Effective medium approximation

In this work recently produced and commercially available glazed ceramic object with metallic lustre decoration was studied by using a spectroscopic ellipsometer with rotating compensator. The thickness and metal content of the surface lustre layers are determined by ion beam analytical techniques, i.e., Rutherford backscattering spectrometry and external beam particleinduced X-ray emission and the results were utilized in the construction of multilayer optical models for the evaluation and interpretation of the spectroellipsometric measurements.

This dissertation presents the results of using different inclusion and granular effective medium models and poroelasticity to predict the elastic properties of rocks with complex microstructures. Effective medium models account for the microstructure and texture of rocks, and can be used to predict the type of rock and microstructure from seismic velocities and densities. We show that if enough information regarding the rock microstructure is available, effective-medium models produce better estimates of the elastic properties of the rock matrix than the average of Hashin-Shtrikman (1963). We introduce the elastic equivalency approach, using the differential effective medium model, to predict the effective elastic moduli of rocks and attenuation. We introduce the porous grain concept and develop rock physics models for rocks with microporosity. We exploit the porous grain concept to describe a variety of arrangements of uncemented and cemented grains with different degrees of hydraulic connectivity in the pore space. We first investigate the accuracy of the differential effective medium and selfconsistent estimations of elastic properties of complex rock matrix using composites as analogs. At low porosity, the elastic moduli of the rock mineral matrix often dominate those of the whole rock. A sedimentary rock matrix may be considered as a composite and may include mineral constituents with very different moduli and shapes. To describe the fabric of these rocks, an unmanageable number of parameters may be needed. We test whether the differential effective-medium (DEM) and selfconsistent (SC) models can accurately estimate the elastic moduli of a complex rock v I would like to distinguish the enduring and insightful support of my adviser Jack Dvorkin, who has provided assistance and guidance without which I would have been unable to complete this dissertation. I would also like to thank Tapan Mukerji, Gary Mavko, Mark Zoback, and David Pollard, for their readiness to serve on my oral exam committee and for their thorough review and constructive comments on my dissertation. Thanks to Claude Reichard who provided valuable input throughout the process of writing this dissertation. Thanks to Tara Ilich and Fuad Nijim for helping me so much with all the paper works for this project. I thank Margaret Muir for her tremendous help all through my first quarter in Stanford.

Effective thermal management is crucial for global sustainability, yet it faces a fundamental challenge: traditional materials cannot dynamically regulate the three coupled heat transfer modes, namely conduction, convection, and radiation, in complex, real-world environments. To overcome this, we present a paradigm shift from material selection to the architectural design of synergistic heat transfer. This perspective explores how multimodal thermal metamaterials, through engineered microstructures and topology, enable programmable control over coupled thermal flows. We highlight how this approach yields advanced functionalities, including directional guidance, adaptive cooling, and waste-heat recovery, across scales ranging from microelectronics to buildings and marine systems. This architectural design framework transcends intrinsic material limits, establishing a foundational pathway toward intelligent, high-efficiency, and sustainable thermal technologies essential for energy sustainability.

We present a theoretical study of light propagation through photonic crystal ͑PhC͒ structures using an effective medium approximation based on equifrequency surface calculations. The procedure is illustrated by calculating bending, splitting and focusing phenomena in a slab of two-dimensional PhC using a Fourier imaging technique. In the passband above the first stop band, wave propagation was found to depend dramatically on both light frequency and incident direction. This propagation anisotropy leads to very large negative refraction along the ͓11͔ crystal direction. Light emitted from a line source outside the PhC slab can be focused, divided into subbeams inside the PhC, bent negatively, and refocused again on the other side the slab. The results agree well with the field calculated using a finite-difference time-domain method and can be straightforwardly applied to more complicated PhC structures, such as three-dimensional PhC structures. The imaging properties of a PhC slab are also discussed.

Complex impedance measurements were used to analyze the influence of ultraviolet and ozone gas on the electronic behaviour of ZnO films grown by rf magnetron sputtering. The data show that UV exposure strongly increases the ac conductivity of the film at very low frequencies, and that after ozone exposure it recovers the original value. At high frequencies, however, UV-light exposure it does not change the conductivity but the ozone acts in the sense to decrease it. Two distinct mechanisms, related to two relaxation time distributions are clearly observed: they are superimposed in the virgin sample, but they split forming two semicircles in the z 00 (f) À z 0 (f) diagrams when the samples are treated with UV and/or ozone gas. A combination of the bruggeman effective medium approximation (BEMA) with the random free energy barrier model is used to fit the data and to explain the ac conductivity variation phenomena observed.

A simple mechanical model of planar fibrous materials with mesoscopic disorder is introduced and an- alyzed. In this scalar model a shear modulus controls the stress transfer in the transverse direction. The system is studied using the effective medium approximation and computer simulations; the comparison between them is quite favorable. In the disorder-controlled regime the stress-strain relation, the number of broken cells at the onset of crack propagation, and the length of the final crack scale with the system size as L, L ", and L, respectively. The mechanical properties are controlled by the interplay between disorder and shear modulus, which is studied in detail.

This paper presents detailed numerical simulations predicting the effective thermal conductivity of spherical monodisperse and polydisperse core-shell particles ordered or randomly distributed in a continuous matrix. First, the effective thermal conductivity of this three-component composite material was found to be independent of the capsule spatial distribution and size distribution. In fact, the study established that the effective thermal conductivity depended only on the core and shell volume fractions and on the core, shell, and matrix thermal conductivities. Second, the effective medium approximation reported by Felske (2004) [21] was in very good agreement with numerical predictions for any arbitrary combination of the above-mentioned parameters. These results can be used to design energy efficient composites, such as microencapsulated phase change materials in concrete and/or insulation materials for energy efficient buildings.

The Landau theory of 180 o domain walls in BaT iO 3 type ferroelectric particles is presented . Results of exact description of domain walls in bulk enabled us to formulate variational approach to theory of domain walls in corresponding small particles. The depolarization field effects and the space-charge layers are taken into account in the samples of the cube form. It was found that at low temperatures well known hyperbolic tangent wall profile is a good approximation for description of domain walls in particles. Near the transition temperature it is more and more appropriate to speak about two walls separating ferroelectric, paraelectric and ferroelectric domains correspondingly as a result of splitting of a single ferroelectric wall into two subwalls in small BaT iO 3 particles. Domain wall energy density, average interwall distance and change of the dielectric response of thick walls in small ferroelectric particles in microcomposites is qualitatively found. Our results qualitatively describe observed dependencies better than those theories which exist up to date. In temperature region near transition from the ferroelectric to paraelectric phase in micrcomposites our quantitative results for response, for Curie-like transition temperature and other parameters may be verified.

We study experimentally the propagation of linear magnetoinductive waves in arrays of split-ring resonators with different orientation and spacing. We summarize our experimental results characterizing the effect of coupling of individual elements in magnetic composite metamaterials. We observe the band broadening due to the excitation of magnetoinductive waves which should impose some limitations on the effective medium approximation used to

For an isotropic and homogeneous nonlinear left-handed materials, for which the effective medium approximation is valid, Maxwell's equations for electric and magnetic fields lead naturally, within the slowly varying envelope approximation, to a system of coupled nonlinear Schrödinger equations. This system is equivalent to the well-known Manakov model that under certain conditions, is completely integrable and admits bright and dark soliton solutions. It is demonstrated that leftand right-handed (normal) nonlinear mediums may have compound bright and dark soliton solutions, respectively. These results are also supported by numerical calculations.

A mathematical model for diffusion and reaction in blocked zeolites is developed which takes into account nonidealities arising from interaction between sorbed molecules as well as the effect of pore and surface blocking. The model combines a microscopic approach, in which expressions for chemical potential and diffusive fluxes are calculated within the lattia-gas framework, with the more traditional continuum approach which takes into account the effect of surface blocking. The effect of pore blocking on the diffusive fluxes is accounted for through an effective medium approximation. The effects of crystal size and blocking on the activity-selectivity characteristics of the crystal are illustrated through an example that is qualitatively similar to industrially important reactions such as alkylation of toluene in blocked ZSM-5 zeolite.

We present numerical simulations of acoustic wave propagation in disordered granular media. Small amplitude oscillations of compressed static configurations of frictionless spherical grains are analyzed. Force chains, while important for the static properties of the granular assemblies, do not play a dominant role in transmitting acoustic waves according to our observations. Reasons include that the stiffness network is less widely distributed than the force network, and the nearby grains are coupled relatively strongly to grains in the force chain. The transmitted acoustic signal can be decomposed to an initial cycle and a more noisy tail, similarly to related experiments.

Mesocrystalline particles have been recognized as a class of multifunctional materials with potential applications in different fields. However, the internal organization of nanocomposite mesocrystals and its influence on the final properties have not yet been investigated. In this paper, a novel strategy based on electrodynamic simulations is developed to shed light on how the internal structure of mesocrystals influences their optical properties. In a first instance, a unified design protocol is reported for the fabrication of hematite/PVP particles with different morphologies such as pseudo-cubes, rods-like and apple-like structures and controlled particle size distributions. The optical properties of hematite/PVP mesocrystals are effectively simulated by taking their aggregate and nanocomposite structure into consideration. The superposition T-Matrix approach accounts for the aggregate nature of mesocrystalline particles and validate the effective medium approximation used in the framework of the Mie theory and electromagnetic simulation such as Finite Element Method. The approach described in our paper provides the framework to understand and predict the optical properties of mesocrystals and more general, of hierarchical nanostructured particles.

Discontinuous metal films on semiconductor surface are very important for future application in single-electronics. Elaborated technology of chemical liquid deposition of metal from aqueous solution of gold salt allows us to obtain as well isolated nanoclusters as some nearly percolated films. Morphology and geometric parameters of metal clusters were examined by atomic force microscopy (AFM) and transmission electron microscopy (TEM). At optical investigations we used both p-polarized light reflection at several angles of incidence in visible and multi-angle of incidence (MAI) ellipsometry. Using the effective optical parameters obtained, we have calculated the dielectric function of this planar structure. Various ways for theoretical description of the dielectric response of an ensemble of metal particles on solid surface in the effective medium approximation (EMA) are considered. The most interest is exhibited to specific optical properties due to the Mie surface plasmon resonance. By AFM and TEM measurements it was found that the Au clusters were flattened in the substrate surface. The Bruggeman's approximation for oblate spheroids or truncated spheres is found as the most preferable in some range of the metal filling factor.

Despite all the support and help I have received, I am solely responsible for any mistakes herein. I also wish to express my appreciation to my brother and sister for their thoughtful care and concerns for me. Last, but certainly not least, my deepest thanks go to my parents for supporting and encouraging me to achieve and be successful. I am forever grateful to them for showing me the value of education.

Organic solar cells with copper pthalocyanine (CuPC) and fullerene (C60) blends with efficiency around 5% have already been demonstrated. However, the data of reliable optical constants of these organic materials and their blends in thin films are not readily available. In this paper, we discuss thin films of CuPC and C60 fabricated using multiple evaporation cells at a base pressure b 10 -8 torr are studied using spectroscopic ellipsometry. Ellipsometric data were obtained in the spectral range of 0.75 eV to 4.5 eV for determining the optical constants. We model CuPC and C60 using Tauc-Lorentz dispersion relation. The blend at the composition ratio of 1:1 were modelled by Maxwell-Garnett and Bruggeman effective medium approximations. In addition, a new approach is taken to model the blend by adding separately all the oscillators for each energy transition for both the composites and were found to fit the raw data better than the Maxwell-Garnett and Bruggeman effective medium approximations. The obtained refractive index data by this approach is then presented. We find that the Q-band and B-band of CuPC and the broad absorption of C60 around 3.56 eV still maintain their optical identity in the blend.