- Title Pages
- Title Pages
- Dedicated to <b>Hartmut Baärnighausen</b> and <b>Hans Wondratschek</b>
- Preface
- List of symbols
- 1 Introduction
- 2 Basics of crystallography, part 1
- 3 Mappings
- 4 Basics of crystallography, part 2
- 5 Group theory
- 6 Basics of crystallography, part 3
- 7 Subgroups and supergroups of point and space groups
- 8 Conjugate subgroups, normalizers and equivalent descriptions of crystal structures
- 9 How to handle space groups
- 10 The group-theoretical presentation of crystal-chemical relationships
- 11 Symmetry relations between related crystal structures
- 12 Pitfalls when setting up group-subgroup relations
- 13 Derivation of crystal structures from closest packings of spheres
- 14 Crystal structures of molecular compounds
- 15 Symmetry relations at phase transitions
- 16 Topotactic reactions
- 17 Group—subgroup relations as an aid for structure determination
- 18 Prediction of possible structure types
- 19 Historical remarks
- Appendices
- A Isomorphic subgroups
- B On the theory of phase transitions
- C Symmetry species
- D Solutions to the exercises
- References
- Glossary
- Index
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
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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- Title Pages
- Title Pages
- Dedicated to <b>Hartmut Baärnighausen</b> and <b>Hans Wondratschek</b>
- Preface
- List of symbols
- 1 Introduction
- 2 Basics of crystallography, part 1
- 3 Mappings
- 4 Basics of crystallography, part 2
- 5 Group theory
- 6 Basics of crystallography, part 3
- 7 Subgroups and supergroups of point and space groups
- 8 Conjugate subgroups, normalizers and equivalent descriptions of crystal structures
- 9 How to handle space groups
- 10 The group-theoretical presentation of crystal-chemical relationships
- 11 Symmetry relations between related crystal structures
- 12 Pitfalls when setting up group-subgroup relations
- 13 Derivation of crystal structures from closest packings of spheres
- 14 Crystal structures of molecular compounds
- 15 Symmetry relations at phase transitions
- 16 Topotactic reactions
- 17 Group—subgroup relations as an aid for structure determination
- 18 Prediction of possible structure types
- 19 Historical remarks
- Appendices
- A Isomorphic subgroups
- B On the theory of phase transitions
- C Symmetry species
- D Solutions to the exercises
- References
- Glossary
- Index
