A new model of three-dimensional grain growth: theory and computer simulation of topology-dependency of individual grain growth rate

A relationship between the growth kinetics and the topology of individual grains in three dimensions, as an equivalent to Von Neumann’s law in two dimensions, was derived theoretically. The relationship depicts that the changing rate of the surface area of an individual three-dimensional grain, other than that of grain volume, is independent of grain size and proportional to (F−Fc), where F is the number of grain faces, and Fc a constant. It should also be pointed out that the new theory is approximate in nature — perhaps an exact three-dimensional law does not exist at all. A modified Monte Carlo algorithm was newly developed by the authors to simulate the three-dimensional normal grain growth process including the quasi-steady stage. The simulated process obeys the power law kinetics with its growth exponent approaching 0.5, and agrees quantitatively well with the experimental observations of topological evolution during the three-dimensional grain growth process in various materials found in the literature. The topology dependency of individual grain growth rate in simulation agrees very well with that predicted by the above-mentioned new three-dimensional theory.