Space Groups for Solid State Scientists

3rd Edition

Authors: Michael Glazer Gerald Burns
Print ISBN: 9780128100615
eBook ISBN: 9780123946157
Imprint: Academic Press
Published Date: 20th February 2013
Page Count: 432
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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 itself. This remains the only book aimed at non-crystallographers that is devoted to teaching them about crystallographic space groups.

Researchers within the solid state frequently need to understand publications that use space group information and are invariably disappointed when they turn, necessarily, to the mammoth eight volume set International Tables of Crystallography - so complete and at the same time so closely written that those not trained explicitly in crystallography cannot understand the explanations given.

Huge sections of the Tables are given over to extremely careful and elaborate explanations and definitions that may be of interest to those crystallographers specialising in symmetry, but tend to obscure the meanings for those who are not so inclined. Five editions have now published since the first compilation in 1983, incorporating a diverse panorama of new content, and even introducing new symmetry elements that had not been considered earlier. In addition, the International Union has recently brought out whole new tranches of content: Volume A1 (on subgroups) and Volume E (on frieze, rod and layer groups – important for the study of 1 and 2 dimensional systems, such as domain walls).

Table of Contents

Front Matter


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 Chalcopy


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About the Author

Michael Glazer

Gerald Burns

Affiliations and Expertise

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