International Tables for Crystallography, Volume B

International Tables for Crystallography, Volume B

Author: Uri Shmueli

Publisher: Springer Science & Business Media

Published: 2008-08-27

Total Pages: 704

ISBN-13: 9781402082054

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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). Volume B presents accounts of the numerous aspects of reciprocal space in crystallographic research. After an introductory chapter, Part 1 presents the reader with an account of structure-factor formalisms, an extensive treatment of the theory, algorithms and crystallographic applications of Fourier methods, and fundamental as well as advanced treatments of symmetry in reciprocal space. In Part 2, these general accounts are followed by detailed expositions of crystallographic statistics, the theory of direct methods, Patterson techniques, isomorphous replacement and anomalous scattering, and treatments of the role of electron microscopy and diffraction in crystal structure determination, including applications of direct methods to electron crystallography. Part 3 deals with applications of reciprocal space to molecular geometry and `best'-plane calculations, and contains a treatment of the principles of molecular graphics and modelling and their applications. A convergence-acceleration method of importance in the computation of approximate lattice sums is presented and the part concludes with a discussion of the Ewald method. Part 4 contains treatments of various diffuse-scattering phenomena arising from crystal dynamics, disorder and low dimensionality (liquid crystals), and an exposition of the underlying theories and/or experimental evidence. Polymer crystallography and reciprocal-space images of aperiodic crystals are also treated. Part 5 of the volume contains introductory treatments of the theory of the interaction of radiation with matter (dynamical theory) as applied to X-ray, electron and neutron diffraction techniques. The simplified trigonometric expressions for the structure factors in the 230 three-dimensional space groups, which appeared in Volume I of International Tables for X-ray Crystallography, are now given in Appendix 1.4.3 to Chapter 1.4 of this volume. Volume B is a vital addition to the library of scientists engaged in crystal structure determination, crystallographic computing, crystal physics and other fields of crystallographic research. Graduate students specializing in crystallography will find much material suitable for self-study and a rich source of references to the relevant literature.


Tables of Irreducible Representations of Space Groups and Co-representations of Magnetic Space Groups

Tables of Irreducible Representations of Space Groups and Co-representations of Magnetic Space Groups

Author: Stanley C. Miller

Publisher:

Published: 1967

Total Pages: 1234

ISBN-13:

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"This volume contains a computer calculation of tables of the irreducible representations of 230 space groups of all prominent symmetry points in the associated Brillouin zones. The characters of the elements of the group of k are included as well as compatibility tables for related symmetry points. A second section gives the irreducible co-representations of the remaining 1421 magnetic space groups and the classification into the degeneracy types discussed by Wigner. A brief introduction to the theory of space groups will be given before the detailed description of the tables is presented. A general knowledge of group theory is assumed."--Intro. Published 1967.


Representation of Crystallographic Space Groups

Representation of Crystallographic Space Groups

Author: Kovalev

Publisher: CRC Press

Published: 1993-12-08

Total Pages: 410

ISBN-13: 9782881249341

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This new edition of Kovalev's renowned text (first English edition, 1965) presents all the irreducible representations (IRs) and irreducible corepresentations (ICRs) for the 230 crystallographic space groups. In order to give readers the opportunity of representing generally the entire crystallographic symmetry, the method of inducing an IR of the local groups is presented first, and then complete lists of induced representations (InRs) which allow the calculation of the microstructure of any crystal (already known or not yet discovered, but geometrically not forbidden) in any physical question. For research students and researchers in theoretical aspects of solid state physics, crystallography, and space group theory. Translated from the second Russian edition of 1987. Annotation copyright by Book News, Inc., Portland, OR


Space Group Representations

Space Group Representations

Author: Nikolai B. Melnikov

Publisher: Springer Nature

Published: 2023-01-01

Total Pages: 343

ISBN-13: 3031139917

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This book is devoted to the construction of space group representations, their tabulation, and illustration of their use. Representation theory of space groups has a wide range of applications in modern physics and chemistry, including studies of electron and phonon spectra, structural and magnetic phase transitions, spectroscopy, neutron scattering, and superconductivity. The book presents a clear and practical method of deducing the matrices of all irreducible representations, including double-valued, and tabulates the matrices of irreducible projective representations for all 32 crystallographic point groups. One obtains the irreducible representations of all 230 space groups by multiplying the matrices presented in these compact and convenient to use tables by easily computed factors. A number of applications to the electronic band structure calculations are illustrated through real-life examples of different crystal structures. The book's content is accessible to both graduate and advanced undergraduate students with elementary knowledge of group theory and is useful to a wide range of experimentalists and theorists in materials and solid-state physics.


Character Tables and Compatibility Relations of the Eighty Layer Groups and Seventeen Plane Groups

Character Tables and Compatibility Relations of the Eighty Layer Groups and Seventeen Plane Groups

Author: D.B. Litvin

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 205

ISBN-13: 1461304954

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Considers the group-theoretical structure of the layer groups and their irreducible representations. Tabulates the properties of the point groups and translation groups associated with the eighty layer groups; gives the nomenclature, symbol, and elements of the eighty layer groups; tabulates the rec


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.


Isotropy Subgroups Of The 230 Crystallographic Space Groups

Isotropy Subgroups Of The 230 Crystallographic Space Groups

Author: Dorian M Hatch

Publisher: World Scientific

Published: 1989-01-01

Total Pages: 621

ISBN-13: 9814522392

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This book gives a rather exhaustive list of isotropy subgroups of the 230 crystallographic space groups. The symmetry changes for the vast majority of observed phase transitions in crystalline solids can be found in the list. With each entry, information is given concerning both physical and abstract characteristics of the phase transitions.


Group Representation Theory For Physicists (2nd Edition)

Group Representation Theory For Physicists (2nd Edition)

Author: Jialun Ping

Publisher: World Scientific Publishing Company

Published: 2002-08-15

Total Pages: 602

ISBN-13: 981310600X

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This book introduces systematically the eigenfunction method, a new approach to the group representation theory which was developed by the authors in the 1970's and 1980's in accordance with the concept and method used in quantum mechanics. It covers the applications of the group theory in various branches of physics and quantum chemistry, especially nuclear and molecular physics. Extensive tables and computational methods are presented.Group Representation Theory for Physicists may serve as a handbook for researchers doing group theory calculations. It is also a good reference book and textbook for undergraduate and graduate students who intend to use group theory in their future research careers.


Group Theory

Group Theory

Author: Mildred S. Dresselhaus

Publisher: Springer Science & Business Media

Published: 2007-12-18

Total Pages: 576

ISBN-13: 3540328998

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This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.


Author:

Publisher: World Scientific

Published:

Total Pages: 564

ISBN-13: 9813104252

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