Modeling of grain growth in two dimensions

Abstract

A detailed consideration of the time-dependent bivariate distribution P R ,n ;t in both the grain size R, and the number of sides n of the grain in two dimensions is given. Using this formalism and the von Neumann law, an explicit form of the Fokker–Planck equation for the marginal distribution F R ,t is provided. Based on available experimental evidence an explicit form of bivariate distribution is also constructed and its consequences are examined. Bivariate analysis shows the crucial importance of the correlation between the grain size and its number of sides and provides a more fundamental underpinning to modeling of Grain Growth.