International Tables For Crystallography Symmetry Relations Between Space Groups

Volume A1 presents a systematic treatment of the maximal subgroups and minimal supergroups of the crystallographic plane groups and space groups. It will be a useful resource for scientists engaged in crystal-structure determination, crystal physics or crystal chemistry.

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science. Each of the eight volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching. This volume presents a systematic treatment of the maximal subgroups and minimal supergroups of the crystallographic plane groups and space groups. It is an extension of and a supplement to Volume A, Space-group symmetry, in which only basic data for sub- and supergroups are provided. Group-subgroup relations, apart from their theoretical interest, are the basis of a number of important applications in crystallographic research: (1) In solid-state phase transitions there often exists a group-subgroup relation between the symmetry groups of the two phases. According to Landau theory, this is in fact mandatory for displacive (continuous, second-order) phase transitions. Group-subgroup relations are also indispensable in cases where the symmetry groups of the two phases are not directly related but share a common subgroup or supergroup. (2) Group-subgroup relations provide a concise and powerful tool for revealing and elucidating relations between crystal structures. They can thus help to keep up with the ever-increasing amount of crystal-structure data. Their application requires knowledge of the relations of the Wyckoff positions of group-subgroup related structures. (3) Group-subgroup relations are of great importance in the study of twinned crystals, domain structures and domain boundaries. (4) These relations can even help to identify errors in space-group assignment and crystal-structure determination. (5) Subgroups of space groups provide a valuable approach to teaching crystallographic symmetry. Volume A1 consists of three parts: Part 1 presents an introduction to the theory of space groups at various levels and with many examples. It includes a chapter on the mathematical theory of subgroups. Part 2 gives for each plane group and space group a complete listing of all maximal subgroups and minimal supergroups. The treatment includes the generators of each subgroup as well as any necessary changes of the coordinate system. Maximal isomorphic subgroups are given in parameterized form as infinite series because of the infinite number for each group. A special feature of the presentation is graphs that illustrate the group-subgroup relations. Part 3 lists the relations between the Wyckoff positions of every space group and its subgroups. Again, the infinite number of maximal isomorphic subgroups of each space group are covered by parameterized series. These data for Wyckoff positions are presented here for the first time. Audience: The volume is a valuable addition to the library of scientists engaged in crystal-structure determination, crystal physics or crystal chemistry. It is essential for those interested in phase transitions, the systematic compilation of crystal structures, twinning phenomena and related fields of crystallographic research.

International Tables for Crystallography are no longer available for purchase from Springer. For further information please contact Wiley Inc. (follow the link on the right hand side of this page). This brief teaching edition is a condensed, inexpensive version of Volume A of International Tables for Crystallography. It consists of: complete descriptions of the 17 plane groups, useful for the teaching of symmetry 24 selected space-group examples, of varying complexity and distributed over all seven crystal systems those basic text sections of Volume A that are necessary for the understanding and handling of space groups (Parts 1, 2, 3 and 5). The purpose of the teaching edition is threefold: It should provide a handy (and inexpensive) tool for researchers and students wishing to familiarize themselves with the use of the space-group tables in Volume A. It is designed for use in classroom teaching, and with this aim in mind the price has been kept as low as possible. In order to achieve this, the material has been reprinted from Volume A without any changes, except for pagination. It may serve as a laboratory handbook because the 24 examples include most of the frequently occurring space groups, for both organic and inorganic crystals. The fifth edition of the brief teaching edition has been reviewed by M. Warren [Mineral. Mag. (2003). 67, 826-827].

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science. Volume A of the series, Space-group symmetry, contains diagrams and tables of data for the 17 plane groups, the 230 space groups and the 32 crystallographic point groups.This new edition is edited by M. I. Aroyo and has been extensively updated and revised. Part 1 of the volume provides an introduction to space-group symmetry. It includes chapters on groups, crystallographic and space-group symmetry, descriptions of space groups, coordinate-system transformations and methods of space-group determination. The final chapter provides a useful introduction to topics treated in more depth in Volumes A1 and E of the series. The chapters in this part have been written with teaching in mind, and will prove invaluable for undergraduates or graduates wishing to learn about symmetry in crystallography, while providing a clear introduction to the topic for researchers from other disciplines. Part 2 of the volume presents the diagrams and tables of plane- and space-group data. The layout of the tables of data, the symbols used in the diagrams and the classification of the space groups are explained in a useful guide. Together these form an essential resource not only for professional crystallographers, but also for chemists, physicists, mineralogists, biologists and material scientists who employ crystallographic methods and who are concerned with the structure and the properties of crystalline materials. Part 3 treats more advanced topics on space-group symmetry, and covers crystal lattices, point groups and crystal classes, space-group symbols and their use, lattice complexes, normalizers of space groups, and magnetic subperiodic groups and magnetic space groups. There are eight new chapters in this 6th edition of Volume A, and five chapters have been revised. The layout of the space-group tables has been simplified as the sub- and supergroup data are now available in Volume A1, and there are new general-position diagrams for the cubic space groups. Additional diagrams showing tilted, perspective views of some of the more complex cubic space groups are also provided. More information on the series can be found at: http://it.iucr.org

This sixth edition of what was previously known as the Brief Teaching Edition of Volume A provides an introduction to the basic crystallographic data for space groups found in Volume A, for symmetry relations between space groups in Volume A1 and for subperiodic groups in Volume E of International Tables for Crystallography, to magnetic space groups and to the symmetry database that forms part of International Tables Online at https://it.iucr.org. It is designed for graduate students and young researchers who are new to the field of crystallographic symmetry, and includes many illustrative examples to help readers to understand and use these different kinds of information. Selected tables of symmetry data from the full volumes in the series are also included, making this a handy aid for classroom teaching. References are also provided to further specialized sources for those who need to go deeper into the subject and to textbooks for those who need more background information.

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science. Each of the eight volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching. Volume A treats crystallographic symmetry in direct or physical space. It contains extensive tabulations and illustrations of the 17 plane groups, the 230 space groups and the 32 crystallographic point groups. Parts 1-5 of the volume present introductory material, including lists of symbols and terms, a guide to the use of the space-group tables, and the determination of space groups. Later parts discuss aspects of symmetry theory, such as crystal lattices and normalizers of space groups. Thoroughly updated and improved, the latest edition of Volume A includes an additional chapter on further properties of lattices.

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.