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Symmetry relationships between crystal structures : applications of crystallographic group theory in crystal chemistry /
This text presents the basic information needed to understand and to organise the huge amount of known structures of crystalline solids. Its basis is crystallographic group theory (space group theory), with special emphasis on the relations between the symmetry properties of crystals.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Oxford University Press,
2013.
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| Colección: | International Union of Crystallography texts on crystallography ;
18. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title Page; Copyright Page; Dedication; Preface; Contents; List of symbols; 1.1 The symmetry principle in crystal chemistry; 1.2 Introductory examples; 1 Introduction; 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; 3.1.1 An example; 3.1.2 Symmetry operations; 3.2 Affine mappings.
- 3.3 Application of (n + 1) × (n + 1) matrices3.4 Affine mappings of vectors; 3.5 Isometries; 3.6 Types of isometries; 3.7 Changes of the coordinate system; 3.7.1 Origin shift; 3.7.2 Basis change; 3.7.3 General transformation of the coordinate system; 3.7.4 The effect of coordinate transformations on mappings; 3.7.5 Several consecutive transformations of the coordinate system; 3.7.6 Calculation of origin shifts from coordinate transformations; 3.7.7 Transformation of further crystallographic quantities; Exercises; 4 Basics of crystallography, part 2.
- 4.1 The description of crystal symmetry in International Tables A: Positions4.2 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 3; 6.1 Space groups and point groups; 6.1.1 Molecular symmetry.
- 6.1.2 The space group and its point group6.1.3 Classification of the space groups; 6.2 The lattice of a space group; 6.3 Space-group symbols; 6.3.1 Hermann-Mauguin symbols; 6.3.2 Schoenflies symbols; 6.4 Description of space-group symmetry in International Tables A; 6.4.1 Diagrams of the symmetry elements; 6.4.2 Lists of the Wyckoff positions; 6.4.3 Symmetry operations of the general position; 6.4.4 Diagrams of the general positions; 6.5 General and special positions of the space groups; 6.5.1 The general position of a space group; 6.5.2 The special positions of a space group.
- 6.6 The difference between space group and space-group typeExercises; 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; 7.2.1 Maximal translationengleiche subgroups; 7.2.2 Maximal non-isomorphic klassengleiche subgroups; 7.2.3 Maximal isomorphic subgroups; 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 structures; 8.1 Conjugate subgroups of space groups; 8.2 Normalizers of space groups.