Elizabeth A. Holm

On misorientation distribution evolution during anisotropic grain growth

In order to study the development of texture and boundary character during annealing, three-dimensional grain crystallography and crystallographically mediated grain boundary properties were incoporated into a finite temperature Monte Carlo model for grain growth. Randomly textured microstructures evolve normally, with growth exponent n=0.96. While texture remains random, the steady-state boundary misorientation distribution favors low-angle boundaries. To first order, low-angle boundaries increase by lengthening, not by proliferating. In contrast, microstructures with a strong single-component texture develop four-grain junctions and highly curved grain boundaries, which alter evolution. The boundary misorientation distribution narrows and shifts to low angles, and no steady state is observed. The accompanying decrease in mean boundary mobility causes growth to slow, resulting in a growth exponent n=0.62. The dependence of the growth exponent on average boundary mobility may explain experimental observations of exponents less than unity.

On abnormal subgrain growth and the origin of recrystallization nuclei

Abnormal subgrain growth has been proposed as the nucleation mechanism for recrystallization. To test this hypothesis, Monte Carlo Potts model simulations of subgrain growth were performed on single-phase, strain-free subgrain structures with experimentally validated microstructure, texture, boundary character, and boundary properties. Results indicate that abnormal growth events emerge spontaneously during evolution in such systems, and abnormal subgrains behave as predicted by mean field theory. An analysis predicts the frequency of abnormal growth events as a function of local neighborhood and the boundary misorientation distribution. A recrystallization model is derived based on the abnormal subgrain growth analysis. Using data for aluminum subgrain structures, the model predicts reasonable recrystallized grain sizes as a function of von Mises strain. The extension of these results to abnormal grain growth is discussed.

How Grain Growth Stops: A Mechanism for Grain-Growth Stagnation in Pure Materials

Taking the Rough with the Smooth Even with extensive annealing at high temperatures, most polycrystalline materials will not become a perfect single crystal, which would represent the thermodynamically preferred state. The stability of the polycrystalline state has been attributed to the presence of impurities that accumulate at the grain boundaries, but even very pure materials show grain growth stagnation. Using simulations, Holm and Foiles (p. 1138) show that grain boundaries can be classified as “rough” and “smooth.” Rough boundaries move continuously with well-defined activation energies, while the smooth boundaries have low mobility and move in a jerky, stepwise manner. With heating, a boundary can change from smooth to rough, but the transition temperature can vary by hundreds of degrees from one grain boundary to the next. These smooth, low-mobility boundaries thus pin the polycrystalline structure, even in the absence of impurities. Smooth, low-mobility grain boundaries limit crystallite growth when a pure metal is heated. The thermodynamic equilibrium state of crystalline materials is a single crystal; however, polycrystalline grain growth almost always stops before this state is reached. Although typically attributed to solute drag, grain-growth stagnation occurs, even in high-purity materials. Recent studies indicate that grain boundaries undergo thermal roughening associated with an abrupt mobility change, so that at typical annealing temperatures, polycrystals will contain both smooth (slow) and rough (fast) boundaries. Mesoscale grain-growth models, validated by large-scale polycrystalline molecular dynamics simulations, show that even small fractions of smooth, slow boundaries can stop grain growth. We conclude that grain-boundary roughening provides an alternate stagnation mechanism that applies even to high-purity materials.

On boundary misorientation distribution functions and how to incorporate them into three-dimensional models of microstructural evolution

The fundamental difficulties of incorporating experimentally obtained boundary misorientation distributions (BMDs) into three-dimensional microstructural models are discussed. An algorithm is described which overcomes these difficulties. The boundary misorientations are treated as a statistical ensemble which is evolved toward the desired BMD using a Monte Carlo method. The application of this algorithm to a number of complex arbitrary BMDs shows that the approach is effective for both conserved and non-conserved textures. The algorithm is successfully used to create the BMDs observed in deformation microstructures containing both incidental dislocation boundaries (IDBs) and geometrically necessary boundaries (GNBs). The application of an algorithm to grain boundary engineering is discussed.

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.

Nonuniform and directional grain growth caused by grain boundary mobility variations

Most derivations of grain growth relations require an assumption of constant grain boundary mobility; in fact, a number of these relations cannot be derived if boundary mobility varies in space or time. Computer simulations of grain growth in which boundary mobility varies in time and/or space have been performed. When mobility varies continuously with position, grains grow with locally normal kinetics. In contrast, when the mobility profile in discontinuous, deviations from normal growth may appear near the mobility discontinuity. When the boundary mobility varies in time as well as in space, different growth morphologies can occur. Under a one-dimensional Gaussian mobility profile moving across the sample with some velocity, three growth regimes can occur. At low and high profile velocities, grain growth is equiaxed and normal. At intermediate velocities, a fully columnar grain structure forms; the width of the columnar grains evolves with normal growth kinetics.

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.

Evolving cellular automata to grow microstructures

The properties of engineering structures such as cars, cell phones or bridges rely on materials and on the properties of these materials. The study of these properties, which are determined by the internal architecture of the material or microstructure, has significant importance for material scientists. One of the things needed for this study is a tool that can create microstructural patterns. In this paper we explore the use of a genetic algorithm to evolve the rules of an effector automata to recreate these microstructural patterns.

Scaling of dislocation cell structures: diffusion in orientation space

This paper examines the idea that the evolution of self-organizing dislocation cells is dominated by random fluctuations in cell orientation. The development of the dislocation cell misorientation distributions during deformation is treated on the basis that noise causes the cell orientations to random walk in orientation space. We solve the orientation equivalent of Ficks second law to get a time-dependent solution for the orientation distributions, misorientation distributions and the strain dependence of the average misorientation angle. In the low-angle limit, average misorientation is proportional to the square root of the strain, and the misorientation distributions scale with the average misorientation angle, in agreement with the experiment. The analysis predicts an infinite number of possible scaling states and not a universal curve, as seen in practice. This discrepancy is discussed.

Heterogeneous diffusion effects in polycrystalline microstructures

Diffusion in polycrystalline microstructures is influenced by two factors that are not considered in a simple continuum material description. These are kinetic effects, where the diffusivities of grain boundaries differ from those of the grains, and free-energy effects, where the driving force for diffusion is dependent on a free energy function that includes the phase of the diffusion medium as well as its composition. Simulation studies of kinetic diffusion effects in two-dimensional polycrystalline microstructures obtained from the Potts model have shown that the compositional gradients resulting from these effects are transitory in nature, and that average diffusivities are dependent on microstructural features such grain size, diffusion bottlenecks in grain boundary paths, and model lattice artifacts. Similar studies of free-energy effects using the phase-field model show that metastable grain boundary segregation of components occurs, and that the rate and nature of grain growth can be influenced by an imposed composition gradient. Collectively, these studies show that the two simulation techniques, finite-difference solutions of fast grain boundary diffusion in the polycrystalline microstructures obtained from the Potts model and phase-field model solutions of diffusion in evolved and evolving microstructures with spatially dependent chemical potentials, are complementary in studying diffusional effects in polycrystalline microstructures.