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

Bergman-type phases in the Na–Au–T (T =
Ga, Ge, and
Sn) systems were synthesized by solid-state means and structurally
characterized by single-crystal X-ray diffraction studies. Two structurally
related (1/1) Bergman phases were found in the Na–Au–Ga
system: (a) a conventional Bergman-type (CB) structure, Na26AuxGa54–x, which features empty innermost icosahedra, as refined with x = 18.1 (3), Im3̅, a = 14.512(2) Å, and Z = 2; (b) a stuffed Bergman-type
(SB) structure, Na26AuyGa55–y, which contains Ga-centered innermost
icosahedra, as refined with y = 36.0 (1), Im3̅, a = 14.597(2) Å, and Z = 2. Although these two subtypes have considerable phase
widths along with respective tie lines at Na ≈ 32.5 and 32.1
atom %, they do not merge into a continuous solid solution. Rather,
a quasicrystalline phase close to the Au-poor CB phase and an orthorhombic
derivative near the Au-rich SB phase lie between them. In contrast,
only Au-rich SB phases exist in the Ge and Sn systems, in which the
innermost icosahedra are centered by Au rather than Ge or Sn. These
were refined for Na26Au40.93(5)Ge14.07(5) (Im3̅, a = 14.581(2) Å,
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 Bergman clusters are rare. Such centering and coloring
correlate with the sizes of the neighboring icosahedra, the size ratios
between electropositive and electronegative components, and the values
of the average valence electron count per atom (e/a). Theoretical
calculations revealed that all of these phases are Hume–Rothery
phases, with evident pseudogaps in the density of states curves that
arise from the interactions between Fermi surface and Brillouin zone
boundaries corresponding to a strong diffraction intensity.

钠-金-T（T=Ga、Ge、Sn）体系中的伯格曼型相（Bergman-type phase）通过固相合成法（solid-state synthesis）制备，并经单晶X射线衍射（single-crystal X-ray diffraction）分析完成结构表征。在Na-Au-Ga体系中发现两种结构相关的（1/1型）伯格曼型相：(a) 常规伯格曼型（CB）结构Na₂₆AuₓGa₅₄₋ₓ，其最内部二十面体为空心结构，精修结果为x=18.1(3)，空间群Im-3，晶胞参数a=14.512(2) Å，Z=2；(b) 填充型伯格曼型（SB）结构Na₂₆AuᵧGa₅₅₋ᵧ，其最内部二十面体以Ga为中心，精修结果为y=36.0(1)，空间群Im-3，晶胞参数a=14.597(2) Å，Z=2。尽管这两种亚型具有较宽的单相区，且各自的结线位于钠原子分数约32.5%和32.1%处，但二者并未形成连续固溶体。相反，在二者之间存在靠近贫金CB相的准晶相（quasicrystalline phase），以及靠近富金SB相的正交晶系衍生相。与之相反，在Ge和Sn体系中仅存在富金SB相，其最内部二十面体的中心为Au原子，而非Ge或Sn原子。上述相分别通过Na₂₆Au₄₀.₉₃(₅)Ge₁₄.₀₇(₅)（空间群Im-3，a=14.581(2) Å，Z=2）和Na₂₆Au₃₉.₈₃(₆)Sn₁₅.₁₇(₆)（空间群Im-3，a=15.009(2) Å，Z=2）完成精修。伯格曼团簇的中心占位情况较为罕见。此类中心占位与原子着色（coloring）、相邻二十面体的尺寸、正电性与负电性组分的尺寸比，以及平均每个原子的价电子数（e/a）密切相关。理论计算表明，上述所有相均为休姆-罗瑟里相（Hume–Rothery phase），其态密度（density of states）曲线中存在显著的赝能隙，该赝能隙源于费米面（Fermi surface）与布里渊区（Brillouin zone）边界的相互作用，对应着较强的衍射强度。