Site Symmetry in Crystals

Theory and Applications

Author: Robert Evarestov,Vyacheslav P. Smirnov

Publisher: Springer Science & Business Media

ISBN: 3642974422

Category: Science

Page: 274

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The history of applications of space group theory to solid state physics goes back more than five decades. The periodicity of the lattice and the definition of a k-space were the corner-stones of this application. Prof. Volker Heine in Vol. 35 of Solid State Physics (1980) noted that, even in perfect crystals, where k-space methods are appropriate, the local properties (such as the charge densi ty, bond order, etc.) are defined by the local environment of one atom. Natural ly, "k-space methods" are not appropriate for crystals with point defects, sur faces and interfaces, or for amorphous materials. In such cases the real-space approach favored by chemists to describe molecules has turned out to be very useful. To span the gulf between the k-space and real space methods it is helpful to recall that atoms in crystalline solids possess a site symmetry defined by the symmetry of the local environment of the atom occupying the site. The site symmetry concept is familiar to crystallographers and commonly used by them in the description of crystalline structures. However, in the application of group theory to solid state physics problems, the site symmetry approach has been used only for the last ten to fifteen years. In our book Methods oj Group Theory in the Quantum Chemistry oj Solids published in Russian in 1987 by Leningrad University Press we gave the first results of this application to the theory of electronic structure of crystals.

Symmetry, Group Theory, and the Physical Properties of Crystals

Author: Richard C Powell

Publisher: Springer

ISBN: 1441975985

Category: Science

Page: 230

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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.

Symmetry in Bonding and Spectra

An Introduction

Author: Bodie E. Douglas,Charles A. Hollingsworth

Publisher: Academic Press

ISBN: 0323139310

Category: Science

Page: 456

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Many courses dealing with the material in this text are called "Applications of Group Theory." Emphasizing the central role and primary importance of symmetry in the applications, Symmetry in Bonding and Spectra enables students to handle applications, particularly applications to chemical bonding and spectroscopy. It contains the essential background in vectors and matrices for the applications, along with concise reviews of simple molecular orbital theory, ligand field theory, and treatments of molecular shapes, as well as some quantum mechanics. Solved examples in the text illustrate theory and applications or introduce special points. Extensive problem sets cover the important methods and applications, with the answers in the appendix.

Quantum Chemistry of Solids

The LCAO First Principles Treatment of Crystals

Author: Robert Evarestov

Publisher: Springer Science & Business Media

ISBN: 3540487484

Category: Science

Page: 560

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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.

Symmetry Relationships Between Crystal Structures

Applications of Crystallographic Group Theory in Crystal Chemistry

Author: Ulrich Müller

Publisher: Oxford University Press

ISBN: 0199669953

Category: Science

Page: 332

View: 6140

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The book presents the basic information needed to understand and to organize the huge amount of known structures of crystalline solids. Its basis is crystallographic group theory (space group theory), with special emphasis on the relations between the symmetry properties of crystals.

Spectroscopic Properties of Rare Earths in Optical Materials

Author: ... Liu-Jacquier,Bernard Jacquier

Publisher: Springer Science & Business Media

ISBN: 9783540238867

Category: Science

Page: 550

View: 7256

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Aimed at researchers and graduate students, this book provides up-to-date information for understanding electronic interactions that impact the optical properties of rare earth ions in solids. Its goal is to establish a connection between fundamental principles and the materials properties of rare-earth activated luminescent and laser optical materials. The theoretical survey and introduction to spectroscopic properties include electronic energy level structure, intensities of optical transitions, ion-phonon interactions, line broadening, and energy transfer and up-conversion. An important aspect of the book lies in its deep and detailed discussions on materials properties and the potential of new applications such as optical storage, information processing, nanophotonics, and molecular probes that have been identified in recent experimental studies. This volume will be a valuable reference book on advanced topics of rare earth spectroscopy and materials science.

Phase Transitions and Crystal Symmetry

Author: I͡Uriĭ Aleksandrovich Izi͡umov,V.N. Syromyatnikov

Publisher: Springer Science & Business Media

ISBN: 9780792305422

Category: Science

Page: 443

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About half a century ago Landau formulated the central principles of the phe nomenological second-order phase transition theory which is based on the idea of spontaneous symmetry breaking at phase transition. By means of this ap proach it has been possible to treat phase transitions of different nature in altogether distinct systems from a unified viewpoint, to embrace the aforemen tioned transitions by a unified body of mathematics and to show that, in a certain sense, physical systems in the vicinity of second-order phase transitions exhibit universal behavior. For several decades the Landau method has been extensively used to an alyze specific phase transitions in systems and has been providing a basis for interpreting experimental data on the behavior of physical characteristics near the phase transition, including the behavior of these characteristics in systems subject to various external effects such as pressure, electric and magnetic fields, deformation, etc. The symmetry aspects of Landau's theory are perhaps most effective in analyzing phase transitions in crystals because the relevant body of mathemat ics for this symmetry, namely, the crystal space group representation, has been worked out in great detail. Since particular phase transitions in crystals often call for a subtle symmetry analysis, the Landau method has been continually refined and developed over the past ten or fifteen years.

Symmetry in Crystallography

Understanding the International Tables

Author: Paolo Radaelli

Publisher: Oxford University Press

ISBN: 0199550654

Category: Mathematics

Page: 126

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A fresh approach to teaching crystallographic symmetry. Rather than being swamped by heavy algebraic notation, the reader is taken through a series of simple and beautiful examples from the visual arts, and taught how to analyse them employing the 'pictorial' diagrams used in the International Tables of Crystallography.

Symmetry and Physical Properties of Crystals

Author: Cécile Malgrange,Christian Ricolleau,Michel Schlenker

Publisher: Springer

ISBN: 9401789932

Category: Science

Page: 522

View: 9868

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Crystals are everywhere, from natural crystals (minerals) through the semiconductors and magnetic materials in electronic devices and computers or piezoelectric resonators at the heart of our quartz watches to electro-optical devices. Understanding them in depth is essential both for pure research and for their applications. This book provides a clear, thorough presentation of their symmetry, both at the microscopic space-group level and the macroscopic point-group level. The implications of the symmetry of crystals for their physical properties are then presented, together with their mathematical description in terms of tensors. The conditions on the symmetry of a crystal for a given property to exist then become clear, as does the symmetry of the property. The geometrical representation of tensor quantities or properties is presented, and its use in determining important relationships emphasized. An original feature of this book is that most chapters include exercises with complete solutions. This allows readers to test and improve their understanding of the material. The intended readership includes undergraduate and graduate students in materials science and materials-related aspects of electrical and optical engineering; researchers involved in the investigation of the physical properties of crystals and the design of applications based on crystal properties such as piezoelectricity, electro-optics, optical activity and all those involved in the characterization of the structural properties of materials.

Structure of Materials

An Introduction to Crystallography, Diffraction and Symmetry

Author: Marc De Graef,Michael E. McHenry

Publisher: Cambridge University Press

ISBN: 1139560476

Category: Technology & Engineering

Page: N.A

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This highly readable, popular textbook for upper undergraduates and graduates comprehensively covers the fundamentals of crystallography and symmetry, applying these concepts to a large range of materials. New to this edition are more streamlined coverage of crystallography, additional coverage of magnetic point group symmetry and updated material on extraterrestrial minerals and rocks. New exercises at the end of chapters, plus over 500 additional exercises available online, allow students to check their understanding of key concepts and put into practice what they have learnt. Over 400 illustrations within the text help students visualise crystal structures and more abstract mathematical objects, supporting more difficult topics like point group symmetries. Historical and biographical sections add colour and interest by giving an insight into those who have contributed significantly to the field. Supplementary online material includes password-protected solutions, over 100 crystal structure data files, and Powerpoints of figures from the book.

Geometry of Crystals, Polycrystals, and Phase Transformations

Author: Harshad K. D. H. Bhadeshia

Publisher: CRC Press

ISBN: 1351629107

Category: Science

Page: 252

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Organized into a two-part structure aimed at readers of differing experience levels, Geometry of Crystals, Polycrystals, and Phase Transformations is accessible to both newcomers and advanced researchers within the field of crystallography. The first part of the text covers what any reader in the material sciences, physics, chemistry, earth sciences and natural sciences in general should know about crystallography. It is intentionally concise and covers sufficient material to form a firm foundation. The second part is aimed at researchers and discusses phase transformations, deformations, and interface crystallography in depth. The phase transformations are limited to those dominated by crystallography. The entire book contains worked examples and uniquely deals not just with crystals but aggregates of crystals and solid-state transformations between crystals.

The Effective Crystal Field Potential

Author: J. Mulak,Z. Gajek

Publisher: Elsevier

ISBN: 9780080530710

Category: Science

Page: 316

View: 8524

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As it results from the very nature of things, the spherical symmetry of the surrounding of a site in a crystal lattice or an atom in a molecule can never occur. Therefore, the eigenfunctions and eigenvalues of any bound ion or atom have to differ from those of spherically symmetric respective free ions. In this way, the most simplified concept of the crystal field effect or ligand field effect in the case of individual molecules can be introduced. The conventional notion of the crystal field potential is narrowed to its non-spherical part only through ignoring the dominating spherical part which produces only a uniform energy shift of gravity centres of the free ion terms. It is well understood that the non-spherical part of the effective potential "seen" by open-shell electrons localized on a metal ion plays an essential role in most observed properties. Light adsorption, electron paramagnetic resonance, inelastic neutron scattering and basic characteristics derived from magnetic and thermal measurements, are only examples of a much wider class of experimental results dependent on it. The influence is discerned in all kinds of materials containing unpaired localized electrons: ionic crystals, semiconductors and metallic compounds including materials as intriguing as high-Tc superconductors, or heavy fermion systems. It is evident from the above that we deal with a widespread effect relative to all free ion terms except those which can stand the lowered symmetry, e.g. S-terms. Despite the universality of the phenomenon, the available handbooks on solid state physics pay only marginal attention to it, merely making mention of its occurrence. Present understanding of the origins of the crystal field potential differs essentially from the pioneering electrostatic picture postulated in the twenties. The considerable development of the theory that has been put forward since then can be traced in many regular articles scattered throughout the literature. The last two decades have left their impression as well but, to the authors' best knowledge, this period has not been closed with a more extended review. This has also motivated us to compile the main achievements in the field in the form of a book.

Symmetry Relationships between Crystal Structures

Applications of Crystallographic Group Theory in Crystal Chemistry

Author: Ulrich Müller

Publisher: OUP Oxford

ISBN: 0191648809

Category: Science

Page: 352

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In crystal chemistry and crystal physics, the relations between the symmetry groups (space groups) of crystalline solids are of special importance. Part 1 of this book presents the necessary mathematical foundations and tools: the fundamentals of crystallography with special emphasis on symmetry, the theory of the crystallographic groups, and the formalisms of the needed crystallographic computations. Part 2 gives an insight into applications to problems in crystal chemistry. With the aid of numerous examples, it is shown how crystallographic group theory can be used to make evident relationships between crystal structures, to set up a systematic order in the huge amount of known crystal structures, to predict crystal structures, to analyse phase transitions and topotactic reactions in the solid state, to understand the formation of domains and twins in crystals, and to avoid errors in crystal structure determinations. A broad range of end-of-chapter exercises offers the possibility to apply the learned material. Worked-out solutions to the exercises can be found at the end of the book.

Outline of Crystallography for Biologists

Author: David Blow

Publisher: Oxford University Press on Demand

ISBN: 0198510519

Category: Medical

Page: 236

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X-ray crystallography is the main method used to determine the structure of biological molecules. X-ray crystallography is explained without maths and reading this text allows biologists to assess the quality and accuracy of biological structures.

Handbook of Electron Spin Resonance

Author: Charles P. Jr. Poole,Horacio A. Farach

Publisher: Springer Science & Business Media

ISBN: 9780387986609

Category: Science

Page: 375

View: 2428

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The continuously expanding field of electron spin resonance (ESR) has broadened our understanding of physics, chemistry, biology, medicine and related sciences over the last fifty years. In the first volume Professors Poole and Farach provided one of the first definitive reference tools for this field. These handbooks bring together wide- ranging data from diverse disciplines within ESR and integrate the data into a comprehesive and definitive resource. In this second volume of the Handbook of Electron Spin Resonance, the authors present a comprehensive source subfields of ESR not covered in the first volume. Topics covered in this volume include: * Sensitivity * Field Swept versus Frequency Swept Spectra * Resonators * Line Shapes * Electron Spin Echo Envelope Modulation * Hamiltonian types and symmetries, including a comprehensive tabulation of transition ion data * ESR Imaging * High Magnetic Fields and High Frequencies Written by recognized experts in the field, and intended for students and researchers, the Handbook of Electron Spin Resonance will prove to be an invaluable reference for all those involved in ESR research.

Applied Group Theory

Selected Readings in Physics

Author: Arthur P. Cracknell

Publisher: Elsevier

ISBN: 1483149382

Category: Science

Page: 430

View: 7975

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Selected Readings in Physics: Applied Group Theory provides information pertinent to the fundamental aspects of applied group theory. This book discusses the properties of symmetry of a system in quantum mechanics. Organized into two parts encompassing nine chapters, this book begins with an overview of the problem of elastic vibrations of a symmetric structure. This text then examines the numbers, degeneracies, and symmetries of the normal modes of vibration. Other chapters consider the conditions under which a polyatomic molecule can have a stable equilibrium configuration when its electronic state has orbital degeneracy. This book discusses as well the effect of an electric field having a given symmetry upon an atom. The final chapter deals with the symmetry of crystals with a magnetic moment. This book is intended to be suitable for final-year students and fresh postgraduate students in physics. Physicists and researcher workers will also find this book extremely useful.

Symmetry of Crystals and Molecules

Author: Mark Ladd

Publisher: Oxford University Press, USA

ISBN: 0199670889

Category: Science

Page: 433

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An eminently readable book on the symmetry of crystals and molecules, starting from first principles

Space Groups for Solid State Scientists

Author: Michael Glazer,Gerald Burns

Publisher: Academic Press

ISBN: 0123946158

Category: Science

Page: 432

View: 9608

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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

Crystal Structures

Lattices and Solids in Stereoview

Author: M Ladd

Publisher: Elsevier

ISBN: 1782420460

Category: Science

Page: 192

View: 7433

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This survey of the important types of inorganic and organic crystal structures treats its subject thoroughly and in sufficient depth for undergraduate modules in chemistry courses. Features of this book are the instructions for 3D stereoviewing which is central to a full appreciation of the presentation. Clear directions for making your own stereo have been provided in the book, which enables readers to examine the plentiful stereo of lattices and crystal structures which are illustrated. The introductory chapter explains point-group and space-group symmetry insofar as required to understand lattices and crystal structures. Crystal structures are sub-divided according to the atomic force mainly responsible for cohesion in the solid state, The descriptions of the structures are gi in crystallographic terms, including data on the space group, molecular symmetry and molecular geometry. Discussions of bonding theory for each sub-division of the structures enhance and strengthen the author’s presentation. The book stems from the author’s successful lecture courses, tested and refined in class teaching. It draws as necessary on equilibrium thermodynamics and other chemical topics, with avoidance of advanced mathematics, A level being the prerequisite. Examines the important types of inorganic and organic crystal structures Includes instructions for making simple stereoviewers and computer programs Draws, as necessary, on equilibrium thermodynamics and other chemical topics, with avoidance of advanced mathematics

Molecular Aggregation

Structure Analysis and Molecular Simulation of Crystals and Liquids

Author: Angelo Gavezzotti

Publisher: OUP Oxford

ISBN: 0198570805

Category: Business & Economics

Page: 425

View: 7153

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The book is divided in two parts, to supply first the basic elements of the language, with short but complete explanations of terms, methods and theories; and then to describe the present status of studies on the processes by which organic molecules aggregate to form observable bodies and to determine their physical and chemical properties.