准晶体中十方晶系点群的对称性与矩阵表示  

The representations of decagonal system's point groups in quasicrystal

作　　者：龙光芝[1] 高彦芳[2] 陈瀛[3] 陈敬中[2] 

机构地区：[1]中国地质大学数学与物理学院,武汉430074 [2]中国地质大学材料科学与化学工程学院,武汉430074 [3]中国地质大学地球科学学院,武汉430074

出　　处：《华中师范大学学报（自然科学版）》2006年第3期347-351,共5页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(4897008249272091)

摘　　要：运用结晶学、群论、线性代数等方法,从理论上对准晶体中十方晶系各点群进行了研究.绘出了各点群的极赤投影图;列出了各点群的所有群元和生成元;填写出了最大的固有点群10 22的群乘表.在自定义的十方坐标系中,导出了十方晶系各点群所有群元的坐标变换矩阵,这40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,±τ.其中,τ=(5+1)/2是反映十方晶系准晶体所具有的准周期性的特殊无理数.The point groups of decagonal system in quasicrystal were studied. All stereographic projections of the point groups were drawn. All symmetry operation and generating operation of the point groups were listed, and their group multiplication table of maximal proper point group 10 22 was filled in. In decagonal coordinate system defined by us, the matrixes of the point groups symmetry operation were derived. There are forty 3× 3 matrixes. The matrixes form are compact, their matrix element possible val- ues are： 0, ± 1, ±τ. Thereinto,τ= （√5＋ 1）/2 is an especial irrational number, which indicated the quasi-periodicity of decagonal system quasicrystal.

关 键 词：准晶体 十方晶系 点群 极赤投影 群乘表 矩阵 

分 类 号：O711[理学—晶体学]