Acid–Base Chemistry in the Formation of Mackay-Type Icosahedral Clusters: μ3-Acidity Analysis of Sc-Rich Phases of the Sc–Ir System

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.

Unpredicted but It Exists: Trigonal Sc2Ru with a Significant Metal-Metal Charge Transfer

The Sc₂Ru compound, obtained by high-temperature synthesis, was found to crystallize in a new trigonal hP45 structure type [space group P3̅m1; a = 9.3583(9) Å and c = 11.285(1) Å]: Ru@Sc₈ cubes, Ru@Sc₁₂ icosahedra, and uncommon Ru@Sc₁₀ sphenocoronae are the building blocks of a unique motif tiling the whole crystal space. According to density functional theory studies, Sc₂Ru is a metallic compound characterized by multicenter interactions: a significant charge transfer occurs from Sc to Ru, indicating an unexpectedly strong ionic character of the interactions between the two transition metals. Energy calculations support our experimental results in terms of stability of this compound, contributing to the recurrent discussion on the limits of the high-throughput first-principles calculations for metallic materials design.

A strong metal (Sc) to metal (Ru) charge transfer occurs for the new Sc2Ru compound, indicating a significant ionic contribution to the bond. The Sc₂Ru trigonal crystal structure features a unique structural motif built up by Ru-centered simple cubes and icosahedra connected through hybrid sphenocorona polyhedra. This investigation represents also a little food for thought on the interplay between the experiments and theoretical prediction in metallic materials design.

Cation Clustering in Intermetallics: The Modular Bonding Schemes of CaCu and Ca2Cu

Electropositive metals such as the alkaline earths or lanthanides are generally assumed to act largely as spectator cations in solid state compounds. In polar intermetallic phases, atoms of such elements are indeed often placed at the peripheries of anions or polyanionic fragments. However, they also show a pronounced tendency to cluster with each other in these peripheral regions in a manner suggestive of multicenter bonding. In this Article, we theoretically investigate the bonding schemes that underlie these cationic cluster arrangements, focusing on CaCu (whose two polymorphs are based on the intergrowth of the FeB- and CrB-types) and Ca₂Cu (a Ca-intercalated derivative of CaCu). The structures of these phases are based on Cu zigzag chains embedded in matrices of Ca atoms arranged into increasingly well-developed fragments of closest-packed arrangements. Using reversed approximation Molecular Orbital (raMO) analysis, the Cu chains of both structures are revealed to be connected via nearly fully occupied Cu-Cu isolobal σ-bonds, such that the Cu atoms control 11.67 of the 13 and 15 electrons/formula unit of CaCu and Ca₂Cu, respectively. Most of the remaining electrons are drawn to multicenter bonding functions in the Ca sublattices despite the availability of additional Cu 4p orbitals, indicating that the electronegativity difference between Ca and Cu is insufficient to achieve formal Cu oxidation states far beyond -1. The metallic nature of the Ca-based bonding subsystem is reflected in the raMO analysis by a plurality of resonance structures that can be generated from the occupied crystal orbitals. Across these bonding schemes, a separation of the electronic structure into largely self-contained Ca-Ca and Ca-Cu states is a consistent theme. This modularity in the bonding can be correlated to the ease with which this and related systems rearrange FeB- and CrB-type features, which may provide clues to identifying other intermetallic families with similar degrees of structural versatility.

Atomic structure of icosahedral quasicrystals: stacking multiple quasi-unit cells

An effective tiling approach is proposed for the structural description of icosahedral quasicrystals based on the original substitution algorithm.