具有10次对称性的准晶结构模型

STRUCTURAL MODEL OF QUASICRYSTAL WITH 10-FOLD SYMMETRY

准晶体不同于晶体晶胞的选取原则,须先考虑选取两种或三种基本菱形单胞,再考虑如何由这类菱形生成的组合准晶胞,既要考虑组合准晶胞的对称性,又要考虑它们铺满2维平面的原则,考虑到三角二十面体分数维生长的优点,又考虑到36°,144°菱形与72°,108°菱形生成Penrose拼图优点,更重要的是组合准晶胞多重分数维生长的优点,在此基础上我们提出一种新的10次对称性的准晶结构模型。(1)以36°,144°菱形与72°,108°菱形为基本单元生成组合准晶胞;(2)以组合准晶胞为单位操作;(3)以2.6180作准周期进行放大、缩小操作,即R_n=R_(n-1)×2.6180;(4)以高次对称轴(10次轴)作旋转操作;(5)生成10次准晶多重分数维结构模型。

Based on analysing and studying the research papers at home and abroad on 2-D quasicrystals, the selection principles of quasicrystal cell of 2-D quasicrystals are put forward. The fundamental property of a 2-D crystal is formed by periodic translation of only one of cells on the plan, while a two -dimensional quasicrystal is formed by quasiperiodic translation of two or three sorts of basic rhombi. The selection principles of quasicrystal cell, therefore, are different from that of crystal cell. These principles are applied respectively to the quasicrystals with 10-fold axis. The paper deduces the corresponding structural models: the structural model of 2 -D quasicrystal with tenfold symmetry as follow. (1) Combining the basic units, 36 ° , 144 ° rhombus and 72 ° , 108 ° rhombus, form the combinational quasicrystal cell; ( 2) Doing the unit operation with the combinational quasicrystal cell; (3) Doing the amplification, or mmification operation with the quasiperiod of 2.6180, that is, Rn = 2.6180 × Rn-1; (4) Doing rotation operation with tenfold axis; ( 5) In this way, multifractal structural model of quasicrystal with tenfold symmetry is gotten.