Three-dimensional grain growth modeling with a Monte Carlo algorithm

Power-law kinetics was obtained previously from grain growth simulations in isotropic, single-phase materials using three-dimensional (3D) Monte Carlo (MC) Potts models but the theoretically expected grain growth exponent was obtained only in the late simulation stages. This paper addresses the grain growth simulated by a modified 3D MC algorithm using 200×200×200 cubic lattices. The grain growth kinetics is analyzed both for the 3D domain and for two-dimensional (2D) cross-sections thereof. The 3D grain growth exponent obtained is found to be in agreement with theoretical predictions for the entire time domain. While the parabolic grain growth kinetics is also obtained for the cross-sections, the grain growth rates calculated for these cross-sections are smaller than that obtained for the 3D domain. A time-invariant grain size distribution is obtained both for the 3D domain and the cross-sections. The grain shape distribution obtained for the cross-sections is time-invariant but the distribution of grain facet numbers changes with time and appears to evolve toward a steady state in the later simulation stages.