Symmetry in crystallography: understanding the international tables
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2011
|
| Series: | IUCr texts on crystallography
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIII, 126 S. Ill., graph. Darst. |
| ISBN: | 9780199550654 |
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| 245 | 1 | 0 | |a Symmetry in crystallography |b understanding the international tables |c Paolo G. Radaelli |
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2011 | |
| 300 | |a XIII, 126 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
PART I SYMMETRY GROUPS: AN INTRODUCTION 1 SYMMETRY AROUND A FIXED POINT
3
1.1 THE SYMMETRIES OF A PARALLELOGRAM, AN ARROW AND A RECTANGLE 3
1.2 WHAT DO THE GRAPHIC SYMBOLS FOR 2 AND M REALLY MEAN? GRAPHS AND
THEIR SYMMETRY 4
1.3 SYMMETRY OPERATORS 4
1.4 GROUP STRUCTURE: A FEW FORMAL DEFINITIONS 6
1.5 MULTIPLICATION TABLES FOR SIMPLE GROUPS 8
1.6 GRAPH SYMMETRY VS. COMPOSITION 9
1.7 CONJUGATION AND CONJUGATION CLASSES 10
1.8 RULES TO OBTAIN 2D MULTIPLICATION TABLES 10
1.9 THE REMAINING 2D POINT GROUPS 11
1.10 GRAPH SYMMETRY, CONJUGATION AND PATTERNS 11
1.11 THE 2D POINT GROUPS IN THE ITC 12
1.12 GROUP-SUBGROUP RELATIONS 17
2 FRIEZE PATTERNS AND FRIEZE GROUPS 19
2.1 SYMBOLS FOR FRIEZE GROUPS 22
2.2 OPERATOR GRAPHS GENERALIZED TO FRIEZE PATTERNS 22
2.3 MORE FORMAL CONCEPTS FOR FRIEZE GROUPS 23
2.4 RELATION BETWEEN GRAPH SYMMETRY AND COMPOSITION 24 2.5 WHY DID WE
INTRODUCE GRAPHS IN THE FIRST PLACE? GRAPHICAL MULTIPLICATION TABLES 24
2.6 A GRAPHICAL MULTIPLICATION TABLE FOR FRIEZE PATTERNS 25 2.7
COMMUTATION: HOW TO SWITCH OPERATORS 27
2.8 INTRODUCING AN ORIGIN: NORMAL FORM FOR OPERATORS 28 2.9 CHOICE OF
ORIGIN 29
2.10 COMPOSITION OF OPERATORS IN NORMAL FORM 30
2.11 POINT GROUPS AND LOCAL SYMMETRY 30
2.12 COORDINATE SYSTEMS FOR FRIEZE GROUPS 30
2.13 FRIEZE GROUPS IN THE ITC 31
3 WALLPAPER (PLANE) GROUPS 35
3.1 TRANSFORMATION OF TRANSLATIONS BY GRAPH SYMMETRY 35 3.2 THE SYMMETRY
OF THE TRANSLATION SET 36
3.3 LATTICES 36
3.4 CRYSTALLOGRAPHIC RESTRICTION 36
IMAGE 2
3.5 BRAVAIS LATTICES IN 2D 38
3.6 UNIT CELLS IN 2D 40
3.7 COMPOSITION RULES IN 2D 41
3.8 GRAPHICAL MULTIPLICATION TABLE IN 2D 43
3.9 NOMENCLATURE FOR WALLPAPER GROUPS 43
3.10 THE 17 WALLPAPER GROUPS 44
3.11 ANALYZING WALLPAPER AND OTHER 2D ART USING WALLPAPER GROUPS 45
3.12 CONSTRUCTING WALLPAPER GROUPS 48
PART II CRYSTALLOGRAPHIC COORDINATE SYSTEMS
4 COORDINATE SYSTEMS IN CRYSTALLOGRAPHY 53
4.1 CHANGE OF ORIGIN AND GENERALIZED COORDINATE TRANSFORMATIONS 56
4.2 THE MOST GENERAL COORDINATE TRANSFORMATION 56
5 THE MATHEMATICAL FORM OF SYMMETRY OPERATORS 57 5.1 SYMMETRY OPERATORS
IN CARTESIAN COORDINATES 57 5.2 ROTATION MATRICES 58
5.3 SYMMETRY OPERATORS IN GENERALIZED CRYSTALLOGRAPHIC COORDINATES 59
6 DISTANCES, ANGLES AND THE REAL AND RECIPROCAL SPACES 61 6.1
DETERMINATION OF DISTANCES AND ANGLES IN REAL SPACE: THE METRIC TENSOR
61
6.2 DUAL BASIS AND COORDINATES: THE RECIPROCAL SPACE 62 6.3 AN AUXILIARY
CARTESIAN SYSTEM 65
7 A PHASE TRANSITION IN TWO DIMENSIONS 67
7.1 LOW-SYMMETRY GROUP 67
7.2 WYCKOFF POSITIONS 67
7.3 BASIS TRANSFORMATION 69
7.4 METRIC TENSOR 70
PART III SYMMETRY IN THREE DIMENSIONS
8 POINT GROUPS IN 3D 75
8.1 GENERALIZED ROTATIONS IN 3D 75
8.2 3D POINT GROUPS WITH A 2D POINT-GROUP PROJECTION 76 8.3 OTHER 3D
POINT GROUPS: THE FIVE CUBIC GROUPS 79
8.4 3D POINT GROUPS IN THE ITC 80
9 THE 14 3D BRAVAIS LATTICES 83
9.1 INTRODUCTION 83
9.2 CONSTRUCTION OF THE 14 BRAVAIS LATTICES 83
10 3D SPACE-GROUP SYMMETRY 89
10.1 ROTO-TRANSLATIONS IN 3D 89
IMAGE 3
10.2 GLIDE PLANES IN 3D 90
10.3 GRAPHICAL NOTATION FOR 3D SYMMETRY OPERATORS 91 10.4 MULTIPLICATION
TABLES IN 3D 92
10.5 CONSTRUCTION OF SPACE GROUPS IN 3D 93
PART IV RECIPROCAL SPACE
11 SYMMETRY AND REFLECTION CONDITIONS IN RECIPROCAL SPACE 101 11.1 REAL
AND RECIPROCAL LATTICE: RECAPITULATION 101
11.2 RECIPROCAL LATTICE - AN ALTERNATIVE DEFINITION 102
11.3 CENTERING EXTINCTIONS 103
11.4 HOLOHEDRY OF THE RECIPROCAL LATTICE 105
11.5 FOURIER TRANSFORM OF LATTICE FUNCTIONS: THE WEIGHED RECIPROCAL
LATTICE AND ITS SYMMETRY 107
11.6 FURTHER EXPLOITATION OF THE RL SYMMETRY 113
12 THE WIGNER-SEITZ CONSTRUCTIONS AND THE BRILLOUIN ZONES 117 12.1 THE
WIGNER-SEITZ CONSTRUCTION AT THE ORIGIN OF RECIPROCAL SPACE 118
12.2 THE EXTENDED WIGNER-SEITZ SCHEME: CONSTRUCTION OF HIGHER-ORDER
BRILLOUIN ZONES 120
REFERENCES 123
INDEX 125
|
| any_adam_object | 1 |
| author | Radaelli, Paolo G. |
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| discipline | Chemie / Pharmazie Physik |
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| institution | BVB |
| isbn | 9780199550654 |
| language | English |
| lccn | 2011026855 |
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| physical | XIII, 126 S. Ill., graph. Darst. |
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| spelling | Radaelli, Paolo G. Verfasser aut Symmetry in crystallography understanding the international tables Paolo G. Radaelli Oxford [u.a.] Oxford Univ. Press 2011 XIII, 126 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier IUCr texts on crystallography 17 Hier auch später erschienene, unveränderte Nachdrucke Crystallography Tables Crystallography, Mathematical Symmetry (Physics) SCIENCE / Crystallography bisacsh Kristallform (DE-588)4287210-8 gnd rswk-swf Kristallographie (DE-588)4033217-2 gnd rswk-swf Kristallmathematik (DE-588)4125615-3 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Kristall (DE-588)4033209-3 gnd rswk-swf Kristall (DE-588)4033209-3 s Kristallform (DE-588)4287210-8 s Kristallmathematik (DE-588)4125615-3 s Kristallographie (DE-588)4033217-2 s Symmetrie (DE-588)4058724-1 s DE-604 IUCr texts on crystallography 17 (DE-604)BV002805877 17 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024497072&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Radaelli, Paolo G. Symmetry in crystallography understanding the international tables IUCr texts on crystallography Crystallography Tables Crystallography, Mathematical Symmetry (Physics) SCIENCE / Crystallography bisacsh Kristallform (DE-588)4287210-8 gnd Kristallographie (DE-588)4033217-2 gnd Kristallmathematik (DE-588)4125615-3 gnd Symmetrie (DE-588)4058724-1 gnd Kristall (DE-588)4033209-3 gnd |
| subject_GND | (DE-588)4287210-8 (DE-588)4033217-2 (DE-588)4125615-3 (DE-588)4058724-1 (DE-588)4033209-3 |
| title | Symmetry in crystallography understanding the international tables |
| title_auth | Symmetry in crystallography understanding the international tables |
| title_exact_search | Symmetry in crystallography understanding the international tables |
| title_full | Symmetry in crystallography understanding the international tables Paolo G. Radaelli |
| title_fullStr | Symmetry in crystallography understanding the international tables Paolo G. Radaelli |
| title_full_unstemmed | Symmetry in crystallography understanding the international tables Paolo G. Radaelli |
| title_short | Symmetry in crystallography |
| title_sort | symmetry in crystallography understanding the international tables |
| title_sub | understanding the international tables |
| topic | Crystallography Tables Crystallography, Mathematical Symmetry (Physics) SCIENCE / Crystallography bisacsh Kristallform (DE-588)4287210-8 gnd Kristallographie (DE-588)4033217-2 gnd Kristallmathematik (DE-588)4125615-3 gnd Symmetrie (DE-588)4058724-1 gnd Kristall (DE-588)4033209-3 gnd |
| topic_facet | Crystallography Tables Crystallography, Mathematical Symmetry (Physics) SCIENCE / Crystallography Kristallform Kristallographie Kristallmathematik Symmetrie Kristall |
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