Atomic-environment classification of the hexagonal “intermetallic” structure types

In this paper we give a complete description of the geometrical atomic environments found in the hexagonal intermetallic structure types. Our analysis of 442 structure types showed that 315 are possible, while the remaining 127 structure types have e.g. improbable interatomic distances or are excluded because they are oxides with no intermetallic compounds crystallizing in these structure types. In addition, we observed that 23 atomic environment types are greatly preferred. Out of 20 131 point-sets investigated, 16 392 (81%) belong to one of these 23 atomic environment types. Of the 5646 compounds crystallizing in one of the 315 structure types, 14% belong to a single-environment group (structures in which all atoms have the same type of environment), 35% combine two environment types, 32% have three environments, 11% have four environments and the rest (7%) have five or more environments. Our systematic and comprehensive analysis of the hexagonal structure types verified all presently known relationships between these structure types but also revealed new non-trivial relationships.