3D MC simulation of grain growth kinetics and the Zener limit in polycrystals

Large scale Potts model Monte Carlo simulation was carried on 3-dimensional square lattices of 100 3 and 200 3 sizes using the Metropolis algorithm to study grain growth behavior. Simulations were carried out to investigate both growth kinetics as well as the Zener limit in two-phase polycrystals inhibited in growth by second phase particles of single-voxel size. Initially the matrices were run to 10,000 Monte Carlo steps (MCS) to check the growth kinetics in both single phase and two-phase poly-crystals. Grain growth exponent values obtained as a result have shown to be highest (similar to 0.4) for mono-phase materials while the value decreases with addition of second phase particles. Subsequently the matrices were run to stagnation in the presence of second phase particles of volume fractions ranging from 0.001 to 0.1. Results obtained have shown a cube root dependence of the limiting grain size over the particle volume fraction thus reinforcing earlier 3D simulation efforts. It was observed that there was not much difference in the values of either growth kinetics or the Zener limit between 100(3) and 200(3) sized matrices, although the results improved mildly with size.