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Symmetry, Group Theory, and the Physical Properties of Crystals

  • Richard C Powell

Part of the Lecture Notes in Physics book series (LNP, volume 824)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Richard C. Powell
    Pages 1-24
  3. Richard C. Powell
    Pages 25-53
  4. Richard C. Powell
    Pages 55-78
  5. Richard C. Powell
    Pages 79-104
  6. Richard C. Powell
    Pages 105-135
  7. Richard C. Powell
    Pages 137-163
  8. Richard C. Powell
    Pages 165-199
  9. Richard C. Powell
    Pages 201-224
  10. Richard C. Powell
    Pages E1-E3
  11. Back Matter
    Pages 225-230

About this book

Introduction

This book demonstrates the importance of symmetry in determining the properties of solids and the power of using group theory and tensor algebra to elucidate these properties. It provides the fundamentals necessary for the reader to understand how to utilize these techniques in many different applications without becoming lost in a heavy formal treatment of the subject matter. The book begins by discussing the concepts of symmetry relevant to crystal structures. This is followed by a summary of the basics of group theory and how it applies to quantum mechanics. Next is a discussion of the description of the macroscopic properties of crystals by tensors and how symmetry determines the form of these tensors. The basic concepts covered in these early chapters are then applied to a series of different examples including crystal field theory treatment of point defects in solids, molecular orbitals, two-photon processes, the optical properties of solids, the nonlinear optical properties of solids, lattice vibrations, the Jahn-Teller effect, and the effects of translational symmetry on electronic energy bands in solids.. Emphasis is placed on showing how group theory and tensor algebra can provide important information about the properties of a system without resorting to first principal quantum mechanical calculations. The book also features a comprehensive set of relevant tables, including crystal symmetries, point group character tables, matter tensors of different rank, and other tensor properties. Key Features: •Serves as a textbook or reference book for solid-state physics, solid-state chemistry, and materials science and engineering •Shows how the physical properties of solids are determined by their symmetry •Demonstrates the applications of group theory •Utilizes the concept of matter tensors •Includes an extensive set of reference tables and end of chapter problems

Keywords

Group Theory Matter Ten Matter Tensors Nonlinear Optics Point group Properties of Solids Symmetry Solid State Physics optics

Authors and affiliations

  • Richard C Powell
    • 1
  1. 1.Optical SciencesUniversity of ArizonaTucsonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7598-0
  • Copyright Information Springer Science+Business Media LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-1-4419-7597-3
  • Online ISBN 978-1-4419-7598-0
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361
  • Buy this book on publisher's site
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