Mason Jeremy K, Schuh Christopher A
Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
Acta Crystallogr A. 2007 Jul;63(Pt 4):315-28. doi: 10.1107/S0108767307021782. Epub 2007 Jul 1.
In polycrystals, there are spatial correlations in grain-boundary species, even in the absence of correlations in the grain orientations, due to the need for crystallographic consistency among misorientations. Although this consistency requirement substantially influences the connectivity of grain-boundary networks, the nature of the resulting correlations are generally only appreciated in an empirical sense. Here a rigorous treatment of this problem is presented for a model two-dimensional polycrystal with uncorrelated grain orientations or, equivalently, a cross section through a three-dimensional polycrystal in which each grain shares a common crystallographic direction normal to the plane of the network. The distribution of misorientations theta, boundary inclinations phi and the joint distribution of misorientations about a triple junction are derived for arbitrary crystal symmetry and orientation distribution functions of the grains. From these, general analytical solutions for the fraction of low-angle boundaries and the triple-junction distributions within the same subset of systems are found. The results agree with existing analysis of a few specific cases in the literature but present a significant generalization.
在多晶体中，即使晶粒取向不存在相关性，由于晶界取向差之间需要晶体学一致性，晶界物种也存在空间相关性。尽管这种一致性要求对晶界网络的连通性有重大影响，但由此产生的相关性的本质通常仅从经验角度来理解。本文针对具有不相关晶粒取向的二维多晶体模型，或者等效地，针对三维多晶体的一个横截面（其中每个晶粒都有一个垂直于网络平面的共同晶体学方向），对这个问题进行了严格的处理。对于任意晶体对称性和晶粒的取向分布函数，推导了取向差θ、边界倾角φ以及围绕三重结的取向差联合分布。由此，找到了同一系统子集中低角度边界分数和三重结分布的一般解析解。结果与文献中少数特定情况的现有分析一致，但有显著的推广。
