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Author: Gertjan Koster
Publisher: Elsevier
ISBN: 0323161170
Category : Science
Languages : en
Pages : 89
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Book Description
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: Gertjan Koster
Publisher: Elsevier
ISBN: 0323161170
Category : Science
Languages : en
Pages : 89
Get Book Here
Book Description
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: George F. Koster
Publisher:
ISBN:
Category : Group theory
Languages : en
Pages : 84
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Book Description
Author: Christopher Bradley
Publisher: Oxford University Press
ISBN: 0199582580
Category : Mathematics
Languages : en
Pages : 758
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Book Description
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: R. Mirman
Publisher: World Scientific
ISBN: 9789810237325
Category : Science
Languages : en
Pages : 768
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Book Description
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: Nikolai B. Melnikov
Publisher: Springer Nature
ISBN: 3031139917
Category : Science
Languages : en
Pages : 343
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Book Description
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:
Publisher: Academic Press
ISBN: 0080864694
Category : Technology & Engineering
Languages : en
Pages : 473
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Book Description
Solid State Physics
Author: Vladimir Dmitriev
Publisher: World Scientific
ISBN: 981450002X
Category : Science
Languages : en
Pages : 416
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Book Description
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.
Author: Wojciech Florek
Publisher: World Scientific
ISBN: 9814554006
Category :
Languages : en
Pages : 508
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Book Description
These proceedings review the recent developments in current research connected with an adequate description of condensed matter in statistics of quasiparticles, topological invariants and self-similar structures.
Author: Dmitriĭ Petrovich Zhelobenko
Publisher: American Mathematical Soc.
ISBN: 9780821886649
Category : Mathematics
Languages : en
Pages : 464
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Book Description
Author: Vladimir Dmitriev
Publisher: World Scientific
ISBN: 1800612931
Category : Science
Languages : en
Pages : 469
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Book Description
Discontinuous (first-order) phase transitions constitute the most fundamental and widespread type of structural transitions existing in Nature, forming a large majority of the transitions found in elemental crystals, alloys, inorganic compounds, minerals and complex fluids. Nevertheless, only a small part of them, namely, weakly discontinuous transformations, were considered by phenomenological theories, leaving aside the most interesting from a theoretical point of view and the most important for application cases. Discontinuous Phase Transitions in Condensed Matter introduces a density-wave approach to phase transitions which results in a unified, symmetry-based, model-free theory of the weak crystallization of molecular mixtures to liquid-crystalline mesophases, strongly discontinuous crystallization from molten metals and alloys to conventional, fully segregated crystals, to aperiodic, quasi-crystalline structures. Assembly of aperiodic closed virus capsids with non-crystallographic symmetry also falls into the domain of applicability of the density-wave approach.The book also considers the applicability domains of the symmetry-based approach in physics of low-dimensional systems. It includes comparisons of stability of different surface superstructures and metal monoatomic coverage structures on the surface of single-crystalline substrates. The example of the twisted graphene bilayer demonstrates how parametrization in the spirit of an advanced phenomenological approach can establish symmetry-controlled, and therefore model-free, links between geometrical parameters of the twisted bilayer structure and reconstruction of its Brillouin zone and energy bands.
