An interpenetrated cluster model of p-type Zn–Mg–Ho icosahedral quasicrystal

Abstract

A six-dimensional (6D) cluster model of p-type Zn–Mg–Ho icosahedral quasicrystal has been proposed. The model consists of three large occupation domains centred at (0, 0, 0, 0, 0, 0), (½, ½, ½, ½, ½, ½), and (½, 0, 0, 0, 0, 0) in the 6D primitive unit cell. The 3D structure is described by three building blocks: rhombic triacontahedron (RTH), obtuse rhombohedron (OR) and acute rhombohedron (AR). The RTH is an extended icosahedral cluster, which includes a Bergman-type cluster inside it. The RTH clusters are placed at a subset of 12-fold vertices of the three-dimensional Penrose tiling with an edge length of about 0.5 nm. A pair of neighbour RTH clusters shares a rhombus face or an OR along 2- or 3-fold connections, respectively. The interstices of the network of RTH clusters are described by combinations of ORs and ARs with atom decorations.