Tiling models for metadislocations in AlPdMn approximants

Abstract

The AlPdMn quasicrystal approximants ξ, ξ′, and ξ′ _n of the 1.6 nm decagonal phase and R, T, and T_n of the 1.2 nm decagonal phase can be viewed as arrangements of cluster columns on two-dimensional tilings. We substitute the tiles by Penrose rhombs and show that alternative tilings can be constructed by a simple cut and projection formalism in three-dimensional hyperspace. It follows that in the approximants there is a phasonic degree of freedom, whose excitation results in the reshuffling of the clusters. We apply the tiling model for metadislocations, which are special textures of partial dislocations.