Conventional and Stuffed Bergman-Type Phases in the Na?Au?T (T = Ga, Ge, Sn) Systems: Syntheses, Structures, Coloring of Cluster Centers, and Fermi Sphere?Brillouin Zone Interactions

摘要

Bergman-type phases in the Na−Au−T (T = Ga, Ge, and Sn) systemsnwere synthesized by solid-state means and structurally characterized by single-crystal X-rayndiffraction studies. Two structurally related (1/1) Bergman phases were found in the Na−nAu−Ga system: (a) a conventional Bergman-type (CB) structure, Na26AuxGa54−x, whichnfeatures empty innermost icosahedra, as refined with x = 18.1 (3), Im3̅, a = 14.512(2) Å,nand Z = 2; (b) a stuffed Bergman-type (SB) structure, Na26AuyGa55−y, which contains Gacenteredninnermost icosahedra, as refined with y = 36.0 (1), Im3̅, a = 14.597(2) Å, and Z =n2. Although these two subtypes have considerable phase widths along with respective tienlines at Na ≈ 32.5 and 32.1 atom %, they do not merge into a continuous solid solution.nRather, a quasicrystalline phase close to the Au-poor CB phase and an orthorhombicnderivative near the Au-rich SB phase lie between them. In contrast, only Au-rich SB phasesnexist in the Ge and Sn systems, in which the innermost icosahedra are centered by Aunrather than Ge or Sn. These were refined for Na26Au40.93(5)Ge14.07(5) (Im3̅, a = 14.581(2)nÅ, and Z = 2) and Na26Au39.83(6)Sn15.17(6) (Im3̅, a = 15.009(2) Å, and Z = 2), respectively. Occupations of the centers of Bergmannclusters are rare. Such centering and coloring correlate with the sizes of the neighboring icosahedra, the size ratios betweennelectropositive and electronegative components, and the values of the average valence electron count per atom (e/a). Theoreticalncalculations revealed that all of these phases are Hume−Rothery phases, with evident pseudogaps in the density of states curvesnthat arise from the interactions between Fermi surface and Brillouin zone boundaries corresponding to a strong diffractionnintensity.