Author(s): Meethong, N (Meethong, Nonglak); Kao, YH (Kao, Yu-Hua); Tang, M (Tang, Ming); Huang, HY (Huang, Hsiao-Ying); Carter, WC (Carter, W. Craig); Chiang, YM (Chiang, Yet-Ming)
Title: Electrochemically Induced Phase Transformation in Nanoscale Olivines Li1-xMPO4 (M = Fe, Mn)
Source: CHEMISTRY OF MATERIALS, 20 (19): 6189-6198 OCT 14 2008
Abstract: The phase stability and phase transformation kinetics of Li1-xMPO4 olivines are critical to their performance as lithium storage electrodes. In this work, nanoscale (< 100 nm primary particle size) Li1-xFePO4 and Li1-xMnPO4 are chosen as model systems for comparison with a coarser-rained LiFePO4 that exhibits a conventional two-phase reaction. The nanoscale materials first exhibit time and state-of-charge dependences of the electrochemical potential and structural parameters which show that stable two-phase coexistence is not reached. The evolution of structural parameters supports the existence of a coherency stress influenced crystal-crystal transformation. However, an additional response, the preferential formation of amorphous phase at nanosize scale, is identified. In Li1-xFePO4, at 34 nm average particle size, at least one amorphous phase of varying Li content coexists with the crystalline phases. In Li1-xMnPO4 of 78 nm particle size, the electrochemically formed delithiated phase is highly disordered. These phenomena are interpreted front the effect Of Surface and bulk energetics on phase stability of a nanoscale material.
DOI: 10.1021/cm801722f

Author(s): Tang, M (Tang, Ming); Ramos, AV (Ramos, Ana V.); Jud, E (Jud, Eva); Chung, SY (Chung, Sung-Yoon); Gautier-Soyer, M (Gautier-Soyer, Martine); Cannon, RM (Cannon, Rowland M.); Carter, WC (Carter, W. Craig); Chiang, YM (Chiang, Yet-Ming)
Title: Nanometer-scale wetting of the silicon surface by its equilibrium oxide
Source: LANGMUIR, 24 (5): 1891-1896 MAR 4 2008
Abstract: Despite the extremely broad technical applications of the Si/SiO2 structure, the equilibrium wetting properties of silicon oxide on silicon are poorly understood. Here, we produce new results in which a solid-state buffer method is used to systematically titrate oxygen activity about the Si/SiO2 coexistence value. The equilibrium morphology at the Si(001) surface over > 8 decades of Po-2 about coexistence is revealed to be a uniform sub-stoichiometric SiOx film of sub-manometer thickness, coexisting with secondary island structures which coarsen with annealing time. A new thermodynamic method using chemical potential to stabilize and control surficial oxides in nanoscale devices is suggested.
DOI: 10.1021/la703331m

Author(s): Dillon, SJ (Dillon, Shen J.); Tang, M (Tang, Ming); Carter, WC (Carter, W. Craig); Harmer, MP (Harmer, Martin P.)
Title: Complexion: A new concept for kinetic engineering in materials science
Source: ACTA MATERIALIA, 55 (18): 6208-6218 OCT 2007
Abstract: Interfaces and the movement of atoms within an interface play a crucial role in determining the processing and properties of virtually all materials. However, the nature of interfaces in solids is highly complex and it has been an ongoing challenge to link material performance with the internal interface structure and related atomic transport mechanisms. Interface complexions offer a missing link to help solve this universal problem. We have theoretically predicted the existence of multiple interface complexions by thermodynamics, but the present work represents the most comprehensive characterization and proof of their existence in a real material system. An interface complexion can be considered as a separate phase, which can be made to transform into different complexions (phases) with vastly different properties by chemistry and heat treatment, thereby enabling the engineering control of material properties on a level not previously realizable. As such, complexions offer a solution to outstanding fundamental scientific mysteries, such as the origin of abnormal grain growth in inorganic materials, a problem which leading researchers in the field have struggled to explain for the past 50 years. It is also described how interface complexions will likely have widespread impact across all branches of material science and related disciplines. (c) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
DOI: 10.1016/j.actamat.2007.07.029

Author(s): Meethong, N (Meethong, Nonglak); Huang, HYS (Huang, Hsiao-Ying Shadow); Speakman, SA (Speakman, Scott A.); Carter, WC (Carter, W. Craig); Chiang, YM (Chiang, Yet-Ming)
Title: Strain accommodation during phase transformations in olivine-based cathodes as a materials selection criterion for high-power rechargeable batteries
Source: ADVANCED FUNCTIONAL MATERIALS, 17 (7): 1115-1123 MAY 7 2007
Abstract: High energy lithium-ion batteries have improved performance in a wide variety of mobile electronic devices. A new goal in portable power is the achievement of safe and durable high-power batteries for applications such as power tools and electric vehicles. Towards this end, olivine-based positive electrodes are amongst the most important and technologically enabling materials. While certain lithium metal phosphate olivines have been shown to be promising, not all olivines demonstrate beneficial properties. The mechanisms allowing high power in these compounds have been extensively debated. Here we show that certain high rate capability olivines are distinguished by having extended lithium nonstoichiometry (up to ca. 20 %), with which is correlated a reduced lattice misfit as the material undergoes an electrochemically driven, reversible, first-order phase transformation. The rate capability in several other intercalation oxides can also be correlated with lattice strain, and suggests that nanomechanics plays an important and previously unrecognized role in determining battery performance.
DOI: 10.1002/adfm.200600938

Author(s): Rajter, RF (Rajter, R. F.); French, RH (French, R. H.); Ching, WY (Ching, W. Y.); Carter, WC (Carter, W. C.); Chiang, YM (Chiang, Y. M.)
Title: Calculating van der Waals-London dispersion spectra and Hamaker coefficients of carbon nanotubes in water from ab initio optical properties
Source: JOURNAL OF APPLIED PHYSICS, 101 (5): Art. No. 054303 MAR 1 2007
Abstract: The van der Waals-London dispersion (vdW-Ld) spectra are calculated for the [9,3,m] metallic and [6,5,s] semiconducting single wall carbon nanotubes (SWCNTs), graphite, and graphene (a single carbon sheet of the graphite structure) using uniaxial optical properties determined from ab initio band structure calculations. The [9,3,m], exhibiting metallic optical properties in the axial direction versus semiconducting optical properties in the radial direction, highlights the strong anisotropic nature of metallic SWCNTs. Availability of both efficient ab initio local density band structure codes and sufficient computational power has allowed us to calculate the imaginary parts of the frequency dependent dielectric spectra, which are then easily converted to the required vdW-Ld spectra for Hamaker coefficient calculations. The resulting Hamaker coefficients, calculated from the Lifshitz quantum electrodynamic theory, show that neither graphite nor graphene are accurate model materials for estimating the Hamaker coefficients of SWCNTs. Additionally, Hamaker coefficients were calculated between pure radial-radial, radial-axial, and axial-axial components of both SWCNTs. Analysis of these coefficients reveals that the vdW-Ld interactions will depend on both chirality and the particular orientation between neighboring SWCNTs. The minimization of energy, with respect to orientation, predicts that vdW-Ld alignment forces will arise as a result of the anisotropic optical properties of SWCNTs. (c) 2007 American Institute of Physics.
DOI: 10.1063/1.2709576

Record 6 of 11
Author(s): Meethong, N (Meethong, Nonglak); Huang, HYS (Huang, Hsiao-Ying Shadow); Carter, WC (Carter, W. Craig); Chiang, YM (Chiang, Yet-Ming)
Title: Size-dependent lithium miscibility gap in nanoscale Li1-xFePO4
Abstract: Olivine compounds have emerged as important and enabling positive electrode materials for high-power, safe, long-life lithium rechargeable batteries. In this work, the miscibility gap in undoped Li1-xFePO4 is shown to contract systematically with decreasing particle size in the nanoscale regime and with increasing temperature at a constant particle size. These effects suggest that the miscibility gap completely disappears below a critical size. In the size-dependent regime, the kinetic response of nanoscale olivines should deviate from the simple size-scaling implicit in Fickian diffusion. (c) 2007 The Electrochemical Society.
DOI: 10.1149/1.2710960

Author(s): Tang, M (Tang, Ming); Carter, WC (Carter, W. Craig); Cannon, RM (Cannon, Rowland M.)
Title: Grain boundary order-disorder transitions
Source: JOURNAL OF MATERIALS SCIENCE, 41 (23): 7691-7695 DEC 2006
Abstract: The conditions for grain boundary (GB) structural transitions are determined from a diffuse interface model that incorporates structural disorder and crystallographic orientation. A graphical construction and numerical calculations illustrate the existence of a first-order GB order-disorder transition below the bulk melting point. When thermodynamic conditions permit their existence, disordered GB structures tend to be stable at higher temperatures and are perfectly wet by liquid at the melting point, while ordered grain boundaries are meta-stable against preferential melting. We calculate GB phase diagrams which are analogous to those for liquid-vapor phase transitions.
DOI: 10.1007/s10853-006-0608-4

Author(s): Maskaly, KR (Maskaly, Karlene Rosera); Hsiao, VKS (Hsiao, Vincent K. S.); Cartwright, AN (Cartwright, Alexander N.); Prasad, PN (Prasad, Paras N.); Lloyd, PF (Lloyd, P. F.); Bunning, TJ (Bunning, Timothy J.); Carter, WC (Carter, W. Craig)
Title: Experimental verification of the applicability of the homogenization approximation to rough one-dimensional photonic crystals using a holographically fabricated reflection grating
Source: JOURNAL OF APPLIED PHYSICS, 100 (6): Art. No. 066103 SEP 15 2006
Abstract: The theoretical reflectance spectrum of a one-dimensional photonic crystal with large amounts of interfacial roughness has been calculated using a previously proposed method, and compared to the actual experimental reflectivity of the structure. The photonic crystal was fabricated using a simple and fast method involving the holographic exposure of a liquid crystal/photosensitive prepolymer syrup via the self-interference patterns from two laser beams. The calculated reflectance spectrum for this structure matched the experimental one extremely well, giving very similar reflectivity peak positions and intensities. Slight discrepancies between the two reflectance spectra are attributed to either small variations in the microstructure of the reflection grating beyond that which is captured in the transmission electron micrograph, or the dispersion of the polymer which was not taken into account. These results serve as experimental verification of the theory for rough photonic crystals reported previously. (c) 2006 American Institute of Physics.
DOI: 10.1063/1.2336346

Record 9 of 11
Author(s): Tang, M (Tang, Ming); Carter, WC (Carter, W. Craig); Cannon, RM (Cannon, Rowland M.)
Title: Grain boundary transitions in binary alloys
Source: PHYSICAL REVIEW LETTERS, 97 (7): Art. No. 075502 AUG 18 2006
Abstract: A thermodynamic diffuse interface analysis predicts that grain boundary transitions in solute absorption are coupled to localized structural order-disorder transitions. An example calculation of a planar grain boundary using a symmetric binary alloy shows that first-order boundary transitions can be predicted as a function of the crystallographic grain boundary misorientation and empirical gradient coefficients. The predictions are compared to published experimental observations.
DOI: 10.1103/PhysRevLett.97.075502

Author(s): Luo, J; Tang, M; Cannon, RM; Carter, WC; Chiang, YM
Title: Pressure-balance and diffuse-interface models for surficial amorphous films
Abstract: Recent observations of nanoscale surficial amorphous films in Bi2O3-doped ZnO are briefly reviewed. The experimental results are modeled with two approaches. A pressure-balance model with the volumetric free energy being the dominant temperature-dependent interaction extended from Clarke's intergranular films model is proposed and numerically evaluated. This quantitative model predicts thicknesses versus temperature behavior for subeutectic films consistent with experimental results. Alternatively, the sequence of adsorption and wetting events as a function of temperature and composition is interpreted as a case of combined surface prewetting and premelting in a two-component system with a bulk eutectic reaction as a generalization of Cahn's critical point wetting model. In this second approach that better represents the through-thickness gradients, diffuse-interface formulation is proposed and analyzed for assessing surficial film stability as well as associated drying and complete wetting transitions. The observation made for Bi2O3 on ZnO can be represented by one of the possible surface prewetting/premelting phase diagrams. (c) 2006 Elsevier B.V. All rights reserved.
DOI: 10.1016/j.msea.2006.01.001

Author(s): Bishop, CM (Bishop, Catherine M.); Tang, M (Tang, Ming); Cannon, RM (Cannon, Rowland M.); Carter, WC (Carter, W. Craig)
Title: Continuum modelling and representations of interfaces and their transitions in materials
Abstract: Evidence for internal and external interface transitions in ceramics and metals is copious. The work described here lays out a framework for predicting interface transitions and including them on bulk phase diagrams. Advances in understanding possible grain boundary transitions in single- and binary-component materials have been made with energetics modelled with the phase-field model due to Kobayashi, Warren and Carter. Analyses inspired by Cahn's critical point wetting work allowed the exploration of the stable, metastable, and unstable grain boundary compositions and structures. A general phase-field model has also been developed that allows the couplings between chemistry, structure, and electrostatics to be explored. This model has been applied to grain boundaries in silicon nitride and indicates that intergranular films can be stabilized below the eutectic temperature. Predictive information from the models presented here could be used to inform material processing routes in order to design for interface structures and so bulk properties. (c) 2006 Elsevier B.V. All rights reserved.
DOI: 10.1016/j.msea.2006.01.013

Author(s): Tang, M; Carter, WC; Cannon, RM Title: Diffuse interface model for structural transitions of grain boundaries Source: PHYSICAL REVIEW B, 73 (2): Art. No. 024102 JAN 2006 Abstract: The conditions for structural transitions at the core of a grain boundary separating two crystals was investigated with a diffuse interface model that incorporates disorder and crystal orientation [Kobayashi , Physica D 140, 141 (2000)]. The model predicts that limited structural disorder near the grain boundary core can be favorable below the melting point. This disordered material is a precursor to a liquid phase and therefore the model represents grain boundary premelting. This model is shown to be isomorphic to Cahn's critical point wetting theory [J.W. Cahn, J. Chem. Phys. 66, 3667 (1977)] and predicts first- and higher-order structural grain boundary transitions. A graphical construction predicts the equilibrium grain boundary core disorder, the grain boundary energy density, and the relative stability of multiple grain boundary "complexions." The graphical construction permits qualitative inference of the effect of model properties, such as empirical homogeneous free energy density and assumed gradient energy coefficients, on properties. A quantitative criterion is derived which determines whether a first-order grain boundary transition will occur. In those systems where first-order transition does occur, they are limited to intermediate grain-boundary misorientations and to a limited range of temperatures below the melting point. Larger misorientations lead to continuously increasing disorder up to the melting point at which the disorder matches a liquid state. Smaller misorientation continuously disorder but are not completely disordered at the melting point. Characteristic grain boundary widths and energies are calculated as is the width's divergence behavior at the melting point. Grain boundary phase diagrams are produced. The relations between the model's predictions and atomistic simulations and with experimental observations are examined.
Author(s): Chatain, D; Lewis, D; Baland, JP; Carter, WC
Title: Numerical analysis of the shapes and energies of droplets on micropatterned substrates
Source: LANGMUIR, 22 (9): 4237-4243 APR 25 2006
Abstract: The shapes and energies of drops on substrates patterned with either holes or posts are computed using Surface Evolver software. The holes and posts are cylindrical in shape and distributed in a 6-fold symmetric pattern. The wetting conditions are such that the liquid does not fill the holes and the interface between the drop and the substrate is composite, i.e., partly solid/liquid and partly liquid/vapor. The sequence of stable drop configurations with increasing volume is analyzed and provides, in part, an explanation for superhydrophobic drop spreading.

Author(s): Upmanyu, M; Srolovitz, DJ; Lobkovsky, AE; Warren, JA; Carter, WC
Title: Simultaneous grain boundary migration and grain rotation
Source: ACTA MATERIALIA, 54 (7): 1707-1719 APR 2006
Abstract: The energy of a polycrystalline network can be reduced by both grain boundary migration and grain rotation. We perform a series of molecular dynamics (M D) simulations of a circular grain embedded in an otherwise single-crystal matrix and monitor both the grain size and the misorientation of the two grains as a function of time. The MID simulations show that grain boundary migration and grain rotation Occur simultaneously. The grains rotate toward local minima or cusps in the grain boundary energy versus misorientation plots. The rate of rotation decreases with increasing grain size. The boundary migration rate is a maximum at the orientations corresponding to cusps in the boundary energy. We use the MD results to fit parameters in a sharp interface limit of a phase field model of simultaneous grain boundary migration and grain rotation. With this parameterization, the phase field model is able to reproduce simultaneously the time dependence of the grain size and misorientation of the initially circular grain. The MID simulations are consistent with the phase field prediction of the grain size dependence of the rotation rate. The implications of the results for grain growth are discussed.

Author(s): Maskaly, GR; Garcia, RE; Carter, WC; Chiang, YM
Title: Ionic colloidal crystals: Ordered, multicomponent structures via controlled heterocoagulation
Source: PHYSICAL REVIEW E, 73 (1): Art. No. 011402 Part 1 JAN 2006
Abstract: A statistical approach for modeling fracture in brittle materials is presented. In particular, a microstructural-based finite element code called OOF is used in conjunction with a stochastic representation of failure that relies on the Weibull law. The OOF code, which maps materials microstructures onto finite element meshes, enables to calculate the local stress states; these stresses are used along with the statistical criterion for brittle fracture in order to determine microcrack formation and propagation. Computer simulations are performed on several microstructures of different materials types, e.g., laminates, particulate composites and polycrystals. The damage accumulation due to microcracking is characterized by the stereological measure of failed material and is investigated in order to assess the effect of microstructural features on the failure mechanism. Moreover, the approach allows to analyze the influence of the characteristic parameters for brittle materials on damage evolution. (c) 2005 Springer Science + Business Media, Inc.

Author(s): Maskaly, KR; Carter, WC; Averitt, RD; Maxwell, JL
Title: Application of the homogenization approximation to rough one-dimensional photonic crystals
Source: OPTICS LETTERS, 30 (21): 2930-2932 NOV 1 2005
Abstract: We show that the homogenization approximation accurately predicts this diminished optical response by comparing results with finite-difference time-domain (FDTD) simulations applied to the same roughened structures. Within the parameter range tested (rms roughness less than 20% and rms wavelengths less than 100% of the photonic crystal periodicity), the homogenization approximation accurately reproduces the reflectivities obtained by the FDTD simulations, which are much more computationally expensive.

Author(s): Maskaly, KR; Carter, WC; Averitt, RD; Maxwell, JL
Title: The effect of interfacial roughness on the normal incidence bandgap of one-dimensional photonic crystals
Source: OPTICS EXPRESS, 13 (21): 8380-8389 OCT 17 2005
Abstract: As discussed previously, interfacial roughness in one-dimensional photonic crystals (1DPCs) can have a significant effect on their normal reflectivity at the quarter-wave tuned wavelength. We report additional finite-difference time-domain (FDTD) simulations that reveal the effect of interfacial roughness on the normal-incidence reflectivity at several other wavelengths within the photonic bandgaps of various 1DPC quarter-wave stacks. The results predict that both a narrowing and red-shifting of the bandgaps will occur due to the roughness features. These FDTD results are compared to results obtained when the homogenization approximation is applied to the same structures. The homogenization approximation reproduces the FDTD results, revealing that this approximation is applicable to roughened 1DPCs within the parameter range tested (rms roughnesses less than 20% and rms wavelengths less than 50% of the photonic crystal periodicity) across the entire normal incidence bandgap.

Author(s): Bishop, CM; Cannon, RM; Carter, WC
Title: A diffuse interface model of interfaces: Grain boundaries in silicon nitride
Source: ACTA MATERIALIA, 53 (18): 4755-4764 OCT 2005
Abstract: A diffuse-interface model for interfaces in multi-component systems with energetic contributions from chemistry, defects, structure, orientation, electrostatics and gradients is proposed. The energy minimizing profiles of planar grain boundaries in the pseudo-binary SiO2-SiN4/3 system are calculated in the SiN4/3-rich single-phase field. Intergranular films are found to be stable below the eutectic temperature. Evidence of first-order grain boundary order-disorder transitions is found in misorientation and chemical potential space. Interface transitions predicted with the model can be plotted on equilibrium phase diagrams to produce "interfacial phase diagrams." These could be a tool for designing processing routes to optimize bulk, polycrystalline material properties through control of grain boundary characteristics.

Author(s): Cannillo, V; Carter, WC
Title: A stochastic model of damage accumulation in complex microstructures
Source: JOURNAL OF MATERIALS SCIENCE, 40 (15): 3993-4004 AUG 2005
Abstract: We propose a new type of ordered colloid, the "ionic colloidal crystal" (ICC), which is stabilized by attractive electrostatic interactions analogous to those in atomic ionic materials. The rapid self-organization of colloids via this method should result in a diversity of orderings that are analogous to ionic compounds. Most of these complex structures would be difficult to produce by other methods. We use a Madelung summation approach to evaluate the conditions where ICC's are thermodynamically stable. Using this model, we compare the relative electrostatic energies of various structures showing that the regions of ICC stability are determined by two dimensionless parameters representing charge balance and the spatial extent of the electrostatic interactions. Parallels and distinctions between ICC's and classical ionic crystals are discussed. Monte Carlo simulations are utilized to examine the glass transition and melting temperatures, between which crystallization can occur, of a model system having the rocksalt structure. These tools allow us to make a first-order prediction of the experimentally accessible regions of surface charge, particle size, ionic strength, and temperature where ICC formation is probable.

Author(s): Siem, EJ; Carter, WC
Title: Orientation-dependent surface tension functions for surface energy minimizing calculations
Source: JOURNAL OF MATERIALS SCIENCE, 40 (12): 3107-3113 JUN 2005
Abstract: Previous numerical methods that calculate equilibrium particle shape to study thermodynamic and kinetic processes depend on interfacial (surface) free energy functions gamma((n) over cap) that have cubic symmetry and thus produce Wulff shapes W of cubic symmetry. This work introduces a construction yielding the minimal surface energy density gamma(convex)(W) that can be determined for any W. Each gamma((n) over cap) that belongs to the equivalence class gamma(W) bounded by gamma(convex)(W) can be used in an energy-minimizing calculation that depends only on W. For practical numerical calculations, this work gives two methods taking directional distance from specified orientation minima as a parameter to produce analytic forms of gamma((n) over cap) giving W as the equilibrium shape for (an otherwise unconstrained) fixed volume. Included are several two- and three-dimensional examples that demonstrate the application and utility of the model gamma((n) over cap) functions. (c) 2005 Springer Science + Business Media, Inc.

Author(s): Bishop, CM; Satet, RL; Cannon, RM; Carter, WC; Roosen, AR
Title: A simple model of fully-faceted grain growth and coarsening with non-linear growth laws
Source: ZEITSCHRIFT FUR METALLKUNDE, 96 (2): 124-134 FEB 2005
Abstract: A numerical simulation of the growth and coarsening of completely faceted particles in a two-dimensional closed system is described. The particles grow from a supersaturated solution with driving forces including an anisotropic-Gibbs-Thompson effect. Linear and non-linear growth laws were incorporated. This allows comparison to data obtained from physical experiments of Si3N4 growing from a glass matrix with additions of various rare earths (La, Y, Lu) where particle growth is more or less anisotropic (depending on the particular rare earth dopant). Simulations explore the ranges of kinetic parameters for which particle shapes tend to be dictated by thermodynamic and/or kinetic anisotropy. Comparison to data taken from a series of experiments indicates that La probably has a non-linear growth effect whereas Lu is less so.

Author(s): Garcia, RE; Langer, SA; Carter, WC
Title: Finite element implementation of a thermodynamic description of piezoelectric microstructures
Abstract: A model and numerical framework is developed for piezoelectric materials. The model treats the piezoelectric and electrostrictive effects by incorporating orientation-dependent, single-crystal properties. The method is implemented in Object Oriented Finite Element program, a public domain finite element code, so it can be applied to arbitrary two-dimensional microstructures with crystallographic anisotropy. The model is validated against analytic solutions. Consistency of the method for known cases permits application of the technique to more complicated two-dimensional systems. The piezoelectric and electrostrictive response is determined for a few simple device geometries and provides insight for design and convergence criteria.

Author(s): Garcia, RE; Carter, WC; Langer, SA
Title: The effect of texture and microstructure on the macroscopic properties of polycrystalline piezoelectrics: Application to barium titanate and PZN-PT
Abstract: The effects of crystallographic texture and microstructure are analyzed for polycrystalline tetragonal BaTiO3, pseudotetragonal PZN-PT, and cubic BaTiO3. For tetragonal BaTiO3 and pseudotetragonal PZN-PT, we demonstrate that a high anisotropy of the single-crystal properties induces an apparent enhancement in the macroscopic piezoelectric response. For tetragonal BaTiO3, the predicted macroscopic piezoelectric constants d(31) and d(33) are enhanced with respect to its single-crystal value at the expense of the spatial contributions from d(15). For samples possessing fiber texture, an optimal response is predicted for samples that are not perfectly textured. Similarly, an apparent enhancement of the macroscopic value of d15 is predicted for PZN-PT. For cubic BaTiO3, the low anisotropy of the underlying crystal properties induces a uniform decrease of the macroscopic electrostrictive constant, Q(11), with decreasing texture. A completely random polycrystal provides 0.85 +/- 0.05 times its single-crystal response.

Author(s): Garcia, RE; Chiang, YM; Carter, WC; Limthongkul, P; Bishop, CM
Title: Microstructural modeling and design of rechargeable lithium-ion batteries
Abstract: The properties of rechargeable lithium-ion batteries are determined by the electrochemical and kinetic properties of their constituent materials as well as by their underlying microstructure. In this paper a method is developed that uses microscopic information and constitutive material properties to calculate the response of rechargeable batteries. The method is implemented in OOF, a public domain finite element code, so it can be applied to arbitrary two-dimensional microstructures with crystallographic anisotropy. This methodology can be used as a design tool for creating improved electrode microstructures. Several geometrical two-dimensional arrangements of particles of active material are explored to improve electrode utilization, power density, and reliability of the LiyC6\LixMn2O4 battery system. The analysis suggests battery performance could be improved by controlling the transport paths to the back of the positive porous electrode, maximizing the surface area for intercalating lithium ions, and carefully controlling the spatial distribution and particle size of active material. (C) 2004 The Electrochemical Society.

Author(s): Chatain, D; Carter, WC
Title: Wetting dynamics - Spreading of metallic drops
Source: NATURE MATERIALS, 3 (12): 843-845 DEC 2004
Abstract: The spreading of metallic liquid drops on flat solid metal or ceramic substrates ranges from milliseconds - comparable to room-temperature spreading of water on glass - to hours. This varying timescale can be understood by what happens - or doesn't happen - at the foot of the drop where the liquid surface contacts the substrate.

Author(s): Maskaly, KR; Maskaly, GR; Carter, WC; Maxwell, JL
Title: Diminished normal reflectivity of one-dimensional photonic crystals due to dielectric interfacial roughness
Source: OPTICS LETTERS, 29 (23): 2791-2793 DEC 1 2004
Abstract: Dielectric reflectors that are periodic in one dimension, also known as one-dimensional photonic crystals (1DPCs), have become extremely useful tools in the optics industry due to the presence of wavelength-tunable photonic bandgaps. However, little is known about the practical effects of manufacturing defects, such as interfacial roughness, on this technologically useful property of 1DPCs. We employ a finite-difference time-domain code to gain further insight into the effect of interfacial roughness on the reflectivity of quarter-wave-tuned 1DPCs in the center of the bandgap at normal incidence. This provides an estimate of the magnitude of the effect of the roughness for even the most-robust incidence conditions. (C) 2004 Optical Society of America.

Author(s): Siem, EJ; Carter, WC; Chatain, D
Title: The equilibrium shape of anisotropic interfacial particles
Source: PHILOSOPHICAL MAGAZINE, 84 (10): 991-1010 APR 1 2004
Abstract: The Wulff construction yields the equilibrium shape of a particle of fixed volume embedded in a single phase at constant temperature. When the particle attaches to an interface ( boundary) between two distinct phases or grains of the same phase, the Wulff construction must be modified to account for the abutment of Wulff shapes at the boundary as well as the boundary energy that is replaced by the particle. If the boundary is non-deformable, a portion of the particle interface is constrained to replace the image (i.e. the exact position) of the boundary that is removed, and the Winterbottom construction yields the equilibrium particle shape. If the boundary can deform, the particle is not constrained to replace the image of removed boundary, and the particle shape is determined by a more general modification of the Wulff construction. In two dimensions, the particle attaches to an initially. at boundary and creates two disjoint segments that remain. at at equilibrium. In three dimensions, the boundary surrounding the particle is contiguous, and numerical calculations show that such a boundary is not necessarily. at but maintains a constant mean curvature of zero at equilibrium.

Author(s): Garcia, RE; Bishop, CM; Carter, WC
Title: Thermodynamically consistent variational principles with applications to electrically and magnetically active systems
Source: ACTA MATERIALIA, 52 (1): 11-21 JAN 5 2004
Abstract: We propose a theoretical framework to derive thermodynamically consistent equilibrium equations and kinetic driving forces to describe the time evolution for electrically and magnetically active materials. This procedure starts from the combined statement of the first and second laws of thermodynamics, naturally incorporates Maxwell's equations, and accommodates the description of continuous phase transformations for conserved and non-conserved order parameters. The kinetics of conserved and non-conserved ordered parameters are introduced, the adequate gradient flow is identified, thus the appropriate kinetics (e.g., Allen-Cahn, Cahn-Hilliard) are derived. Example applications of this theory include the electromechanical fields of piezoelectric materials and the wave equation in the limit of chemically homogeneous solids. Moreover, we derive a thermodynamically consistent set of partial differential equations which describe the transport of charged species in conductive, non-polarizable, magnetizable solids, and in polarizable, electrically insulating, non-magnetizable solids. (C) 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Author(s): Maldovan, M; Carter, WC; Thomas, EL
Title: Three-dimensional dielectric network structures with large photonic band gaps
Source: APPLIED PHYSICS LETTERS, 83 (25): 5172-5174 DEC 22 2003
Abstract: Several three-dimensional dielectric network structures possessing large photonic band gaps are presented. Two of these photonic crystals show gaps as large as 26% of the midgap frequency for a refractive index contrast 3.6:1. Four of the proposed structures consist of three-connected networks and a fifth structure has a mixture of three- and four-connected nodes. The realization of these structures using block polymer self-assembly, interference lithography and layer-by-layer lithography is briefly discussed. (C) 2003 American Institute of Physics.

Author(s): Warren, JA; Kobayashi, R; Lobovsky, AE; Carter, WC
Title: Extending phase field models of solidification to polycrystalline materials
Source: ACTA MATERIALIA, 51 (20): 6035-6058 DEC 8 2003
Abstract: We present a two-dimensional phase field model of grain boundary statics and dynamics. We begin with a brief description and physical motivation of the crystalline phase field model. The description is followed by characterization and analysis of several microstructural implications: the grain boundary energy as a function of misorientation, the liquid-grain-grain triple junction behavior, the wetting condition for a grain boundary and stabilized widths of intercalating phases at these boundaries, and evolution of a polycrystalline microstructure by solidification and impingement, followed by both grain boundary migration and grain rotation. Simulations that demonstrate these implications are presented, with a description of the numerical methods that were used to obtain them. (C) 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Author(s): Maldovan, M; Ullal, CK; Carter, WC; Thomas, EL
Title: Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups
Source: NATURE MATERIALS, 2 (10): 664-667 OCT 2003
Abstract: T he promise of photonic crystals and their potential applications(1,2) has attracted considerable attention towards the establishment of periodic dielectric structures that in addition to possessing robust complete bandgaps, can be easily fabricated with current techniques. A number of theoretical structures have been proposed(3-15). To date, the best complete photonic bandgap structure is that of diamond networks having Fd3m symmetry (2-3 gap). The only other known complete bandgap in a face-centred- cubic (f.c.c.) lattice structure is that of air spheres in a dielectric matrix (8-9 gap; the so called 'inverseopal' structure). Importantly, there is no systematic approach to discovering champion photonic crystal structures. Here we propose a level-set approach based on crystallography to systematically examine for photonic bandgap structures and illustrate this approach by applying it to the 11 f.c.c. groups. This approach gives us an insight into the effects of symmetry and connectivity. We classify the F-space groups into four fundamental geometries on the basis of the connectivity of high-symmetry Wyckoff sites. Three of the fundamental geometries studied display complete bandgaps including two: the F-RD structure with Fm (3) over barm symmetry and a group 216 structure with F (4) over bar 3m symmetry that have not been reported previously. By using this systematic approach we were able to open gaps between the 2-3,5-6 and 8-9 bands in the f.c.c. systems.

Author(s): Maldovan, M; Bockstaller, MR; Thomas, EL; Carter, WC
Title: Validation of the effective-medium approximation for the dielectric permittivity of oriented nanoparticle-filled materials: effective permittivity for dielectric nanoparticles in multilayer photonic composites
Source: APPLIED PHYSICS B-LASERS AND OPTICS, 76 (8): 877-884 JUL 2003
Abstract: A formula for the effective permittivity for two-dimensional particles embedded in a host matrix is derived and a method for its numerical evaluation is described. The method is applied to specific cases of circular, square, rectangular and triangular particles. Shapes are assumed for the inclusion particles. Data for obtaining the effective permittivity is provided for a wide range of filling fractions, geometries and dielectric contrasts between the particles and the matrix under the assumption of the quasi-static approximation, that is, the wavelength of the electric field is assumed to be much larger than the particle size. Metallic particles with complex and frequency-dependent dielectric constants are treated, as well as no-loss dielectric inclusions. Calculations are validated by comparing the results of the reflectivity obtained for a composite layer using the transfer-matrix method, assuming the layer to be an effective medium, to those using the finite-element method and accounting for the heterogeneous material.

Author(s): Lee, ML; Li, Y; Feng, YP; Carter, WC
Title: Frequency-dependent complex modulus at the glass transition in Pd40Ni10Cu30P20 bulk amorphous alloys
Source: PHYSICAL REVIEW B, 67 (13): Art. No. 132201 APR 1 2003
Abstract: We report frequency-dependent measurements of the dynamic elastic modulus of a Pd40Cu30Ni10P20 bulk amorphous phase near its glass transition temperature. The storage and loss moduli exhibit a structural relaxation similar to those observed by other characterization techniques. Parameters obtained by fitting to the Vogel-Fulcher-Tamman equation and the Kohlrausch-Williams-Watts model exhibit similar behaviors to those other methods.
Author(s): Bishop CM, Garcia RE, Carter WC
Title: Effect of charge separation on the stability of large wavelength fluctuations during spinodal decomposition
Source: ACTA MATERIALIA 2003, Vol 51, Iss 6, pp 1517-1524
Abstract: stability analysis of phase separation of charged species by spinodal decomposition is presented. The charge effects introduce a short wave number cutoff for linear perturbations about the homogeneous, neutral solution. Phase field calculations using a semi-implicit spectral method support this conclusion. This suggests that coarsening is limited in ionic solid systems that are unstable with respect to charged-phase separation.

Author(s): Bishop, CM Carter, WC
Title: Relating atomistic grain boundary simulation results to the phase-field model
Source: Comput. Mater. Sci. 25, 3, 378--386 2003
Abstract: A coarse-graining method for mapping discrete data to a continuous structural order parameter is presented. This method is intended to provide a useful and consistent method of utilizing structural data from molecular simulations in continuum models, such as the phase field model. The method is based on a local averaging of the variation of a Voronoi tessellation of the atomic positions from the Voronoi tessellation of a perfect crystal (the Wigner-Seitz cell). The coarse-graining method is invariant to coordinate frame rotation. The method is illustrated with a simple two- dimensional example and then applied to a three-dimensional relaxation simulation using the silicon EDIP potential of a Sigma5 grain boundary. Calculated results indicate that a continuous structural parameter is obtained that has grain boundary characteristics similar to phase-field models of grain boundaries. Comparisons to other coarse-graining measures of structure are discussed as well as applications to experimental data sets.

Author(s): Siem, EJ Carter, WC
Title: The stability of several triply periodic surfaces
Source: Interface Sci. 10, 4, 287--296 2002
Abstract: The stability of six triply periodic surfaces of constant mean curvature (CMC) is investigated. The relative energy and curvature values of the surfaces comprising the P (Pm (3) over barm), I-WP (Im (3) over barm), and G (I4(1)32) families are numerically calculated with K. Brakke's Surface Evolver. Regions where the I-WP surface can exist metastable to a complementary I-WP surface are found. This type of metastability is also found in the F-RD surface. Bifurcation points marking the stability limits of the P, I-WP, and G families are also calculated with Evolver. Modes of instability which may occur in the six CMC families are classified. Bifurcations in the P, G, I-WP, C(P), D, and F-RD families are attributed to fundamental instabilities. Lattices of spheres (LOS) are possible extremal surfaces at the bifurcations. It is determined that both the CMC surfaces and the LOS configurations are unstable to coarsening. Because the variation in curvature is lowest for the G family, it is the most robust of the six families to coarsening when the surfaces are otherwise equivalent.

Author(s): Urbas, AM Thomas, EL Maldovan, M Carter, WC
Title: Three dimensionally periodic block copolymer photonic crystals.
Source: Abstr. Pap. Am. Chem. Soc.

Author(s): Maldovan, M Urbas, AM Yufa, N Carter, WC Thomas, EL
Title: Photonic properties of bicontinuous cubic microphases
Source: Phys. Rev. B 65(16) pg 165123 2002
Abstract: Band structures of three dimensionally periodic bi- and tricontinuous cubic structures have been calculated using the plane-wave method for solving Maxwell's equations. In particular, we consider the single primitive, single diamond, single gyroid, double primitive, double gyroid, and double diamond level surface families as examples of such structures found in self-organizing systems. We also provide design guidelines for creating three-dimensional photonic crystals with a complete photonic band gap from block copolymer systems and other self-organizing systems.

Author(s): Chatain, D Wynblatt, P Hagege, S Siem, EJ Carter, WC
Title: Wetting in multiphase systems with complex geometries
Source: Interface Sci. 9 (3-4) 191--197 2001
Abstract: We address the shape and distribution of two-phase systems embedded within a third phase. To motivate this work, we begin by describing transmission electron microscopy observations of the configurations adopted by the solid and vapor phases of lead when these are confined together within a silicon cavity. We then perform analytical calculations of the stability of various possible configurations of two-phase systems confined in a cubic-shaped cavity. The most stable configurations are a function of the volume ratio of the two phases in the cavity, and of a parameter describing the wetting behavior in the three-phase system. The wealth of configurations obtained for embedded solid/fluid or condensed/fluid phases within a solid cavity is presented. Wetting anisotropy on the walls of the cavity, and the faceted or isotropic character of the interface between the two embedded phases, are shown to be physical parameters that determine the number of possible stable configurations.

Author(s): Vedula, VR Glass, SJ Saylor, DM Rohrer, GS Carter, WC Langer, SA Fuller, ER
Title: Residual-stress predictions in polycrystalline alumina
Source: J. Am. Ceram. Soc. 84(12) 2947--2954 2001
Abstract: Microstructure-level residual stresses occur in polycrystalline ceramics during processing, as a result of thermal expansion anisotropy and crystallographic misorientation across the grain boundaries. Depending on the grain size, the magnitude of these stresses can be sufficiently high to cause spontaneous microcracking when cooled from the processing temperature. They are also likely to affect where cracks initiate and propagate under macroscopic loading. The magnitudes of residual stresses in untextured and textured alumina samples have been predicted using experimentally determined grain orientations and object- oriented finite-element analysis. The crystallographic orientations have been obtained using electron-backscattered diffraction. The residual stresses are lower and the stress distributions are narrower in the textured samples, in comparison with those in the untextured samples. Crack initiation and propagation also have been simulated, using a Griffith-like fracture criterion. The grain-boundary- energy:surface-energy ratios required for computations are estimated using atomic-force-microscopy thermal-groove measurements.

Author(s): Cannillo, V Manfredini, T Corradi, A Carter, WC
Title: Numerical models of the effect of heterogeneity on the behavior of graded materials
Source: EURO CERAMICS VII, PT 1-3, 2163--2166 2002
Abstract: ABSTRACT

Author(s): Langer SA; Fuller E; Carter WC
Title: OOF: An image-based finite-element analysis of material microstructures
Source: COMPUTING IN SCIENCE & ENGINEERING 2001, Vol 3, Iss 3, pp 15-23
Abstract: Determining a material's macroscopic properties given its microscopic structure is of fundamental importance to materials science, The authors describe two public-domain programs that jointly predict macroscopic behavior. The programs start from an image of the microstructure and end with results from finite-element calculations.

Author(s): Zimmermann A; Carter WC; Fuller ER
Title: Damage evolution during microcracking of brittle solids
Source: ACTA MATERIALIA 2001, Vol 49, Iss 1, pp 127-137
Abstract: Microcracking due to thermal expansion and elastic anisotropy is examined via computer simulations with a microstructural-based finite element model. Random polycrystalline microstructures are generated via Monte Carlo Potts-model simulations. Microcrack formation and propagation due to thermal expansion anisotropy is investigated in these microstructures using a Griffith-type failure criterion in a microstructural-based finite element model called OOF. Effects of the grain size distribution on the accumulation of microcrack damage, as well as on the threshold for microcrack initiation, are analysed. Damage evolution is rationalised by statistical considerations, i.e. damage accumulation is correlated with the statistical distributions of microstructural parameters. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Author(s): Kitayama M; Narushima T; Carter WC; Cannon RM; Glaeser AM
Title: The Wulff shape of alumina: I. Modeling the kinetics of morphological evolution
Source: JOURNAL OF THE AMERICAN CERAMIC SOCIETY 2000, Vol 83, Iss 10, pp 2561-2571
Abstract: The rate at which fully facetted nonequilibrium shaped particles and pores approach their equilibrium (Wulff) shape via surface diffusion was modeled, and calculations relevant to alumina were performed to guide experimental studies. The modeling focuses on 2-D features, and considers initial particle/pore shape, size, surface energy anisotropy, and temperature (surface diffusivity) as variables. The chemical potential differences driving the shape change are expressed in terms of facet-to-facet differences in weighted mean curvature, Two approaches to modeling the surface flux are taken. One linearizes the difference in the mean chemical potential of adjacent facets, and assumes the flux is proportional to this difference. The other approach treats the surface chemical potential as a continuous function of position, and relates the displacement rate of the surface to the divergence of the surface flux. When consistent values for the relevant materials parameters are used, the predictions of these two modeling approaches agree to within a factor of 1.5, As expected, the most important parameters affecting the evolution times are the cross-sectional area (volume in 3-D) and the temperature through its effect on the surface diffusivity, Pores of micrometer size are predicted to reach near-equilibrium shapes in reasonable times at temperatures as low as 1600 degrees C. The detailed geometry of the initial nonequilibrium shape and the Wulff shape appear to have relatively minor effects on the times required to reach a near-equilibrium shape.

Author(s): Cannillo V; Carter WC
Title: Computation and simulation of reliability parameters and their variations in heterogeneous materials
Source: ACTA MATERIALIA 2000, Vol 48, Iss 13, pp 3593-3605
Abstract: Two numerical methods for reliability assessment for composite microstructures under arbitrary loading are presented: a Monte Carlo (MC) technique that assigns discrete failure probabilities from local stresses and empirical failure probabilities, and a parametric probability product (PP) method where the joint probability of survival is from a product over a set of heterogeneous finite elements. The two methods are verified for known cases and then applied to random composite microstructures that are not amenable to direct analysis. While the MC method is computationally more expensive and less accurate than the PP method, it produces a distribution of failure predictions. The distribution places confidence intervals on survival probabilities or estimates for the number of physical experiments required to predict Weibull parameters. A composite microstructure does not have a failure distribution of the same form as its homogeneous composite parts, but its form is readily understood. (C) 2000 Acra Metallurgica inc. Published by Elsevier Science Ltd. All rights reserved.

Author(s): Kobayashi R; Warren JA; Carter WC
Title: A continuum model of grain boundaries
Source: PHYSICA D 2000, Vol 140, Iss 1-2, pp 141-150
Abstract: A two-dimensional frame-invariant phase field model of grain boundaries is developed. One-dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed. With an appropriate choice of functional dependencies; the grain boundary energy takes the same analytic form as the microscopic (dislocation) model of Read and Shockley [W.T. Read, W. Shockley, Phys. Rev. 78 (1950) 275]. In addition, dynamic tone-dimensional) solutions are presented, showing rotation of a small grain between two pinned grains and the shrinkage and rotation of a circular grains embedded in a larger crystal. (C) 2000 Elsevier Science B.V. All rights reserved.

Author(s): Warren JA; Kobayashi R; Carter WC
Title: Modeling grain boundaries using a phase-field technique
Source: JOURNAL OF CRYSTAL GROWTH 2000, Vol 211, Iss 1-4, pp 18-20
Abstract: We propose a two-dimensional phase-field model of grain boundary dynamics. One-dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed. By comparison with microscopic models of dislocation walls. insights into the physical accuracy of this model can be obtained. Indeed, for a particular choice of functional dependencies in the model, the grain boundary energy takes the same analytic form as the microscopic (dislocation) model of Read and Shockley. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Author(s): Josell D; Carter WC; Bonevich JE
Title: Stability of multilayer structures: Capillary effects
Source: NANOSTRUCTURED MATERIALS 1999, Vol 12, Iss 1-4, pp 387-390
Abstract: The long term stability of multilayer materials composed of nonreactive, immiscible materials is related to the equilibrium shapes of the individual grains within the layers. These shapes are determined by the free energies and locations of the interfaces within the multilayer. We link the results of zero creep experiments with measured grain boundary groove angles to understand experimental observations of multilayer stability. (C) 1999 Acta Metallurgica Inc.

Author(s): Blendell JE; Carter WC; Handwerker CA
Title: Faceting and wetting transitions of anisotropic interfaces and grain boundaries
Source: JOURNAL OF THE AMERICAN CERAMIC SOCIETY 1999, Vol 82, Iss 7, pp 1889-1900
Abstract: A three-dimensional construction is presented that illustrates conditions under which anisotropic interfaces will be fully wetted, partially wetted, or not wetted by a second phase. Recent experimental observations on the equilibrated morphologies of solid or fluid "wetting" phases along anisotropic interfaces and grain boundaries reveal features that are predicted-and, in some cases, required-by the construction. Theory distinguishes between cases where surfaces are smoothly curved and where there are facets, edges, and corners. In the latter case, the conventional comparison of the surface energy of the original surface with the sum of the surface energy of the two surfaces of the wetting layer leads to erroneous predictions. The correct predictions are obtained by comparing the Wulff shape of the original surface with a carefully defined "sum" of Wulff shapes of the surfaces of the wetting layer, Where orientations that are wetted join with those that are not, an abrupt change of orientation usually is present. Faceting on two hierarchical levels can occur. Microscopic morphology changes along macroscopically curved surfaces follow well-defined rules that are predicted by the theory, The analogy between the thermodynamics of surface faceting and phase transformations allows the well-known concepts of phase equilibria to be used to understand the predicted structures.

Author(s): Hsueh CH; Fuller ER; Langer SA; Carter WC
Title: Analytical and numerical analyses for two-dimensional stress transfer
Abstract: Both analytical modeling and numerical simulations were performed to analyze the stress transfer in platelet-reinforced composites in a two-dimensional sense. In the two-dimensional model, an embedded elongated plate bonded to a matrix along its long edges was considered. The system was subjected to both tensile loading parallel to the plate's long edges and residual thermal stresses. The ends of the plate can be debonded from or bonded to the matrix during loading, and both cases were considered in the analysis. Good agreement was obtained between the present analytical and numerical solutions. However, better agreement between analytical and numerical models was obtained for the case of bonded ends than for debonded ends. (C) 1999 Elsevier Science S.A. All rights reserved.

Author(s): Hsueh CH; Haynes JA; Lance MJ; Becher PF; Ferber MK; Fuller ER; Langer SA; Carter WC; Cannon WR
Title: Effects of interface roughness on residual stresses in thermal barrier coatings
Source: JOURNAL OF THE AMERICAN CERAMIC SOCIETY 1999, Vol 82, Iss 4, pp 1073-1075
Abstract: Using a newly developed object-oriented finite-element analysis method, both an actual microstructure and model microstructures of a plasma-sprayed thermal barrier coating system were numerically simulated to analyze the fullfield residual stresses of this coating system, Residual stresses in the actual microstructure were influenced by both the irregular top-coat/bond-coat interface and cracks in the top coat. By treating the microcracked top coat as a more-compliant solid microstructure, the effects of the irregular interface on residual stresses were examined. These results then could be compared to results that have been obtained by analyzing a model microstructure with a sinusoidal interface, which has been considered by some earlier investigators.

Author(s): Warren JA; Carter WC; Kobayashi R
Title: A phase field model of the impingement of solidifying particles
Source: PHYSICA A 1998, Vol 261, Iss 1-2, pp 159-166
Abstract: We propose a model of the impingement of solidifying crystalline particles, the ensuing grain boundary formation, and grain coarsening. This model improves upon previous theoretical descriptions of this phenomenon, in that it has the proper behavior under rotations and is easy to implement numerically. Also, insight into the model is straightforward since the parameters are physically motivated, and anisotropy in both the liquid-solid and grain boundary energies can be introduced in a natural manner. A one dimensional analytic solution is presented. (C) 1998 Elsevier Science B.V. All rights reserved.

Author(s): Roosen AR; Carter WC
Title: Simulations of microstructural evolution: anisotropic growth and coarsening
Source: PHYSICA A 1998, Vol 261, Iss 1-2, pp 232-247
Abstract: Two-dimensional calculations of anisotropic growth and coarsening are illustrated. This model is intended to simulate the development of microstructure in materials like silicon nitride. The model is comprised of an ensemble of polygonal particles with anisotropic surface energies and growth mobilities. Particle growth is modeled by linear kinetics with a driving force proportional to a difference between local supersaturation and an equilibrium chemical potential which depends on particle geometry and surface tension. The competition for solute for particle growth is calculated via the diffusion equation, and conservation laws determine the strength of sources (or sinks) in the diffusion equation. Statistics of particles size distributions are obtained and regimes of kinetic behavior are related to transitions from non-equilibrium to near-equilibrium kinetics. Computed microstructures are qualitatively comparable to those observed experimentally. (C) 1998 Elsevier Science B.V. All rights reserved.

Author(s): Carter WC
Title: Computing macroscopic properties from microstructures of materials.

Author(s): Kobayashi R; Warren JA; Carter WC
Title: Mathematical models for solidification and grain boundary formation
Source: ACH-MODELS IN CHEMISTRY 1998, Vol 135, Iss 3, pp 287-295
Abstract: We propose a model which can calculate solidifying crystalline particles with different orientations simultaneously and their impingement. It is achieved by the vectorization of phase field by which the direction of solid-liquid interfaces can be measured in the crystalline frame. This makes the phase field model behave properly under rotation. In this article, one dimensional simulation of the model and two dimensional one of the simplified model will be presented.

Author(s): Kobayashi R; Warren JA; Carter WC
Title: Vector-valued phase field model for crystallization and grain boundary formation
Source: PHYSICA D 1998, Vol 119, Iss 3-4, pp 415-423
Abstract: We propose a new model for calculation of the crystalliztation and impingement of many particles with differing orientations. Based on earlier phase field models, a vector order parameter is introduced, and thus orientation of crystal/disordered interfaces can be determined relative to a crystalline frame. This model improves upon previous attempts to describe this phenomenon, as it requires far fewer equations of motion, and is energetically invariant under rotations. In this report a one-dimensional simulation of the model will be presented along with preliminary investigations of two-dimensional simulations. (C) 1998 Elsevier Science B.V.

Author(s): Roosen AR; McCormack RP; Carter WC
Title: Wulffman: A tool for the calculation and display of crystal shapes
Source: COMPUTATIONAL MATERIALS SCIENCE 1998, Vol 11, Iss 1, pp 16-26
Abstract: A computational tool called Wulffman has been developed to determine, quickly and easily, the shape with minimal surface energy (Wulff shape) for solids of arbitrary crystallographic symmetry. The Wulff shape is often the equilibrium or growth shape of the crystal and can be an important contributor in determining the physical properties of a material. Input quantities to the software are the point group symmetry of the shape and several crystal facet directions (along with their energies). Wulffman generates all symmetry-equivalent planes and then computes the Wulff shape. This shape is sent to a public domain 3D visualization environment (Geomview) where it can be viewed and manipulated. The software allows users to interactively see the effects of changes in surface energy. Users may also simulate partially-faceted shapes and 'cleavage' of the Wulff shape. Wulffman is public domain software available via the World-Wide Web. (C) 1998 Elsevier Science B.V.

Author(s): Bullard JW; Garboczi EJ; Carter WC
Title: Interplay of capillary and elastic driving forces during microstructural evolution: Applications of a digital image model
Source: JOURNAL OF APPLIED PHYSICS 1998, Vol 83, Iss 8, pp 4477-4486
Abstract: A recently developed model of curvature-driven, two-dimensional microstructure evolution is modified to include elastic strain energy at solid-fluid interfaces as an additional driving force for mass transport. Local phase distributions within a digital image of the microstructure are used to interpolate an isopotential contour that represents the equivalent sharp surface, along which local properties such as curvature are calculated. To determine the strain energy distribution, a finite element method is employed, using the pixel grid as the mesh. Interface-reaction-controlled mass transport is simulated using a finite difference approach along the interface. Calculations of the strain energy density and chemical potential distributions within simple systems show reasonable agreement with analytical results, and the predicted stability and evolution of such systems also agree with the predictions of other investigators. The model is also applied to a more complex system for which neither analytical nor other numerical methods can be readily used, and useful quantitative information is obtained on the energetics and structural changes. (C) 1998 American Institute of Physics.

Author(s): Saigal A; Fuller ER; Langer SA; Carter WC; Zimmerman MH; Faber KT
Title: Effect of interface properties on microcracking of iron titanate
Source: SCRIPTA MATERIALIA 1998, Vol 38, Iss 9, pp 1449-1453

Author(s): Carter WC; Taylor JE; Cahn JW
Title: Variational methods for microstructural-evolution theories
Abstract: Recent progress in variational methods helps to provide general principles for microstructural evolution. Especially when several processes are interacting, such general principles are useful to formulate dynamical equations and to specify rules for evolution processes. Variational methods provide new insight and apply even under conditions of nonlinearity, nondifferentiability, and extreme anisotropy. Central to them is the concept of gradient flow with respect to an inner product. This article shows, through examples, that both well-known kinetic equations and new triple junctions motions fit in this context.

Author(s): Alexander JID; Delafontaine S; Resnick A; Carter WC
Title: Stability of non-axisymmetric liquid bridges
Source: MICROGRAVITY SCIENCE AND TECHNOLOGY 1996, Vol 9, Iss 3, pp 193-200
Abstract: The stability of non-axisymmetric liquid bridges held between equidimensional coaxial disks of radius R and separated by a distance L is examined. The stability limits for lateral and axial acceleration are considered. The lateral acceleration stability limit is defined in terms of loss of stability by breaking. This limit is determined for both large and small values of the relative volume, V. The stability limit can be divided into two basic segments. One segment appears to be indistinguishable from part of the margin for the zero Bond number case. The other segment belongs to a one-parameter family of curves which, for a given Bond number and a fixed value of slenderness Lambda = L/2R, have a maximum and minimum stable relative volume. The maximum volume stability limit tends to infinity as Lambda --> 0. For any given lateral Bond number, the minimum volume stability limit is decreased and becomes indistinguishable from the zero Bond number limit when Lambda becomes sufficiently small.

Author(s): Argento C; Jagota A; Carter WC
Title: Surface formulation for molecular interactions of macroscopic bodies
Source: JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1997, Vol 45, Iss 7, pp 1161-1183
Abstract: The determination of forces resulting from molecular interactions between macroscopic bodies is important for the analysis of a variety of processes such as sintering, adhesion, and fracture. Body forces resulting from these interactions are usually concentrated near the surfaces of the bodies and are responsible for phenomena such as surface tension and surface energy. In the formulation presented here, the volume integrated intermolecular force between bodies is partitioned to obtain a distribution of effective surface tractions. This new surface formulation eliminates the geometrical restrictions associated with the commonly used Derjaguin approximation. The influence of each body on the surface of any other body is represented by a new quantity: the inter-surface stress tensor. Additional forces resulting from interactions within the body, the surface tension, have been considered for liquid-like materials. These self interactions are modeled by the classical Young-Laplace equation relating the effective traction on a surface to the energy of the surface and its curvature. The surface formulation offers considerable reduction in computational complexity compared to a formulation. based on body forces. The efficacy of the technique is demonstrated using several examples. (C) 1997 Elsevier Science Ltd.

Author(s): Choi JH; Kim DY; Hockey BJ; Wiederhorn SM; Handwerker CA; Blendell JE; Carter WC; Roosen AR
Title: Equilibrium shape of internal cavities in sapphire
Source: JOURNAL OF THE AMERICAN CERAMIC SOCIETY 1997, Vol 80, Iss 1, pp 62-68
Abstract: The equilibrium shape of internal canities in sapphire was determined through the study of submicrometer internal cavities in single crystals, Cavities formed from indentation cracks during annealing at 1600 degrees C, Equilibrium could be reached only for cavities that were smaller than approximate to 100 nm, Excessive times mere required to achieve equilibrium for cavities larger than approximate to 1 mu m. Five equilibrium facet planes were observed to bound the cavities: the basal (C) {0001}, rhombohedral (R) {<(1)over bar 012>}, prismatic (A) {<1(2)over bar 10>}, pyramidal (P) {<11(2)over bar 3>}, and structural rhombohedral (S) {<10(1)over bar 1>}. The surface energies for these planes relative to the surface energy of the basal plane mere gamma(R) = 1.05, gamma(A) = 1.12, gamma(P) = 1.06, gamma(S) = 1.07, These energies mere compared with the most recent theoretical calculations of the surface energy of sapphire, The comparison was not within experimental scatter for any of the surfaces, with the measured relative surface energies being lower than the calculated energies, Although the prismatic (M) {<10(1)over bar 0>} planes are predicted to be a low-energy surface, facets of this orientation mere not observed.

Author(s): Moon KW; BOettinger WJ; Williams ME; Josell D; Murray BT; Carter WC; Handwerker CA
Title: Dynamic aspects of wetting balance tests
Source: JOURNAL OF ELECTRONIC PACKAGING 1996, Vol 118, Iss 3, pp 174-183
Abstract: The relationships between the force measured during wetting balance tests and the observed changes of contact angle and meniscus shape are studied. Experiments using silicone oil at 25, 50, and 100 degrees C on glass plates as,cell as Pb-Sn eutectic solder on Au-coated glass plates are reported. Discrepancies between the measured force and height and those expected for a static meniscus are detailed. Equilibrium meniscus shapes are computed for wide plates using the elastica solution and for narrow plates using the public-domain software package, ''Surface Evolver'' For room temperature experiments with oil, the measured force discrepancy disappears when the meniscus rise is complete. Thus, the force discrepancy may be due to shear stress exerted on the sample by fluid rising up the sample. For static menisci with heated liquids, force and meniscus height discrepancies do not disappear when the meniscus rise is complete. These discrepancies can be explained by Marangoni flow due to temperature gradients in the fluid for the oil experiments but not for the solder experiments.

Author(s): Searcy AW; Bullard JW; Carter WC
Title: Possible explanations of transient neck formation between pairs of{100} faceted particles
Source: JOURNAL OF THE AMERICAN CERAMIC SOCIETY 1996, Vol 79, Iss 9, pp 2443-2451
Abstract: Rankin and Boatner have observed that {100} faceted MgO particles in contact along either corners or edges developed, on heating, necks that initially grew, but then shrank and broke, General thermodynamic models are provided that predict this transient neck formation for any cubic particles that share only a small fraction of an edge and for particles that share an edge that is less than 0.6 times as long as the orthogonal edges, A third model, which assumes that reaction of MgO particles with their carbon substrate removes MgO from the MgO-carbon interface at a constant rate, explains the observation that the neck shrinkage rate greatly exceeds the neck growth rate, Application of the theory to explaining the seeming prevalence of rounded surfaces in sintering powders is described.

Author(s): Cahn JW; Carter WC
Title: Crystal shapes and phase equilibria: A common mathematical basis
Abstract: Geometrical constructions, such as the tangent construction on the molar free energy for determining whether a particular composition of a solution is stable, are related to similar tangent constructions on the orientation-dependent interfacial energy for determining stable interface orientations and on the orientation dependence of the crystal growth rate which tests whether a particular orientation appears on a growing crystal. Subtle differences in the geometric constructions for the three fields arise from the choice of a metric (unit of measure). Using results from studies of extensive and convex functions, we demonstrate that there isa common mathematical structure for these three disparate topics and use this to find new uses for well-known graphical methods for all three topics. Thus, the use of chemical potentials for solution thermodynamics is very similar to known vector formulations for surface thermodynamics and the method of characteristics which tracks the interfaces of growing crystals; the Gibbs-Duhem equation is analogous to the Cahn-Hoffman equation. The Wulff construction for equilibrium crystal shapes can be modified to construct a ''phase shape'' from solution free energies that is a potentially useful method of numerical calculations of phase diagrams from known thermodynamical data.

Source: ACTA METALLURGICA ET MATERIALIA 1995, Vol 43, Iss 12, pp 4309-4323
Abstract: The evolution of two-dimensional shapes to equilibrium shapes is investigated for two kinetic mechanisms, surface diffusion and surface attachment limited kinetics. Qualitative differences are found that may be used in experiments for easy distinction among the two mechanisms, and find topological changes not expected for the corresponding isotropic problems. We take advantage of the mathematical developments for surface evolution and equilibration problems when surface energy anisotropy is ''crystalline'', so extreme that crystals are fully faceted. We confirm the prediction that with this anisotropy these problems are more easily solvable than for lesser anisotropies, and the techniques developed may even be useful for approximating isotropic problems.

Source: COMPUTATIONAL MATERIALS SCIENCE 1995, Vol 4, Iss 2, pp 103-116
Abstract: A procedure is described for computing the mean curvature along condensed phase interfaces in two or three dimensions, without knowledge of the spatial derivatives of the interface. For any point P on the interface, the method consists of computing the portion of volume enclosed by a small template sphere, centered on P, that lies on one side of the interface. That portion of the template volume is shown to be linear in the mean curvature of the surface, relative to the phase lying on the opposite side of the interface, to within terms that can usually be made negligible. An analogous procedure is described in two dimensions. Application of the procedure to compute the mean curvature along a digitized surface is demonstrated. A burning algorithm can be included to improve computational accuracy for interfaces having sharp curvature fluctuations. A minor extension of the method allows computation of the orientation of an interfacial element relative to a fixed reference frame.

Source: ACTA METALLURGICA ET MATERIALIA 1995, Vol 43, Iss 9, pp 3511-3524
Abstract: In a previous paper, a new model called the Binary Model was formulated to describe the behavior of textile composites with three-dimensional (3D) reinforcement. Here, detailed prescriptions are given for the constitutive laws of the computational elements in terms of the properties of the constituent materials and the geometry of the fiber reinforcement. The application studied is to woven composites with 3D interlock reinforcement. Predicted macroscopic elastic constants agree with experimental values without the use of adjustable parameters. The Binary Model also shows how the waviness of nominally straight tows in 3D weaves affects the statistics of local stresses. Through-thickness reinforcement also disorders local stresses, but its effect is found generally to be much less than that of tow waviness for current 3D woven composites. For predicting the onset of failure, it is inferred that treating the stochastic effects of tow irregularity is much more important than modeling the influence of local tow configurations in great detail.

Source: ACTA METALLURGICA ET MATERIALIA 1994, Vol 42, Iss 10, pp 3463-3479
Abstract: This paper presents a finite element model of polymer composites with three-dimensional (3D) reinforcement. The model performs Monte Carlo simulations of failure under monotonic and fatigue loading. The formulation of the model is guided by extensive prior experimental observations of 3D woven composites. Special emphasis is placed on realistic representation of the pattern of reinforcing tows, random irregularity in tow Positioning, randomness of the strengths of constituent elements, and the mechanics of stress redistribution around sites of local failure. The constitutive properties of model elements (or their distributions) are based on micromechanical models of observed failure events. Material properties that are appropriately analyzed by the model are contrasted with those amenable to much simpler models. Some illustrative model simulations are presented. Prescriptions for the calibration of the model for design and reliability applications and details of its performance in simulating the elastic and damaged regimes of 3D woven composites will appear in subsequent papers.

Source: ACTA METALLURGICA ET MATERIALIA 1993, Vol 41, Iss 5, pp 1633-1642
Abstract: In diffusion-induced recrystallization (DIR), diffusion of a misfitting solute produces coherency strains in a solid and can lead to nucleation of new grains. The local interface velocity of the newly nucleated grains depends only on the magnitude of the reduction in the elastic energy density of the coherently stressed solid ahead of the migrating grain boundary, which in turn depends only on the local interface normal of the shrinking grain. Real-space calculations of the orientation-dependent elastic energy density are outlined in general and specific results are given for cubic systems. The method of characteristics described recently by Cahn, Taylor and Handwerker is employed to obtain predictions of the evolution in grain shape with time and the range of possible limiting growth shapes in terms of the edges and comers which develop on any growing grain. When the growing grain is free of elastic strains, the possible morphologies depend on only two parameters: the elastic anisotropy alpha(=2(s11 - s12)/s44), and normalized linear compressibility beta(=(s11 + 2s12)/s44). When the elastic anisotropy alpha > 1, the morphology tends to be cuboidal, but the exact shape is found to depend on the value of the linear compressibility. For alpha < 1, the morphology tends to be octahedral.

Source: SCRIPTA METALLURGICA ET MATERIALIA 1991, Vol 25, Iss 3, pp 579-584

Source: ACTA METALLURGICA ET MATERIALIA 1990, Vol 38, Iss 11, pp 2327-2336

Source: PHYSICAL REVIEW B-CONDENSED MATTER 1990, Vol 41, Iss 13, pp 8698-8701

Source: JOURNAL OF THE AMERICAN CERAMIC SOCIETY 1989, Vol 72, Iss 8, pp 1550-1555

Author(s): CARTER WC
Source: ACTA METALLURGICA 1988, Vol 36, Iss 8, pp 2283-2292


Source: AMERICAN CERAMIC SOCIETY BULLETIN 1984, Vol 63, Iss 8, pp 993-993

Source: JOURNAL OF THE AMERICAN CERAMIC SOCIETY 1984, Vol 67, Iss 6, pp C124-C127