Stochastic Modeling of Grain Growth and Coarsening

Abstract

AbstractRecent developments in the modeling of grain growth and coarsening are briefly considered. Common characteristics of both these phenomena are briefly pointed out. A formulation based on stochastic consideration is proposed. This formulation assumes that the rate of growth of an individual grain or a precipitate is not entirely determined by its size but has a random component to it. This leads to a Fokker-Planck Equation for the size distribution. It can then be shown that there is indeed a unique state (the self-similar state) which is in general reached from an arbitrary initial state. The case of two dimensional grain growth is treated in detail as an example. Grain size distribution is obtained from these considerations, which is in good agreement with experiments.