Double antisymmetry and the rotation-reversal space groups

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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/.

Original languageEnglish (US)
Pages (from-to)24-38
Number of pages15
JournalActa Crystallographica Section A: Foundations and Advances
Volume70
Issue number1
DOIs
StatePublished - Jan 2014

Fingerprint

antisymmetry
Crystal symmetry
symmetry
Crystals
Group theory
Magnetic structure
Silicon Dioxide
Perovskite
crystals
Crystal structure
Silica
group theory
Research
tetrahedrons

All Science Journal Classification (ASJC) codes

  • Structural Biology
  • Biochemistry
  • Materials Science(all)
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Inorganic Chemistry

Cite this

@article{fb386d8e976b4d2b9c5c5e7c3e7b7f6b,
title = "Double antisymmetry and the rotation-reversal space groups",
abstract = "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/.",
author = "Vanleeuwen, {Brian K.} and Venkatraman Gopalan and Litvin, {Daniel B.}",
year = "2014",
month = "1",
doi = "10.1107/S2053273313023176",
language = "English (US)",
volume = "70",
pages = "24--38",
journal = "Acta Crystallographica Section A: Foundations and Advances",
issn = "0108-7673",
publisher = "John Wiley and Sons Inc.",
number = "1",

}

Double antisymmetry and the rotation-reversal space groups. / Vanleeuwen, Brian K.; Gopalan, Venkatraman; Litvin, Daniel B.

In: Acta Crystallographica Section A: Foundations and Advances, Vol. 70, No. 1, 01.2014, p. 24-38.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Double antisymmetry and the rotation-reversal space groups

AU - Vanleeuwen, Brian K.

AU - Gopalan, Venkatraman

AU - Litvin, Daniel B.

PY - 2014/1

Y1 - 2014/1

N2 - 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/.

AB - 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/.

UR - http://www.scopus.com/inward/record.url?scp=84905656522&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905656522&partnerID=8YFLogxK

U2 - 10.1107/S2053273313023176

DO - 10.1107/S2053273313023176

M3 - Article

C2 - 24419168

AN - SCOPUS:84905656522

VL - 70

SP - 24

EP - 38

JO - Acta Crystallographica Section A: Foundations and Advances

JF - Acta Crystallographica Section A: Foundations and Advances

SN - 0108-7673

IS - 1

ER -