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Symmetry Groups of Cyclic Systems in Crystals
Author(s) -
Evarestov R. A.,
Leko A. V.,
Smirnov V. P.
Publication year - 1985
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221280132
Subject(s) - group (periodic table) , symmetry operation , symmetry (geometry) , irreducible representation , symmetry group , space (punctuation) , crystal (programming language) , mathematics , unit (ring theory) , space group , simple (philosophy) , pure mathematics , theoretical physics , crystallography , physics , quantum mechanics , chemistry , geometry , diffraction , computer science , x ray crystallography , philosophy , epistemology , programming language , operating system , mathematics education
Abstract The symmetry group of a cyclic system in a crystal is defined. Its relation to the space group of an infinite crystal is cleared up. It is shown that all the irreducible representations of the cyclic system symmetry group can be found from the definite representations of the space group. The connection between Herring's and reduction group methods developed in the space group representation theory and the large unit cell method is established. A simple and efficient method of the symmetry‐adapted atomic orbitals generation is proposed and illustrated by the examples for α‐quartz and β‐cristobalite crystals (space group D 6 3 and O 7 h ).