Download or read book Tensor Properties of Materials Generalized Compliance and Conductivity written by A. R. Billings and published by . This book was released on 1969 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tensor Properties of Materials written by Alan Reginald Billings and published by John Wiley & Sons. This book was released on 1969 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Properties of Materials written by Robert E. Newnham and published by Oxford University Press. This book was released on 2005 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Crystals are sometimes called 'Flowers of the Mineral Kingdom'. In addition to their great beauty, crystals and other textured materials are enormously useful in electronics, optics, acoustics and many other engineering applications. This richly illustrated text describes the underlying principles of crystal physics and chemistry, covering a wide range of topics and illustrating numerous applications in many fields of engineering using the most important materials today. Tensors, matrices, symmetry and structure-property relationships form the main subjects of the book. While tensors and matrices provide the mathematical framework for understanding anisotropy, on which the physical and chemical properties of crystals and textured materials often depend, atomistic arguments are also needed to quantify the property coefficients in various directions. The atomistic arguments are partly based on symmetry and partly on the basic physics and chemistry of materials. After introducing the point groups appropriate for single crystals, textured materials and ordered magnetic structures, the directional properties of many different materials are described: linear and nonlinear elasticity, piezoelectricity and electrostriction, magnetic phenomena, diffusion and other transport properties, and both primary and secondary ferroic behavior. With crystal optics (its roots in classical mineralogy) having become an important component of the information age, nonlinear optics is described along with the piexo-optics, magneto-optics, and analogous linear and nonlinear acoustic wave phenomena. Enantiomorphism, optical activity, and chemical anisotropy are discussed in the final chapters of the book.
Download or read book Physical Properties of Crystals written by J. F. Nye and published by Oxford University Press. This book was released on 1985 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensor Properties of Materials written by Alan Reginald Billings and published by John Wiley & Sons. This book was released on 1969 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tensor Properties of Solids written by Richard F. Tinder and published by Morgan & Claypool Publishers. This book was released on 2008 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor Properties of Solids presents the phenomenological development of solid state properties represented as matter tensors in two parts: Part I on equilibrium tensor properties and Part II on transport tensor properties. Part I begins with an introduction to tensor notation, transformations, algebra, and calculus together with the matrix representations. Crystallography, as it relates to tensor properties of crystals, completes the background treatment. A generalized treatment of solid-state equilibrium thermodynamics leads to the systematic correlation of equilibrium tensor properties. This is followed by developments covering first-, second-, third-, and higher-order tensor effects. Included are the generalized compliance and rigidity matrices for first-order tensor properties, Maxwell relations, effect of measurement conditions, and the dependent coupled effects and use of interaction diagrams. Part I concludes with the second- and higher-order effects, including numerous optical tensor properties. Part II presents the driving forces and fluxes for the well-known proper conductivities. An introduction to irreversible thermodynamics includes the concepts of microscopic reversibility, Onsager's reciprocity principle, entropy density production, and the proper choice of the transport parameters. This is followed by the force-flux equations for electronic charge and heat flow and the relationships between the proper conductivities and phenomenological coefficients. The thermoelectric effects in solids are discussed and extended to the piezothermoelectric and piezoresistance tensor effects. The subjects of thermomagnetic, galvanomagnetic, and thermogalvanomagnetic effects are developed together with other higher-order magnetotransport property tensors. A glossary of terms, expressions, and symbols are provided at the end of the text, and end-of-chapter problems are provided on request. Endnotes provide the necessary references for further reading.
Download or read book Tensor Properties of Solids Part One written by Richard Tinder and published by Springer Nature. This book was released on 2022-05-31 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor Properties of Solids presents the phenomenological development of solid state properties represented as matter tensors in two parts: Part I on equilibrium tensor properties and Part II on transport tensor properties. Part I begins with an introduction to tensor notation, transformations, algebra, and calculus together with the matrix representations. Crystallography, as it relates to tensor properties of crystals, completes the background treatment. A generalized treatment of solid-state equilibrium thermodynamics leads to the systematic correlation of equilibrium tensor properties. This is followed by developments covering first-, second-, third-, and higher-order tensor effects. Included are the generalized compliance and rigidity matrices for first-order tensor properties, Maxwell relations, effect of measurement conditions, and the dependent coupled effects and use of interaction diagrams. Part I concludes with the second- and higher-order effects, including numerous optical tensor properties. Part II presents the driving forces and fluxes for the well-known proper conductivities. An introduction to irreversible thermodynamics includes the concepts of microscopic reversibility, Onsager's reciprocity principle, entropy density production, and the proper choice of the transport parameters. This is followed by the force-flux equations for electronic charge and heat flow and the relationships between the proper conductivities and phenomenological coefficients. The thermoelectric effects in solids are discussed and extended to the piezothermoelectric and piezoresistance tensor effects. The subjects of thermomagnetic, galvanomagnetic, and thermogalvanomagnetic effects are developed together with other higher-order magnetotransport property tensors. A glossary of terms, expressions, and symbols are provided at the end of the text, and end-of-chapter problems are provided on request. Endnotes provide the necessary references for further reading. Table of Contents: I. Equilibrium Tensor Properties of Solids / Introduction / Introduction to Tensor Notation, Tensor Transformations, Tensor Calculus, and Matrix Representation / Crystal Systems, Symmetry Elements, and Symmetry Transformations / Generalized Thermostatics and the Systematic Correlation of Physical Properties / The Dependent Coupled Effects and the Interrelationships Between First-Order Tensor Properties - Use of Interaction Diagrams / Third- and Fourth-Rank Tensor Properties - Symmetry Considerations / Second- and Higher-Order Effects - Symmetry Considerations / II. Transport Properties of Solids / Introduction to Transport Properties and the Thermodynamics of Irreversible Processes / Thermoelectric, Piezothermoelectric, and Diffusive Effects in Solids / Effect of Magnetic Field on the Transport Properties / Appendix A: Magnetic Tensor Properties, Magnetic Crystals, and the Combined Space-Time Transformations / Endnotes / Glossary / Biography / Index
Download or read book Tensor Properties of Crystals written by D Lovett and published by CRC Press. This book was released on 2018-05-04 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of single crystals for scientific and technological applications is now widespread in solid-state physics, optics, electronics, materials science, and geophysics. An understanding of the variation of physical properties with crystalline direction is essential to maximize the performance of solid-state devices. Written from a physical viewpoint and avoiding advanced mathematics, Tensor Properties of Crystals provides a concise introduction to the tensor properties of crystals at a level suitable for advanced undergraduate and graduate students. While retaining the successful basic format of the well-known first edition, this second edition brings the material up to date with the latest developments in nonlinear optics and modulated structures. Because of the increasing importance of nonlinear optics, a new chapter on optoelectronics has been added. This edition also includes a short discussion on incommensurate modulated structures in the final chapter because they are relevant to high temperature superconductors and to ferroelectric and ferromagnetic materials. The book extensively contains diagrams, worked examples, and problems with answers throughout.
Download or read book Tensor Properties of Crystals written by D. R. Lovett and published by Institute of Physics Publishing (GB). This book was released on 1989 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tensor Properties of Solids Part Two written by Richard Tinder and published by Springer Nature. This book was released on 2022-05-31 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor Properties of Solids presents the phenomenological development of solid state properties represented as matter tensors in two parts: Part I on equilibrium tensor properties and Part II on transport tensor properties. Part I begins with an introduction to tensor notation, transformations, algebra, and calculus together with the matrix representations. Crystallography, as it relates to tensor properties of crystals, completes the background treatment. A generalized treatment of solid-state equilibrium thermodynamics leads to the systematic correlation of equilibrium tensor properties. This is followed by developments covering first-, second-, third-, and higher-order tensor effects. Included are the generalized compliance and rigidity matrices for first-order tensor properties, Maxwell relations, effect of measurement conditions, and the dependent coupled effects and use of interaction diagrams. Part I concludes with the second- and higher-order effects, including numerous optical tensor properties. Part II presents the driving forces and fluxes for the well-known proper conductivities. An introduction to irreversible thermodynamics includes the concepts of microscopic reversibility, Onsager's reciprocity principle, entropy density production, and the proper choice of the transport parameters. This is followed by the force-flux equations for electronic charge and heat flow and the relationships between the proper conductivities and phenomenological coefficients. The thermoelectric effects in solids are discussed and extended to the piezothermoelectric and piezoresistance tensor effects. The subjects of thermomagnetic, galvanomagnetic, and thermogalvanomagnetic effects are developed together with other higher-order magnetotransport property tensors. A glossary of terms, expressions, and symbols are provided at the end of the text, and end-of-chapter problems are provided on request. Endnotes provide the necessary references for further reading. Table of Contents: I. Equilibrium Tensor Properties of Solids / Introduction / Introduction to Tensor Notation, Tensor Transformations, Tensor Calculus, and Matrix Representation / Crystal Systems, Symmetry Elements, and Symmetry Transformations / Generalized Thermostatics and the Systematic Correlation of Physical Properties / The Dependent Coupled Effects and the Interrelationships Between First-Order Tensor Properties - Use of Interaction Diagrams / Third- and Fourth-Rank Tensor Properties - Symmetry Considerations / Second- and Higher-Order Effects - Symmetry Considerations / II. Transport Properties of Solids / Introduction to Transport Properties and the Thermodynamics of Irreversible Processes / Thermoelectric, Piezothermoelectric, and Diffusive Effects in Solids / Effect of Magnetic Field on the Transport Properties / Appendix A: Magnetic Tensor Properties, Magnetic Crystals, and the Combined Space-Time Transformations / Endnotes / Glossary / Biography / Index
Download or read book Representation Surfaces for Physical Properties of Materials written by Manuel Laso and published by Springer Nature. This book was released on 2020-04-04 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents all the mathematical and physical concepts needed to visualize and understand representation surfaces, providing readers with a reliable and intuitive understanding of the behavior and properties of anisotropic materials, and a sound grasp of the directionality of material properties. They will learn how to extract quantitative information from representation surfaces, which encode tremendous amounts of information in a very concise way, making them especially useful in understanding higher order tensorial material properties (piezoelectric moduli, elastic compliance and rigidity, etc.) and in the design of applications based on these materials. Readers will also learn from scratch concepts on crystallography, symmetry and Cartesian tensors, which are essential for understanding anisotropic materials, their design and application. The book describes how to apply representation surfaces to a diverse range of material properties, making it a valuable resource for material scientists, mechanical engineers, and solid state physicists, as well as advanced undergraduates in Materials Science, Solid State Physics, Electronics, Optics, Mechanical Engineering, Composites and Polymer Science. Moreover, the book includes a wealth of worked-out examples, problems and exercises to help further understanding.
Download or read book Symmetry Group Theory and the Physical Properties of Crystals written by Richard C Powell and published by Springer. This book was released on 2010-12-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Symmetry and Physical Properties of Crystals written by Cécile Malgrange and published by Springer. This book was released on 2014-12-04 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensors for Material Science written by Nitin Kanani and published by Independently Published. This book was released on 2020-03-02 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor analysis is the type of subject that can make even the best of students shudder. My ownpost-graduate instructor in the subject took away much of the fear by speaking of an implicitrhythm in the peculiar notation traditionally used, and helped me to see how this rhythm plays itsway throughout the various formalisms.Prior to taking that class, I had spent many years "playing" on my own with tensors. I found thegoing to be tremendously difficult, but was able, over time, to back out some physical andgeometrical considerations that helped to make the subject a little more transparent. Today, it issometimes hard not to think in terms of tensors and their associated concepts.This article, prompted and greatly enhanced by Marlos Jacob, whom I've met only by e-mail, isan attempt to record those early notions concerning tensors. It is intended to serve as a bridgefrom the point where most undergraduate students "leave off" in their studies of mathematics tothe place where most texts on tensor analysis begin. A basic knowledge of vectors, matrices, andphysics is assumed. A semi-intuitive approach to those notions underlying tensor analysis isgiven via scalars, vectors, dyads, triads, and similar higher-order vector products. The readermust be prepared to do some mathematics and to think.For those students who wish to go beyond this humble start, I can only recommend myprofessor's wisdom: find the rhythm in the mathematics and you will fare pretty well. At the heart of all mathematics are numbers.If I were to ask how many marbles you had in a bag, you might answer, "Three." I would findyour answer perfectly satisfactory. The 'bare' number 3, a magnitude, is sufficient to provide theinformation I seek.If I were to ask, "How far is it to your house?" and you answered, "Three," however, I wouldlook at you quizzically and ask, "Three what?" Evidently, for this question, more information isrequired. The bare number 3 is no longer sufficient; I require a 'denominate' number - a numberwith a name.Suppose you rejoindered, "Three km." The number 3 is now named as representing a certainnumber of km. Such numbers are sometimes called scalars. Temperature is represented by ascalar. The total energy of a thermodynamic system is also represented by a scalar.If I were next to ask "Then how do I get to your house from here?" and you said, "Just walkthree km," again I would look at you quizzically. This time, not even a denominate number issufficient; it is necessary to specify a distance or magnitude, yes, but in which direction? NASA/TM2002-211716 2"Just walk three km due north." The denominate number 3 km now has the required additionaldirectional information attached to it. Such numbers are called vectors. Velocity is a vector sinceit has a magnitude and a direction; so is momentum. Quite often, a vector is represented bycomponents. If you were to tell me that to go from here to your house I must walk three blockseast, two blocks north, and go up three floors, the vector extending from "here" to "your house"would have three spatial components: - Three blocks east, - Two blocks north, - Three floors up.
Download or read book Physical Components of Tensors written by Wolf Altman and published by CRC Press. This book was released on 2018-10-08 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrating the important aspects of tensor calculus, and highlighting its most practical features, Physical Components of Tensors presents an authoritative and complete explanation of tensor calculus that is based on transformations of bases of vector spaces rather than on transformations of coordinates. Written with graduate students, professors, and researchers in the areas of elasticity and shell theories in mind, this text focuses on the physical and nonholonomic components of tensors and applies them to the theories. It establishes a theory of physical and anholonomic components of tensors and applies the theory of dimensional analysis to tensors and (anholonomic) connections. This theory shows the relationship and compatibility among several existing definitions of physical components of tensors when referred to nonorthogonal coordinates. The book assumes a basic knowledge of linear algebra and elementary calculus, but revisits these subjects and introduces the mathematical backgrounds for the theory in the first three chapters. In addition, all field equations are also given in physical components as well. Comprised of five chapters, this noteworthy text: Deals with the basic concepts of linear algebra, introducing the vector spaces and the further structures imposed on them by the notions of inner products, norms, and metrics Focuses on the main algebraic operations for vectors and tensors and also on the notions of duality, tensor products, and component representation of tensors Presents the classical tensor calculus that functions as the advanced prerequisite for the development of subsequent chapters Provides the theory of physical and anholonomic components of tensors by associating them to the spaces of linear transformations and of tensor products and advances two applications of this theory Physical Components of Tensors contains a comprehensive account of tensor calculus, and is an essential reference for graduate students or engineers concerned with solid and structural mechanics.
Download or read book The Structure of Materials written by Samuel M. Allen and published by John Wiley & Sons. This book was released on 1999-03-22 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are You Looking for a Unified and Concise Approach to Teaching and Learning the Structure of Materials? Allen and Thomas present information in a manner consistent with the way future scientists and engineers will be required to think about materials' selection, design, and use. Students will learn the fundamentals of three different states of condensed matter-glasses, crystals, and liquid crystals-and develop a set of tools for describing all of them. Above all, they'll gain a better understanding of the principles of structure common to all materials. Key concepts, such as symmetry theory, are introduced and applied to provide a common viewpoint for describing structures of ceramic, metallic, and polymeric materials. Structure-sensitive properties of real materials are introduced. The text also includes a variety of worked example problems. Other texts available in the MIT Series: Thermodynamics of Materials, Vol I, Ragone, 30885-4 Thermodynamics of Materials, Vol II: Kinetics, Ragone, 30886-2 Physical Ceramics: Principles for Ceramics Science and Engineering, Chiang, Birnie, Kingery, 59873-9 Electronic Properties of Engineering Materials, Livingston, 31627-X
Download or read book Directional Properties of Materials written by Hans Joachim Bunge and published by . This book was released on 1988 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
