Stróz Kazimierz
Institute of Material Science, University of Silesia, Poland.
Acta Crystallogr A. 2007 Nov;63(Pt 6):447-54. doi: 10.1107/S0108767307044789. Epub 2007 Oct 17.
Automatically generated orientation-location parts, or coordinate triplets describing the geometric elements, differ frequently from the corresponding parts of the symmetry-operation symbols listed in International Tables for Crystallography [(1983), Vol. A, Space-Group Symmetry, edited by Th. Hahn. Dordrecht: Reidel]. An effective algorithm enabling the derivation of standard orientation-location parts from any symmetry matrix is described and illustrated. The algorithm is based on a new concept alternative to the 'invariant points of reduced operation'. First, the geometric element that corresponds to a given symmetry operation is oriented and located in a nearly convention free manner. The application of the direction indices [uvw] or Miller indices (hkl) gives a unique orientation provided the convention about the positive direction is defined. The location is fixed by the specification of a unique point on the geometric element, i.e. the point closest to the origin. Next, both results are converted into the standard orientation-location form. The standardization step can be incorporated into other existing methods of derivation of the symmetry-operation symbols. A number of standardization examples are given.
自动生成的取向 - 位置部分，或描述几何元素的坐标三元组，常常与《晶体学国际表》[(1983年)，A卷，空间群对称性，由Th. Hahn编辑。多德雷赫特：里德尔出版社]中列出的对称操作符号的相应部分不同。本文描述并举例说明了一种能从任何对称矩阵推导出标准取向 - 位置部分的有效算法。该算法基于一种替代“约化操作的不变点”的新概念。首先，以几乎不受约定限制的方式对与给定对称操作相对应的几何元素进行取向和定位。只要定义了关于正方向的约定，方向指数[uvw]或密勒指数(hkl)的应用就能给出唯一的取向。位置通过在几何元素上指定一个唯一点来确定，即最接近原点的点。接下来，将这两个结果都转换为标准取向 - 位置形式。标准化步骤可以纳入其他现有的对称操作符号推导方法中。文中给出了多个标准化示例。
