Physical Properties of Crystals: Their Representation by Tensors and Matrices

Features

• Cover Type: Paperback with 352 pages
• Published by: Oxford University Press, USA July 11, 1985
• Written in: English
• ISBN 10 Number: 0198511655
• ISBN 13 Number: 978-0198511656
• Book Dimensions: 9.1 x 6.1 x 0.8 inches
• Weighs: 1.2 pounds

Product Review
'We all have to be grateful to Dr Nye for giving us such a clearly conceived and well written text.' Journal of Mechanics and Physics of Solids 'Dr Nye is to be warmly congratulated on an great book, which it is a pleasure to handle and read.' Mathematical Gazette

Product Description
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.

Reader Reviews
Because it's difficult or impossible to calculate the properties of solid matter by use of quantum mechanics ("ab initio method"), scientists and engineers turn to alternative methods. One such method, continuum mechanics, assumes that the material under consideration is continuously distributed throughout its volume and completely fills the space it occupies. Obviously this assumption is false: in reality, the atoms of a solid are arranged in symmetrical patterns called crystals (with the exception of glasses) and there is considerable space between the atoms. Properties of the unit cell of each crystal can be measured (with respect to appropriate reference axes), and the data can be put to use by scientists and engineers. In this method, the physical and chemical properties are represented by tensors and matrices. But let's be clear: the experimental values have to be input as components of a tensor--the theory does not in any way allow us to actually calculate the properties of matter. Furthermore, the tensor relates the response to the applied force in a linear manner. Thus the nonlinearity of many phenomena cannot be captured by this method (although there are valiant attempts to use second and higher order effects, as per a Taylor series expansion). Also, the components of the tensor are assumed to be constant, but in many cases they are not. Finally, the orientation of the crystal is arbitrary (though usually certain conventions are followed), which means that the components of the tensor are coupled with the choice of reference axes and will change with a different choice. What I like about Prof. Nye's book is that he admits all of this up front, unlike some other books on material tensors or continuum mechanics. On p. xvi of the Introduction, he says "It is, of course, part of the task of physics to explain the values of these tensors for any particular crystal in terms of its atomic and crystalline structure. That is, in a sense, the next stage. Here we are less ambitious; we concern ourselves more with the form and general significance of the tensors than with their actual numerical values." Part 1 of the book reviews the basics of vectors and tensors, and states Neumann's Principle ("The symmetry elements of any physical property of a crystal must include the symmetry elements of the point group of the crystal.") Part 2 covers equilibrium properties (paramagnetic and diamagnetic susceptibility, electric polarization, stress and strain and elasticity, and piezoelectricity). Part 3 covers transport properties (thermal and electrical conductivity and thermoelectricity), and Part 4 covers crystal optics and optical activity. Each chapter of each part ends with a summary (and some chapters have an additional summary in the middle). Exercises with real data are scattered throughout the text; solutions to some of them are given in the back of the book. There are numerous appendices, a bibliography, supplementary references and notes, and one index for authors and another for subjects. The treatment of elasticity is traditional: Hooke's Law (which assumes a linear relation between stress and strain) is stated, and a fourth-order tensor is derived. In reality of course, Bridgman's experiments have shown that solid volume is inversely proportional to the square root of the applied pressure. The real variables are pressure and volume, which are scalar. What actually happens is that the applied pressure reduces the interatomic distance between the atoms, but the atomic forces resist this change. Overall, however, this is a very fine book and recommended for all solid-state physicists, chemists, and engineers. Just don't expect to be able to actually calculate the properties of matter with it...