The Tsai vs. Bergman Cluster Stability in ZnMgSc 1/1 Periodic Approximant Crystal

Quasicrystals with icosahedral symmetry can be classified into two main groups: Bergman-type and Tsai-type. While these are considered as distinct phases, they share a common feature of being constructed from atomic clusters, either Tsai or Bergman. In this study, we employ Density Functional Theory to perform electronic structure calculations on the Zn_84.79Mg_0.86Sc_14.35 periodic approximant crystal phase. Our investigation involves systematically displacing atoms from Tsai cluster sites to Bergman cluster sites, allowing us to explore modifications in the electronic structure. Our findings reveal that the stability of the phase is influenced by the interaction between Zn-4p and Sc-3d orbitals. We observe that the sp-d hybridization effect may play a more crucial role rather than Hume-Rothery stabilization, as this observation holds true regardless of the presence or absence of periodic boundary conditions. Notably, the additional atom present in the Tsai structure serves as a significant electron acceptor in low-energy orbitals. Its absence in Bergman structures results in a composition with fewer atoms possessing high-energy d orbitals. This discovery provides a rationale for the frequent occurrence of Bergman phases with transition metals or rare earth elements, which occupy less than 10 % of the sites in the structure.