Space Group Representations

Author : Kovalev
Publisher : CRC Press
Page : 410 pages
File Size : 55,6 Mb
Release : 1993-12-08
Category : Science
ISBN : 2881249345

Get Book

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 : Nikolai B. Melnikov,Boris I. Reser
Publisher : Springer Nature
Page : 343 pages
File Size : 40,9 Mb
Release : 2023-01-01
Category : Science
ISBN : 9783031139918

Get Book

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 : George F. Koster
Publisher : Unknown
Page : 84 pages
File Size : 47,8 Mb
Release : 1964
Category : Group theory
ISBN : LCCN:11902445

Get Book

Space Groups and Their Representations by George F. Koster Pdf

Author : R. Mirman
Publisher : World Scientific
Page : 768 pages
File Size : 40,5 Mb
Release : 1999
Category : Science
ISBN : 9810237324

Get Book

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.

Author : Oleg Vladimirovich Kovalev
Publisher : Routledge
Page : 176 pages
File Size : 52,5 Mb
Release : 1965
Category : Mathematics
ISBN : UOM:39015003435271

Get Book

Irreducible Representations of the Space Groups by Oleg Vladimirovich Kovalev Pdf

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

Get Book

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 : Uri Shmueli
Publisher : Springer Science & Business Media
Page : 704 pages
File Size : 40,7 Mb
Release : 2008-08-27
Category : Science
ISBN : 1402082053

Get Book

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 : Joshua Zak
Publisher : Addison Wesley Longman
Page : 296 pages
File Size : 54,7 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:39015017273874

Get Book

The Irreducible Representations of Space Groups by Joshua Zak Pdf

Author : Gertjan Koster
Publisher : Elsevier
Page : 89 pages
File Size : 43,7 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323161176

Get Book

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 : Mildred S. Dresselhaus,Gene Dresselhaus,Ado Jorio
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 54,6 Mb
Release : 2007-12-13
Category : Science
ISBN : 9783540328971

Get Book

Group Theory by Mildred S. Dresselhaus,Gene Dresselhaus,Ado Jorio Pdf

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 : Robert A. Evarestov
Publisher : Springer Science & Business Media
Page : 559 pages
File Size : 53,8 Mb
Release : 2007-08-16
Category : Science
ISBN : 9783540487487

Get Book

Quantum Chemistry of Solids by Robert A. Evarestov Pdf

This book delivers a comprehensive account of the main features and possibilities of LCAO methods for the first principles calculations of electronic structure of periodic systems. The first part describes the basic theory underlying the LCAO methods applied to periodic systems and the use of wave-function-based, density-based (DFT) and hybrid hamiltonians. The second part deals with the applications of LCAO methods for calculations of bulk crystal properties.

Author : Stanley C. Miller,William F. Love
Publisher : Unknown
Page : 1234 pages
File Size : 46,7 Mb
Release : 1967
Category : Crystal lattices
ISBN : UOM:39015018448426

Get Book

Tables of Irreducible Representations of Space Groups and Co-representations of Magnetic Space Groups by Stanley C. Miller,William F. Love Pdf

"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.

Author : Anonim
Publisher : Academic Press
Page : 322 pages
File Size : 40,9 Mb
Release : 1975-11-05
Category : Mathematics
ISBN : 0080956254

Get Book

An Introduction to Group Representation Theory by Anonim Pdf

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Author : Yurii I. Lyubich
Publisher : Birkhäuser
Page : 231 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034891691

Get Book

Introduction to the Theory of Banach Representations of Groups by Yurii I. Lyubich Pdf

The theory of group representations plays an important roie in modern mathematics and its applica~ions to natural sciences. In the compulsory university curriculum it is included as a branch of algebra, dealing with representations of finite groups (see, for example, the textbook of A. I. Kostrikin [25]). The representation theory for compact, locally compact Abelian, and Lie groups is co vered in graduate courses, concentrated around functional analysis. The author of the present boo~ has lectured for many years on functional analysis at Khar'kov University. He subsequently con tinued these lectures in the form of a graduate course on the theory of group representations, in which special attention was devoted to a retrospective exposition of operator theory and harmo nic analysis of functions from the standpoint of representation theory. In this approach it was natural to consider not only uni tary, but also Banach representations, and not only representations of groups, but also of semigroups.

Author : Pierre Tol‚dano,Vladimir Dmitriev
Publisher : World Scientific
Page : 424 pages
File Size : 41,7 Mb
Release : 1996
Category : Science
ISBN : 9810223641

Get Book

Reconstructive Phase Transitions by Pierre Tol‚dano,Vladimir Dmitriev Pdf

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.