采用Potts模型Monte Carlo方法对3种现存的三维个体晶粒长大速率拓扑依赖性 方程进行了仿真验证. 结果表明, Rivier速率方程认为晶粒 体积变化率dVf/dt与晶粒面数f成线性关系, 与仿真 结果明显不符, 不适用于描述三维晶粒长大过程的动力 学. 当晶粒面数f≥8时, Yu-Liu速率方程和 MacPherson-Srolovitz速率方程均与仿真结果很好吻合, 表明这两者均可以用来定量描述三维晶粒长大过程的动力学；当 f＜8时, 这两个方程均与仿真结果有显著差异.
Three existing topological dependence equations for the growth rate of three-dimensional individual grains have been testified using a new Potts model Monte Carlo simulation. The result shown that the volume change rate dVf/dt is related to the face number f by a curve, and thus, Rivier’s grain growth rate equation that predicts dVf/dt ∝f is not confirmed. Yu-Liu’s grain growth rate equation and MacPherson-Srolovitz’s grain growth rate equation are confirmed by mean of the simulation in the case of the face number f≥8. Yu-Liu’s grain growth rate equation and MacPherson-Srolovitz’s grain growth rate equation are not valid in the case of the face number f<8.
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