Space Groups and Their Representations

Space Groups and Their Representations

Author: Gertjan Koster

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 89

ISBN-13: 0323161170

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Space Groups and Their Representations focuses on the discussions on space groups and their corresponding numerical and analytical representations. Divided into six chapters, the book starts with the presentation of the nature and properties of space groups. This topic includes orthogonal transformations and Bravais lattices, such as cubic system, triclinic system, trigonal and hexagonal systems, monoclinic systems, and tetragonal systems. The book then proceeds with the discussion on the irreducible representations of space groups, and then covers the general theory, simplification, and introduction. Discussions on various examples of space groups are given in the third chapter. Numerical representations are provided to support the validity of the different space groups, including discussions on double groups. The book also points out that the irreducible representation of space groups and the application of representation theory to them manifest the latest developments on geometrical crystallography. The text is a vital source of data for scholars and readers who are interested to study space groups and crystallography.


The Mathematical Theory of Symmetry in Solids

The Mathematical Theory of Symmetry in Solids

Author: Christopher Bradley

Publisher: Oxford University Press

Published: 2010

Total Pages: 758

ISBN-13: 0199582580

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This classic book gives, in extensive tables, the irreducible representations of the crystallographic point groups and space groups. These are useful in studying the eigenvalues and eigenfunctions of a particle or quasi-particle in a crystalline solid. The theory is extended to the corepresentations of the Shubnikov groups.


Point Groups, Space Groups, Crystals, Molecules

Point Groups, Space Groups, Crystals, Molecules

Author: R Mirman

Publisher: World Scientific Publishing Company

Published: 1999-05-14

Total Pages: 744

ISBN-13: 9813105364

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This book is by far the most comprehensive treatment of point and space groups, and their meaning and applications. Its completeness makes it especially useful as a text, since it gives the instructor the flexibility to best fit the class and goals. The instructor, not the author, decides what is in the course. And it is the prime book for reference, as material is much more likely to be found in it than in any other book; it also provides detailed guides to other sources. Much of what is taught is folklore, things everyone knows are true, but (almost?) no one knows why, or has seen proofs, justifications, rationales or explanations. (Why are there 14 Bravais lattices, and why these? Are the reasons geometrical, conventional or both? What determines the Wigner–Seitz cells? How do they affect the number of Bravais lattices? Why are symmetry groups relevant to molecules whose vibrations make them unsymmetrical? And so on). Here these analyses are given, interrelated, and in-depth. The understanding so obtained gives a strong foundation for application and extension. Assumptions and restrictions are not merely made explicit, but also emphasized. In order to provide so much information, details and examples, and ways of helping readers learn and understand, the book contains many topics found nowhere else, or only in obscure articles from the distant past. The treatment is (often completely) different from those elsewhere. At least in the explanations, and usually in many other ways, the book is completely new and fresh. It is designed to inform, educate and make the reader think. It strongly emphasizes understanding. The book can be used at many levels, by many different classes of readers — from those who merely want brief explanations (perhaps just of terminology), who just want to skim, to those who wish the most thorough understanding. Request Inspection Copy


Space Groups for Solid State Scientists

Space Groups for Solid State Scientists

Author: Michael Glazer

Publisher: Academic Press

Published: 2013-01-03

Total Pages: 423

ISBN-13: 0123946158

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This comprehensively revised – essentially rewritten – new edition of the 1990 edition (described as "extremely useful" by MATHEMATICAL REVIEWS and as "understandable and comprehensive" by Scitech) guides readers through the dense array of mathematical information in the International Tables Volume A. Thus, most scientists seeking to understand a crystal structure publication can do this from this book without necessarily having to consult the International Tables themselves. This remains the only book aimed at non-crystallographers devoted to teaching them about crystallographic space groups. - Reflecting the bewildering array of recent changes to the International Tables, this new edition brings the standard of science well up-to-date, reorganizes the logical order of chapters, improves diagrams and presents clearer explanations to aid understanding - Clarifies, condenses and simplifies the meaning of the deeply written, complete Tables of Crystallography into manageable chunks - Provides a detailed, multi-factor, interdisciplinary explanation of how to use the International Tables for a number of possible, hitherto unexplored uses - Presents essential knowledge to those needing the necessary but missing pedagogical support and detailed advice – useful for instance in symmetry of domain walls in solids


Quantum Groups and Their Representations

Quantum Groups and Their Representations

Author: Anatoli Klimyk

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 568

ISBN-13: 3642608965

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This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.


Landau Theory Of Phase Transitions, The: Application To Structural, Incommensurate, Magnetic And Liquid Crystal Systems

Landau Theory Of Phase Transitions, The: Application To Structural, Incommensurate, Magnetic And Liquid Crystal Systems

Author: Pierre Toledano

Publisher: World Scientific Publishing Company

Published: 1987-08-01

Total Pages: 471

ISBN-13: 9813103949

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The contents of this book stems from three different objectives. First, it is an introduction to the basic principles and techniques of Landau's theory, which is intended for teaching purposes. A second purpose of the book provides the practical methods for applying Landau's theory to complex systems. The last objective of the book is to incorporate the developments which have arisen in the last fifteen years from the extensive application of the theory to a variety of physical systems.


Reconstructive Phase Transitions: In Crystals And Quasicrystals

Reconstructive Phase Transitions: In Crystals And Quasicrystals

Author: Vladimir Dmitriev

Publisher: World Scientific

Published: 1996-09-30

Total Pages: 416

ISBN-13: 981450002X

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This book deals with the phenomenological theory of first-order structural phase transitions, with a special emphasis on reconstructive transformations in which a group-subgroup relationship between the symmetries of the phases is absent. It starts with a unified presentation of the current approach to first-order phase transitions, using the more recent results of the Landau theory of phase transitions and of the theory of singularities. A general theory of reconstructive phase transitions is then formulated, in which the structures surrounding a transition are expressed in terms of density-waves, providing a natural definition of the transition order-parameters, and a description of the corresponding phase diagrams and relevant physical properties. The applicability of the theory is illustrated by a large number of concrete examples pertaining to the various classes of reconstructive transitions: allotropic transformations of the elements, displacive and order-disorder transformations in metals, alloys and related structures, crystal-quasicrystal transformations.