Space Groups for Solid State Scientists

Space Groups for Solid State Scientists, 3rd Edition

Space Groups for Solid State Scientists, 3rd Edition,Michael Glazer,Gerald Burns,ISBN9780123946157


Academic Press



Cuts the heavy mathematics of the International Tables into bite-size form, enabling solid-state scientists of whatever stripe to readily interpret symmetry information in crystal structures

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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


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.

Information about this author is currently not available.

Gerald Burns

Affiliations and Expertise

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

View additional works by Gerald Burns

Space Groups for Solid State Scientists, 3rd Edition

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 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


Quotes and reviews

Praise for First Edition
"Space Groups for Solid State Scientists fills a definite need and fills it well....The book is clearly written, in a very readable style. It is lavishly illustrated and well printed. It contains many examples to illustrate the points being made, and these, together with the problems for solution at the end of each chapter, make it suitable for use as a textbook at the graduate level. In addition to its role as a guide to the International Tables the book is valuable for the research scientist because of the many tables it presents."--PHYSICS TODAY
"An understandable and comprehensive guide...Of particular interest in this new edition are the discussions of space groups application to such timely topics as high-temperature superconductors, phase transitions, semiconductor superlattices, incommensurate modulation, and icosahedral symmetry."--SCITECH
"The book will be extremely useful to those who are interested in improving their knowledge of space groups for the determination of complicated structures."--MATHEMATICAL REVIEWS
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