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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.
The law of three-dimensional grain growth is one of the core issues in material science research. In this paper, by considering the heterogeneity of grain boundary energy and grain boundary mobility and anisotropy in actual polycrystalline structure, The general three-dimensional von Neumann equation suitable for convex grains is deduced based on the relationship between the average curvature and the average cut diameter of the grain boundary in classical stereology. The results show that the accuracy of the actual convex grains The rate of growth can be expressed as the mean tangent diameter of the grains, the total length of the tri-crystal edges, and the dihedral angle at the tri-crystal edges.The resulting equations are validated by Kelvin tetrahedron and five regular polyhedra, and for the three-dimensional von Neumann equation Nature, 2007, 446: 1053) is of great importance for further promotion and application in practical metal and ceramic materials.