Evaluation of topology-dependent growth rate equations of three-dimensional grains using realistic microstructure simulations

Understanding the laws of grain (or bubble, cell) growth in two and three dimensions (2D and 3D) is one of the classic and important problems in the fields of mathematics, Physics, materials sciences and biology. Studies related to the evaluation of topology-dependent grain growth rate models are very limited so far. Those who reported about the evaluation of the growth rate models used synthetic structure grain data generated from Monte Carlo–Potts model simulations. In this paper, topology-dependent growth rate models for 3D grains are evaluated by using realistic microstructure grain growth simulation data. The results show that, except Wang –Liu's equation [H Wang and G Q Liu EPL 96, 38003 (2011)], all the other topology-dependent growth rate models have their limitations to describe the average growth rate of 3D grains, those models are not applicable for grains having number of faces less than 7; however, Yu–Liu's equation [G Q Liu and H B Yu Chin. Sci. Bull. 41, 2000 (1996)], Glazier's equation [J A Glazier Phys. Rev. Lett. 70, 2170 (1993)] and MacPherson–Srolovitz's topology-dependent equation [R D Macpherson and D J Srolovitz Nature (London) 446, 1053 (2007)] fit well to the realistic simulation data for grains having number of faces greater than 7. The Wang –Liu's equation [H Wang and G Q Liu EPL 96, 38003 (2011)] is applicable for all grains in the system and hence it is the best choice to study the average growth rate of individual grains in microstructures. The results also show that the Monte Carlo–Potts model simulations have very close correspondence with the evolution of real structures. (paper)