Topology of Intermetallic Crystals: Classification, Uniformity, and Transitions

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We have analyzed the crystal structures of 7551 binary intermetallic compounds, which are deposited in the inorganic crystal structure database, using a combined geometrical-topological approach as implemented in our program package ToposPro. We represented each crystal structure with two models: (i) the topological model of periodic atomic net and (ii) the geometrical model of the Voronoi partition of crystal space. Within the former model, we have classified all intermetallics into 949 topological types, 20 of which cover 57% of the whole sample. Using our recently developed topological network model of reconstructive solid-state transformations, we have described possible mechanisms of displacive transitions between the most abundant topological types and revealed a key role of the body-centered lattice in these transitions. The Voronoi partition model enabled us to introduce the concept of uniformity of the overall structure and the environment of separate atoms; the uniformity is estimated by the second moment of inertia of atomic Voronoi polyhedra. We have shown that the structures with a low uniformity value either contain mistakes in the crystallographic data or have significantly directed interatomic bonds. The proposed uniformity criteria can serve for the estimation of the robustness of an intermetallic structure.