Normal Grain Growth in Three Dimensions: Monte Carlo Potts Model Simulation and Mean-Field Theory
A modified Monte Carlo Potts model algorithm for single-phase normal grain growth in three dimensions in presented, which enables an extensive statistical analysis of the growth kinetics and topological properties of the microstructure within the quasi-stationary self-similar coarsening regime. From the mean-field theory an analytical grain size distribution function is derived, which is based on a quadratic approximation of the average self-similar volumetric rate of change as a function of the relative grain size as it has been determined from the simulation. The analytical size distribution function is found to be in excellent agreement with the simulation results.
P. B. Prangnell and P. S. Bate
D. Zöllner and P. Streitenberger, "Normal Grain Growth in Three Dimensions: Monte Carlo Potts Model Simulation and Mean-Field Theory", Materials Science Forum, Vol. 550, pp. 589-594, 2007