中文摘要：

以MacPherson-Srolovitz提出的三维个体晶粒长大拓扑依赖速率方程以及三维晶粒组织的晶粒尺寸-晶粒面数间的抛物线型统计关系为基础，导出了相应的描述三维准稳态晶粒尺寸分布的函数族．采用纯Fe实验数据以及顶点法、基元演化法、相场模型和MonteCarlo法进行了验证，结果表明，函数族中峰值左偏的函数适合三维准稳态晶粒尺寸分布的定量表述．将该函数与Liu等提出的2种三维准稳态晶粒尺寸分布函数进行的对比表明：此3种函数的解析表达形式有所不同，但其曲线图在一定条件下相互吻合．此外，MacPherson—Srolovitz三维拓扑依赖速率方程、Hillert三维速率方程及Yu—Liu三维速率方程尽管表达形式不同均能较好地反映三维正常晶粒长大的动力学规律．

英文摘要：

Based on a new 3D topology-related grain growth rate equation proposed recently by MacPherson and Srolovitz and the grain topology-size relationship, a set of analytical functions describing quasi-stationary grain size distributions were obtained. One of such functions, its peak position shifted to left side, can be used to describe satisfactorily the 3D quasi-stationary grain size distribution obtained from experimental results for pure iron by serial sectioning, and those obtained from computer simulations by vertex dynamics method, surface evolver method, phase field method and Monte Carlo method with Potts model. By adopting appropriate parameters, the grain size distribution curve corresponding to this function is very similar with those of two quasi-stationary grain size distributions based on Hillert rate equation and Yu-Liu topology-related rate equation, respectively. It is implied that all the three normal grain growth rate equations, i.e., Hillert rate equation, Yu-Liu rate equation and MacPherson-Srolovitz topology-related rate equation, can describe well the 3D grain growth kinetics, despite their different forms.