Atomic environment classification of the tetragonal 'intermetallic' structure types

In this paper we give a complete description of the geometrical atomic environments found in the tetragonal intermetallic structure types. We analyzed the 404 structure types, having 4471 compounds crystallizing in them with, all together, 18233 point sets, for their geometrical correctness. Our analysis showed that 294 are possible, with 4264 compounds and 17157 point sets, while the remaining 110 structure types have for example improbable interatomic distances or are excluded because they are oxides with no intermetallic compounds crystallizing in these structure types. In addition, we observed that in the 294 structure types 23 atomic environment types are greatly preferred. Out of 17157 investigated point sets, 14194 (83%) belong to one of these 23 atomic environment types. Of the 4264 compounds crystallizing in one of the 294 structure types, 16% belong to a single environment group (structures in which all atoms have the same type of environment), 17% combine two environment types, 42% have three environments, 13% have four environments and the rest (12%) have five or more environments. Our systematic and comprehensive analysis of the tetragonal structure types verified all presently known relationships between these structure types but also revealed new non-trivial relationships.