Modeling of grain growth characteristics in three-dimensional domains and two-dimensional cross sections

In the modeling of grain growth of isotropic, single-phase materials using three-dimensional (3-D) Monte Carlo (MC) Potts algorithm, the theoretically expected grain growth exponent was obtained only in the late simulation stages. This article addresses the grain growth simulated by a modified MC Potts model using simple cubic lattices. The grain growth kinetics was analyzed both for the 3-D domain and for two-dimensional (2-D) cross sections. Regression analyses of the grain size data averaged over time, multiple simulations runs, and three cross sections showed that both the Louat function and the log-normal function can be fitted to the data. It was clearly observed that the log-normal function allows a better fit to the 3-D simulation data, while the Louat function is more suited to the cross-sectional data. Furthermore, parabolic grain growth kinetics was obtained both for the 3-D domain and for the cross sections, but the grain growth rates calculated for these cross sections were smaller than that obtained for the 3-D domain.