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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

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

Ulrich Müller

Oxford University Press

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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