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Space Groups and Their Representations - 1st Edition - ISBN: 9780123954985, 9780323161176

Space Groups and Their Representations

1st Edition

Author: Gertjan Koster
eBook ISBN: 9780323161176
Imprint: Academic Press
Published Date: 1st January 1957
Page Count: 88
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Space Groups and Their Representations focuses on the discussions on space groups and their corresponding numerical and analytical representations. Divided into six chapters, the book starts with the presentation of the nature and properties of space groups. This topic includes orthogonal transformations and Bravais lattices, such as cubic system, triclinic system, trigonal and hexagonal systems, monoclinic systems, and tetragonal systems. The book then proceeds with the discussion on the irreducible representations of space groups, and then covers the general theory, simplification, and introduction. Discussions on various examples of space groups are given in the third chapter. Numerical representations are provided to support the validity of the different space groups, including discussions on double groups. The book also points out that the irreducible representation of space groups and the application of representation theory to them manifest the latest developments on geometrical crystallography. The text is a vital source of data for scholars and readers who are interested to study space groups and crystallography.

Table of Contents

I. Nature and Properties of the Space Groups

1. Orthogonal Transformations

2. Space Groups

3. Point Groups

4. Bravais Lattices

a. Cubic System

b. Tetragonal System

c. Orthorhombic System

d. Monoclinic System

e. Triclinic System

f. Trigonal and Hexagonal Systems

II. Irreducible Representations of Space Groups

1. Introduction

2. General Theory

3. Simplifications

III. Examples

1. Simple Cubic Oλ1

a. General Point

b. General Points in a Symmetry Plane

2. Body-Centered Cubic Oλ9

a. General Point on the Surface

3. Face-Centered Cubic Oλ5

a. General Point on the Surface

4. Zincblende Structure Td2

a. General Point

b. General Point on a Symmetry Plane

5. Diamond Structure Oλ7

a. General Point

b. General Points on Symmetry Planes

6. Hexagonal Close-Packed D6λ4

a. General Point

IV. Double Groups

1. General

V. Time Reversal

VI. History


No. of pages:
© Academic Press 1957
1st January 1957
Academic Press
eBook ISBN:

About the Author

Gertjan Koster

Gertjan Koster is Associate Professor at the University of Twente, The Netherlands.

Affiliations and Expertise

University of Twente, The Netherlands

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