Symmetry relationships between crystal structures: applications of crystallographic group theory in crystal chemistry
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2013
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | IUCr texts on crystallography
18 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 332 S. Ill., graph. Darst |
| ISBN: | 9780199669950 |
Internformat
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| 100 | 1 | |a Müller, Ulrich |d 1940- |e Verfasser |0 (DE-588)130176184 |4 aut | |
| 245 | 1 | 0 | |a Symmetry relationships between crystal structures |b applications of crystallographic group theory in crystal chemistry |c Ulrich Müller |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2013 | |
| 300 | |a XVI, 332 S. |b Ill., graph. Darst | ||
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Datensatz im Suchindex
| _version_ | 1804150468156325888 |
|---|---|
| adam_text | Titel: Symmetry relationships between crystal structures
Autor: Müller, Ulrich, 1940 July 6-
Jahr: 2013
Contents
List of Symbols xvi
1 Introduction 1
1.1 The symmetry principle in crystal chemistry 2
1.2 Introductory examples 4
1 Crystallographic Foundations 9
2 Basics of crystallography, part 1 11
2.1 Introductory remarks 11
2.2 Crystals and lattices 11
2.3 Appropriate coordinate Systems, crystal coordinates 13
2.4 Lattice directions, net planes, and reciprocal lattice 15
2.5 Calculation of distances and angles 16
3 Mappings 19
3.1 Mappings in crystallography 19
3.1.1 Anexample 19
3.1.2 Symmetry Operations 19
3.2 Affine mappings 20
3.3 Application of (n +1) x (n +1) matrices 23
3.4 Affine mappings of vectors 24
3.5 Isometries 25
3.6 Types of isometries 27
3.7 Changes of the coordinate System 30
3.7.1 Originshift 30
3.7.2 Basis change 31
3.7.3 General transformation of the coordinate System 32
3.7.4 The effect of coordinate transformations on mappings 33
3.7.5 Several consecutive transformations of the coordinate
system 36
3.7.6 Calculation of origin shifts from coordinate transfor-
mations 38
3.7.7 Transformation of further crystallographic quantities 39
Exercises 40
4 Basics of crystallography, part 2 41
4.1 The description of crystal symmetry in International Tables A:
Positions 41
4.2 Crystallographic symmetry Operations 41
4.3 Geometrie interpretation of the matrix-column pair (W,w) of
a crystallographic symmetry Operation 45
4.4 Derivation of the matrix-column pair of an isometry 47
Exercises 48
5 Group theory 49
5.1 Two examples of groups 49
5.2 Basics of group theory 51
5.3 Coset decomposition of a group 53
5.4 Conjugation 56
5.5 Factor groups and homomorphisms 57
5.6 Action of a group on a set 59
Exercises 61
6 Basics of crystallography, part 3 63
6.1 Space groups and point groups 63
6.1.1 Molecular symmetry 63
6.1.2 The space group and its point group 66
6.1.3 Classification of the space groups 67
6.2 The lattice of a space group 69
6.3 Space-group Symbols 70
6.3.1 Hermann-Mauguin Symbols 70
6.3.2 Schoenflies symbols 74
6.4 Description of space-group symmetry in International Tables A 76
6.4.1 Diagrams of the symmetry elements 76
6.4.2 Lists of the Wyckoff positions 79
6.4.3 Symmetry Operations of the general position 80
6.4.4 Diagrams of the general positions 80
6.5 General and special positions of the space groups 81
6.5.1 The general position of a space group 82
6.5.2 The special positions of a space group 83
6.6 The difference between space group and space-group type 84
Exercises 85
7 Subgroups and supergroups of point and space groups 87
7.1 Subgroups of the point groups of molecules 87
7.2 Subgroups of the Space groups 89
7.2.1 Maximal translationengleiche subgroups 91
7.2.2 Maximal non-isomorphic klassengleiche subgroups 93
7.2.3 Maximal isomorphic subgroups 93
7.3 Minimal supergroups of the space groups 94
7.4 Layer groups and rod groups 96
Exercises 99
Conjugate subgroups, normalizers and
equivalent descriptions of crystal structures 101
8.1 Conjugate subgroups of space groups 101
8.2 Normalizers of space groups 103
8.3 The number of conjugate subgroups. Subgroups on a par 106
8.4 Standardized description of crystal structures 110
8.5 Equivalent descriptions of crystal structures 110
8.6 Chirality 113
8.7 Wrongly assigned space groups 115
8.8 Isotypism 117
Exercises 119
How to handle space groups 121
9.1 Wyckoff positions of space groups 121
9.2 Relations between the Wyckoff positions in group-subgroup
relations 122
9.3 Non-conventional settings of space groups 123
9.3.1 Orthorhombic space groups 123
9.3.2 Monoclinic space groups 125
9.3.3 Tetragonal space groups 127
9.3.4 Rhombohedral space groups 129
9.3.5 Hexagonal space groups 129
Exercises 130
II Symmetry Relations between Space Groups as a
Tool to Disclose Connections between Crystal Structures 131
10 The group-theoretical presentation of crystal-chemical
relationships 133
11 Symmetry relations between related crystal structures 137
11.1 The space group of a structure is a translationengleiche maxi-
mal subgroup of the space group of another structure 137
11.2 The maximal subgroup is klassengleiche 141
11.3 The maximal subgroup is isomorphic 145
11.4 The subgroup is neither translationengleiche nor klassengleiche 148
11.5 The space groups of two structures have a common supergroup 149
11.6 Large families of structures 151
Exercises 156
12 Pitfalls when setting up group-subgroup relations 159
12.1 Originshifts 160
12.2 Subgroups on a par 162
12.3 Wrong cell transformations 162
12.4 Different paths of symmetry reduction 163
12.5 Forbidden addition of symmetry Operations 165
Exercises 166
13 Derivation of crystal structures from dosest packings of spheres 167
13.1 Occupation of interstices in dosest packings of spheres 167
13.2 Occupation of octahedral interstices in the hexagonal-closest
packing of spheres 168
13.2.1 Rhombohedral hettotypes 168
13.2.2 Hexagonal and trigonal hettotypes of the hexagonal-
closest packing of spheres 174
13.3 Occupation of octahedral and tetrahedral interstices in the cubic-
closest packing of spheres 178
13.3.1 Hettotypes of the NaCl type with doubled unit cell 178
13.3.2 Hettotypes of the CaF2 type with doubled unit cell 180
Exercises 183
14 Crystal structures of molecular Compounds 185
14.1 Symmetry reduction due to reduced point symmetry of
building blocks 186
14.2 Molecular packings after the pattern of sphere packings 187
14.3 The packing in tetraphenylphosphonium salts 191
Exercises 195
15 Symmetry relations at phase transitions 197
15.1 Phase transitions in the solid State 197
15.1.1 First- and second-order phase transitions 198
15.1.2 Structural Classification of phase transitions 199
15.2 On the theory of phase transitions 200
15.2.1 Lattice vibrations 200
15.2.2 The Landau theory of continuous phase transitions 202
15.3 Domains and twinned crystals 205
15.4 Can a reconstructive phase transition proceed via a common
subgroup? 207
15.5 Growth and transformation twins 210
15.6 Antiphase domains 211
Exercises 214
16 Topotactic reactions 217
16.1 Symmetry relations among topotactic reactions 218
16.2 Topotactic reactions among lanthanoid halides 220
Exercises 224
17 Group-subgroup relations as an aid for structure determination 227
17.1 What space group should be chosen? 228
17.2 Solving the phase problem of protein structures 228
17.3 Superstructure reflections, suspicious structural features 229
17.4 Detection of twinned crystals 230
Exercises 233
18 Prediction of possible structure types 235
18.1 Derivation of hypothetical structure types with the aid of
group-subgroup relations 235
18.2 Enumeration of possible structure types 239
18.2.1 The total number of possible structures 239
18.2.2 The number of possible structures depending on sym-
metry 241
18.3 Combinatorial computation of distributions of atoms among
given positions 245
18.4 Derivation of possible crystal structure types for a given mole-
cular structure 249
Exercises 253
19 Historical remarks 255
Appendices 259
A Isomorphic subgroups 261
Exercises 267
B On the theory of phase transitions 269
B.l Thermodynamic aspects conceming phase transitions 269
B.2 About Landau theory 271
B.3 Renormalization-group theory 274
B.4 Discontinuous phase transitions 276
C Symmetry species 279
D Solutions to the exercises 281
References 301
Glossary 323
Index 327
|
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| id | DE-604.BV041092039 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:39:24Z |
| institution | BVB |
| isbn | 9780199669950 |
| language | English |
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| physical | XVI, 332 S. Ill., graph. Darst |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Oxford Univ. Press |
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| series | IUCr texts on crystallography |
| series2 | IUCr texts on crystallography |
| spelling | Müller, Ulrich 1940- Verfasser (DE-588)130176184 aut Symmetry relationships between crystal structures applications of crystallographic group theory in crystal chemistry Ulrich Müller 1. ed. Oxford Oxford Univ. Press 2013 XVI, 332 S. Ill., graph. Darst txt rdacontent n rdamedia nc rdacarrier IUCr texts on crystallography 18 Kristallstruktur (DE-588)4136176-3 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Kristallstruktur (DE-588)4136176-3 s Gruppentheorie (DE-588)4072157-7 s DE-604 IUCr texts on crystallography 18 (DE-604)BV002805877 18 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026068613&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Müller, Ulrich 1940- Symmetry relationships between crystal structures applications of crystallographic group theory in crystal chemistry IUCr texts on crystallography Kristallstruktur (DE-588)4136176-3 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4136176-3 (DE-588)4072157-7 |
| title | Symmetry relationships between crystal structures applications of crystallographic group theory in crystal chemistry |
| title_auth | Symmetry relationships between crystal structures applications of crystallographic group theory in crystal chemistry |
| title_exact_search | Symmetry relationships between crystal structures applications of crystallographic group theory in crystal chemistry |
| title_full | Symmetry relationships between crystal structures applications of crystallographic group theory in crystal chemistry Ulrich Müller |
| title_fullStr | Symmetry relationships between crystal structures applications of crystallographic group theory in crystal chemistry Ulrich Müller |
| title_full_unstemmed | Symmetry relationships between crystal structures applications of crystallographic group theory in crystal chemistry Ulrich Müller |
| title_short | Symmetry relationships between crystal structures |
| title_sort | symmetry relationships between crystal structures applications of crystallographic group theory in crystal chemistry |
| title_sub | applications of crystallographic group theory in crystal chemistry |
| topic | Kristallstruktur (DE-588)4136176-3 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Kristallstruktur Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026068613&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002805877 |
| work_keys_str_mv | AT mullerulrich symmetryrelationshipsbetweencrystalstructuresapplicationsofcrystallographicgrouptheoryincrystalchemistry |