三维晶粒的拓扑构形和拓扑相关性研究

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.

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。

单相多晶体材料中三维晶粒的拓扑构形复杂多样，其相关研究具有非常重要的科学意义，因此本项目重点对三维晶粒拓扑构形和邻接晶粒之间拓扑相关性开展了研究，联合采用了理论预测、计算机仿真和三维重建实验手段，取得了一些重要结果：完善了本项目组提出的一种新的基于矩阵理论的三维晶粒拓扑学表示方法，并计算出了界面数为4-14的三维晶粒的所有可能的拓扑构形，其中的多种构形为首次提出；利用系列截面法实验完成了纯铁晶粒构形的三维重建，研究了拓扑构形的分布情况，并首次实验发现了7种新的晶粒拓扑构形，证实了本工作中的理论计算结果的可靠性；利用关键的纯铁晶粒三维重建数据和Monte Carlo晶粒长大仿真数据，证实了“一般性Aboav-Weaire关系”和新的拓扑依赖型晶粒长大速率方程的可靠性。本项目的研究结果有助于人们深刻理解三维晶粒拓扑学，为金属材料的晶粒组织演化等相关研究提供了关键数据支持。