基于三维个体晶粒表面积的变化率与晶粒拓扑性质之间的定量关系和 晶粒尺寸-面数关系的假设, 推导了一个拓扑相关的个体晶粒长大速 率方程. 该方程表明, 个体晶粒的尺寸变化率不仅与其自身尺寸有关, 而且也与拓扑特征有关. 在此基础上, 借鉴最新的关于粒子粗化理论 中的晶粒长大连续方程, 对三维晶粒长大过程准稳态阶段的晶粒尺寸 分布进行了求解. 结果显示, 所得准稳态三维晶粒尺寸分布是一个单 参数函数族. 该结论得到了顶点法、基元演化法、相场模型和Monte Carlo法 这4种晶粒长大仿真方法所得三维准稳态晶粒尺寸分布数据的支持.
A new topology-related individual grain growth rate equation was derived under the assumption of the statistical grain model. It depicts that the changing rate of grains is related to the grain size and topological properties. The continuity equation from the particle coarsening theory was adapted to grain growth. Based on the grain growth rate equation and the continuity equation, an asymptotic solution was obtained. The solution is an one-parameter family of distributions other than a unique distribution function, which is supported by quasi-stationary grain size distributions obtained from simulations of vertex model, surface evolver, phase-field model and Monte Carlo method.
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