Keywords:
Crystals -- Structure.
;
Symmetry (Physics).
;
Electronic books.
Description / Table of Contents:
The book presents the basic information needed to understand and to organize 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.
Type of Medium:
Online Resource
Pages:
1 online resource (349 pages)
Edition:
1st ed.
ISBN:
9780191648793
Series Statement:
International Union of Crystallography Texts on Crystallography Series ; v.18
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=1192571
DDC:
548.81
Language:
English
Note:
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 system -- Exercises -- 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 3 -- 6.1 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 structures -- 8.1 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 Structures -- 10 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 -- Exercises -- 12 Pitfalls when setting up group-subgroup relations -- 12.1 Origin shifts -- 12.2 Subgroups on a par -- 12.3 Wrong cell transformations -- 12.4 Different paths of symmetry reduction -- 12.5 Forbidden addition of symmetry operations -- Exercises -- 13 Derivation of crystal structures from closest packings of spheres -- 13.1 Occupation of interstices in closest packings of spheres -- 13.2 Occupation of octahedral interstices in the hexagonal-closest packing of spheres -- 13.3 Occupation of octahedral and tetrahedral interstices in the cubicclosest packing of spheres -- Exercises.
,
14 Crystal structures of molecular compounds -- 14.1 Symmetry reduction due to reduced point symmetry of building blocks -- 14.2 Molecular packings after the pattern of sphere packings -- 14.3 The packing in tetraphenylphosphonium salts -- Exercises -- 15 Symmetry relations at phase transitions -- 15.1 Phase transitions in the solid state -- 15.2 On the theory of phase transitions -- 15.3 Domains and twinned crystals -- 15.4 Can a reconstructive phase transition proceed via a common subgroup? -- 15.5 Growth and transformation twins -- 15.6 Antiphase domains -- Exercises -- 16 Topotactic reactions -- 16.1 Symmetry relations among topotactic reactions -- 16.2 Topotactic reactions among lanthanoid halides -- Exercises -- 17 Group-subgroup relations as an aid for structure determination -- 17.1 What space group should be chosen? -- 17.2 Solving the phase problem of protein structures -- 17.3 Superstructure reflections, suspicious structural features -- 17.4 Detection of twinned crystals -- Exercises -- 18 Prediction of possible structure types -- 18.1 Derivation of hypothetical structure types with the aid of group-subgroup relations -- 18.2 Enumeration of possible structure types -- 18.3 Combinatorial computation of distributions of atoms among given positions -- 18.4 Derivation of possible crystal structure types for a given molecular structure -- Exercises -- 19 Historical remarks -- Appendices -- A: Isomorphic subgroups -- Exercises -- B: On the theory of phase transitions -- B.1 Thermodynamic aspects concerning phase transitions -- B.2 About Landau theory -- B.3 Renormalization-group theory -- B.4 Discontinuous phase transitions -- C: Symmetry species -- D: Solutions to the exercises -- References -- Glossary -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- W -- Index -- A -- B -- C -- D -- E -- F.
,
G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.
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