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

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.

In crystal chemistry and crystal physics, the relations between the symmetry groups (space groups) of crystalline solids are of particular importance. Part I 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 II 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 the 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 chemical reactions in the solid state, to understand the formation of domains and twins in crystals, and to avoid errors in crystal structure determinations. Part III delves further into some specific topics, namely the isomorphic subgroups of space groups, the theory of phase transitions, and computer programs dedicated to crystallographic group theory. In this new edition, several topics have been extended to cover the latest scientific findings, a new chapter has been added dealing with pertinent computer programs, and references have been updated.