Crystal Properties Via Group Theory

This book deals with the effect of crystal symmetry in determining the tensor properties of crystals. Although this is a well-established subject, the author provides a new approach using group theory and, in particular, the method of symmetry coordinates, which has not been used in any previous book. Using this approach, all tensors of a given rank and type can be handled together, even when they involve very different physical phenomena. Applications to technologically important phenomena as diverse as the electro-optic, piezoelectric, photoelastic, piezomagnetic, and piezoresistance effects, as well as magnetothermoelectric power and third-order elastic constants, are presented. Attention is also given to 'special magnetic properties', that is those that require the concepts of time reversal and magnetic symmetry, an important subject not always covered in other books in this area. This book will be of interest to researchers in solid-state physics and materials science, and will also be suitable as a text for graduate students in physics and engineering taking courses in solid-state physics.

This book provides a rigorous account on the fundamentals and applications of Group Theory to chemical physics.

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.

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

Unlike existing texts, this book blends for the first time three topics in physics - symmetry, condensed matter physics and computational methods - into one pedagogical textbook. It includes new concepts in mathematical crystallography; experimental methods capitalizing on symmetry aspects; non-conventional applications such as Fourier crystallography, color groups, quasicrystals and incommensurate systems; as well as concepts and techniques behind the Landau theory of phase transitions. Adopting a computational approach to the application of group theoretical techniques to solving symmetry related problems, it dramatically alleviates the need for intensive calculations usually found in the presentation of symmetry. Writing computer programs helps the student achieve a firm understanding of the underlying concepts, and sample programs, based on Mathematica, are presented throughout the book. Containing over 150 exercises, this textbook is ideal for graduate students in condensed matter physics, materials science, and chemistry. Solutions and computer programs are available online at www.cambridge.org/9780521828451.

This book deals with the role played by symmetry in the understanding of the physical world, beginning with the notion of geometric symmetries of the ancient Greek philosophers and mathematicians. The recognition of the existence of symmetries led to the notion of transformations, which led from one state of the system to another. It was then realized that such transformations, under the operation of multiplication, constitute an interesting set, whose study led to the branch of mathematics known as Group Theory. With the emergence of quantum mechanics, this theory became much more interesting and led to some additional applications. The theory got another boost with the need for of the internal degrees of freedom in describing physical systems. This way the notion of symmetry is no longer purely geometric and evolved into a useful tool in the study of all physical sciences.For practical reasons as well as pedagogical reasons, group theory is usually split into two parts. The first deals with discrete groups, with the group elements being countable, usually finite in number, while the second deals with continuous groups, whose elements depend on continuous parameters. This volumefocuses the discussion on discrete groups. Given that group theory should be presented from a unified perspective, involving not only the mathematical rigor and beauty of symmetries, but also the ability to use it as a tool for applications, either currently popular or expected to become so in the future, this approach will surely be more beneficial to the dedicated reader. It is not intended for those who would like to just look up a formula or use the results of a table, without understanding their derivation.