Monte Carlo Potts Model Simulation and Statistical Theory of 3D Grain Growth
An improved Monte Carlo (MC) Potts model algorithm has been implemented allowing an extensive simulation of three-dimensional (3D) normal grain growth. It is shown that the simulated microstructure reaches a quasi-stationary state, where the growth of grains can be described by an average self-similar volumetric rate of change, which depends only on the relative grain size. Based on a quadratic approximation of the volumetric rate of change a generalized analytic mean-field theory yields a scaled grain size distribution function that is in excellent agreement with the simulation results.
S.-J.L. Kang, M.Y. Huh, N.M. Hwang, H. Homma, K. Ushioda and Y. Ikuhara
D. Zöllner and P. Streitenberger, "Monte Carlo Potts Model Simulation and Statistical Theory of 3D Grain Growth", Materials Science Forum, Vols. 558-559, pp. 1219-1224, 2007