The equivalence of Tsai and Bergman clusters in 1/1 and 2/1 periodic approximant crystals

The atomic structure of icosahedral quasicrystal is conveniently described by packing of clusters with concentric shells. Three types of those clusters are known to exist in quasicrystals: Mackay, Bergman and Tsai. Here we focus on the tetrahedral close-packed Bergman-and Tsai-type structures. In 2/1 cubic ap-proximant crystal of the icosahedral AgInYb quasicrystal, it was discovered that Tsai and Bergman clusters can be used equivalently to describe the atomic structure. We further explore this possibility by in-vestigating both 1/1 and 2/1 cubic approximants crystals in ScZnMg, CdYb Tsai-type structures, and AlZnMgLi, AlZnMg representing Bergman-type structure. In all the analyzed structures, both Bergman and Tsai clusters are equivalent in a sense that both can be used as structure-building units. The coexistence of two cluster types does not negate the fact that phases are not isostructural. The discrepancy between structures natively regarded as Bergman-or Tsai-type manifests in varying the positional disorder in the shell structure. Bergman structures have an ordered soccer ball polyhedral shell with atoms located in vertices of polyhedron whereas in Tsai-type structure this shell is disordered with a significant atomic displacement from vertex sites. The reverse occurs in Tsai structures. Additionally, a systematic formation of vacancies distinguishes both phases. Because the vertex of the rhombic triacontahedral shell of the Tsai cluster is located in the center of the Bergman cluster (joint with the a - linkage) the unoccupied cluster center results in vacancy at the rhombic triacontahedron. The Tsai-Bergman cluster linkage result in for-mation of extra positions at the center of pentagonal faces of the dodecahedron in the Tsai cluster and off mid-edges sites at icosahedron in the Bergman cluster. The geometric similarity of Tsai and Bergman structures can be used to understand the conditions of their stabilization.(c) 2023 Elsevier B.V. All rights reserved.