Symmetry relationships between crystal structures : applications of crystallographic group theory in crystal chemistry / Ulrich Muller.

Format:

Book

Author/Creator:

Müller, Ulrich, 1940 July 6-

Series:

International Union of Crystallography texts on crystallography ; 18.

IUCr Texts on Crystallography ; 18

Language:

English

Subjects (All):

Crystals--Structure.

Crystals.

Symmetry (Physics).

Physical Description:

1 online resource (349 p.)

Place of Publication:

Oxford, England : Oxford University Press, c2013.

Language Note:

English

Summary:

In crystal chemistry and crystal physics, the relations between the symmetry groups (space groups) of crystalline solids are of special importance. Part 1 of this book presents the necessary mathematical foundations and tools: the fundamentals of crystallography with special emphasis on symmetry, the theory of the crystallographic groups, and the formalisms of the needed crystallographic computations. Part 2 gives an insight into applications to problems in crystal chemistry. Withthe aid of numerous examples, it is shown how crystallographic group theory can be used to make evident relationshi

Contents:

Cover; Contents; List of symbols; 1 Introduction; 1.1 The symmetry principle in crystal chemistry; 1.2 Introductory examples; I: Crystallographic Foundations; 2 Basics of crystallography, part 1; 2.1 Introductory remarks; 2.2 Crystals and lattices; 2.3 Appropriate coordinate systems, crystal coordinates; 2.4 Lattice directions, net planes, and reciprocal lattice; 2.5 Calculation of distances and angles; 3 Mappings; 3.1 Mappings in crystallography; 3.2 Affine mappings; 3.3 Application of (n+1) X (n + 1) matrices; 3.4 Affine mappings of vectors; 3.5 Isometries; 3.6 Types of isometries

3.7 Changes of the coordinate systemExercises; 4 Basics of crystallography, part 2; 4.1 The description of crystal symmetry in International Tables A: Positions; 4.2 Crystallographic symmetry operations; 4.3 Geometric interpretation of the matrix-column pair (W,w) of a crystallographic symmetry operation; 4.4 Derivation of the matrix-column pair of an isometry; Exercises; 5 Group theory; 5.1 Two examples of groups; 5.2 Basics of group theory; 5.3 Coset decomposition of a group; 5.4 Conjugation; 5.5 Factor groups and homomorphisms; 5.6 Action of a group on a set; Exercises

6 Basics of crystallography, part 36.1 Space groups and point groups; 6.2 The lattice of a space group; 6.3 Space-group symbols; 6.4 Description of space-group symmetry in International Tables A; 6.5 General and special positions of the space groups; 6.6 The difference between space group and space-group type; Exercises; 7 Subgroups and supergroups of point and space groups; 7.1 Subgroups of the point groups of molecules; 7.2 Subgroups of the space groups; 7.3 Minimal supergroups of the space groups; 7.4 Layer groups and rod groups; Exercises

8 Conjugate subgroups, normalizers and equivalent descriptions of crystal structures8.1 Conjugate subgroups of space groups; 8.2 Normalizers of space groups; 8.3 The number of conjugate subgroups. Subgroups on a par; 8.4 Standardized description of crystal structures; 8.5 Equivalent descriptions of crystal structures; 8.6 Chirality; 8.7 Wrongly assigned space groups; 8.8 Isotypism; Exercises; 9 How to handle space groups; 9.1 Wyckoff positions of space groups; 9.2 Relations between the Wyckoff positions in group-subgroup relations; 9.3 Non-conventional settings of space groups; Exercises

II: Symmetry Relations between Space Groups as a Tool to Disclose Connections between Crystal Structures10 The group-theoretical presentation of crystal-chemical relationships; 11 Symmetry relations between related crystal structures; 11.1 The space group of a structure is a translationengleiche maximal subgroup of the space group of another structure; 11.2 The maximal subgroup is klassengleiche; 11.3 The maximal subgroup is isomorphic; 11.4 The subgroup is neither translationengleiche nor klassengleiche; 11.5 The space groups of two structures have a common supergroup

11.6 Large families of structures

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from title page (ebrary, viewed July 9, 2013).

Description based on publisher supplied metadata and other sources.

ISBN:

0-19-164880-9

0-19-880720-1

0-19-164879-5

0-19-966995-3

OCLC:

850162150