Buffering Octahedra in Mo₄Zr₉P: Intergrowth as a Solution to the Frustrated Packing of Tricapped Trigonal Prisms and Icosahedra

Atomic packings based on icosahedra and tricapped trigonal prisms are prone to frustrationindeed, these polyhedra represent common configurations in metallic glasses. In this Article, we illustrate how these packing issues can serve as a driving force for the formation of modular intermetallic structures. Using Density Functional Theory-Chemical Pressure (DFT-CP) analysis, we relate the Hf₉Mo₄B-type structure of Mo₄Zr₉P to interatomic pressures experienced by the atoms in two parent structures: Zr₃P, whose structure is built from tricapped trigonal prisms, and ZrMo₂, a Laves phase containing icosahedra. CP analysis of Zr₃P reveals that it has particularly frustrated packing because of the entangling of its tricapped trigonal prisms. In the ternary phase, the frustration is significantly relieved as the units become isolated from each other. Further analysis points to the stabilizing effect of a face-sharing network of octahedra in Mo₄Zr₉P that largely separates the structure into Zr–Mo and Zr–P domains and serves as a buffering region for the relaxation of interatomic distances. These conclusions are generalized to the broader members of this structure type with the examination of the CP schemes for the isostructural Mo₄Zr₉B, Al₅Co₂, and Mg₅Pd₂ phases. Finally, we screen the structural literature using the ToposPro software to identify three additional structure types that have similar intergrowth patterns: the Dy₄CoCd, La₂₃Ni₇Mg₄, and Gd₁₄Co₃In₃ types. An analysis of the interatomic distances within the octahedral networks of these structures suggests that these networks commonly facilitate the reconciliation of packing incompatibilities in intermetallic chemistry.