Discussion on the Hillert Theory of Normal Grain Growth with a Modified Monte Carlo Simulation

On the basis of analyzing some limitations in the existing algorithm, a modified Monte Carlo method was proposed to simulate two-dimensional normal grain growth. With the modified method. the simulated time exponent of grain growth attained n=0.49±0.01, which is very close to the theoretical value of the steady grain growth n=0.5, indicating the possibility to investigate the total process of normal grain growth. The relation between the Hillert and the von Neumann equations were studied and identified, the Hillert's basic equation has been found to hold during the normal grain growth. The grain size distribution was found to van continuously and slowly with the simulated time in the total growth process, the lognormal and the Hillert functions may be two types of the expression forms during its transition, and the later seemingly corresponds at the distribution of the steady stage were n≈0.50.