Cellular automata simulation of grain growth in three dimensions based on the lowest-energy principle

The microstructure and morphology evolution of grain growth were studied by 3D simulation using the cellular automata (CA) model based on the lowest-energy principle. In the present CA model, the transition of cells during the grain growth has a typical physical meaning due to the application of the lowest-energy principle. The results show that the kinetics of grain growth follows Burke equation with the growth exponent as 2. The average number of grain faces is 13.6 and the highest frequency of grain faces is 10 faces. The grain size distribution follows Weibull function. The relationship between the number of faces of a grain and the average number of faces of its adjacent grains follows the Aboav–Weaire law. There is a correlation between the topologies of the simulated 2D and 3D grain growth. The average number of sides per face for all grains is 5.65 and the average number of sides per face is about equal to 6 when the grain aces is larger than 35.