Semimetallic Band Structure and Cluster-Based Description of a Cubic Quasicrystalline Approximant in the Al–Cu–Ir System

Abstract

Density functional calculations were performed for a cubic quasicrystalline approximant in the Al–Cu–Ir system. A semimetallic band structure was developed and analyzed on the basis of Wannier functions constructed from the valence and a part of the conduction band manifold. The Wannier functions were s- and p-like orbitals centered on either the centers of conventional clusters or the icosahedron-like vertices of pseudo-Mackay clusters, and d-like orbitals centered on the transition metals. Grouping the orbitals according to their center, we considered a small cluster for each group of the orbitals. Most of the orbitals contribute to the density of states only within the valence bands, i.e., they are valence states. The exceptions are some of p-like orbitals centered on the icosahedron-like vertices of the pseudo-Mackay clusters, and they contribute to both valence and conduction bands. Each of these p-like orbitals forms a covalent bond with one centered on the neighboring small cluster. The resulting bonding and antibonding orbitals are valence and conduction states, respectively. The number of valence bands (173) of our Al39Cu8Ir15 model was then decomposed in terms of the numbers of transition metals (23), clusters (16), and covalent bonds between the clusters (6) as \(23 \times 5 + 16 \times 4 - 6 = 173\). The description for the valence-band formation may also be applicable to some of the group 13 element–transition metal intermetallic compounds, such as RuAl2.