- 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
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
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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- 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
