Large-scale limit of Monte-Carlo simulations of grain growth

Abstract

This chapter presents a paper that studies the large-scale limit of 2D Monte Carlo simulations of grain growth with isotropic grain boundary energy and mobility in low-temperature regime and shows that it converges to a deterministic simulation model defined by the Mullins equation of curvature-driven growth and the Herring balance condition. There has been considerable interest in the modeling of grain growth in polycrystalline materials by various computer simulation techniques. This paper focuses on two such models—a deterministic curvature driven model and the Monte Carlo model. In 2D, the Monte Carlo model in the low-temperature regime approaches the deterministic model as the relative grain size increases. In a deterministic model, the grain boundary is moved according to the Mullins equation. There are apparent algorithmic differences between the two models. A comparison of the statistical properties that the two models produce—such as the mean grain size and the relative grain size distribution—suggests that they are related. This paper explores this relation in detail.