Group-theoretical definition of crystal-structure types

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  • Group theoretical definition of crystal

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A mathematically unambiguous definition is given to crystal-structure types for the first time. This enables us to enumerate all the possible crystal-structure types systematically. The classification system is also presented which consists of species, genuses, and families. A species is a refined concept of crystal-structure type, while a genus is a set of crystals whose chemical formulae for primitive cells are similar to each other. The numbers of species in genus A, AB, and A_2 are shown to be 14, 51, and 29 respectively. Atomic arrangements of these structures are given in tables and figures.

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