Fundamentals of crystallography:
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2008
|
| Edition: | 2. ed., reprinted |
| Series: | International Union of Crystallography texts on crystallography
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | CD-ROM-Titel: An interactive book on general crystallography |
| Physical Description: | XIX, 825 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 019850957X 0198509588 |
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| 245 | 1 | 0 | |a Fundamentals of crystallography |c ed. by C. Giacovazzo |
| 246 | 1 | 3 | |a An interactive book on general crystallography |
| 250 | |a 2. ed., reprinted | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2008 | |
| 300 | |a XIX, 825 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International Union of Crystallography texts on crystallography |v 7 | |
| 490 | 0 | |a Oxford science publications | |
| 500 | |a CD-ROM-Titel: An interactive book on general crystallography | ||
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| _version_ | 1804139177327984640 |
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| adam_text | Contents
List of contributors
xxi
1
Symmetry in crystals
ι
Carmelo
Giacovazzo
1.1
The crystalline state and isometric operations
1
1.2
Symmetry elements
3
1.2.1
Axes of rotational symmetry
3
1.2.2
Axes of rototranslation or screw axes
5
1.2.3
Axes of inversion
5
1.2.4
Axes of rotoreflection
5
1.2.5
Reflection planes with translational component
(glide planes)
6
1.3
Lattices
6
1.4
The rational properties of lattices
7
1.4.1
Cry stallographic directions
8
1.4.2
Crystallographic planes
8
1.5
Symmetry restrictions due to the lattice periodicity
and vice versa
10
1.6
Point groups and symmetry classes
12
1.6.1
Point groups in one and two dimensions
18
1.7
The
Laue
classes
18
1.8
The seven crystal systems
18
1.9
The
Bravais
lattices
19
1.9.1
Plane lattices
19
1.9.2
Space lattices
20
1.10
The space groups
24
1.11
The plane and line groups
32
1.12
On the matrix representation of symmetry operators
32
Appendices
38
LA The isometric transformations
38
1
.A.
1
Direct movements
38
1
.A.2 Opposite movements
39
l.B Some combinations of movements
40
LC Wigner-Seitz cells
44
1
.D The space-group matrices
44
1
.E Symmetry groups
47
I.E.I Subgroups
49
1.E.2 Cosets
50
1.E.3 Conjugate classes
51
1.E.4 Conjugate subgroups
52
Contents
I.E.
5 Normal
subgroups and factor groups
52
1.E.6 Maximal subgroups and minimal supergroups
54
1.E.7 Maximal subgroups and minimal supergroups
for three-dimensional crystallographic point groups
55
1
.E.8 Limiting groups in two and three dimensions
56
1.E.9 Representation of a group
57
I.E.
10
Opposite movements
58
l.F Symmetry generalization
59
l.F.l The symmetry groups
G„m 59
l.F.
2
The G1 groups
59
1.F.3 The G2 groups
59
1.F.4 The G3 groups
60
1.F.5 The G4 groups
63
l.F.
6
The groups of colour symmetry
63
References
64
2
Crystallographic computing
67
Carmelo
Giacovazzo
2.1
Introduction
67
2.2
The metric matrix
67
2.3
The reciprocal lattice
69
2.4
Basis transformations
72
2.5
Transformation from triclinic to
orthonormal
axes
74
2.6
Rotations in Cartesian systems
76
2.7
Some simple crystallographic calculations
80
2.7.1
Torsion angles
81
2.7.2
Best plane through a set of points
81
2.7.3
Best line through a set of points
82
2.7.4
Principal axes of a quadratic form
83
2.8
Metric considerations on the lattices
85
2.8.1
Niggli reduced cell
85
2.8.2
Sublattices and superlattices
88
2.8.3
Coincidence-site lattices
89
2.9
Calculation of the electron density function
91
2.10
Calculation of the structure factor
93
2.11
The method of least squares
95
2.11.1
Linear least squares
95
2.11.2
Linear least squares with constraints
98
2.11.3
Non-linear (unconstrained) least squares
99
2.11.4
Least-squares refinement of crystal structures
100
2.11.5
Practical considerations on crystallographic
least squares
104
2.11.6
Constraints and restraints in crystallographic
least squares 111
2.12
Alternatives to the method of least squares
115
2.12.1
Maximum likelihood refinement
116
2.12.2
Gradient methods
118
Contents xi
2.13
Rietveld
refinement
120
2.13.1
Preliminary steps
120
2.13.2
The basis of the
Rietveld
refinement
122
2.13.3
Some practical aspects of
Rietveld
refinement
125
2.14
Analysis of thermal motion
130
2.15
The effect of thermal motion on bond lengths and angles
133
2.16
About the accuracy of the calculated parameters
135
Appendices
137
2.A Some metric relations between direct and
reciprocal lattices
137
2.
В
Some geometrical calculations concerning
directions and planes
138
2.
С
Some transformation matrices
141
2.D Reciprocity of
F
and I lattices
141
2.E Transformations of crystallographic
quantities in rectilinear spaces
142
2.F Derivation of the normal equations
144
2.
G
Derivation of the variance-covariance
matrix Mv
145
2.H Derivation of the unbiased estimate of MY
145
2.1
The FFT algorithm and its crystallographic
applications
146
References
147
3
The diffraction of X-rays by crystals
153
Carmelo
Giacovazzo
3.1
Introduction
153
3.2
Basic properties of X-rays
153
3.3
Thomson scattering
154
3.4
Compton scattering
156
3.5
Interference of scattered waves
157
3.6
Scattering by atomic electrons
158
3.7
Scattering by atoms
160
3.8
The temperature factor
161
3.9
Scattering by a molecule or by a unit cell
163
3.10
Diffraction by a crystal
164
3.11
Bragg slaw
168
3.12
The reflection and the limiting spheres
168
3.13
Symmetry in reciprocal space
169
3.13.1
Friedellaw
170
3.13.2
Effects of symmetry operators in the reciprocal space
170
3.13.3
Determination of the
Laue
class
170
3.13.4
Determination of reflections with restricted
phase values
171
3.13.5
Systematic absences
173
3.13.6
Unequivocal determination of the space group
176
x¡¡
Contents
3.14
Diffraction
intensities i76
3.15
Anomalous
dispersion
180
3.16
The Fourier synthesis and the
phase
problem
185
Appendices
1°
3.A Mathematical background
187
3.A.1 Dirac delta function 18V
3.A.2 A mathematical model for the lattice
189
3.A.3 Convolutions
19°
3.A.4 Some properties of convolutions
193
3.A.5 The Fourier transform
194
3.A.6 Some examples of Fourier transform
196
3.A.7 Fourier transform of spherically symmetric functions
200
3.A.8 Deconvolution of spectra
201
3.B Scattering and related topics
202
3.B.1 Compton scattering
202
3.B.2 The anisotropic temperature factor
202
3.B.3 Symmetry restrictions on the anisotropic
temperature factors
205
3.B.4 The Renninger effect and experimental phase
determination by means of multiple
diffraction experiments
208
3.B.5 Electron diffraction
213
3.B.6 Neutron scattering
216
3.C About electron density mapping
220
References
224
4
Beyond ideal crystals
227
Carmelo
Giacovazzo
4.1
Introduction
227
4.2
Ordering types
228
4.3
Crystal twins
229
4.4
Diffuse scattering
236
4.4.1
Thermal diffuse scattering
237
4.4.2
Disorder diffuse scattering
239
4.5
Modulated crystal structures
244
4.6
Quasicrystals
247
4.6.1
Introductory remarks
247
4.6.2
A mathematical basis
248
4.6.3
Aperiodic tiling and quasicrystals
250
4.6.4
Embedding quasicrystals in higher-dimensional space
253
4.7
Liquid crystals (or mesomorphic phases)
256
4.8
The paracrystal
260
4.9
Amorphous and liquid states
262
4.9.1
Diffraction from a finite statistically homogeneous
object
263
4.9.2
Diffraction from a finite statistically homogeneous
object with equal atoms
265
Contents xiii
4.9.3
Diffraction
from an
isotropie
statistically
homogeneous object
268
4.9.4
The Debye formula
268
4.10
Diffraction by gases
270
4.11
Diffraction by liquids and amorphous bodies
272
4.12
Small-angle scattering
274
Appendices
278
4.
A Examples of twin laws
278
4.A.
1
Cubic system
278
4.A.2 Tetragonal system
278
4.A.3 Hexagonal and trigonal systems
278
4.A.4 Orthorhombic system
280
4.
A.
5
Monoclinic system
280
4.A.6 Triclinic system
280
4.
В
How to recognize and treat twins
281
4.C Embedding of modulated structures in
higher-dimensional space
285
4.D About Fibonacci numbers and sequences
289
References
291
Experimental methods in X-ray and
neutron crystallography
295
Hugo L. Monaco and
Gilberto
Artioii
5.1
Introduction
295
5.2
X-ray sources
295
5.2.1
Conventional generators
295
5.2.2
Synchrotron radiation
300
5.2.3
X-ray optics: monochromatization, collimation,
and focusing of X-rays
306
5.3
Neutron sources
313
5.3.1
Nuclear reactors
314
5.3.2
Pulsed neutron sources
315
5.3.3
Neutron optics
317
5.4
X-ray and neutron detectors
318
5.4.1
X-ray detectors
320
5.4.2
Neutron detectors
328
5.5
Data collection techniques for single crystals
329
5.5.1
The
Laue
method
330
5.5.2
The single crystal cameras
331
5.5.3
The single crystal diffractometer
335
5.6
Data collection techniques for polycrystalline materials
348
5.6.1
Diffraction of polycrystalline materials
348
5.6.2
Cameras used for polycrystalline materials
352
5.6.3
Diffractometers used for polycrystalline materials
357
5.6.4
Applications of powder diffraction
362
x¡v
Contents
5.7 In situ
measurements in non-ambient conditions
369
5.7.1
High-temperature polycrystalline diffraction
372
5.7.2
Low-temperature single crystal diffractometry
373
5.7.3
High-pressure experiments
374
5.8
Data Reduction
376
5.8.1
Lorentz
correction
377
5.8.2
Polarization correction
378
5.8.3
Absorption correction
380
5.8.4
Radiation damage correction
383
5.8.5
Relative scaling
386
Appendices
388
5.A Determination of the number of molecules
in the unit cell of a crystal
388
5.
В
The cylindrical film cameras geometry
390
5.
С
The precession camera geometry
396
5.
D
The rotation method geometry
399
References
403
6
Solution and refinement of crystal structures
413
Davide
Viterbo
6.1
Introduction
413
6.2
Statistical analysis of structure-factor amplitudes
415
6.3
The Patterson function and its use
419
6.3.1
The heavy atom method
424
6.4
Direct methods
432
6.4.1
Introduction
432
6.4.2
Structure invariants and semi-invariants
434
6.4.3
Probability methods
438
6.4.4
Fixing the origin and the enantiomorph
444
6.4.5
Phase determination procedures
448
6.5
Completing and refining the structure
465
6.5.1
Difference Fourier method
465
6.5.2
Least-squares method
467
6.5.3
Absolute configuration
475
Appendices
476
6.A Structure-factor probability distributions
476
6.B Patterson vector methods
479
6.C Probability formulae for triplet invariants
486
6.D Pseudotranslational symmetry
489
6.E Magic integers
490
6.F New multisolution techniques
491
6.G Procedures for completing a partial model
493
6.G.
1
Weights for Fourier syntheses
493
6.G.2 Syntheses for completing a partial model
495
References
496
Contents
xv
7
Mineral and inorganic crystals
503
Giovanni Ferraris
7.1
Introduction
503
7.2
Bonding aspects
505
7.2.1
Chemical bond and solid-state properties
505
7.2.2
Melting
506
7.2.3
Cleavage
507
7.2.4
Structure and morphology
508
7.2.5
Morphology and optical properties
509
7.2.6
Representing crystal structures
509
7.2.7
The ionic radii
510
7.2.8
Packing of spheres
512
7.2.9
Coordination polyhedra
516
7.2.10
Interstitial sites
516
7.2.11
Ionic radii and coordination polyhedra
518
7.2.12
Electrostatic bond strength and Pauling s rules
521
7.2.13
Bond strength versus bond length
524
7.2.14
The charge distribution (CD) method
525
7.2.15
Applications of CD and ECoN
528
7.2.16
Bond valence and hydrogen bond
530
7.2.17
Bond valence and hydrates
531
7.2.18
Bond strength of the
О
· · ·
О
hydrogen bond
532
7.2.19
Polymorphism
533
7.2.20
Solid solutions
534
7.2.21
Solid solutions, order/disorder and crystal-chemical
formula
536
7.3
Structure types
538
7.3.1
Closest- and close-packing type structures
538
7.3.2
Packing spheres only
538
7.3.3
Filling tetrahedral sites
539
7.3.4
Filling octahedral sites
543
7.3.5
Filling octahedral and tetrahedral sites
549
7.3.6
More cp structures
550
7.4
Structures with complex anions
552
7.4.1
Orthosilicates
552
7.4.2
Disilicates and ring silicates
554
7.4.3
Chain silicates (inosilicates)
555
7.4.4
Layer (sheet) silicates (phyllosilicates)
556
7.4.5
Tectosfficates
559
7.4.6
More materials of technological interest
561
7.5
Modular structures
561
7.5.1
Polytypism
561
7.5.2
Modelling the structure of
OD
polytypes
562
7.5.3
Identification of long-period polytypes
564
7.5.4
Polysomatic series
567
7.5.5
Modelling structures of polysomes
568
7.5.6
Modular series and homology
571
7.5.7
Intersecting modular series
573
XVI
Contents
7.5.8
Miscellany of
modular
structures
574
7.5.9
Modulated structures
575
7.6
Real structures
575
7.6.1
Symmetry domains
576
7.6.2
Unmixing phenomena
578
References
580
8
Molecules and molecular crystals
585
Gastone Gilli
8.1
Chemistry and X-ray crystallography
585
8.1.1
Crystal and molecular structure
585
8.1.2
The growth of structural information
587
8.2
The nature of molecular crystals
588
8.2.1
Intermolecular forces
588
8.2.2
A more detailed analysis of intermolecular forces
596
8.2.3
Thermodynamics of molecular crystals
600
8.2.4
Free and lattice energy of a crystal from
atom-atom potentials
603
8.2.5
Polymorphism
606
8.2.6
The prediction of the crystal structures
606
8.3
Elements of classical stereochemistry
610
8.3.1
Structure: constitution, configuration, and
conformation
610
8.3.2
Isomerism
612
8.3.3
Ring conformations
617
8.3.4
Ring conformation and group theory
618
8.3.5
Computation of puckering coordinates
624
8.4
Molecular structure and chemical bond
625
8.4.1
Introduction
625
8.4.2
Quantum-mechanical methods
626
8.4.3
Qualitative bonding theories
628
8.4.4
The VSEPR theory
630
8.4.5
VB theory
632
8.4.6
Molecular mechanics (MM)
634
8.4.7
Molecular mechanics, force fields, and
molecular modelling
637
8.5
Molecular hermeneutics: the interpretation of
molecular structures
639
8.5.1
Correlation methods in structural analysis
639
8.5.2
Some three-centre-four-electron linear systems
641
8.5.3
Nucleophilic addition to organometallic compounds
642
8.5.4
Nucleophilic addition to the carbonyl group
644
8.5.5
Conformational rearrangements
645
8.5.6
Advances in hydrogen bond theory by
structure-correlation methods
650
References
657
Contents xvii
9 Protein
crystallography
667
Giuseppe Zanotti
9.1
Introduction
667
9.2
Biological macromolecules
669
9.2.1
Globular proteins
669
9.2.2
Protein folding: general rules
670
9.2.3
Levels of organization of proteins: secondary structure
671
9.2.4
Representation of the polypetide chain conformation
676
9.2.5
Higher levels of organization: tertiary and quaternary
structure, domains, and subunits
676
9.2.6
The influence of the medium
678
9.2.7
Groups other than amino-acids
679
9.2.8
Protein classification
681
9.2.9
Nucleic acids
683
9.3
Protein crystals
683
9.3.1
Principles of protein crystallization
685
9.3.2
Crystallization methods
686
9.3.3
Testing the conditions: factorial approaches
687
9.3.4
The solvent content of protein crystals
689
9.3.5
Cryotechniques
691
9.3.6
Preparation of isomorphous heavy-atom derivatives
692
9.3.7
How isomorphous are isomorphous derivatives?
693
9.4
The solution of the phase problem
694
9.4.1
The isomorphous replacement method
694
9.4.2
The determination of heavy-atom positions
695
9.4.3
The single isomorphous replacement (SIR) method
696
9.4.4
The classical solution of the problem of phase
ambiguity: the MIR technique
698
9.4.5
Anomalous scattering: a complementary (or alternative)
approach to the solution of the phase problem
699
9.4.6
The optimal choice of wavelength and the multiple
anomalous dispersion (MAD) technique
701
9.4.7
The use of anomalous scattering in the determination
of the absolute configuration of the
macromolecule
703
9.4.8
The treatment of errors
705
9.4.9
The refinement of heavy atoms parameters
709
9.4.10
Maximum-likelihood and Bayesian estimates: an
alternative approach in phase refinement
711
9.4.11
Picking up minor heavy-atom sites: the
difference-Fourier synthesis
712
9.4.12
Density-modification: how to solve the phase
ambiguity and improve the electron density map
713
9.4.13
Rotation and translation functions and the
molecular replacement method
716
9.4.14
The first step in molecular replacement: the
rotation function
718
9.4.15
The rotation matrix
С
and the choice of variables
720
9.4.16
Translation functions
720
xviii Contents
9.4.17
Self-rotation and self-translation functions:
improving the electron density maps
723
9.4.18
Practical hints in molecular replacement
725
9.4.19
The direct methods in macromolecular
crystallography
725
9.5
The interpretation of the electron density maps and the
refinement of the model
728
9.5.1
The interpretation of the electron density maps
728
9.5.2
Interactive computer graphics and model building
729
9.5.3
The refinement of the structure
731
9.5.4
Constrained versus restrained least-squares
732
9.5.5
Restrained and constrained least-squares
735
9.5.6
Crystallographic refinement by molecular dynamics
736
9.5.7
The strategy of the refinement of protein structures
737
9.5.8
R
factor and J?free: structure validation.
739
9.5.9
Thermal parameters and disordered structures
741
9.5.10
The organization of solvent
743
9.5.11
The influence of crystal packing
744
9.5.12
Dynamical studies: time-resolved crystallography
744
Appendices
746
9.A Some formulae for isomorphous
replacement and anomalous dispersion
746
9.
В
Translation functions
748
9.C Macromolecular least-squares refinement
and the conjugate-gradient algorithm
749
9.
D
Conventions and symbols for
amino
acids
and peptides
751
References
752
10
Physical properties of crystals:
Phenomenology and modelling
759
Michele Catti
10.1
Introduction
759
10.2
Crystal anisotropy and tensors
760
10.2.1
Tensorial
quantities
761
10.2.2
Symmetry of
tensorial
properties
763
10.3
Overview of physical properties
765
10.4
Electrical properties of crystals
766
10.4.1
Pyroelectricity
767
10.4.2
Dielectric impermeability and optical properties
768
10.5
Elastic properties of crystals
769
10.5.1
Crystal strain
770
10.5.2
Inner deformation
773
10.5.3
Stress tensor
775
10.5.4
Elasticity tensor
775
10.5.5
Examples and applications
779
10.6
Piezoelectricity
781
10.6.1
Symmetry properties of the piezoelectric tensor
783
Contents xix
10.7
Modelling
of structural and elastic behaviour
785
10.7.1
Atomistic potential functions
785
10.7.2
Athermal equation of state
787
10.7.3
Elastic constants
789
10.8
Crystal defects
791
10.9
Experimental methods
792
10.10
Planar defects
794
10.11
Line defects: dislocations
797
10.11.1
The Burgers circuit
799
10.11.2
X-ray topography of dislocations
799
10.11.3
Energy of a dislocation
801
10.11.4
Motion and interaction of dislocations
802
10.11.5
Partial dislocations
803
10.11.6
Small-angle grain boundaries
804
10.12
Point defects
805
10.13
Thermal distribution of defects
806
10.14
Diffusion
807
10.15
Ionic conductivity
808
Appendices
810
10.A.1 Properties of second-rank tensors
810
10.A.2 Eigenvalues and eigenvectors
810
10.A.3 Representation surfaces and their properties
811
References
813
Index
815
|
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| discipline | Chemie / Pharmazie Geowissenschaften Physik |
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| spelling | Fundamentals of crystallography ed. by C. Giacovazzo An interactive book on general crystallography 2. ed., reprinted Oxford [u.a.] Oxford Univ. Press 2008 XIX, 825 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier International Union of Crystallography texts on crystallography 7 Oxford science publications CD-ROM-Titel: An interactive book on general crystallography Kristallographie Kristallographie (DE-588)4033217-2 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content 2\p (DE-588)4016928-5 Festschrift gnd-content Kristallographie (DE-588)4033217-2 s DE-604 Giacovazzo, Carmelo Sonstige oth International Union of Crystallography texts on crystallography 7 (DE-604)BV002805877 7 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017594571&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fundamentals of crystallography International Union of Crystallography texts on crystallography Kristallographie Kristallographie (DE-588)4033217-2 gnd |
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| title | Fundamentals of crystallography |
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| title_auth | Fundamentals of crystallography |
| title_exact_search | Fundamentals of crystallography |
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| title_full_unstemmed | Fundamentals of crystallography ed. by C. Giacovazzo |
| title_short | Fundamentals of crystallography |
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