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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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The group-theoretical presentation of crystal-chemical relationships

The group-theoretical presentation of crystal-chemical relationships

Chapter:
(p.132) (p.133) 10 The group-theoretical presentation of crystal-chemical relationships
Source:
Symmetry Relationships between Crystal Structures
Author(s):

Ulrich Müller

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199669950.003.0010

A Bärnighausen tree is set up according to a given scheme by combining steps of maximal group-subgroup relations. Translationengleiche, klassengleiche and isomorphic subgroups are distinguished, and basis transformations and origin shifts must be marked. The data for all crystal structures, specially the atomic coordinates, should be presented in strict correspondence with each other, even if nonconventional space group settings are then required.

Keywords:   Bärnighausen tree, translationengleiche, klassengleiche, isomorphic subgroups, basis transformations, atomic coordinates, nonconventional space group settings

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