Symmetry Group Theory and the Physical Properties of Crystals

Author: Richard C Powell
Publisher: Springer
ISBN: 1441975985
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Complete with reference tables and sample problems, this volume serves as a textbook or reference for solid-state physics and chemistry, materials science, and engineering. Chapters illustrate symmetry, and its role in determining solid properties, as well as a demonstration of group theory.

Group Theory with Applications in Chemical Physics

Author: Patrick W. M. Jacobs
Publisher: Cambridge University Press
ISBN: 9780521642507
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Group Theory is an indispensable mathematical tool in many branches of chemistry and physics. This book provides a self-contained and rigorous account on the fundamentals and applications of the subject to chemical physics, assuming no prior knowledge of group theory. The first half of the book focuses on elementary topics, such as molecular and crystal symmetry, whilst the latter half is more advanced in nature. Discussions on more complex material such as space groups, projective representations, magnetic crystals and spinor bases, often omitted from introductory texts, are expertly dealt with. With the inclusion of numerous exercises and worked examples, this book will appeal to advanced undergraduates and beginning graduate students studying physical sciences and is an ideal text for use on a two-semester course.

Group Theory

Author: Mildred S. Dresselhaus
Publisher: Springer Science & Business Media
ISBN: 3540328998
Format: PDF, ePub
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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.

Group Theory and Its Applications in Physics

Author: Teturo Inui
Publisher: Springer Science & Business Media
ISBN: 3642800211
Format: PDF, Mobi
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This book has been written to introduce readers to group theory and its ap plications in atomic physics, molecular physics, and solid-state physics. The first Japanese edition was published in 1976. The present English edi tion has been translated by the authors from the revised and enlarged edition of 1980. In translation, slight modifications have been made in. Chaps. 8 and 14 to update and condense the contents, together with some minor additions and improvements throughout the volume. The authors cordially thank Professor J. L. Birman and Professor M. Car dona, who encouraged them to prepare the English translation. Tokyo, January 1990 T. Inui . Y. Tanabe Y. Onodera Preface to the Japanese Edition As the title shows, this book has been prepared as a textbook to introduce readers to the applications of group theory in several fields of physics. Group theory is, in a nutshell, the mathematics of symmetry. It has three main areas of application in modern physics. The first originates from early studies of crystal morphology and constitutes a framework for classical crystal physics. The analysis of the symmetry of tensors representing macroscopic physical properties (such as elastic constants) belongs to this category. The sec ond area was enunciated by E. Wigner (1926) as a powerful means of handling quantum-mechanical problems and was first applied in this sense to the analysis of atomic spectra. Soon, H.

Physical Properties of Crystals

Author: J. F. Nye
Publisher: Oxford University Press
ISBN: 9780198511656
Format: PDF
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First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.

Crystal Symmetry Lattice Vibrations and Optical Spectroscopy of Solids

Author: Baldassare Di Bartolo
Publisher: World Scientific
ISBN: 9814579238
Format: PDF, Mobi
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This book provides a comprehensive treatment of the two fundamental aspects of a solid that determine its physical properties: lattice structure and atomic vibrations (phonons). The elements of group theory are extensively developed and used as a tool to show how the symmetry of a solid and the vibrations of the atoms in the solid lead to the physical properties of the material. The uses of different types of spectroscopy techniques that elucidate the lattice structure of a solid and the normal vibrational modes of the atoms in the solid are described. The interaction of light with solids (optical spectroscopy) is described in detail including how lattice symmetry and phonons affect the spectral properties and how spectral properties provide information about the material's symmetry and normal modes of lattice vibrations. The effects of point defects (doping) on the lattice symmetry and atomic vibrations and thus the spectral properties are discussed and used to show how material symmetry and lattice vibrations are critical in determining the properties of solid state lasers. Contents:Symmetry of CrystalsIntroductionConcepts of Group TheoryCrystal SymmetriesGroup Theoretical Treatment of Crystal SymmetriesScattering of X-Rays by CrystalsLattice Vibrations of CrystalsLattice Vibrations of CrystalsThermodynamics of Lattice VibrationsEffects of Lattice Vibrations on X-Ray Scattering and Neutron ScatteringOptical Spectroscopy of Crystals:Interaction of Radiation with MatterOptical Spectra of Impurities in Solids IOptical Spectra of Impurities in Solids IIInteraction of Light with Lattice Vibrations: Infrared Absorption and Inelastic Light ScatteringLattice Vibrations and Lasers Readership: This book is an ideal upper undergraduate/graduate textbook for students in solid state physics courses as well as researchers in this area. Key Features:No other solid state physics textbook deals with lattice vibrations and their effects on the interaction of radiation with matter in the detail that this book doesNo other solid state physics book has the strong focus on symmetry and group theory that this book doesNo other book on group theory provides the variety of detailed examples of how to use group theory that is found in this bookKeywords:Symmetry;Group Theory;Phonons;Spectroscopy;Crystals;Lasers;Solid State Physics

Advanced Mineralogy

Author: A.S. Marfunin
Publisher: Springer Science & Business Media
ISBN: 3642785239
Format: PDF, Docs
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All existing introductory reviews of mineralogy are written accord ing to the same algorithm, sometimes called the "Dana System of Mineralogy". Even modern advanced handbooks, which are cer tainly necessary, include basic data on minerals and are essentially descriptive. When basic information on the chemistry, structure, optical and physical properties, distinguished features and para genesis of 200-400 minerals is presented, then there is practically no further space available to include new ideas and concepts based on recent mineral studies. A possible solution to this dilemma would be to present a book beginning where introductory textbooks end for those already famil iar with the elementary concepts. Such a volume would be tailored to specialists in all fields of science and industry, interested in the most recent results in mineralogy. This approach may be called Advanced Mineralogy. Here, an attempt has been made to survey the current possibilities and aims in mineral matter investigations, including the main characteristics of all the methods, the most important problems and topics of mineral ogy, and related studies. The individual volumes are composed of short, condensed chap ters. Each chapter presents in a complete, albeit condensed, form specific problems, methods, theories, and directions of investigations, and estimates their importance and strategic position in science and industry.

Symmetries and Group Theory in Particle Physics

Author: Giovanni Costa
Publisher: Springer
ISBN: 3642154824
Format: PDF, ePub, Mobi
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Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures.

Group Theory and Quantum Mechanics

Author: Michael Tinkham
Publisher: Courier Corporation
ISBN: 0486131661
Format: PDF, Docs
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Graduate-level text develops group theory relevant to physics and chemistry and illustrates their applications to quantum mechanics, with systematic treatment of quantum theory of atoms, molecules, solids. 1964 edition.

Point Groups Space Groups Crystals Molecules

Author: R Mirman
Publisher: World Scientific Publishing Company
ISBN: 9813105364
Format: PDF, ePub
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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