Evaluation of growth rate equations of three-dimensional grains using large-scale Monte Carlo simulation

Three-dimensional normal grain growth process was simulated in scale of 300×300×300 on the basis of Monte Carlo–Potts model to study topology-dependent growth rate equations for individual grains. The results show that those growth rate equations solely dependent on the grain face number (f) are not applicable for grains with face number f<8; however, Glazier’s equation [J. A. Glazier, Phys. Rev. Lett. 70, 2170 (1993)], MacPherson–Srolovitz’s topology-dependent equation [R. D. MacPherson and D. J. Srolovitz, Nature (London) 446, 1053 (2007)], and Yu–Liu’s equation [G. Q. Liu and H. B. Yu, Chin. Sci. Bull. 41, 2000 (1996)] describe the simulation data well for grains with face number f>8.