Effect of impurities on tiling in a two-dimensional dodecagonal quasicrystal

Abstract

Langevin dynamics simulations are performed to examine how impurities affect two-dimensional dodecagonal quasicrystals. We assumed that the interaction potential between two particles is the Lennard–Jones–Gauss potential if at least one of these particles is a matrix particle and that the interaction potential between two impurities is the Lennard–Jones potential. Matrix particles and impurities impinge with constant rates on the substrate created by a part of a dodecagonal quasicrystal consisting of square and triangular tiles. The dependences of the twelve-fold rotational order and the number of shield-like tiles on the impurity density are examined after sufficient solid layers are grown. While the change in the twelve-fold rotational symmetry is small, the number of shield-like tiles in the solid increases greatly with increasing impurity density.