Veena Tikare

Comparison of phase-field and Potts models for coarsening processes

We have compared the phase-field model to the Potts model for two coarsening processes, grain growth and Ostwald ripening, both in two-dimensions. The Potts model is a discrete, statistical mechanical numerical simulation technique. In contrast, the phase-field model is a continuum, thermodynamic numerical simulation technique. The similarities and differences in microstructures, kinetics, and grain size distributions obtained for grain growth and Ostwald ripening by the phase-field model and by the Potts model were investigated. Both models gave very similar kinetic, topological and grain size distribution results for grain growth and Ostwald ripening in spite of their different approaches. In this paper, we review each model and its application to coarsening processes, present the results of grain growth and Ostwald ripening and finally, discuss how the physics of grain growth and Ostwald ripening is incorporated into these two different models.

Numerical simulation of grain growth in liquid phase sintered materials—I. Model

The simulation technique based on the Potts model, originally applied to microstructural coarsening by Srolovitz et al. [Scripta metall., 1983, 17, 241] has been extended to study grain growth by Ostwald ripening in liquid phase sintered materials. The model, which makes no assumptions about solid fractions, grain shapes or diffusion fields around grains, has been developed and characterized in this investigation. A two-dimensional, square lattice is used to digitize the microstructure. The representation of the two phases, solid grains in a liquid matrix, were achieved by populating the lattice with a two-component, canonical ensemble, where the two components were designated as A and B. Grain growth was driven by the reduction in interfacial free energy, which was defined by the bond energies between neighboring sites. The solution-reprecipitation mechanism was simulated by allowing neighboring sites to exchange places via the classical Metropolis algorithm.

Modeling and Simulation of Nuclear Fuel Materials

We review the state of modeling and simulation of nuclear fuels with emphasis on the most widely used nuclear fuel, UO2. The hierarchical scheme presented represents a science-based approach to modeling nuclear fuels by progressively passing information in several stages from electronic structure calculations to continuum level simulations. Such an approach is essential to overcome the challenges posed by radioactive materials handling, experimental limitations in modeling extreme conditions and accident scenarios, and the small time and distance scales of fundamental processes. When used in conjunction with experimental validation, this multiscale modeling scheme can provide valuable guidance to development of fuel for advanced reactors to meet rising global energy demand.

Numerical simulation of grain growth in liquid phase sintered materials—II. Study of isotropic grain growth

Abstract The Potts model was used to study grain growth in liquid phase sintered materials. Its application to the study of isotropic grain growth by Ostwald ripening in a fully wetting system will be presented. The interpretation of the simulation results will be described and discussed. It was found that the set of simulation parameters used gave diffusion-controlled grain growth for solid fraction ranging from 0.30 to 0.90. The grain size distribution varied with solid fraction, becoming broader and more peaked with increasing solid fraction. The skewness was near zero at solid fraction of 0.41 and shifted to larger grain sizes with increasing solid fraction. This shift in the skewness of grain size distribution is not predicted by previous analytical or numerical models; however, it is consistent with experimental data collected by Fang and Patterson [ Acta metall. , 1993, 41, 2017] in the WNiFe system

Modelling of anisotropic sintering in crystalline ceramics

We present a model that describes anisotropic shrinkage during sintering in a powder compact of aligned, elongated particles by deriving the anisotropic sintering stress and the anisotropic generalized viscosity as a function of material and geometric parameters. The powder compact consists of elongated particles, which are perfectly aligned and simply packed with elliptical pores at all the quadra-junctions between the particles. The model considers mass transport by grain boundary diffusion and surface diffusion. Shrinkage rates are calculated for a variety of geometries and are compared to kinetic Monte Carlo simulations.

Monte Carlo simulation of ferroelectric domain structure and applied field response in two dimensions

A two-dimensional, lattice-Monte Carlo approach, based upon the energy minimization of an ensemble of electric dipoles, was developed to simulate ferroelectric domain behavior. The model utilizes a Hamiltonian for the total energy based upon electrostatic terms involving dipole–dipole interactions, local polarization gradients, and the influence of applied electric fields. The impact of boundary conditions on the domain configurations obtained was also examined. In general, the model exhibits domain structure characteristics consistent with those observed in a tetragonally distorted ferroelectric. The model was also extended to enable the simulation of ferroelectric hysteresis behavior. Simulated hysteresis loops were found to be very similar in appearance to those observed experimentally in actual materials. This qualitative agreement between the simulated hysteresis loop characteristics and real ferroelectric behavior was also confirmed in simulations run over a range of simulation temperatures and appl...

Crossing the Mesoscale No-Man's Land via Parallel Kinetic Monte Carlo

The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution.

Crack healing of alumina with a residual glassy phase: strength, fracture toughness and fatigue

Abstract The crack-healing behavior of identation cracks and large precracks in 96 wt.% alumina was studied as a function of annealing temperature in air and inert environments. Crack healing occurred at annealing temperatures of 800 °C and above in both air and inert (argon) environments, indicating its cause as transport of existing material to the crack plane, and resulted in increased strength and fracture toughness. However, the resulting phase assemblage in the crack plane was susceptible to fatigue at room temperature in distilled water, as evidenced by a somewhat low fatigue parameter of N = 68. Furthermore, polished-and-annealed samples were more susceptible to fatigue at room temperature in air than as-polished samples.

The sintering behavior of close-packed spheres

The sintering behavior of close-packed spheres is investigated using a numerical model. The investigated systems are the body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed spheres (hcp). The sintering behavior is found to be ideal, with no grain growth until full density is reached for all systems. During sintering, the grains change shape from spherical to tetrakaidecahedron, similar to the geometry analyzed by Coble [R.L. Coble, J. Appl. Phys. 32 (1961) 787].

Microstructure dependence of diffusional transport

A simple and eAective numerical method is proposed for simulating the temporal diAusive mass transport process through a microstructure with arbitrary complexity described by a phase-field approach. The mass diAusion through a given microstructure is modeled by a diAusion equation with a variable diAusion coeAcient, which is solved by an eAcient and accurate semi-implicit spectral method. It is shown that it is possible to extract the eAective diAusion coeAcient for any given microstructure from the temporal concentration profiles. The method is used to simulate the grain boundary diAusion in a single-phase polycrystalline grain structure and the heterogeneous diAusion in a twophase microstructure with diAerent diAusion coeAcient in each phase. Results are compared with existing analytical theories and computer simulations. ” 2001 Elsevier Science B.V. All rights reserved.