中文摘要：

三维晶粒长大规律是材料科学研究的核心问题之一,本文通过考虑实际多晶组织中晶界能和晶界迁移率的不均匀性和各向异性因素对晶粒三晶棱处两面角大小的影响,借助经典体视学中晶粒界面积分平均曲率与平均切直径的关系,经推导得到了适合于凸形晶粒的一般性三维von Neumann方程,结果表明实际凸形晶粒的准确长大速率可以表示为晶粒的平均切直径、三晶棱总长度和三晶棱处两面角的函数.所得方程经过了Kelvin十四面体和5种规则多面体验证,对于三维von Neumann方程（Nature,2007,446：1053）进一步推广并应用于实际金属和陶瓷材料具有重要的意义.

英文摘要：

Understanding the laws of grain growth in three dimensions is one of the classic problems of materials science.By considering the anisotropy in real polycrystalline structure and the relationship between the integral of surface mean curvature and the mean caliper diameter of a convex individual grain,three-dimensional von Neumann equation for accurate grain growth rate is studied.The result shows that accurate grain growth rate of a convex grain is related to the grain mean caliper diameter,the sum of the length of grain edges and the corresponding dihedral exterior angles.This result is verified by Kelvin tetrakaidecahedron and the only five convex regular polyhedra.