中文摘要：

由晶粒长大过程的曲率驱动本质出发,以不同于MacPherson和Srolovitz的方法,推导出凸型多面体晶粒的三维von Neumann关系式,无任何其他形状假设及晶粒尺寸分布或拓扑分布要求.在应用于凸型多面体晶粒时,本文结果与MacPherson和Srolovitz给出的结果完全一致.对于凸型多面体晶粒,三维个体晶粒长大速率是晶粒平均切直径和晶粒棱总长度的函数,符合Kinderlehrer指出的n维体积的变化速率仅与胞的（n-2）维特征量有关的规律.

英文摘要：

Based on the capillarity-driven nature of the grain growth,the exact 3D von Neumann relation for a convex polyhedron grain was obtained in a simpler method than that reported by MacPherson and Srolovitz,which is independent of any additional assumptions concerning any grain size distribution,topology distribution or grain shape.It is shown that the 3D growth rate of a convex polyhedron grain is related to two one-dimensionai quantities,the grain＇s mean caliper diameter and the sum of the length of its edges,which agrees with the property pointed by Kinderlehrer that the rate of change of n-dimensionai volume is related to（n-2）-dimensionai features of the cell and no others.