Space Groups for Solid State Scientists

Space Groups for Solid State Scientists

3rd Edition - January 3, 2013

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  • Authors: Michael Glazer, Gerald Burns
  • Paperback ISBN: 9780128100615
  • eBook ISBN: 9780123946157

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This comprehensively revised – essentially rewritten – new edition of the 1990 edition (described as "extremely useful" by MATHEMATICAL REVIEWS and as "understandable and comprehensive" by Scitech) guides readers through the dense array of mathematical information in the International Tables Volume A. Thus, most scientists seeking to understand a crystal structure publication can do this from this book without necessarily having to consult the International Tables themselves. This remains the only book aimed at non-crystallographers devoted to teaching them about crystallographic space groups.

Key Features

  • Reflecting the bewildering array of recent changes to the International Tables, this new edition brings the standard of science well up-to-date, reorganizes the logical order of chapters, improves diagrams and presents clearer explanations to aid understanding
  • Clarifies, condenses and simplifies the meaning of the deeply written, complete Tables of Crystallography into manageable chunks
  • Provides a detailed, multi-factor, interdisciplinary explanation of how to use the International Tables for a number of possible, hitherto unexplored uses
  • Presents essential knowledge to those needing the necessary but missing pedagogical support and detailed advice – useful for instance in symmetry of domain walls in solids

Table of Contents

  • Chapter 1. Point Symmetry Operations

    What is Symmetry?

    1.1 Symmetry Operations

    1.2 Point Symmetry Operations

    1.3 Hexagonal Coordinates

    Chapter 2. Crystal Systems

    Haüy’s Legacy

    2.1 Lattice

    2.2 Unit Cell

    2.3 Crystal Structure

    2.4 Crystal Systems

    2.5 Summary

    Chapter 3. Bravais Lattices

    Symmetry and Lattices

    3.1 Centering of Lattices

    3.2 The 14 Bravais Lattices

    3.3 Primitive Cells of the 14 Bravais Lattices

    3.4 The Wigner–Seitz Unit Cell

    3.5 Two-Dimensional Lattices

    Chapter 4. Crystallographic Point Groups

    Introduction to Groups

    4.1 Development of Crystallographic Point Groups

    4.2 The Point Groups for Each Crystal System

    4.3 The 32 Point Groups from Holohedries

    4.4 Laue Classes and Groups

    4.5 Point Group Notation

    Chapter 5. Development of Space Groups

    Space Group Operators

    5.1 The Symmorphic Space Groups

    5.2 Non-Symmorphic Operations

    5.3 Point Group of a Space Group

    5.4 Space Groups

    5.5 Derivation of Space Groups

    5.6 Space Group Classifications

    5.7 Two-Dimensional Space Groups

    5.8 Subperiodic Groups


    Chapter 6. Reading the Tables

    What Does the ITA Tell Us?

    6.1 Crystal Structure and Space Groups

    6.2 ‘Typical’ Pages of the ITA

    6.3 Example Pages from the ITA

    6.4 Subgroups and Supergroups

    6.5 Space Group Symmetry Operations

    6.6 Hall Space Group Symbols

    Chapter 7. Space Group Applications

    And Now Atoms

    7.1 Face-Centered Cubic Structures

    7.2 Primitive Cubic Structures

    7.3 Body-Centered Cubic Structures

    7.4 Diamond Structure

    7.5 Spinel Structure

    7.6 Zinc Sulphide Structure

    7.7 Chalcopyrite

    7.8 Semiconductor Superlattices

    7.9 Structural Phase Transitions in Crystals

    7.10 Displacive SPTs

    7.11 Proteins

    7.12 Crystallographic Information File

    7.13 Ferroic Phase Transitions

    7.14 Surface Structure Plane and Layer Groups

    7.15 Diffusion, Disordered Structures and Point Defects

    7.16 Euclidean normalizers

    7.17 Non-Crystallographic Symmetry

    7.18 Structures with Z′ > 1

    7.19 Icosahedral Symmetry

    7.20 Incommensurate Modulations

    7.21 Charge Density Wave

    7.22 Quasicrystals

    Chapter 8. Antisymmetry

    Bicolor Symmetry

    8.1 Black and White Antisymmetry Groups

    8.2 Effect on Vectors

    8.3 Magnetic Point Groups

    8.4 Translational Subgroups of Magnetic Groups

    8.5 Black and White Space Groups

    8.6 Magnetic Space Groups

    8.7 Examples of Magnetic Structures

    8.8 Representation Method

    8.9 OG/BNS Magnetic Group Symbols

    Appendix 1. Matrices Representing the Symmetry Operations

    Jones’ Faithful Representation Symbols

    Appendix 2. Crystal Families, Systems, and Bravais Lattices

    Appendix 3. The 14 Bravais Lattices

    24 Wigner–Seitz Cells

    Appendix 4. The 32 Crystallographic Point Groups

    Appendix 5. Diagrams for the 32 Point Groups


    Some Shapes Illustrating the 32 Point Groups

    Appendix 6. Symbols

    Symbols of Symmetry Planes

    Symbols of Symmetry Axes

    Order of Symbols

    Three-dimensional lattices

    Two-dimensional lattices

    Appendix 7. The Space Groups

    11 Enantiomorphic Space Group Pairs

    The 230 Space Groups

    Triclinic System

    Monoclinic System

    Orthorhombic System

    Orthorhombic System

    Tetragonal System

    Tetragonal System

    Trigonal System Hexagonal System

    Cubic System

    Appendix 8. The Reciprocal Lattice and Diffraction

    Scattering from Disordered Structures

    Appendix 9. Some Interesting Structures

    A9-1 CeM2Si2

    A9-2 Rutile

    A9-3 Nickel Arsenide

    A9-4 Cuprite

    A9-5 Nb3Sn

    A9-6 Perovskites and Their Superstructures

    A9-7 Perovskite-like Phases

    A9-8 Strukturbericht Notation

    Appendix 10. Translational Subgroups of Magnetic Space Groups

    Appendix 11. Cubic Space Group Diagrams

    Appendix 12. Pitfalls



    Chapter 1

    Chapter 2

    Chapter 3

    Chapter 4

    Chapter 5

    Chapter 6

    Chapter 7

    Chapter 8

    Formula Index

Product details

  • No. of pages: 432
  • Language: English
  • Copyright: © Academic Press 2013
  • Published: January 3, 2013
  • Imprint: Academic Press
  • Paperback ISBN: 9780128100615
  • eBook ISBN: 9780123946157

About the Authors

Michael Glazer

Gerald Burns

Affiliations and Expertise

IBM Thomas J. Watson Research Center, Yorktown Heights, New York

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