The Monte Carlo simulation of microstructural evolution in metals

The Monte Carlo simulation method is now widely applied to materials science and engineering. This review surveys recent developments in mesoscale and atomistic Monte Carlo simulation based on statistical mechanics. Fundamentals of simulation techniques and dynamical and topological behaviors of microstructural evolutions are described. The simulation of grain growth based on Potts' model is described as an mesoscale simulation example. Kinetics of interface migration can be traced by flipping of spin variables. Scaling behaviors of domain structure are given by cluster analysis method. As an atomistic scale simulation example, the ordering of f.c.c. to L1₂ structure in Ni base alloy is introduced. Ordering kinetics is controlled by a direct exchange of neighbouring single atoms. The ordering kinetics, the temporal evolution of atomic arrangement, the site occupancy of alloying elements are predicted by the model.