- 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
How to handle space groups
How to handle space groups
- Chapter:
- (p.121) 9 How to handle space groups
- Source:
- Symmetry Relationships between Crystal Structures
- Author(s):
Ulrich Müller
- Publisher:
- Oxford University Press
Among the Wyckoff positions of a space group there often are different positions that are mutually equivalent in the Euclidean normalizer of the space group. Origin shifts or basis transformations can cause an interchange among these Wyckoff positions. The relations between the Wyckoff positions are uniquely determined for every group-subgroup pair. Nonconventional settings of space groups differ from those listed in International Tables for Crystallography. They result from interchange or transformation of the basis vectors and have different Hermann-Mauguin symbols and atomic coordinates.
Keywords: Wyckoff positions, Hermann-Mauguin symbols, space group
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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
