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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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Group—subgroup relations as an aid for structure determination

Group—subgroup relations as an aid for structure determination

Chapter:
(p.226) (p.227) 17 Group—subgroup relations as an aid for structure determination
Source:
Symmetry Relationships between Crystal Structures
Author(s):

Ulrich Müller

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199669950.003.0017

If X-ray diffraction data do not allow a unique assignment of the space group, but the structure of a similar compound is known, group-subgroup relations can help to decide which space group is correct. If the crystal structure of a protein is known and the space group of crystals of another protein is a subgroup or supergroup thereof, the relation can be used to solve the crystal structure. If superstructure reflections are present, the correct space group is a klassengleiche subgroup of the space group without the superstructure reflections. Suspicious parameters of ‘thermal motion’ indicate that the chosen space group may be wrong and a subgroup should be chosen. The initially wrong choice often is a consequence of a twinned crystal. Often, the correct space group then is a subgroup of the initially chosen space group, but it may also be a supergroup.

Keywords:   space group, group-subgroup relations, superstructure, thermal motion, twinned crystal

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