Approximant Phases and an Icosahedral Quasicrystal in the Ca–Au–Ga System. The Influence of Size over Electronic Factors

Two crystalline approximants (ACs) and their corresponding icosahedral quasicrystal (i-QC) are obtained in the Ca−Au−Ga system through conventional solid-state exploratory syntheses. Single crystal structural analyses reveal that the 1/1 AC, Ca3AuxGa19-x (x = ∼ 9.3−12.1) [Im3̅, a = 14.6941(6)−14.7594(6) Å], has the empty cubes in the prototypic YCd6 (= Y3Cd18) now fully occupied by Ga, resulting in a 3:19 stoichiometry. In parallel, the distorted cubes in the 2/1 AC, Ca13Au57.1Ga23.4 [Pa3̅, a = 23.9377(8) Å] are fully or fractionally occupied by Ga. The valence electron count per atom (e/a) for the 2/1 AC (1.64) is smaller than that over the 1/1 AC composition range (1.76−2.02), and the e/a of the Ca15.2Au50.3Ga34.5 i-QC, 1.84, is somewhat distant from typical values for Tsai-type i-QCs (∼ 2.0). Comparisons of the gallium results with the corresponding In phases suggest that the structural differences result mainly from size rather than electronic factors. The 1/1 and 2/1 appear to be thermodynamically stable on slow cooling, as usual, whereas the i-QC isolated by quenching decomposes on heating at ∼660 °C, mainly into 2/1 AC and Ca3(Au,Ga)11. Calculations of the electronic structure of 1/1 AC suggest that the Fermi sphere−Brillouin zone interactions remain important for the Ca−Au−Ga i-QC