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Symmetry, Group Theory, and the Physical Properties of Crystals

  • Book
  • © 2010

Overview

Authors:
  1. Richard C Powell

    1. Optical Sciences, University of Arizona, Tucson, USA

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  • 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
  • Includes supplementary material: sn.pub/extras
  • Request lecturer material: sn.pub/lecturer-material

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Symmetry in Solids

    • Richard C. Powell
    Pages 1-24

  3. Group Theory

    • Richard C. Powell
    Pages 25-53

  4. Tensor Properties of Crystals

    • Richard C. Powell
    Pages 55-78

  5. Symmetry Properties of Point Defects in Solids

    • Richard C. Powell
    Pages 79-104

  6. Symmetry and the Optical Properties of Crystals

    • Richard C. Powell
    Pages 105-135

  7. Nonlinear Optics

    • Richard C. Powell
    Pages 137-163

  8. Symmetry and Lattice Vibrations

    • Richard C. Powell
    Pages 165-199

  9. Symmetry and Electron Energy Levels

    • Richard C. Powell
    Pages 201-224

  10. Erratum to: Tensor Properties of Crystals

    • Richard C. Powell
    Pages E1-E3

  11. Back Matter

    Pages 225-230
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Keywords

About this book

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

Authors and Affiliations

  • Optical Sciences, University of Arizona, Tucson, USA

    Richard C Powell

About the author

I. Symmetry in Solids II. Group Theory III. Tensor Properties of Crystals IV. Symmetry Properties of Point Defects in Solids V. Symmetry and the Optical Properties of Solids VI. Nonlinear Optics VII. Symmetry and Lattice Vibrations VIII. Symmetry and Electron Energy Levels

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