变换矩阵（变形、方向、对应）、它们的连续形式及其变体
The transformation matrices (distortion, orientation, correspondence), their continuous forms, and their variants
摘要：
位移相变的晶体学可以用三种类型的矩阵来描述：晶格畸变矩阵、取向关系矩阵和对应矩阵。本文给出了它们在晶体基、正交基、倒易基中的表示公式，并说明了如何利用它们推导逆变换矩阵。在硬球假设的情况下，可以确定畸变矩阵的连续形式，并且其导数被识别为连续介质力学中使用的速度梯度。通过具有相交组的陪集分解来确定失真、方向和对应变量，所述相交组取决于相位的点组和变换矩阵的类型。马氏体相变唯象理论所要求的拉伸变量应与对应变量区分开来。定向变量和对应变量也是不同的;它们分别由几何对称和代数对称定义。在热循环过程中的取向（IR）可逆性的概念进行了简要和部分处理，通过推广的n-陪集和图形的取向变量。通过一些简单的例子，说明了畸变变体、取向变体和对应变体的数目之间没有一般的关系，并阐明了热循环形成取向变体的概念。
英文摘要：
The crystallography of displacive phase transformations can be described with three types of matrices: the lattice distortion matrix, the orientation relationship matrix, and the correspondence matrix. The paper gives some formula to express them in crystallographic bases, orthonormal bases, and reciprocal bases, and it explains how to use them to deduce the matrices of inverse transformation. In the case of hard-sphere assumption, a continuous form of the distortion matrix can be determined, and its derivative is identified to the velocity gradient used in continuum mechanics. The distortion, the orientation and the correspondence variants are determined by coset decomposition with intersection groups that depend on the point groups of the phases and on the type of transformation matrix. The stretch variants required in the phenomenological theory of martensitic transformation should be distinguished from the correspondence variants. The orientation variants and the correspondence variants are also different; they are defined from the geometric symmetries and algebraic symmetries, respectively. The concept of orientation (ir)reversibility during thermal cycling is briefly and partially treated by generalizing the orientation variants with n-cosets and graphs. Some simple examples are given to show that there is no general relation between the numbers of distortion, orientation and correspondence variants, and to illustrate the concept of orientation variants formed by thermal cycling.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
