Mathematical Model for Structure of Ideal Quasicrystal Lattices

In this paper, a mathematical model for structure of ideal quasicrystal lattices is set up. This Model describes very beautifully the following phenomena which is shown in the electron micrograph of the Mn-Al quasicrystal obtained by Hiraga et al. In some local areas, ten bright dots groups are distributed in concentric circles; sixteen bright dots are distributed the surroundings of every two neighbourhood righs of bright dots; and fourteen bright dots arc distributed the surroundings of every double overlapping rings of bright dots. Therefore, it seems that this model can explain more phenomena in Mn-Al alloy quasicrystal than those reported by Hiraga et al, and could offer some new ideas for the theoretical research of structure of quasicrystal.