Space Groups And Their Representations

Author : Gertjan Koster
Publisher : Elsevier
Page : 89 pages
File Size : 54,6 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323161176

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Space Groups and Their Representations by Gertjan Koster Pdf

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.

Author : Kovalev
Publisher : CRC Press
Page : 410 pages
File Size : 46,6 Mb
Release : 1993-12-08
Category : Science
ISBN : 2881249345

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Representation of Crystallographic Space Groups by Kovalev Pdf

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

Author : Anonim
Publisher : Academic Press
Page : 454 pages
File Size : 55,7 Mb
Release : 1957-01-01
Category : Technology & Engineering
ISBN : 0080864694

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Solid State Physics by Anonim Pdf

Solid State Physics

Author : George F. Koster
Publisher : Unknown
Page : 84 pages
File Size : 40,8 Mb
Release : 1964
Category : Group theory
ISBN : LCCN:11902445

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Space Groups and Their Representations by George F. Koster Pdf

Author : Nikolai B. Melnikov,Boris I. Reser
Publisher : Springer Nature
Page : 343 pages
File Size : 53,8 Mb
Release : 2023-01-01
Category : Science
ISBN : 9783031139918

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Space Group Representations by Nikolai B. Melnikov,Boris I. Reser Pdf

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.

Author : Uri Shmueli
Publisher : Springer Science & Business Media
Page : 704 pages
File Size : 42,9 Mb
Release : 2008-08-27
Category : Science
ISBN : 1402082053

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International Tables for Crystallography, Volume B by Uri Shmueli Pdf

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.

Author : Hugo F. Franzen
Publisher : Springer Science & Business Media
Page : 108 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642489471

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Second-Order Phase Transitions and the Irreducible Representation of Space Groups by Hugo F. Franzen Pdf

The lecture notes presented in this volume were developed over a period of time that originated with the investigation of a research problem, the distortion from NiAs-type to MnP-type, the group-theoretical implications of which were investigated in collaboration with Professors F. Jellinek and C. Haas of the Laboratory for Inorganic Chemistry at the University of Groningen during the 1973-1974 year. This distortion provides the major example that is worked through in the notes. The subject matter of the notes has been incorporated in part in the lectures of a course in Solid State Chemistry taught several times at Iowa State University, and formed the basis of a series of lectures presented at the Max-Planck Institute for Solid State Research in Stuttgart during 1981- 19821 and as part of a Solid State Chemistry course taught during the spring of 1982 at Arizona State University in Tempe. I wish here to express my gratitude to the Max-Planck Institute for Solid State Research and to Arizona State University for the opportunity and support they provided during the time I was developing and writing the lecture notes of this volume. I wish also to thank the many colleagues and students who have offered comments and suggestions that have improved the accuracy and readability of the notes, and who have provided stimulation through discussion of the ideas presented here. am especially indebted to Professors C. Haas and F.

Author : Uri Shmueli,Professor of Chemistry Uri Shmueli
Publisher : Oxford University Press
Page : 283 pages
File Size : 54,6 Mb
Release : 2007-06-07
Category : Language Arts & Disciplines
ISBN : 019921350X

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Theories and Techniques of Crystal Structure Determination by Uri Shmueli,Professor of Chemistry Uri Shmueli Pdf

The book is a detailed but concise exposition of crystal structure determination at a graduate level. Discussions range from geometrical principles of crystallography, through relevant experimental methods, to techniques of reliable and accurate determination of crystal structures.

Author : Oleg Vladimirovich Kovalev
Publisher : Routledge
Page : 176 pages
File Size : 55,5 Mb
Release : 1965
Category : Mathematics
ISBN : UOM:39015003435271

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Irreducible Representations of the Space Groups by Oleg Vladimirovich Kovalev Pdf

Author : R Mirman
Publisher : World Scientific Publishing Company
Page : 744 pages
File Size : 40,8 Mb
Release : 1999-05-14
Category : Science
ISBN : 9789813105362

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Point Groups, Space Groups, Crystals, Molecules by R Mirman Pdf

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

Author : Dmitriĭ Petrovich Zhelobenko
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 44,5 Mb
Release : 1973-01-01
Category : Mathematics
ISBN : 0821886649

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Compact Lie Groups and Their Representations by Dmitriĭ Petrovich Zhelobenko Pdf

Author : Christopher Bradley,Arthur Cracknell
Publisher : Oxford University Press
Page : 758 pages
File Size : 44,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780199582587

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The Mathematical Theory of Symmetry in Solids by Christopher Bradley,Arthur Cracknell Pdf

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.

Author : Anatoli Klimyk,Konrad Schmüdgen
Publisher : Springer Science & Business Media
Page : 568 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642608964

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Quantum Groups and Their Representations by Anatoli Klimyk,Konrad Schmüdgen Pdf

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.

Author : Joshua Zak
Publisher : Addison Wesley Longman
Page : 296 pages
File Size : 49,5 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:39015017273874

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The Irreducible Representations of Space Groups by Joshua Zak Pdf

Author : Michael Glazer,Gerald Burns
Publisher : Academic Press
Page : 432 pages
File Size : 54,7 Mb
Release : 2013-01-03
Category : Science
ISBN : 9780123946157

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Space Groups for Solid State Scientists by Michael Glazer,Gerald Burns Pdf

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