| 对称点群操作和对称操作变换矩阵 |
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| 摘 要： | 在结晶学和晶体结构测定中,由于计算上的某种需要,常常把原来的坐标系以原点为中心,按照某种方式转动某一角度而成为一种新坐标系。由于新、老坐标系有共同的原点,因此它们之间必然存在着某种内在上的联系,也就是说它们中的一种坐标系的某些量可以用另一个坐标的某些量的数学式来表示。坐标系变换后,结晶学中的一系列指数,如点群,晶面指数(hkl),晶棱方向指数uvw],倒易点阵矢量等都会跟着变换。本文试图从数学出发,揭示这种变换关系,即变换矩阵。
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| 关 键 词： | 结晶学 晶体结构测定 对称操作 对称变换 |
SYMMETRY POINT GROUP OPERATIONS AND TRANSFORMATION MATRIXES FOR THE SYMMETRY OPERATIONS |
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| Authors: | Zhang Busheng |
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| Institution: | Zhang Busheng |
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| Abstract: | Owing to the requirements of calculation and determination of crystal structure, We often transform the original ordination system into a new ordination system by rotation of axes around original point. So a methematical relation exists between the new and the old ordination systems, in respects of Miller indices of crystal faces, symbols for zones and zone axes, and axes of reciprocal lattice. We may express this relation by means of transformation matrix. Of course, the transformation matrixes are adapted to the symmetry operations of point group in crystallography.This paper discusses how to find transformation matrix and the application of transformation metrix to the symmetry point group. |
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| Keywords: | Crystallography Crystal structure determination Symmetry operation Symmetry transformation |
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