Symmetry Relationships between Crystal Structures

Auteur
Ulrich Müller studied chemistry at Technische Hochschule in Stuttgart, Germany from 1959 to 1966 and gained a PhD in Inorganic Chemistry. He worked as a Scientific assistant at Universität Karlsruhe, Germany, with H. Bärnighausen from 1967 to 1970 and was a Professor of Inorganic Chemistry at Universität Marburg, Germany, from 1972 to 1992 and 2000 to 2005. He was a Professor of Inorganic Chemistry at Universität Kassel, Germany, from 1992 to 2000, and a visiting Professor at Universidad de Costa Rica, 1975 to 1977. He retired in 2005. Gemma de la Flor studied physics at the University of the Basque Country, Spain from 2004 to 2009 and gained a PhD in Physics at the University of the Basque Country in 2014. She was a post-doc and a lecturer at the University of the Basque Country from 2014 to 2016. She held a post-doc position at Universität Hamburg, Germany, with Professor Boriana Mihailova from 2016 to 2018. Since 2019 she has been a research associate in the petrophysics department at the Karlsruher Institut für Technologie, Germany.

Texte du rabat

An essential property of crystalline solids are their symmetries, which are covered by mathematical groups called space groups. This book explains the corresponding mathematical tools and how the space groups can be used to make evident the relationships between crystal structures and to analyse physical phenomena such as structural transitions.

Contenu

• 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 and normalizers of space groups

• 9: Equivalent descriptions of crystal structures and chirality

• Part II - Symmetry Relations between Space Groups as a Tool to Disclose Connections between Crystal Structures

• 10: How to handle space groups

• 11: The group-theoretical presentation of crystal-chemical relationships

• 12: Symmetry relations between related crystal structures

• 13: Pitfalls when setting up group-subgroup relations

• 14: Derivation of crystal structures from closest packings of spheres

• 15: Crystal structures of molecular compounds

• 16: Symmetry relations at phase transitions

• 17: Topotactic reactions

• 18: Group-subgroup relations as an aid for structure determination

• 19: Prediction of possible structure types

• 20: Historical remarks

• Part III - Widening Excurses to Special Topics

• 21: Isomorphic subgroups

• 22: On the theory of phase transitions

• 23: Symmetry species

• 24: The Bilbao Crystallographic Server

• Appendices