Topology of Intermetallic Structures: From Statistics to Rational Design.

More than 38 000 substances made only of metal atoms are collected in modern structural databases; we may call them intermetallic compounds. They have important industrial applications, and yet they are terra incognita for most of our undergraduate students. Their structural complexity and synthesis are not easily adaptable to first years laboratories, keeping them away from the standard curricula. They have been described over the years following alternative and complementary views such as coordination polyhedra, atomic layers, and polyatomic clusters. All of these descriptions, albeit relying on grounded principles, have been applied on a subjective basis and never implemented as a strict computational algorithm. Sometimes, the authors generated multiple views of the same structure reported with beautifully drawn figures and/or photos of hand-crafted models in seminal works of the precomputer age. With the use of our multipurpose crystallochemical program package ToposPro, we explored the structural chemistry of intermetallics with objective and reproducible topological methods that allow us to reconcile different structure descriptions. After computing the connectivity patterns between the metal atoms on the basis of Voronoi partitioning of the crystal space, we were able to group the 38 000 intermetallic compounds into 3700 sets of crystal structures with the same topology of atomic net. We have described the different views used in the literature and shown that 12-vertex polyhedra are the most frequent (33%) and that almost half of them are icosahedron-like (46%), followed by cuboctahedron (25%) and, unexpectedly, by bicapped pentagonal prism (13%). Looking for layers, we have found that the hexagonal lattice, which corresponds to the closest packing of spheres on a plane, exists in more than 11 000 crystal structures, confirming the close-packed nature of intermetallics. We have also applied the nanocluster approach, which goes beyond the first coordination sphere and looks for structural units as multishell clusters that assemble the whole structure. This approach shows that 41% of intermetallics can be assembled with a single nanocluster and that 22.4% of these are packed according to the face-centered cubic motif of the closest packing of spheres in three-dimensional space. We have shown that our approach can easily adopt any other building model and hence could become a platform for a universal predictive scheme. Within this scheme, all of the structural descriptors can be related to experimental data and theoretical modeling results and then can be used to synthesize new intermetallic compounds and to foresee novel materials.