Symmetry Relationships between Crystal Structures Applications of Crystallographic Group Theory in Crystal Chemistry

Ulrich Müller, Retired Professor of Inorganic Chemistry, Philipps-Universität Marburg,Gemma de la Flor, Research Associate, Institut für Angewandte Geowissenschaften, Karlsruher Institut für Technologie

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.

1. IntroductionPart I - Crystallographic Foundations2. Basics of crystallography, part 13. Mappings4. Basics of crystallography, part 25. Group theory6. Basics of crystallography, part 37. Subgroups and supergroups of point and space groups8. Conjugate subgroups and normalizers of space groups9. Equivalent descriptions of crystal structures and chiralityPart II - Symmetry Relations between Space Groups as a Tool to Disclose Connections between Crystal Structures10. How to handle space groups11. The group-theoretical presentation of crystal-chemical relationships12. Symmetry relations between related crystal structures13. Pitfalls when setting up group-subgroup relations14. Derivation of crystal structures from closest packings of spheres15. Crystal structures of molecular compounds16. Symmetry relations at phase transitions17. Topotactic reactions18. Group-subgroup relations as an aid for structure determination19. Prediction of possible structure types20. Historical remarksPart III - Widening Excurses to Special Topics21. Isomorphic subgroups22. On the theory of phase transitions23. Symmetry species24. The Bilbao Crystallographic ServerAppendices