Physical Properties of Crystals

Their Representation by Tensors and Matrices

Author: J. F. Nye

Publisher: Oxford University Press

ISBN: 9780198511656

Category: Mathematics

Page: 329

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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.

Properties of Materials

Anisotropy, Symmetry, Structure

Author: Robert E. Newnham

Publisher: Oxford University Press on Demand

ISBN: 0198520751

Category: Science

Page: 378

View: 1817

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Tensors, matrices, symmetry, and structure-property relationships form the main subjects of the book. While tensors and matrices provide the mathematical framework for understanding anistropy, on which the physical and chemical properties of crystals and textured materials often depend, atomistic arguments are also needed to qualify the property coefficients in various directions. The atomistic arguments are partly based on symmetry and party on the basic physics and chemistry of materials.

Symmetry and Physical Properties of Crystals

Author: Cécile Malgrange,Christian Ricolleau,Michel Schlenker

Publisher: Springer

ISBN: 9401789932

Category: Science

Page: 522

View: 4140

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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.

Crystal Chemistry

From Basics to Tools for Materials Creation

Author: Gérard Ferey

Publisher: World Scientific Publishing Company

ISBN: 9813144211

Category:

Page: 264

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Devoted to a diverse group of solid state scientists, the book has two objectives, both relating to structural chemistry: (i) a progressive analytic familiarization with the main parameters that govern the organization of crystallized matter and related crystal structures, (ii) a study of what are the various ways to 'read' a structure far beyond its representation in scientific articles. Hence, the reader will, from numerous examples illustrated in color, analyze what are the main characteristics of these structures, from their geometric characteristics, their coordination polyhedra, their connections with the resulting dimensionalities of these solids, including also the defects they exhibit, before looking at possibilities to classify structures, within which recurrence laws can emerge. Chemists are required to understand the potentials of a new structure for becoming future materials scientists. The first part of the book is by no means a database for known structures, but facilitates a progressive understanding of the organization of the solid state. With these tools in hand, the reader is invited in the later part of the book to analyze new structures, and to also use new concepts for viewing structures in a more synthetic way for the future. Such new vision is already leading to the creation of completely new solids with outstanding characteristics that find applications in societal problems concerning energy, energy savings, environment and health. The content is not exclusively academic but relates to the creation of innovative materials, through a more physical approach, that might condition the future of materials.

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.

The Basics of Crystallography and Diffraction

Author: Christopher Hammond

Publisher: OUP Oxford

ISBN: 019156771X

Category: Science

Page: 448

View: 6285

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This book provides a clear introduction to topics which are essential to students in a wide range of scientific disciplines but which are otherwise only covered in specialised and mathematically detailed texts. It shows how crystal structures may be built up from simple ideas of atomic packing and co-ordination, it develops the concepts of crystal symmetry, point and space groups by way of two dimensional examples of patterns and tilings, it explains the concept of the reciprocal lattice in simple terms and shows its importance in an understanding of light, X-ray and electron diffraction. Practical examples of the applications of these techniques are described and also the importance of diffraction in the performance of optical instruments. The book is also of value to the general reader since it shows, by biographical and historical references, how the subject has developed and thereby indicates some of the excitement of scientific discovery.

Structure and Bonding in Crystalline Materials

Author: Gregory S. Rohrer

Publisher: Cambridge University Press

ISBN: 9780521663793

Category: Science

Page: 540

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A graduate level textbook for materials scientists that describes the established principles of crystallography and bonding.

X-Ray Diffraction

Author: B. E. Warren

Publisher: Courier Corporation

ISBN: 0486141616

Category: Science

Page: 400

View: 2253

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Rigorous graduate-level text stresses modern applications to nonstructural problems such as temperature vibration effects, order-disorder phenomena, crystal imperfections, more. Problems. Six Appendixes include tables of values. Bibliographies.

Solid State Physics

Author: Gerald Burns

Publisher: Academic Press

ISBN: 1483288269

Category: Science

Page: 755

View: 2826

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The objective of Solid State Physics is to introduce college seniors and first-year graduate students in physics, electrical engineering, materials science, chemistry, and related areas to this diverse and fascinating field. I have attempted to present this complex subject matter in a coherent, integrated manner, emphasizing fundamental scientific ideas to give the student a strong understanding and "feel" for the physics and the orders of magnitude involved. The subject is varied, covering many important, sophisticated, and practical areas, which, at first, may appear unrelated but which are actually built on the same foundation: the bonding between atoms, the periodic translational symmetry, and the resulting electron energy levels. The text is comprehensive enough so that the basics of broad areas of present research are covered, yet flexible enough so that courses of varying lengths can be satisfied. the exercises at the end of each chapter serve to reinforce and extend the text.

An Introduction to Crystallography

Author: F. C. Phillips

Publisher: Horney Press

ISBN: 9781447417002

Category: Reference

Page: 312

View: 5735

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This classic book offers a comprehensive introduction to the subject of crystallography. Split into two parts: 'The External Symmetry of Crystals' and the 'Symmetry of the Internal Arrangement', and each broken down into many chapters, this book would make an invaluable addition to the bookshelf of anyone with an interest in the subject. Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

Crystallography

Author: Christian Bök

Publisher: Coach House Books

ISBN: 9781552451199

Category: Science

Page: 157

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Crystallography is the mineral science whose name means 'lucid writing.' Long out of print, but now available again in an elegant revised edition, this extraordinary work of avant-garde literature explores the boundary between science and poetry, suggesting that to write with clarity in either discipline involves the most intense thought, much like an act of 'lucid dreaming.' The book reveals that, within the sediment of everyday language, poems are the crystalline formations. -- Back cover.

Tensors

Geometry and Applications

Author: J. M. Landsberg

Publisher: American Mathematical Soc.

ISBN: 0821869078

Category: Mathematics

Page: 439

View: 2886

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Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

Theoretical Physics

Author: Georg Joos,Ira Maximilian Freeman

Publisher: Courier Corporation

ISBN: 9780486652276

Category: Science

Page: 885

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Among the finest, most comprehensive treatments of theoretical physics ever written, this classic volume comprises a superb introduction to the main branches of the discipline and offers solid grounding for further research in a variety of fields. Students will find no better one-volume coverage of so many essential topics; moreover, since its first publication, the book has been substantially revised and updated with additional material on Bessel functions, spherical harmonics, superconductivity, elastomers, and other subjects. The first four chapters review mathematical topics needed by theoretical and experimental physicists (vector analysis, mathematical representation of periodic phenomena, theory of vibrations and waves, theory of functions of a complex variable, the calculus of variations, and more). This material is followed by exhaustive coverage of mechanics (including elasticity and fluid mechanics, as well as relativistic mechanics), a highly detailed treatment of electromagnetic theory, and thorough discussions of thermodynamics, kinetic theory and statistical mechanics, quantum mechanics and nuclear physics. Now available for the first time in paperback, this wide-ranging overview also contains an extensive 40-page appendix which provides detailed solutions to the numerous exercises included throughout the text. Although first published over 50 years ago, the book remains a solid, comprehensive survey, so well written and carefully planned that undergraduates as well as graduate students of theoretical and experimental physics will find it an indispensable reference they will turn to again and again.

Crystallography of Quasicrystals

Concepts, Methods and Structures

Author: Walter Steurer,Sofia Deloudi

Publisher: Springer Science & Business Media

ISBN: 3642018998

Category: Science

Page: 384

View: 1459

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From tilings to quasicrystal structures and from surfaces to the n-dimensional approach, this book gives a full, self-contained in-depth description of the crystallography of quasicrystals. It aims not only at conveying the concepts and a precise picture of the structures of quasicrystals, but it also enables the interested reader to enter the field of quasicrystal structure analysis. Going beyond metallic quasicrystals, it also describes the new, dynamically growing field of photonic quasicrystals. The readership will be graduate students and researchers in crystallography, solid-state physics, materials science, solid- state chemistry and applied mathematics.

Atomistic Properties of Solids

Author: Dinker Sirdeshmukh,Lalitha Sirdeshmukh,K. G. Subhadra

Publisher: Springer Science & Business Media

ISBN: 3642199712

Category: Science

Page: 618

View: 5502

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The book deals with atomistic properties of solids which are determined by the crystal structure, interatomic forces and atomic displacements influenced by the effects of temperature, stress and electric fields. The book gives equal importance to experimental details and theory. There are full chapters dedicated to the tensor nature of physical properties, mechanical properties, lattice vibrations, crystal structure determination and ferroelectricity. The other crystalline states like nano-, poly-, liquid- and quasi crystals are discussed. Several new topics like nonlinear optics and the Rietveld method are presented in the book. The book lays emphasis on the role of symmetry in crystal properties. Comprehensiveness is the strength of the book; this allows users at different levels a choice of chapters according to their requirements.