三维晶粒的拓扑构形和拓扑相关性研究

单相多晶体材料中，三维晶粒究竟有哪些拓扑构形以及邻接晶粒之间的拓扑相关性如何，是当前晶粒拓扑学研究领域的两个重要科学问题。文献中至今仅报道了9个面以下的小晶粒的部分拓扑构形，缺乏对9个面以上的大晶粒的拓扑构形的全面认识和研究，并且最新提出的描述晶粒拓扑相关性的“一般性Aboav-Weaire关系”和新的拓扑依赖型三维晶粒长大速率方程均有待实验证实。鉴于此，本项目拟利用申请人提出的一种基于矩阵理论的表征三维晶粒拓扑学的新方法，对面数大于9的晶粒的全部拓扑构形进行理论预测，同时利用系列截面法实验和计算机仿真手段，研究各种晶粒拓扑构形在不同类型显微组织中的分布情况、择优出现的拓扑构形的特点和晶粒拓扑构形的演化规律，实验验证和完善 “一般性Aboav-Weaire关系”和新的拓扑依赖型晶粒长大速率方程。研究结果将有望帮助人们深入理解三维晶粒的拓扑学和拓扑演变规律，使我国在此类研究中处于国际前列。

The study on the topological forms and correlations of three-dimensional grains in single-phase polycrystalline materials is of great importance in the field of grain topology. Although some topological forms for grains with faces less than 9 have been reported, there still lacks of the understanding of the topological forms for grains with faces more than 9. The generalized Aboav-Weaire relation and a newly proposed topology dependent grain growth rate equation have not been experimentally verified. In this project, we aim to predict all the possible topological forms for grains with faces more than 9 with the aid of a new efficient method of which used a series of the matrices to describe the complete grain topology. The serial sectioning method and computer simulation will be used to study the distributions of every grain forms, the features of the frequently occurring forms and the evolutions of grain forms in different microstructures. Meanwhile, the generalized Aboav-Weaire relation and the topology dependent grain growth rate equation will be verified by experimental data from different materials. The results will assist in a better understanding of three-dimensional grain topology and its evolution.