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晶体空间群推演是晶体结构描述和表达的关键环节,也是理论印证实验晶体结构的手段。因涉及数学方法、物理技术和图形软件,所以不仅是晶体结构教学的重点也是难点。本文基于六方硫化钒晶体结构测定的基本结构数据,用自编晶体学程序cryst 2015在图形软件上再现硫化钒的晶体结构。在点空间和三维实向量空间中,由线性映射表达平移和非平移对称操作,得到硫化钒的空间群和对应的矩阵表示群。由生成元的幂次连乘导出空间群群元素的生成顺序,以及由空间群导致的晶体学分类。这种借助实例的连贯推演方法,有助于建立晶体学知识结构框架,尤其能帮助初学者理解晶体学的科学思想体系。
Crystal space group deduction is the key to the description and expression of crystal structure, which is also a means of theoretically confirming the experimental crystal structure. Because of the mathematical methods, physics and graphics software, it is not only the focus but also the difficulty of the teaching of the crystal structure. Based on the basic structural data of the hexagonal vanadium sulfide crystal structure determination, Crystal 2015 was used to reproduce the crystal structure of vanadium sulfide by the crystallographic program cryst 2015. In point space and three-dimensional real vector space, the linear mapping expresses the translational and non-translational symmetric operations to obtain the space group and corresponding matrix representation group of vanadium sulfide. The order of generation of spatial group elements is derived from the power multiplication of generators, and the crystallographic classification caused by space group. This coherent deduction method with examples helps to establish the structural framework of crystallographic knowledge, especially to help beginners understand the scientific system of crystallography.