Application of group theory to the lattice dynamics of magnesium stannide

Abstract

The germanides Sr7Ge6 and Ba7Ge6 as well as the stannide Ba3Sn2 were prepared by arc melting and annealing in welded tantalum ampoules using induction as well as resistance furnaces. The compounds were investigated by powder and single crystal X-ray diffraction. Sr7Ge6 and Ba7Ge6 crystallize in the Ca7Sn6 structure type (space group Pmna, Z=4: a=7.777(2) Å, b=23.595(4) Å, c=8.563(2) Å, wR2=0.081 (all data), 2175 independent reflections, 64 variable parameters for Sr7Ge6 and a=8.0853(6) Å, b=24.545(2) Å, c=8.9782(8) Å, wR2=0.085 (all data), 2307 independent reflections, 64 variable parameters for Ba7Ge6). Ba3Sn2 crystallizes in an own structure type with the space group P43212, Z=4, a=6.6854(2) Å, c=17.842(2) Å, wR2=0.037 (all data), 1163 independent reflections, 25 variable parameters.In Sr7Ge6 and Ba7Ge6 the Ge atoms are arranged as Ge2 dumbbells and Ge4 four-membered atom chains. Their crystal structures cannot be rationalized according to the (8-N) rule. In contrast, Ba3Sn2 presents Sn2 dumbbells as a main structural motif and thereby can be described as an electron precise Zintl phase. The chemical bonding situation in these structures is discussed on the basis of partial and total Density Of States (DOS) curves, band structures including fatbands, topological analysis of the Electron Localization Function (ELF) as well as Bader analysis of the bond critical points using the programs TB-LMTO-ASA and Wien2k. While Ba3Sn2 reveals semiconducting behaviour, all germanides Ae7Ge6 (Ae=Ca, Sr, and Ba) show metallic properties and a considerable π-bonding character between the Ge atoms of the four-membered chains and the dumbbells. The π-bonding character of the germanides is best reflected by the resonance hybrid structures {[Ge–Ge]6−/[Ge–....Ge–....Ge–....Ge]8−}↔{[Ge=Ge]4−/[Ge–Ge–Ge–Ge]10−}.