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Symmetry Relationships between Crystal StructuresApplications of Crystallographic Group Theory in Crystal Chemistry$
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Ulrich Müller

Print publication date: 2013

Print ISBN-13: 9780199669950

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199669950.001.0001

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Symmetry relations between related crystal structures

Symmetry relations between related crystal structures

(p.137) 11 Symmetry relations between related crystal structures
Symmetry Relationships between Crystal Structures

Ulrich Müller

Oxford University Press

This chapter first presents details concerning Bärnighausen trees for translationengleiche subgroups. For klassengleiche subgroups, it discusses special aspects concerning subgroups on a par, subgroups with an enlarged unit cell, and subgroups with loss of centring. For isomorphic subgroups, the distinction between space group and space group type is important. A general subgroup is neither translationengleiche nor klassengleiche; it cannot be a maximal subgroup. Crystal structures can also be related if their space groups have a common supergroup. The modular way to put together Bärnighausen trees permits the construction of trees for large families of structures. The hettotypes result either from atomic substitutions or from structural distortions, including distortions due to phase transitions.

Keywords:   Bärnighausen tree, translationengleiche subgroup, klassengleiche subgroup, isomorphic subgroup, general subgroup, common supergroup, hettotypes

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