三角十六面体的几何参数与八次对称准晶体

1987年8月王宁等报道具有八次对称轴准晶的高分辨图象,呈现出正八边形相嵌的图案。本文认为从配位多面体理论上对八次对称存在的可能性加以研究是有必要的,为此提出了具有十次配位的等腰三角十六面体和一系列带帽反棱柱,精确地求出了这些十六面体的顶点间的夹角、棱长和晶面法线与四次轴间的夹角等几何参数,作为应用对于Cr—V—Ni—Si八次对称准晶,设Ni原子（简称原子A）位于多面体中心,而V,Cr,Si原子（简称原子B）位于顶点上,原子A和B之半径分别为1.24（?）和1.32（?）,间隙0≤（?）（?）≤0.6（?）.则:（1）若原子A和B按等腰三角十六面体配位且A,B的键长为（2.56+δ）（?）,则原子B间的键长为1.08（2.56+δ）（?）或1.29（2.56+δ）（?）;（2）若原子A和B按带帽反棱柱配位且呈“紧密堆积”,则原子A和B之间的键长为（2.56+δ）（?）或（2.56+δ）(0.511+（0.261+0.08/（2.56+δ）]n）1/2（?）

GEOMETRICAL PARAMETERS TO HEXAKAIDECAHEDRONS AND EIGHTFOLD SYMMETRY QUASICRYSTAL

A 2D quasicrystal pattern with an eightfold rotational axis has been found recently by N. Wang et al.. It is a significant breakthrough in the experimental field of quasicrystal. The authors hold that it is necessary to investigate the possibility on eightfold rotational symmetry by means of coordinational polyhedron theory as investigating the fivefold rotational symmetry by the icosahedr?on. This paper has suggested a so-called "isosceles trigonal hexakaidecahedron" and a series of bicapped antiprism. By using strictly mathematics methods, the authors have accuratly calculated the angles and edge lengths between vertexes, angles between old axis and normal line of the faces, and the other geometrical parameters of hexakaidecahedrons. As an applications in Cr-Ni 8-fold symmety quasicrystal, we suppose the atom Ni (abbreviated as atom A) is located at the center of hexakaideca-hedrons,and atom V. , Cr. , and Si. (abbreviated as atoms B) coordinated with atom A are located respectively a-t the vertexes C, Cand Ci (l i 8),(see fig. 1.). Let the radii of atom A and B be respectively rA = 1. 24A and rB=1.32A (&A. is the space between atom A and B,where A )?Then the following conclusions can be arrived at: (1) if atom A and B are isosceles hexakaidecahedron coordination, then the bonding lengths between A and B :is (2. 56+ )A, and the bonding lengths be-tween B are 1. 08(2. 56+6)A and 1.29(2.56+6)A; (2) if atom A and B are bicapped antiprism coordination and closed-acked, then we have:(a) the bonding length between atom A and atom B which is located at the vertexe of antiprism is (2. 56+5)A ; (b) the bonding length between atom A and atom B which is located at the vertexe of pyramid is (2. 56 + &) (0. 511 +.