Symmetry of crystals and molecules:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2014
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturverz. S. [422] |
| Beschreibung: | XXI, 433 S. Ill., zahlr. graph. Darst. |
| ISBN: | 9780199670888 |
Internformat
MARC
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| 100 | 1 | |a Ladd, M. F. C. |d 1926- |e Verfasser |0 (DE-588)132263378 |4 aut | |
| 245 | 1 | 0 | |a Symmetry of crystals and molecules |c Mark Ladd |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2014 | |
| 300 | |a XXI, 433 S. |b Ill., zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. [422] | ||
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| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027175587&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
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Datensatz im Suchindex
| _version_ | 1804152010940874752 |
|---|---|
| adam_text | This book provides a comprehensive study of the
symmetry and geometry of crystals and molecules,
starting from first principles. The pre-knowledge
assumed is mathematics and physical science to
about
А
-level; additional mathematical topics are
discussed in appendices. It is copiously illustrated,
including many stereoviews, with instructions both
for stereoviewing and for constructing
a
stereoviewer.
Problems for each chapter are provided, with fully worked
tutorial solutions. A suite of associated computer programs
has been devised and is available through the publisher s
website, for assisting both the study of the text and the solutions
to the problems. The applicability of symmetry in everyday life as well
as in science is stressed. Point groups and space groups are first discussed and
derived in a semi-analytical manner, and later by use of group theory. The basic principles of group
theory are discussed, together with applications to symmetry, chemical bonding, and aspects of
vibrations of molecules and crystals. The book is addressed to those studying the physical sciences
and meeting the subject of crystallography for the first time, and it brings the reader to a level of
appreciation for the definitive works produced by the International Union of Crystallography,
such as the International Tables for X-ray Crystallography,
Voli
(1965)
and the International Tables for
Crystallography,
Vol
A
{2006).
Mark Ladd was formerly Head of Chemical Physics at the University of Surrey.
This book should tell you everything you need to know about crystal and molecular symmetry.
Ladd adopts an integrated approach so that the relationships between crystal symmetry, molecular
symmetry, and features of chemical interest are maintained and reinforced. The theoretical aspects
of bonding and symmetry are also well represented, as are symmetry-dependent physical properties
and the applications of group theory. The comprehensive coverage will make this book a valuable
resource for a broad range of readers.
Alexander Blake, School of Chemistry, University of Nottingham
This book successfully combines a thorough treatment of molecular and crystal symmetry with
a simple and informal writing style. By means of familiar examples the author helps to provide
the reader with those conceptual tools necessary for the development of a clear understanding of
what are often regarded as difficult topics. Christopher Hammond, University of Leeds
Cover image: The cover illustration, representing the symmetry group
235
(I), is reproduced by courtesy of
Professor Chaim Goodman-Strauss, University of Arkansas, co-author with John Conway and Heidi Burgiel of
a copiously illustrated, fascinating book entitled The Symmetries of Things, published by
А К
Peters
/
CKC Press
(2008).
ISBN
978-0-19-967088-8
OXTORD
UNIVERSITY PRESS
7888
www.oup.com
Contents
Physical data, notation, and online materials
xix
1
Symmetry everywhere l
1.1
Introduction
1
1.2
Looking at symmetry
2
1.3
Some symmetrical objects
3
1.4
Defining symmetry
4
1.5
Symmetry in science
5
1.6
Symmetry in music
8
1.7
Symmetry in architecture
9
1.8
Summary and notation
10
1.8.1
Introducing symmetry notation
10
References
1 10
Problems
1 11
2
Geometry of crystals and molecules
із
2.1
Introduction
13
2.2
Reference axes
15
2.2.1
Crystallographic axes
17
2.3
Equation of a plane
18
2.4
Miller indices
19
2.4.1
Miller-Bravais indices
20
2.5
Zones
20
2.5.1
Weiss zone equation
21
2.5.2
Addition rule for crystal planes
22
2.6
Projection of three-dimensional features
23
2.6.1
Stereographic projection
24
2.6.2
Calculations in stereographic projections
30
2.6.3
Axial ratios and
interaxial
angles
35
2.7
Molecular geometry: VSEPR theory
36
2.8
Molecular geometry: experimental determination
38
2.8.1
Interatomic distances and angles
39
2.8.2
Conformational parameters
41
2.8.3
Internal coordinates
44
2.8.4
Errors and precision
46
2.9
Molecular geometry: theoretical determination
49
2.9.1
The
Schrödinger
equation
49
2.9.2
Atomic
orbitais
50
xii
Contents
2.9.3
Normalization
51
2.9.4
Probability distributions
52
2.9.5
Atomic
s
and
ρ
orbitais
53
2.9.6
Chemical species and molecular
orbitais
55
2.10
Crystal packing
56
References
2 60
Problems
2 61
3
Point group symmetry
3.1
Introduction
b.
3.2
Symmetry elements, symmetry operations and symmetry operators
b?
3.3
Point groups
65
3.4
Symmetry in two dimensions
fl5
3.4
Л
Rotation symmetry
<>s
3.4.2
Reflection symmetry
Ml
3.4.3
Combinations of symmetry operations in two dimensions
6<>
3.4.4
Two-dimensional systems and point group notation
67
3.4,5
Subgroups
W
3.5
Three-dimensional point groups
(Ý)
3.5.1
Rotation symmetry in three dimensions
(Ý)
3.5.2
Reflection symmetry in three dimensions
W
3.5.3
Roto-inversion symmetry
70
3.5.4
Stereogram
representations of three-dimensional
point groups
70
3.5.5
Crystallographic point groups
71
3.5.6
Crystal classes
71
3.5.7
Crystal systems
72
3.6
Derivation of point groups
73
3.6.1
Ten simple point groups
75
3.6.2
Combinations of symmetry operations
in three dimensions
76
3.6.3
Euler s construction
78
3.6.4
Centrosymmetric point groups
(Laue
groups) and
Laue
classes
82
3.6.5
Projected symmetry
82
3.7
Point groups and physical properties of crystals and molecules
83
3.7.1
Enantiomorphism and chirality
83
3.7.2
Optical properties
85
3.7.3
Pyroelectricity and piezoelectricity
88
3.7.4 Dipole
moments
89
3.7.5
Infrared and Raman activity
89
3.8
Point groups and chemical species
90
3.8.1
Point groups
R
90
3.8.2
Point groups
Ä
90
3.8.3
Point groups
RÏ
92
3.8.4
Point groups /?2
93
3.8.5
Point groups Rm
93
Contents xiii
3.8.6 Point
groups Rm
93
3.8.7 Point
groups
R2 and
Î
94
3.9 Non-crystallographic
point groups
95
3.10 Hermann-Mauguin and Schönflies
point group symmetry notations
96
3.10.1
Roto-reflection (alternating) axis of symmetry
99
3.10.2
The two symmetry notations compared
100
3.11
Point group recognition
100
3.12
Matrix representation of point group symmetry operations
101
3.12.1
Rotation matrices
104
3.13
Non-periodic crystals
105
3.13.1
Quasicrystals
105
3.13.2
Buckyballs
112
3.13.3
Icosahedral symmetry
113
References
3 115
Problems
3 116
119
119
119
120
121
121
122
123
124
124
125
125
127
129
129
130
131
132
133
136
139
140
140
142
143
143
144
145
145
146
147
147
4
Lattices
4.1
Introduction
4.2
One-dimensional lattice
4.3
Two-dimensional lattices
4.3.1
Choice of unit cell
4.3.2
Nets in the oblique system
4.3.3
Nets in the rectangular system
4.3.4
Square and hexagonal nets
4.3.5
Unit cell centring
4.4
Three-dimensional lattices
4.4.1
Triclinic lattice
4.4.2
Monoclinic lattices
4.4.3
Orthorhombic lattices
4.4.4
Tetragonal lattices
4.4.5
Cubic lattices
4.4.6
Hexagonal lattice
4.4.7
Trigonal lattices
4.5
Lattice
directions
4.6
Law of rational intercepts:
reticular
density
4.7
Reciprocal lattice
4.8
Rotational symmetry of lattices
4.9
Lattice
transformations
4.9.1
Bravais
lattice unit cell vectors
4.9.2
Zone symbols and lattice directions
4.9.3
Coordinates of points in the direct unit cell
4.9.4
Miller indices
4.9.5
Reciprocal unit cell vectors
4.9.6
Volume relationships
4.9.7
Reciprocity of
F
and
/
unit cells
4.9.8
Wigner-Seitz cells
References
4
Problems
4
xiv Contents
5 Space
groups
149
5.1
Introduction l49
5.2
One-dimensional space groups
150
5.3
Two-dimensional space groups
150
5.3.1
Plane groups in the oblique system
152
5.3.2
Plane groups in the rectangular system
154
5.3.3
Limiting conditions on X-ray reflections
155
5.3.4
Plane groups in the square and hexagonal systems
158
5.3.5
The seventeen plane groups summarized
159
5.3.6
Comments on notation
160
5.4
Three-dimensional space groups
160
5.4.1
Triclinic space groups 1
60
5.4.2
Monoclinic space groups
161
5.4.3
Space groups related to point group
2 162
5.4.4
Screw axes
164
5.4.5
Space groups related to point group m: glide planes
164
5.4.6
Space groups related to point group
lim
1
66
5.4.7
Summary of the monoclinic space groups 1
68
5.4.8
Half-shift rule
169
5.4.9
Orthorhombic space groups
170
5.4.10
Change of origin
177
5.4.11
Standard and alternative settings of space groups 1
77
5.4.12
Tetragonal space groups
179
5.4.13
Space groups in the trigonal and hexagonal systems 1
87
5.4.14
Cubic space groups
192
5.4.15
Space groups and crystal structures
197
5.5
Matrix representation of space group symmetry operations
20
1
5.6
Black-white and colour symmetry
203
5.6.1
Black-white symmetry: potassium chloride
204
5.6.2
Colour symmetry
207
5.7
The international tables and other crystallographic compilations
209
5.7.1
The international tables for crystallography, Vol. A
209
References
5 214
Problems
5 215
6
Symmetry and X-ray diffraction
218
6.1
Introduction
218
6.2
X-ray diffraction
219
6.3
Recording X-ray diffraction spectra
220
6.4
Reciprocal lattice and
Ewald
s
construction
220
6.5
X-ray intensity data collection
221
6.5.1 Laue
X-ray photography
221
6.5.2 Laue
projection symmetry
222
6.5.3
X-ray precession photography
223
6.5.4
Diffractometric and image plate recording of X-ray intensities
226
Contents xv
6.6
X-ray scattering by a crystal: the structure factor
227
6.6.1
Limiting conditions and the structure factor
229
6.6.2
Geometrical structure factor for a centrosymmetric crystal
230
6.6.3
Geometrical structure factor for an
/
centred unit cell
230
6.6.4
Geometrical structure factor for space group P2 /c
231
6.6.5
Geometrical structure factor for space group Pmal
231
6.6.6
Geometrical structure factor for space group
Рб^/т
233
6.7
Using X-ray diffraction information
235
References
6 236
Problems
6 237
7
Elements of group theory
239
7.1
Introduction
239
7.2
Group requirements
240
7.3
Group definitions
241
7.4
Examples of groups
243
7.4.1
Group multiplication tables
243
7.4.2
Reference axes in group theory
246
7.4.3
Subgroups and cosets
246
7.4.4
Similarity transformations, conjugates and
symmetry classes
247
7.5
Representations and character tables
251
7.5.1
Representations on position vectors
251
7.5.2
Representations on basis vectors
253
7.5.3
Representations on atom vectors
255
7.5.4
Representations on functions
259
7.6
A first look at character tables
260
7.6.1
Transformation of atomic
orbitais
261
7.6.2
Orthonormality and orthogonality
262
7.6.3
Notation for irreducible representations
262
7.6.4
Complex characters
263
7.6.5
Linear groups
264
7.6.6
Some properties of character tables
265
7.7
The great orthogonality theorem
266
7.8
Reduction of reducible representations
270
7.9
Constructing a character table
272
7.9.1
Summary of the properties of character tables
272
7.9.2
Constructing the character table for point group D3/,
273
7.9.3
Handling complex characters
274
7.10
Direct products
276
7.10.1
Representations on direct product functions
277
7.10.2
Formation of a character table by direct products
278
7.10.3
How the direct product has been used
279
References
7 280
Problems
7 280
xvi
Contents
8
Applications of group theory
283
8.1
Introduction
283
8.2
Structure and symmetry in molecules and ions
284
8.2.1
Application of models
284
8.2.2
Application of diffraction studies
285
8.2.3
Application of theoretical studies
287
8.2.4
Monte Carlo and molecular dynamics techniques
289
8.2.5
Symmetry adapted molecular
orbitais
292
8.2.6
Transition metal compounds: crystal-field and
ligand-field theories
301
8.2.7
The hexacyanoferrateCII) ion
304
8.3
Vibrational studies
307
8.3.1
Symmetry of normal modes
30K
8.3.2
Boron trifluoride
309
8.3,3
Selection rules for infrared and Raman activity:
dipole
moment and polarizability
311
8.3.4
Harmonics and combination vibrations
31?
8.4
Group theory and point groups
31í.
8.4.1
Cyclic point groups
3
1
7
8.4.2
Dihedral point groups
317
8.4.3
Cubic rotation point groups
3IS
8.4.4
Point groups from combinations of operators
3ľ>
8.5
Group theory and space groups
320
8.5.1
Triclinic and monoclinic space groups
321
8.5.2
Orthorhombic space groups
32 :
8.5.3
Tetragonal space groups
12
λ
8.5.4
Cubic space groups
324
8.6
Factor groups
325
8.6.1
Factor group analysis of iron(II) sulphide
32ŕ>
8.6.2
Symmetry ascent and correlation
327
8.6.3
Site group and factor group analyses
327
References
8
329
Problems
8
330
9
Computer-assisted studies
ззз
9.1
Introduction
333
9.2
Derivation of point groups
333
9.3
Recognition of point groups
334
9.4
Internal and Cartesian coordinates
334
9.5
Molecular geometry
334
9.6
Best-fit plane
335
9.7
Reduction of a representation
in point group Dbh
335
9.8
Unit cell reduction
335
9.9
Matrix operations
335
9.10
Zone symbol or Miller indices
336
9.11
Linear least squares
336
Reference
9 336
Contents xvii
Al
Stereoviews
and crystal models
337
Al.l
Stereoviews
and stereoviewing
337
Al.
2
Crystal models
337
References
340
A2 Analytical geometry of direction cosines
341
A2.
1
Direction cosines of
а
line
341
A2.2 Angle between two lines
342
A3
Vectors and matrices
343
A3.1 Introduction
343
A3.2 Vectors
343
A3.3 Volume of
а
parallelepiped
345
A3.4
Matrices
346
A3.5 Normal to a plane (hkl)
351
A3.6
Solution of linear simultaneous equations
352
A3.7 Useful matrices
352
A4 Stereographic
projection of a circle is a circle
356
A5 Best-fit plane
358
Reference
358
AÓ
General rotation matrices
359
A7 Trigonometric identities
36
1
A8 Spherical polar coordinates
362
A8.1 Polar coordinates
362
A8.2 Volume element
363
A9 The gamma function,
Γ(η)
364
References
365
Al
0
Point group character tables and related data
366
A
10.1
Introduction
366
A10.2 Character tables
366
xv¡¡¡
Contents
A10.3
Direct
products of irreducible representations and
other related data
377
A10.4 Other useful relationships
378
Al
1
Linear, unitary and projection operators
379
Al
1.1
Linear operators
379
Al
1.2
Operators in function space
380
Al
1,3
Unitary operators
381
Al
1.4
Projection operators
382
Al
2
Vanishing integrals
385
A
12.1
Introduction
385
АИД
Spectroscopie
applications
386
References
337
A13
Affine
groups 388
A13.1 Introduction 3gg
A13.2 Linear mappings 3gg
A13.3
Affine
mappings and
affine
groups
389
A13.4 Space groups and space group types
339
A
13,5
Conclusion
References
Tutorial solutions
_
General bibliography
Index
423
|
| any_adam_object | 1 |
| author | Ladd, M. F. C. 1926- |
| author_GND | (DE-588)132263378 |
| author_facet | Ladd, M. F. C. 1926- |
| author_role | aut |
| author_sort | Ladd, M. F. C. 1926- |
| author_variant | m f c l mfc mfcl |
| building | Verbundindex |
| bvnumber | BV041728758 |
| classification_rvk | RB 10103 UQ 1300 VE 5300 VE 5700 |
| classification_tum | PHY 620f |
| ctrlnum | (OCoLC)882430998 (DE-599)OBVAC11328233 |
| discipline | Chemie / Pharmazie Physik Geographie |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV041728758 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:03:55Z |
| institution | BVB |
| isbn | 9780199670888 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027175587 |
| oclc_num | 882430998 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-703 DE-11 DE-29T DE-355 DE-BY-UBR DE-19 DE-BY-UBM |
| owner_facet | DE-91 DE-BY-TUM DE-703 DE-11 DE-29T DE-355 DE-BY-UBR DE-19 DE-BY-UBM |
| physical | XXI, 433 S. Ill., zahlr. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Ladd, M. F. C. 1926- Verfasser (DE-588)132263378 aut Symmetry of crystals and molecules Mark Ladd 1. ed. Oxford [u.a.] Oxford Univ. Press 2014 XXI, 433 S. Ill., zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [422] Kristallsymmetrie (DE-588)4136175-1 gnd rswk-swf Molekülsymmetrie (DE-588)4170385-6 gnd rswk-swf Kristallographie (DE-588)4033217-2 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Molekülsymmetrie (DE-588)4170385-6 s DE-604 Kristallsymmetrie (DE-588)4136175-1 s Kristallographie (DE-588)4033217-2 s Symmetrie (DE-588)4058724-1 s Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027175587&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027175587&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Ladd, M. F. C. 1926- Symmetry of crystals and molecules Kristallsymmetrie (DE-588)4136175-1 gnd Molekülsymmetrie (DE-588)4170385-6 gnd Kristallographie (DE-588)4033217-2 gnd Symmetrie (DE-588)4058724-1 gnd |
| subject_GND | (DE-588)4136175-1 (DE-588)4170385-6 (DE-588)4033217-2 (DE-588)4058724-1 |
| title | Symmetry of crystals and molecules |
| title_auth | Symmetry of crystals and molecules |
| title_exact_search | Symmetry of crystals and molecules |
| title_full | Symmetry of crystals and molecules Mark Ladd |
| title_fullStr | Symmetry of crystals and molecules Mark Ladd |
| title_full_unstemmed | Symmetry of crystals and molecules Mark Ladd |
| title_short | Symmetry of crystals and molecules |
| title_sort | symmetry of crystals and molecules |
| topic | Kristallsymmetrie (DE-588)4136175-1 gnd Molekülsymmetrie (DE-588)4170385-6 gnd Kristallographie (DE-588)4033217-2 gnd Symmetrie (DE-588)4058724-1 gnd |
| topic_facet | Kristallsymmetrie Molekülsymmetrie Kristallographie Symmetrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027175587&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027175587&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT laddmfc symmetryofcrystalsandmolecules |