem.html, an industrial leader in the use of this M. (1990) Electroceramics, Chapman and Hall, London, technique. p. 147. Figure 29.10 Data from Brice, J.C. (1986) Crystal Figure 30.24 Data from Koller, A. (1994) Structure and Growth Processes, Blackie, Glasgow, p. 56. Properties of Ceramics, Elsevier, Amsterdam, p. 474. Figure 29.13 Ramachandran, D., Basu, J., & CBC. Figure 30.25 Data from Duffy, J.A. (1990) Bonding, Figure 29.19b Reprinted from Varghese, O.K., Gong, Energy Levels and Bands in Inorganic Solids, Longman D., Paulose, M., Grimes, C.A., and Dickey, E.D. (2003) Scientific and Technical, Harlow, Essex, UK. p. 138. 712 ................................................................................................................................ D e ta i l s f o r F i g u r e s a n d Ta b l e s Figure 30.26 Data from Kingery, W.D., Bowen, H.K., Table 31.6 Data compiled by Yanagida, H., Koumoto, and Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd K., and Miyayama, M. (1996) The Chemistry of Ceramics, Ed., Wiley, New York, p. 156. Wiley, New York, p. 213. Table 30.2 Data compiled by Kingery, W.D., Bowen, Table 31.9 Data from Electronic Industries Association H.K., and Uhlmann, D.R. (1976) Introduction to Ceram- RS-198 (1958), American Standard Requirements for ics, 2nd Ed., Wiley, New York, p. 853. Ceramic Dielectric Capacitors, Classes 1 and 2, American Table 30.3 Data compiled by Barsoum, M.W., Funda- Standards Association, New York. mentals of Ceramics, Institute of Physics, Bristol, p. 43 Table 31.12 Data compiled by Lovell, M.C., Avery, A. and Hench, L.L. and West J.K. (1990) Principles of Elec- J., and Vernon, M.W. (1976) Physical Properties of Mate- tronic Ceramics, Wiley, New York, p. 91. rials, Van Nostrand Reinhold, New York. Table 30.4 Data compiled by Kingery, W.D., Bowen, H.K., and Uhlmann, D.R. (1976) Introduction to Ceram- Chapter 32 ics, 2nd Ed., Wiley, New York, p. 869 and Hench, L.L. and West J.K. (1990) Principles of Electronic Ceramics, Wiley, Figure 32.3 Data from Kingery, W.D., Bowen, H.K., New York, p. 111. and Uhlmann, D.R. (1976) Introduction to Ceramics 2nd Table 30.6 Data compiled by Moulson, A.J. and Herbert, Ed., Wiley, New York, p. 647. J.M. (1990) Electroceramics, Chapman and Hall, London, Figure 32.5a Data from Kingery, W.D., Bowen, H.K., p. 141. and Uhlmann, D.R. (1976) Introduction to Ceramics 2nd Table 30.7 Data compiled by Hench, L.L. and West J.K. Ed., Wiley, New York, p. 651. (1990) Principles of Electronic Ceramics, Wiley, New Figure 32.5b Data from Kingery, W.D., Bowen, H.K., York, p. 114. and Uhlmann, D.R. (1976) Introduction to Ceramics 2nd Table 30.8 Data compiled by Hench, L.L. and West J.K. Ed., Wiley, New York, p. 652. (1990) Principles of Electronic Ceramics, Wiley, NY, Figure 32.6 Data from Kingery, W.D., Bowen, H.K., p. 116. and Uhlmann, D.R. (1976) Introduction to Ceramics 2nd Table 30.10 Data compiled by Colell, H. and Cook, B. Ed., Wiley, New York, p. 653. (1999) “Fuel cells—Power for the future” Education in Figure 32.16 Modified from Izawa, T. and Sudo, S. Chem., 36, 123. (1987) Optical Fibers: Materials and Fabrication, KTK, Table 30.12 Data compiled by Cyrot, M., and Pavuna, Scientific, Tokyo, Japan. D. (1992) Introduction to Superconductivity and High-Tc Figure 32.17 Modified from Izawa, T. and Sudo, S. Materials, World Scientific, Singapore, p. 174. (1987) Optical Fibers: Materials and Fabrication, KTK, Table 30.13 Data compiled by Cyrot, M. and Pavuna, Scientific, Tokyo, Japan. D. (1992) Introduction to Superconductivity and High-Tc Figure 32.11 Data from Lee, D.W. and Kingery W.D. Materials, World Scientific, Singapore, pp. 24 and 38. (1960) “Radiation energy transfer and thermal conductiv- ity of ceramic oxides”, J. Am. Ceram. Soc. 43, 594. Figure 32.12 Data from Kingery, W.D., Bowen, H.K., Chapter 31 and Uhlmann, D.R. (1976) Introduction to Ceramics 2nd Figure 31.9 Data from Kay, H.F. and Vousden P. (1949) Ed., Wiley, New York, p. 657. Phil. Mag. 40, 1019. http://www.tandf.co.uk/journals Figure 32.28 Aizenberg, J. and Hendler, G. (2004) Figure 31.10 Data from Moulson, A.J. and Herbert, J. “Designing efficient microlens arrays: Lessons from M. (1990) Electroceramics, Chapman and Hall, London. nature.” J. Mater. Chem. 14, 2066. Reproduced by permis- p. 76. sion of The Royal Society of Chemistry. Figure 31.14 Data from Merz, W.J. (1949) Phys. Rev. Table 32.2 Data compiled by Kingery, W.D., Bowen, 76, 1221. H.K., and Uhlmann, D.R. (1976) Introduction to Ceram- Figure 31.15 Data from Moulson, A.J. and Herbert, J. ics, 2nd Ed., Wiley, New York, p. 662. M. (1990) Electroceramics, Chapman and Hall, London. Table 32.4 Data compiled by Bloor, D., Brook, R.J., p. 78. Flemings, M.C., and Mahajan, S. (1994) editors, The Figure 31.16 Data from Moulson, A.J. and Herbert, J. Encyclopedia of Advanced Materials, Pergamon Press, M. (1990) Electroceramics, Chapman and Hall, London. Oxford, p. 451. p. 77. Table 32.5 Data compiled by Bloor, D., Brook, R.J., Figure 31.21 Data from Jaffe, B., Cook, W.R., and Jaffe, Flemings, M.C., and Mahajan, S. (1994) editors, The H. (1971) Piezoelectric Ceramics, Academic Press, London. Encyclopedia of Advanced Materials, Pergamon Press, Figure 31.22 Courtesy of Ted Charles Norton and the Oxford, p. 452. University of Washington Medical Center. Table 32.7 Data compiled by Yanagida, H., Koumoto, Table 31.4 Data compiled by Walther, G.C. and Hench K., and Miyayama, M. (1996) The Chemistry of Ceramics, L.L. (1971) “Dielectric breakdown of Ceramics” in Physics Wiley, New York. of Electronic Ceramics, L.L. Hench and D.B. Dove, eds. Table 32.8 Data compiled by Bloor, D., Brook, R.J., Part A, Dekker, New York. Flemings, M.C., and Mahajan, S. (1994) editors, The D e ta i l s f o r F i g u r e s a n d Ta b l e s ............................................................................................................................... 713 Encyclopedia of Advanced Materials, Pergamon Press, Chapter 34 Oxford, p. 274. Figure 34.1 Data from Kingery, W.D., Bowen, H.K., Table 32.10 Data compiled by Bever, M.B. (1986) editor- and Uhlmann, D.R. (1976) Introduction to Ceramics in-chief, Encyclopedia of Materials Science and Engi- 2nd. Ed., Wiley, New York, p. 586. neering, Pergamon Press, Oxford, p. 2507. Figure 34.2 Data from Kingery, W.D., Bowen, H.K., Table 32.11 Data compiled by Bever, M.B. (1986) editor- and Uhlmann, D.R. (1976) Introduction to Ceramics in-chief, Encyclopedia of Materials Science and Engi- 2nd. Ed., Wiley, New York, p. 588. neering, Pergamon Press, Oxford, p. 2507. Figure 34.3 Data from Berman, R. (1951) “The Thermal Table 32.12 Data compiled by Engineered Materials Conductivities of Some Dielectric Solids at Low Tempera- Handbook, Vol. 4, Ceramics and Glasses, ASM Interna- tures—Experimental”, Proc. R. Soc. Lond A 208, 90 and tional (1991) p. 1129. Lee, D.W. and Kingery, W.D. (1960) “Radiation Energy Transfer and Thermal Conductivity of Ceramic Oxides”, Chapter 33 J. Am. Ceram. Soc. 43, 594. Figure 34.4 Data from Kingery, W.D., Bowen, H.K., Figure 33.1 Courtesy of Stan Sherer. and Uhlmann, D.R. (1976) Introduction to Ceramics Figure 33.6 Data from Standley, K.J. (1962) Oxide 2nd. Ed., Wiley, New York, p. 617. Magnetic Materials, Clarendon Press, Oxford, p. 89. Figure 34.6 Data from Kingery, W.D., Bowen, H.K., Figure 33.15 Adapted from Hench, L.L., and West, J.K. and Uhlmann, D.R. (1976) Introduction to Ceramics (1990) Principles of Electronic Ceramics, Wiley, New 2nd. Ed., Wiley, New York, p. 623. York. p. 321. Figure 34.7 Data from Kingery, W.D., Bowen, H.K., Figure 33.18 Reprinted from Jakubovics, J.P. (1994) and Uhlmann, D.R. (1976) Introduction to Ceramics Magnetism and Magnetic Materials, 2nd. Ed., The Insti- 2nd. Ed., Wiley, New York, p. 620. tute of Materials, London, p. 82. By permission of Maney Figure 34.11 Data from Van Uitert, L.G., et al (1977) Publishing. Mater. Res. Bull. 12, 261. Figure 33.19 Reprinted with permission from Wolfe, Figure 34.12 Data from Kingery, W.D., Bowen, H.K., R., Gyorgy, E.M., Lieberman, R.A., Fratello, V.J., Licht, and Uhlmann, D.R. (1976) Introduction to Ceramics 2nd. S.J., Deeter, M.N., and Day, G.W. (1992) “High-frequency Ed., Wiley, New York, p. 593. magnetic-field sensors based on the Faraday-effect in Figure 34.13 Data from Shirane G. and Takeda, A. garnet thick-films” Appl. Phys. Lett. 60, p. 2048. Copy- (1952) J. Phys. Soc. Japan 7, 1. right 1992, American Institute of Physics. Figure 34.15 Data from Richerson, D.W. (1992) Modern Figure 33.22a–c Data from Moulson, A.J. and Herbert, Ceramic Engineering: Properties, Processing, and Use in J.M. (1990) Electroceramics, Chapman & Hall, London, Design, 2nd. Ed., Marcel Dekker, New York, p. 147. p. 358. Figure 34.16 Data from Kingery, W.D., Bowen, H.K., Figure 33.23 Redrawn after Moulson, A.J. and Herbert, and Uhlmann, D.R. (1976) Introduction to Ceramics 2nd. J.M. (1990) Electroceramics, Chapman & Hall, London, Ed., Wiley, New York, p. 597. p. 363. Table 34.2 Data compiled by Barsoum, M.W. (1997) Figure 33.26 Redrawn after Moulson, A.J. and Herbert, Fundamentals of Ceramics, McGraw-Hill, New York, J.M. (1990) Electroceramics, Chapman & Hall, London, p. 97. p. 367. Table 34.9 Data compiled by Barsoum, M.W. (1997) Figure 33.27 After Perez et al (cited in Chapter). Fundamentals of Ceramics, McGraw-Hill, p. 103–4. Table 33.3 Data from Jakubovics, J.P. (1994) Magne- Table 34.10 Data compiled by Kingery, W.D., Bowden, tism and Magnetic Materials, 2nd. Ed., The Institute of H.K., and Uhlmann, D.R. (1976) Introduction to Ceramics Materials, London. p. 15. 2nd Ed., Wiley, New York, p. 594. Table 33.4 Data from Handbook of Chemistry and Physics, 61st Ed., CRC Press, Boca Raton, FL. Chapter 35 Table 33.5 Data from Handbook of Chemistry and Physics, 61st Ed., CRC Press, Boca Raton, FL. Figure 35.1 Data from Hulbert, S.F., Hench, L.L., Table 33.6 Data compiled by Barsoum, M.W. (1997) Forbers, D., and Bowman, L.S. (1982–83) Ceramurgia Fundamentals of Ceramics, McGraw-Hill, New York. Intl. 8–9, 131. p. 585. Figure 35.2 Redrawn after Hench, L.L. and Wilson, J. Table 33.9 Data compiled by ASM Handbook Vol. 2, K. (1993) in: An Introduction to Bioceramics, Hench, L. Properties and Selection: Nonferrous Alloys and Special- L. and Wilson, J.K. (editors) World Scientific, Singapore, Purpose Materials, ASM International (1990). p. 2. Table 33.10 Data compiled by Metals Handbook: Prop- Figure 35.4 Redrawn after Hench, L.L. and Wilson, J. erties and Selection: Stainless Steels, Tool Materials and K. (1993) in: An Introduction to Bioceramics, Hench, L. Special Purpose Metals, Vol. 3, 9th Ed., D. Benjamin, L. and Wilson, J.K. (editors) World Scientific, Singapore, Senior Editor, ASM, 1980. p. 13. 714 ................................................................................................................................ D e ta i l s f o r F i g u r e s a n d Ta b l e s Figure 35.6 Reprinted from Richerson, D.W. (2000) Figure 36.6a Reprinted from Read, P.G. (1999) Gem- The Magic of Ceramics, The American Ceramic Society, mology 2nd Ed., Butterworth-Heinemann, Oxford. With Westerville, OH, p. 175. By permission of the American permission from Elsevier. Ceramic Society. Figure 36.7 Reprinted from Read, P.G. (1999) Gemmol- Figure 35.7 Data from Bonfield, W., Grynpas, M.D., ogy 2nd Ed., Butterworth-Heinemann, Oxford. With per- Tully, A.E., Bowman, J., and Abram, J. (1981) ‘Hydroxy- mission from Elsevier. apatite Reinforced Polyethylene—A Mechanically Com- Figure 36.8a Courtesy of A.Krüss Optronic GmbH, patible Implant’ Biomaterials 2, 185. Hamburg, Germany (Karin Leibrock). Figure 35.8 Reprinted from Wang, Q., Huang, W., Figure 36.8b Redrawn after Read, P.G. (1999) Gem- Wang. D., Darvell. B.W., Day, D.E., and Rahaman, mology. 2nd Ed., Butterworth-Heinemann, Oxford. M.N. (2006) “Preparation of hollow hydroxyapatite Figure 36.9 Adapted from Read, P.G. (1999) Gemmol- microspheres,” J Mater. Sci.: Mater. Med. (2006) 17, ogy 2nd Ed., Butterworth-Heinemann, Oxford, plate 10. 641, with permission from Springer. With permission from Elsevier. Figure 35.9 Courtesy of Medical Carbon Research Figure 36.11b Reprinted from Read, P.G. (1999) Gem- Institute, LLC the maker of On-X prosthetic heart mology 2nd Ed., Butterworth-Heinemann, Oxford. With valves. permission from Elsevier. Figure 35.10 Reprinted from Dejneka, M.J., Streltsov, Figure 36.12b Reprinted from Read, P.G. (1999) Gem- A., Pal, S., Frutos, A.G., Powell, C.L., Yost, K., Yuen, P. mology 2nd Ed., Butterworth-Heinemann, Oxford, p. 114. K., Müller, U., and Lahiri, J. (2003) “Rare earth-doped With permission from Elsevier. glass microbarcodes,” PNAS 100, 389. Copyright 2003 Figure 36.19 Courtesy of Ryan Thompson. See also National Academy of Sciences, USA. http://famousdiamonds.tripod.com/cullinandiamonds. Figure 35.12a Redrawn after: Lin, A. and Meyers, M. html. A. (2005) “Growth and structure in abalone shell,” Mater. Figure 36.22 Reprinted from Keller, P.C. (1992) Gem- Sci. Eng. A 390 27. stones of East Africa Geoscience Press, Figure 8.1. With Figure 35.12b Reprinted from Lin, A. and Meyers, M. permission from Geosciences Press. A. (2005) “Growth and structure in abalone shell,” Mater. Figure 36.23 Riesterer, J.L & CBC. Sci. Eng. A 390 27. Copyright (2005), with permission Figure 36.26 Reprinted from Sofianides, A.S. and from Elsevier. Harlow, G.E. (1990) Gems & Crystals from the American Figure 35.13 Reprinted from Chakrabarti, O., Weisensel, Museum of Natural History, Simon and Schuster, New L., and Sieber, H. (2005) “Reactive Melt Infiltration Pro- York, p. 82. With permission from the American Museum cessing of Biomorphic Si–Mo–C Ceramics from Wood,” of Natural History. Copyright Van Pelt Photographers/ J. Am. Ceram. Soc. 88(7), 1792–1798. With permission AMNH. from the American Ceramic Society. Figure 36.34 Redrawn after the summary table in Table 35.2 Data compiled by Ravaglioli, A. and Hughes, R.W. (1997) Ruby & Sapphire, RWH Publishing, Krajewski, A. (1992) Bioceramics: Materials, Properties, Boulder CO. and Application, Chapman and Hall, London, p. 44. Figure 36.33 Reprinted from Hurlbut, C.S. and Kam- Table 35.4 Data compiled by Hench, L.L. and Wilson, merling, R.C. (1991) Gemology 2nd Ed., Wiley, New York. J. (1993) An Introduction to Bioceramics, World Scien- Plate I image 6. With permission from Wiley-VCH tific, Singapore, p. 12. Verlag. Table 35.5 Data compiled by Hulbert, S.F. (1993) Figure 36.34 Redrawn after Hughes, R.W. (1997) Ruby “The Use of Alumina and Zirconia in Surgical & Sapphire, RWH Publishing, Boulder CO. Implants” in: An Introduction to Bioceramics, Hench, L. Table 36.1 Data from Read, P.G. (1999) Gemmology. 2nd L. and Wilson, J.K. (editors) World Scientific, Singapore, Ed., Butterworth-Heinemann, Oxford P27. p. 26. Table 36.3 Data compiled by Read, P.G. (1999) Table 35.6 Data compiled by Höland, W. and Vogel, W. Gemmology. 2nd Ed., Butterworth-Heinemann, Oxford (1993) in: An Introduction to Bioceramics, Hench, L.L. p. 219, app G and www.matls.com/search/GetProperty. and Wilson, J.K. (editors) World Scientific, Singapore, asp. p. 126. Table 36.4 Data compiled by Hurlbut, C.S. and Table 35.7 Data compiled by LeGeros, R.Z. and Kammerling, R.C. (1991) Gemmology, 2nd Ed., John Wiley, LeGeros, J.P. (1993) in: An Introduction to Bioceramics, New York. Hench, L.L. and Wilson, J.K. (editors) World Scien- Table 36.5 Data compiled by Read, P.G. (1999) Gem- tific, Singapore, p. 145. mology. 2nd Ed., Butterworth-Heinemann, Oxford, p. 73. Table 36.7 Data compiled by Read, P.G. (1999) Gemmology. 2nd Ed., Butterworth-Heinemann, Oxford, Chapter 36 p. 7. Figure 36.1 Courtesy of Richard Hughes. See also his Table 36.10 Data from Yavuz, F., Gültekin, A.H., and web site www.ruby-sapphire.com. Karakaya, M.Ç. (2002) “CLASTOUR: a computer D e ta i l s f o r F i g u r e s a n d Ta b l e s ............................................................................................................................... 715 program for the classification of the minerals of the D.N. (2006) “High yield synthesis and lithography of tourmaline group”, Computers and Geosci. 28, 1017. silica-based nanosprings,” Nanotechnology, 17, S298. Table 36.11 Data compiled by Nassau, K. (1994) Gem- Figure 37.11 Redrawn from DOE. Basic Research stone Enhancement, 2nd Ed., Butterworth-Heinemann, Needs for Solar Energy, Report of the Basic Energy Sci- Oxford. ences Workshop on Solar Energy Utilization, April 18–21, 2005. Defining the direction for U.S. solar energy research, p. 30. Table 37.1 Data compiled by Kenney, G.B. and Bowen, Chapter 37 H.K. (1983) ‘High tech ceramics in Japan: Current and Figure 37.2 Data from Dow Whitney, E. (1976) “New future markets,’ Am. Ceram. Soc. Bull. 62, 590. advances in ceramic tooling,” SME Technical Report, Table 37.2 Data from Ceramic Industry, August 1993, MRR76-15, Society of Manufacturing Engineers, Dear- p. 43. born, MI 1976. Table 37.4 Data from Schoenung, J.M. (1991) “Analysis Figure 37.3 Data from Reynolds, III, T.G. (2001) “Elec- of the economics of silicon nitride powder production,” tronic ceramic materials,” Am. Ceram. Soc. Bull. 80, 30. Am. Ceram. Soc. Bull. 70, 114. Figure 37.4 Data from Reynolds, III, T.G. (2001) “Elec- Table 37.5 Data from Business Communications Co., tronic ceramic materials,” Am. Ceram. Soc. Bull. 80, 31. Inc. Reprinted in Am. Ceram. Soc. Bull., March 2002, 71, Figure 37.5 Reprinted from Eakins, D.E., Held, M., 34. Norton, M.G., and Bahr, D.F. (2003) “A study of fracture Table 37.6 Data from Advanced Ceramics Technology and defects in single crystal YAG,” J. Cryst. Growth 267, Roadmap—Charting Our Course. December 2000. Spon- 502. Copyright 2003, with permission from Elsevier. sored by United States Advanced Ceramic Association Figure 37.6 Data from New Scientist, 30 August 2003, and the U.S. Department of Energy, p. 16. p. 16. Table 37.7 Data compiled by Hummel, R.E. (1998) Figure 37.7 Reprinted from McKernan S. and Kotula, Understanding Materials Science, Springer, New York, p. P.G. (1992) in: Norton, M.G. and Carter, C.B., “Grain and 372. interphase boundaries in ceramics and ceramic compos- Table 37.8 Data compiled by Hummel, R.E. (1998) Under- ites,” Chapter 4 in Materials Interfaces: Atomic-level standing Materials Science, Springer, New York, p. 373. Structure and Properties, Wolf, D. and Yip, S. Eds., Table 37.9 Data from Siikamäki, R. and Hupa, L. (2001) Chapman and Hall, London, p. 186. With permission from “Utilization of EOL CRT-glass as a glaze raw material,” Springer. in: Recycling and Reuse of Glass Cullet, Dhir, R.K., Lim- Figure 37.9 McIlroy, D.N. & MGN. See also Wang, L., bachiya, M.C., and Dyer, T.D., Eds., Thomas Telford, Major, D., Paga, P., Zhang, D., Norton, M.G., and McIlroy, London, p. 136. 716 ................................................................................................................................ D e ta i l s f o r F i g u r e s a n d Ta b l e s