摘要
从理论上对准晶体中八方晶系各点群进行了研究.运用八方晶系各点群的极赤投影图,列出了各点群的所有对称操作;填出了固有点群822的群乘表.运用坐标变换和群论在自定义的八方坐标系中,推导出八方晶系点群所有对称操作的矩阵.这32个3×3矩阵的结构是相当简洁的,它们的矩阵元只有5种可能取值:0,±1,±2.其中2是反映八方晶系准晶体所具有的准周期性的特殊无理数.
The point groups of octagonal system in quasicrystal are studied. By using stereographic projection of each point group, all symmetry operation and generating operation of the point groups are listed, and group multiplication table of maximal proper point group 822 is filled in. In octagonal coordinate system defined by us, the matrixes of the point groups symmetry operation are derived. There are thirty-two 3 × 3 matrixes. The marixes form are compact, their matrix element possible values are ：0, ± 1, ±√2. Therein,√2 is an especial irrational number,which indicated the quasi-periodicity of octagonal system quasicrystal.
出处
《大学物理》
北大核心
2006年第3期17-20,37,共5页
College Physics
基金
国家自然科学基金资助项目(48970082
49272091)
关键词
准晶体
八方晶系
点群
极赤投影图
群乘表
矩阵
quasicrystal
octagonal system
point group
stereographic projection
group multiplication
matrix
