Symmetry Relationships between Crystal Structures

Description

The book presents the basic information needed to understand and to organize the huge amount of known structures of crystalline solids. Its basis is crystallographic group theory (space group theory), with special emphasis on the relations between the symmetry properties of crystals.

• Presents the basics of the symmetry of crystals (space groups) and the application of crystallographic group theory
• Gives a thorough treatment of crystallographic group-subgroup relations
• Emphasis on theory and applications
• Numerous exercices offer the possibility to apply the learned material

About the Author(s)

Ulrich Müller, Fachbereich Chemie, Philipps-Universität Marburg, Germany

Ulrich Müller was born in Colombia in 1940. He studied chemistry in Germany. His Ph.D. work (1964 - 1966) was performed in Inorganic Chemistry, partly at the University of Stuttgart, Germany, partly at Purdue University, Indiana, USA. After post-doctoral work at the University of Karlsruhe, Germany, he was appointed as professor of Inorganic Chemistry at the University of Marburg, Gemany, in 1972. From 1992 to 1999 he was professor of solid state chemistry at the University of Kassel, Germany, and then returned to the University of Marburg. He is now retired since 2005. He is the author of several textbooks in chemistry for beginners and advanced students.

Table of Contents

1:Introduction
Part I: Crystallographic Foundations
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
Part II: Symmetry Relations between Space Groups as a Tool to disclose Connections between Crystal Structures
10:The group-theoretical presentation of crystal-chemical relationships
11:Symmetry relations between 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
Appendix A: Isomorphic subgroups
Appendix B: On the theory of phase transitions
Appendix C: Symmetry species
Appendix D: Solutions to the exercises
References
Glossary
Index

Reviews

"Here we have ... a rigorous, carefully checked and polished text which ... we have a reference text which, with its numerous examples and exercises, also perfectly fits the purpose of self-study, provided the reader is sufficiently familiar with space-group theory ... This is a book that every crystallographer taking seriously his job should have on his shelf." - Acta Crystallographica B

"Structural crystallographers in biology, chemistry and physics meet symmetry and sometimes relatively complicated cases. More can be made of symmetry relations too. This book takes the reader beyond structure. The book shows how to make use of the symmetry relations described in International Tables as well as understand e.g. crystal structure types, analyse phase transitions, domain formation and twinning in crystals as well as to avoid errors in crystal structure determinations such as choice of incorrect space group. Numerous chapter exercises are a distinctive feature and offer the possibility to apply the material that has been learnt; solutions to the exercises are at the end of the book." - John R. Helliwell, School of Chemistry, The University of Manchester