Atomic environment classification of the rhombohedral “intermetallic” structure types

In this paper we give a complete description of the geometrical atomic environments found in the rhombohedral intermetallic structure types. Our analysis of 195 structure types showed that 144 are possible, while the remaining 51 structure types have e.g. improbable interatomic distances or are excluded because they are oxides with no intermetallic compounds crystallizing in this structure type. In addition, we observed that 14 atomic environment types are greatly preferred. Out of 6356 investigated point sets, 4482 (71%) belong to one of these 14 atomic environment types. Of the 1324 compounds crystallizing in one of the 144 structure types, 19% belong to a single-environment group (structures in which all atoms have the same type of environment), 15% combine two environment types, 25% have three environments, 34% have four environments and the rest (7%) have five or more environments. Our systematic and comprehensive analysis of the rhombohedral structure types verified all known relationships between these structure types but also revealed new non-trivial relationships.