International Tables for Crystallography, Symmetry Relations between Space Groups / Edition 1

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Overview

  • This extension to Volume A presents a systematic treatment of the maximal subgroups and minimal supergroups of the crystallographic plane groups and space groups
  • The second edition contains new chapters on building trees of group-subgroup relations for crystal structures that can be derived from an aristotype and on the Bilbao Crystallographic Server, and a detailed discussion of the listed supergroup data
  • Essential for those interested in phase transitions, the systematic compilation of crystal structures and twinning phenomena
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Product Details

Table of Contents

Foreword.

Scope of this Volume.

Computer Production of Parts 2 and 3.

List of Symbols and Abbreviations used in this Volume.

PART 1 SPACE GROUPS AND THEIR SUBGROUPS.

1.1 Historical Introduction (M.I. Aroyo, U. Müller and H. Wondratschek).

1.1.1 The Fundamental Laws of Cystallography.

1.1.2 Symmetry and Crystal-Structure Determination.

1.1.3 Development of the Theory of Group–Subgroup Relations.

1.1.4 Applications of Group–Subgroup Relations.

1.2 General Introduction to the Subgroups of Space Groups (H. Wondratschek).

1.2.1 General Remarks.

1.2.2 Mappings and Matrices.

1.2.3 Groups.

1.2.4 Subgroups.

1.2.5 Space Groups.

1.2.6 Types of Subgroups of Space Groups.

1.2.7 Application to Domain Structures.

1.2.8 Lemmata on Subgroups of Space Groups.

1.3 Remarks on Wyckoff Positions (U. Müller).

1.3.1 Introduction.

1.3.2 Crystallographic Orbits and Wyckoff Positions.

1.3.3 Derivative Structures and Phase Transitions.

1.3.4 Relations Between the Positions in Group–Subgroup Relations.

1.4 Computer Checking of the Subgroup Data (F. Gähler).

1.4.1 Introduction.

1.4.2 Basic Capabilities of the Cryst package.

1.4.3 Computing Maximal Subgroups.

1.4.4 Description of the Checks.

1.5 The Mathematical Background of the Subgroup Tables (G. Nebe).

1.5.1 Introduction.

1.5.2 The Affine Space.

1.5.3 Groups.

1.5.4 Space Groups.

1.5.5 Maximal Subgroups.

1.5.6 Quantitative Results.

1.5.7 Qualitative Results.

PART 2 MAXIMAL SUBGROUPS OF THE PLANE GROUPS AND SPACE GROUPS.

2.1 Guide to the Subgroup Tables and Graphs (H. Wondratschek and M.I. Aroyo).

2.1.1 Contents and Arrangement of the Subgroup Tables.

2.1.2 Structure of the Subgroup Tables.

2.1.3 I Maximal Translationengleiche Subgroups (t-Subgroups).

2.1.4 II Maximal Klassengleiche Subgroups (k-Subgroups).

2.1.5 Series of Maximal Isomorphic Subgroups (Y. Billiet).

2.1.6 Minimal Supergroups.

2.1.7 The Subgroup Graphs.

2.2 Tables of Maximal Subgroups of the Plane Groups (Y. Billiet, M.I. Aroyo and H. Wondratschek).

2.3 Tables of Maximal Subgroups of the Space Groups (Y. Billiet, M.I. Aroyo and H. Wondratschek).

2.4 Graphs for Translationengleiche Subgroups (V. Gramlich and H. Wondratschek).

2.4.1 Graphs of the Translationengleiche Subgroups with a Cubic Summit.

2.4.2 Graphs of the Translationengleiche Subgroups with a Tetragonal Summit.

2.4.3 Graphs of the Translationengleiche Subgroups with a Hexagonal Summit.

2.4.4 Graphs of the Translationengleiche Subgroups with an Orthorhombic Summit.

2.5 Graphs for Klassengleiche Subgroups (V. Gramlich and H. Wondratschek).

2.5.1 Graphs of the Klassengleiche Subgroups of Monoclinic and Orthorhombic Space Groups.

2.5.2 Graphs of the Klassengleiche Subgroups of Tetragonal Space Groups.

2.5.3 Graphs of the Klassengleiche Subgroups of Trigonal Space Groups.

2.5.4 Graphs of the Klassengleiche Subgroups of Hexagonal Space Groups.

2.5.5 Graphs of the Klassengleiche Subgroups of Cubic Space Groups.

PART 3 RELATIONS BETWEEN THE WYCKOFF POSITIONS.

3.1 Guide to the Tables (U. Müller).

3.1.1 Arrangement of the Entries.

3.1.2 Cell Transformations.

3.1.3 Origin Shifts.

3.1.4 Nonconventional Settings of Orthorhombic Space Groups.

3.1.5 Conjugate Subgroups.

3.1.6 Monoclinic and Triclinic Subgroups.

3.2 Tables of the Relations of the Wyckoff Positions (U. Müller).

Appendix. Differences in the Presentation of Parts 2 and 3 (U. Müller and H. Wondratschek).

References.

Subject Index.

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