Verification of topological relationship in 2-D grain growth process by simulation

Behaviors of the quasi-steady state grain size distribution and the corresponding topological relationship were investigated using the Potts Monte Carlo method to simulate the normal grain growth process. The observed quasi-steady state grain size distribution can be well fit by the Weibull function rather than the Hillert distribution. It is also found that the grain size and average number of grain sides are not linearly related. The reason that the quasi-steady state grain size distribution deviates from the Hillert distribution may contribute to the nonlinearity of the relation of the average number of grain sides with the grain size. The results also exhibit the reasonability of the relationship deduced by Mullins between the grain size distribution and the average number of grain sides.