Normal Grain Growth: Monte Carlo Potts Model Simulation and Mean-Field Theory

Abstract

Grain growth in polycrystals is modelled using an improved Monte Carlo Potts model algorithm. By extensive simulation of three-dimensional normal grain growth it is shown that the simulated microstructure reaches a quasi-stationary self-similar coarsening state, where especially the growth of grains can be described by an average self-similar growth law, which depends only on the number of faces described by a square-root law. Together with topological considerations a non-linear effective growth law results. A generalized analytic mean-field theory based on the growth law yields a scaled grain size distribution function that is in excellent agreement with the simulation results. Additionally, a comparison of simulation and theory with experimental results is performed.