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Double antisymmetry and the rotation‐reversal space groups
Author(s) -
VanLeeuwen Brian K.,
Gopalan Venkatraman,
Litvin Daniel B.
Publication year - 2014
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273313023176
Subject(s) - antisymmetry , symmetry operation , symmetry (geometry) , symmetry number , rotation (mathematics) , rotational symmetry , space group , space (punctuation) , physics , group (periodic table) , one dimensional symmetry group , octahedral symmetry , symmetry group , octahedron , global symmetry , crystallography , crystal structure , geometry , mathematics , quantum mechanics , chemistry , symmetry breaking , spontaneous symmetry breaking , x ray crystallography , computer science , diffraction , philosophy , ion , linguistics , operating system
Rotation-reversal symmetry was recently introduced to generalize the symmetry classification of rigid static rotations in crystals such as tilted octahedra in perovskite structures and tilted tetrahedra in silica structures. This operation has important implications for crystallographic group theory, namely that new symmetry groups are necessary to properly describe observations of rotation-reversal symmetry in crystals. When both rotation-reversal symmetry and time-reversal symmetry are considered in conjunction with space-group symmetry, it is found that there are 17,803 types of symmetry which a crystal structure can exhibit. These symmetry groups have the potential to advance understanding of polyhedral rotations in crystals, the magnetic structure of crystals and the coupling thereof. The full listing of the double antisymmetry space groups can be found in the supplementary materials of the present work and at http://sites.psu.edu/gopalan/research/symmetry/.