On the Nature of Ge–Pb Bonding in the Solid State. Synthesis, Structural Characterization, and Electronic Structures of Two Unprecedented Germanide-Plumbides

Structures of Three Alkaline-Earth Metal Germanides Refined from Single-Crystal X-ray Diffraction Data

The calcium- and strontium- alumo-germanides SrxCa1–xAl2Ge2 (x ≈ 0.4) and SrAl2Ge2 have been synthesized and structurally characterized. Additionally, a binary calcium germanide CaGe has also been identified as a byproduct. All three crystal structures have been established from single-crystal X-ray diffraction methods and refined with high accuracy and precision. The binary CaGe crystallizes with a CrB-type structure in the orthorhombic space group Cmcm (no. 63; Z = 4; Pearson symbol oC8), where the germanium atoms are interconnected into infinite zigzag chains, formally [Ge]2−. The calcium atoms are arranged in monocapped trigonal prisms, centered by Ge atoms. SrxCa1−xAl2Ge2 (x ≈ 0.4) and SrAl2Ge2 have been confirmed to crystallize with a CaAl2Si2-type structure in the trigonal space group P3¯m1 (no. 164; Z = 1; Pearson symbol hP5), where the germanium and aluminum atoms form puckered double-layers, formally [Al2Ge2]2−. The calcium atoms are located between the layers and reside inside distorted octahedra of Ge atoms. All presented structures have a valence electron count satisfying the octet rules (e.g., Ca2+Ge2− and Ca2+[Al2Ge2]2−) and can be regarded as Zintl phases.

First principles investigation on how site preference and entropy affect the stability of (EuxM1–x)2Ge2Pb (M = Ca, Sr, Ba) polar intermetallics

Density functional theory calculations have been carried out to analyze the factors contributing to the stabilities of a set of recently synthesized quaternary polar intermetallic compounds, (EuxM1–x)2Ge2Pb with M = Ca, Sr, and Ba. Experiments showed that these preferentially crystallized with Pbam (M = Ca) or Cmmm (M = Sr, Ba) symmetry. We systematically explored how the electronic energies of these structures depended on how they were “colored” by the europium/M ions for a wide composition range. It was found that whereas there was very little site preference in the Cmmm structure, the “B” site in the Pbam structure strongly preferred smaller cations. The configurational entropy was also found to play a role in determining which structures might be preferred. However, the experimentally obtained product ratios could only be fully rationalized by the Gibbs free energies of structures containing M:Eu ratios resembling those that were synthesized experimentally. Our results highlight the importance of calculating vibrational contributions to the entropy for realistic structure models (in terms of coloring and composition) to explain product ratios for syntheses carried out at high temperatures.