Spatial and Atomic Occupancy Disorders in Tsai-Type 1/1 Approximant Crystals

Tsai-type phases, built from concentric polyhedral shells, represent one of the most structurally prominent families of quasicrystal-related materials. Despite their prevalence, many reported Au-based 1/1 approximants have structural features that may not be fully refined, due in part to unaccounted atomic occupancy disorders and/or incomplete treatment of cubic interstices and because of the large atomic scattering factor of Au compared to the other constituent elements in the various crystalline approximant systems, which obscure subtle spatial and structural disorders inherent to these compounds. In this work, we review and analyse the crystallographic details of Au-containing Tsai-type 1/1 approximants, with particular emphasis on the nature of atomic occupancy disorders that lead to deviations from integer stoichiometric chemical compositions, and the role of interstitial occupancies in conjunction with electronic structure theory. A comparison against several reported structures is presented, and a unified model is proposed to describe the crystallographic disorders among these phases. Furthermore, a reinvestigation of the Gd-Au-Ge 1/1 approximant reveals that subtle differences in the concentric clustering and partial atomic occupancies may lead to compositional and symmetry changes.