正多面体的结晶学分类及等大正二十面体共角顶连接的准晶结构模型

本文将正四面体、正八面体、正六面体归为结晶类,将正二十面体、正十二面体归为准晶类。大小相近的原子倾向于形成正二十面体配位;再将正二十面体看成球体,那末符合m35对称的理想堆垛方式是以等大正二十面体共角顶连接,形成大一级的正二十面体。继续按照这一规律连接将不断形成更大一级的正二十面体,从而获得理想准晶结构模型。此模型很好地解释了Al—Mn准晶体的高分辨结构图及Penrose拼图与准晶体的高分辨结构图的密切关系。

CRYSTALLOGRAPHICAL CLASSIFICATION OF REGULAR POLY-HEDRA AND THE QUASI-CRYSTAL STRUCTURE MODEL IN TERMS OF CORNER-CONNECTED REGULAR ICOSAHEDRA OF EQUAL SIZE

The regular tetrahedron, hexahedron and octahedron fall into the crystal, while the regular pentagon-dodecahedron and icosahedron into the quasi-crystal. Equal-sized atoms tend to form regular icosahedra in 12-folded coordination. When regarded as equal-sized balls in coincidence with the symmetry of m35,the ideal stacking of equal-sized regular icosahedra is that they are corner-connected to form a regular icosahedron of a higher order. The continuation of the process produces icosahedra of higher orders. Application of these two principles to the quasi-crystal leads us to its structural model.