von Neumann–Mullins equation in the Potts model of two-dimensional grain growth

In this study, the validity of von Neumann–Mullins equation was examined for the Potts model of two-dimensional grain growth. Simple geometric consideration of the lattice in the model confirmed that the Potts model used in this study naturally satisfies von Neumann–Mullins equation, and provided the exact value of the grain boundary mobility. Monte Carlo simulation of a single grain growth demonstrated that the grain area growth rate is statistically constant for a given vertex number. The simulated grain boundary mobility agreed with its analytical prediction. The kinetics of individual grains in a polycrystalline structure was also investigated. The area change rate of the individual grains was not uniform over a short time interval, and then yielded large errors of the grain boundary mobility. Some of estimation techniques were tried to reduce the errors. Regardless of the methods we exploited, the average value of the simulated mobilities was a good approximation of the results from analytical prediction or single grain growth simulations.