GEOMETRICAL PARAMETERS TO HEXAKAIDECAHEDRONS AND EIGHTFOLD SYMMETRY QUASICRYSTAL
Min Lequan (University of Science and Technology Beijing) Shi Nicheng (China University of Geoseinces)
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 +.
【Fund】： 国家自然科学基金;; 北京科技大学科研基金