Symmetry Relationships between Crystal Structures: Applications of Crystallographic Group Theory in Crystal Chemistry [Hardcover]

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.In crystal chemistry and crystal physics, the relations between the symmetry groups (space groups) of crystalline solids are of special importance. Part 1 of this book presents the necessary mathematical foundations and tools: the fundamentals of crystallography with special emphasis on symmetry, the theory of the crystallographic groups, and the formalisms of the needed crystallographic computations. Part 2 gives an insight into applications to problems in crystal chemistry. With the aid of numerous examples, it is shown how crystallographic group theory can be used to make evident relationships between crystal structures, to set up a systematic order in the huge amount of known crystal structures, to predict crystal structures, to analyse phase transitions and topotactic reactions in the solid state, to understand the formation of domains and twins in crystals, and to avoid errors in crystal structure determinations.A broad range of end-of-chapter exercises offers the possibility to apply the learned material. Worked-out solutions to the exercises can be found at the end of the book.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, normalizers and equivalent descriptions of crystal structures9. How to handle space groupsPart II: Symmetry Relations between Space Groups as a Tool to disclose Connections between Crystal Structures10. The group-theoretical presentation of crystal-chemical relationships11. Symmetry relations between between relatedl#*