Growth rate distributions for regular two-dimensional grains with Read–Shockley grain boundary energy

Abstract

Understanding the effects of an anisotropic grain boundary energy model is difficult analytically, so simulations provide a valuable insight into the dynamics and characteristics of grain structure evolution. A brute-force analysis of the common Read–Shockley model in two dimensions for grains of the topological class of n-sided grains with 3 ⩽ n ⩽ 8 is performed. In this approach, we rotate all cubic two-dimensional crystal lattices of n-sided grain neighbors stepwise with high resolution in two dimensions, and compute the growth rates of each configuration to obtain detailed growth rate distributions. To perform the computationally intense task of computing the growth rates for billions of configurations, a vertex type model and a supercomputer are utilized. Modern computation facilities deliver the required computation power to carry out such studies in a reasonable amount of time. The vertex model is validated by comparison with 700 phase-field simulations. Our findings support the isotropic behavior of grain structures with randomly oriented lattices and Read–Shockley grain boundary energy, where the average values of the growth rate distributions follow the isotropic Neumann–Mullins relation. Further, all computed growth rate distributions are not symmetric and adapt a normal distribution for n → 8. Abnormal grain growth does not occur for the Read–Shockley model with neighbors in the range 3 ⩽ n ⩽ 8. The brute-force method of scanning the parameter space in high resolution reaches its limit fast, but contributes a new perspective.