Monte Carlo Simulation of Grain Growth Taking into Account the Influence of Temperature

Abstract

The influence of temperature on the grain growth behavior in Monte Carlo simulation has been studied based on the original Potts model proposed by Anderson et al. Grain growth kinetics in Monte Carlo simulation are represented in the non-dimensional form by non-dimensional grain radius and the ratio of Monte Carlo step to total orientation number Q. It has been revealed that the influence of temperature in Monte Carlo simulation could be mainly introduced through the correspondent relationship between Monte Carlo Step and real time, rather than through the transition probability of re-orientation attempts. A new equation for the relationship between Monte Carlo Step and real time has been derived based on the idea of the law of similitude in grain growth. The grain growth during cooling for the actual time–length system has been estimated using newly derived equation and the estimated grain size as a function of temperature showed quantitatively good agreement with the observed results reported in the literature when lattice constant in the calculation system as a characteristic length for conversion was set to be 0.015 cm which was a half of the initial grain diameter in the real system.