Fundamentals of crystallography:
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2011
|
| Edition: | 3. ed. |
| Series: | International Union of Crystallography texts on crystallography
15 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXI, 842 S. Ill., graph. Darst. |
| ISBN: | 9780199573653 9780199573660 |
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| 084 | |a GEO 420f |2 stub | ||
| 130 | 0 | |a Introduzione alla cristallografia moderna | |
| 245 | 1 | 0 | |a Fundamentals of crystallography |c ed. by C. Giacovazzo |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2011 | |
| 300 | |a XXI, 842 S. |b Ill., graph. Darst. | ||
| 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 15 | |
| 490 | 0 | |a Oxford science publications | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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| 700 | 1 | |a Giacovazzo, Carmelo |e Sonstige |4 oth | |
| 830 | 0 | |a International Union of Crystallography texts on crystallography |v 15 |w (DE-604)BV002805877 |9 15 | |
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| adam_text | Contents
List of contributors
xxii
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
8
1.4.1
Crystallographic 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
19
1.8
The seven crystal systems
19
1.9
The
Bravais
lattices
20
1.9.1
Plane lattices
20
1.9.2
Space lattices
21
1.10
The space groups
24
1.11
The plane and line groups
30
1.12
On the matrix representation of symmetry operators
33
Appendices
39
1
.A The isometric transformations
39
1
.A.
1
Direct movements
39
1
.A.2 Opposite movements
40
1
.B Some combinations of movements
41
l.C Wigner-Seitz cells
45
l.D The space-group matrices
45
1
.E Symmetry groups
49
1
.E.
1
Subgroups
51
1.E.2 Cosets
52
1
.E.3 Conjugate classes
53
xii
Contents
1.E.4 Conjugate subgroups
53
1
.E.5 Normal subgroups and factor groups
53
1
.E.6 Maximal subgroups and minimal supergroups
55
1.E.7 Maximal subgroups and minimal supergroups for
three-dimensional crystallographic point groups
57
1
.E.8 Limiting groups in two and three dimensions
57
1
.E.9 Representation of a group
58
I.E.
10
Character tables
59
1
.F Symmetry generalization
59
l.F.
1
The symmetry groups GJf
60
1.F.2 The G1 groups
60
1.F.3 The G2 groups
60
1.F.4 The G3 groups
60
1.F.5 The G^ groups
62
1
.F.6 The groups of colour symmetry
62
References
65
Crystallographic computing
66
Carmelo
Giacovazzo
2.1
Introduction
66
2.2
The metric matrix
66
2.3
The reciprocal lattice
69
2.4
Basis transformations
71
2.5
Transformation from triclinic to
orthonormal
axes
73
2.6
Rotations in Cartesian systems
75
2.7
Some simple crystallographic calculations
80
2.7.1
Torsion angles
80
2.7.2
Best plane through a set of points
80
2.7.3
Best line through a set of points
82
2.7.4
Principal axes of a quadratic form
82
2.8
Metric considerations on the lattices
84
2.8.1
Niggli reduced cell
84
2.8.2
Sublattices and superlattices
87
2.8.3
Coincidence-site lattices
88
2.9
Calculation of the electron density function
90
2.10
Calculation of the structure factor
92
2.11
The method of least squares
94
2.11.1
Linear least squares
95
2.11.2
Linear least squares with constraints
97
2.11.3
Non-linear (unconstrained) least squares
98
2.11.4
Least-squares refinement of crystal structures
99
2.11.5
Practical considerations on crystallographic least squares
104
2.11.6
Constraints and restraints in crystallographic
least squares
110
2.12
Alternatives to the method of least squares
114
2.12.1
Maximum likelihood refinement
115
Contents xiii
2.12.2 Gradient
methods
117
2.13
Powder crystallography: techniques for structural analysis
119
2.13.1
Phasing via powder diffraction
119
2.13.2
The basis of the
Rietveld
refinement
125
2.13.3
Some practical aspects of
Rietveld
refinement
128
2.14
Analysis of thermal motion
133
2.15
The effect of thermal motion on bond lengths and angles
136
2.16
About the accuracy of the calculated parameters
138
Appendices
141
2.A Some metric relations between direct and reciprocal lattices
141
2.B Some geometrical calculations concerning directions and planes
142
2.C Some transformation matrices
144
2.D Reciprocity of
F
and I lattices
144
2.E Transformations of crystallographic quantities in rectilinear spaces
146
2.F Derivation of the normal equations
148
2.G Derivation of the variance-covariance matrix Mx
148
2.
H
Derivation of the unbiased estimate of Mx
149
2.1
The FFT algorithm and its crystallographic applications
149
References
151
3
The diffraction of X-rays by crystals
157
Carmelo
Giacovazzo
3.1
Introduction
157
3.2
Basic properties of X-rays
157
3.3
Thomson scattering
158
3.4
Compton scattering
160
3.5
Interference of scattered waves
161
3.6
Scattering by atomic electrons
162
3.7
Scattering by atoms
164
3.8
The temperature factor
165
3.9
Scattering by a molecule or by a unit cell
167
3.10
Diffraction by a crystal
168
3.11
Bragg slaw
171
3.12
The reflection and the limiting spheres
172
3.13
Symmetry in reciprocal space
173
3.13.1
Friedellaw
174
3.13.2
Effects of symmetry operators in the reciprocal space
174
3.13.3
Determination of the
Laue
class
174
3.13.4
Determination of reflections with restricted phase values
176
3.13.5
Systematic absences
178
3.13.6
Unequivocal determination of the space group
180
3.14
Diffraction intensities
181
3.15
Anomalous dispersion
184
3.16
The Fourier synthesis and the phase problem
189
Appendices
192
3.A Mathematical background
192
3.A.1 Dirac delta function
193
xiv Contents
3.A.2
A mathematical model for the lattice
194
3.A.3 Convolutions: the mathematical model of a crystal
195
3.A.4 Some properties of convolutions
197
3.A.5 The Fourier transform
198
3.A.6 Some examples of Fourier transform
200
3.A.7 Fourier transform of spherically symmetric functions
204
3.A.8 Deconvolution of spectra
205
3.B Scattering and related topics
206
3.B.1 Compton scattering
206
3.B.2 The anisotropic temperature factor
206
3.B.3 Symmetry restrictions on the anisotropic
temperature factors
209
3.B.4 The Renninger effect and experimental phase
determination by means of multiple
diffraction experiments
211
3.B.5 Electron diffraction
216
3.B.6 Neutron scattering
220
3.B.7 Electron, neutron and X-ray diffraction: comparison
and perspectives
224
3.C About electron density mapping
228
References
232
4
Beyond ideal crystals
235
Carmelo
Giacovazzo
4.1
Introduction
235
4.2
Ordering types
236
4.3
Crystal twins
237
4.4
Diffuse scattering
244
4.4.1
Thermal diffuse scattering
244
4.4.2
Disorder diffuse scattering
248
4.5
Modulated crystal structures
251
4.6
Quasi-crystals
254
4.6.1
Introductory remarks
254
4.6.2
A mathematical basis
255
4.6.3
Aperiodic tiling and quasi-crystals
258
4.6.4
Embedding quasi-crystals in higher-dimensional space
261
4.7
Liquid crystals (or mesomorphic phases)
264
4.8
The paracrystal
267
4.9
Amorphous and liquid states
270
4.9.
і
Diffraction from a finite statistically homogeneous object
271
4.9.2
Diffraction from a finite statistically homogeneous
object with equal atoms
272
4.9.3
Diffraction from an
isotropie
statistically
homogeneous object
275
4.9.4
The Debye formula
276
4.10
Diffraction by gases
277
4.11
Diffraction by liquids and amorphous bodies
28
1
Contents xv
4.12
Small-angle scattering
282
Appendices
285
4.A Examples of twin laws
285
4.A.
1
Cubic system
285
4.A.2 Tetragonal system
285
4.A.3 Hexagonal and trigonal systems
285
4.A.4 Orthorhombic system
287
4.A.5 Monoclinic system
287
4.A.6 Triclinic system
288
4.B How to recognize and treat twins
288
4.C Embedding of modulated structures in higher-dimensional
space
292
4.D About Fibonacci numbers and sequences
295
References
297
Experimental methods in X-ray and neutron
crystallography
301
Hugo L. Monaco and
Gilberto Artioli
5.1
Introduction
301
5.2
X-ray sources
301
5.2.1
Conventional generators
301
5.2.2
Synchrotron radiation
306
5.2.3
X-ray optics: monochromatization, collimation,
and focusing of X-rays
312
5.3
Neutron sources
319
5.3.1
Nuclear reactors
320
5.3.2
Pulsed neutron sources
321
5.3.3
Neutron optics
323
5.4
X-ray and neutron detectors
324
5.4.1
X-ray detectors
326
5.4.2
Neutron detectors
333
5.5
Data-collection techniques for single crystals
334
5.5.1
The
Laue
method
335
5.5.2
The single-crystal cameras
336
5.5.3
The single-crystal diffractometer
340
5.6
Data-collection techniques for polycrystalline materials
351
5.6.1
Diffraction of polycrystalline materials
351
5.6.2
Cameras used for polycrystalline materials
355
5.6.3
Diffractometers used for polycrystalline materials
361
5.6.4
Applications of powder diffraction
366
5.7
In situ measurements at non-ambient conditions
374
5.7.1
High-temperature polycrystalline diffraction
376
5.7.2
Low-temperature single-crystal diffractometry
377
5.7.3
Humidity control of macromolecular crystals
379
5.7.4
High-pressure experiments
379
5.8
Data reduction
381
5.8.1
Lorentz
correction
381
xvi Contents
5.8.2
Polarization correction
383
5.8.3
Absorption correction
385
5.8.4
Radiation-damage correction
388
5.8.5
Relative scaling
390
Appendices
392
5.
A Determination of the number of molecules or formula units in the
unit cell of a crystal
392
5.B The cylindrical-film camera geometry
394
5.
С
The precession camera geometry
400
5.D The rotation method geometry
403
References
406
6
Solution and refinement of crystal structures
417
Marco Milanesio and
Davide Viterbo
6.1
Introduction
417
6.2
Statistical analysis of structure factor amplitudes
419
6.3
Direct space methods
423
6.3.1
The Patterson function and its use
423
6.3.2
Electron density modification methods
435
6.4
Reciprocal space methods (direct methods)
442
6.4.1
Introduction
442
6.4.2
Structure invariants
444
6.4.3
Probability methods
445
6.4.4
Direct methods procedures
452
6.5
Using the dual space procedures
457
6.6
Completing and refining the structure
461
6.6.1
Difference Fourier method
461
6.6.2
Least-squares method
463
6.6.3
Absolute structure and resonant scattering
474
Appendices
476
6.A Structure factor probability distributions
476
6.B Patterson vector methods
478
6.C Difference electron density modification (DEDM)
486
6.D Phase-retrieval methods in optics and their use in
crystallography
488
6.E Effects of phase errors on electron density maps
491
6.F Probability formulae for triplet invariants
492
6.G Early direct method procedures
495
6.G.1 Fixing the origin and the enantiomorph
495
6.G.2 Phase-determination procedures
498
6.H Pseudotranslational symmetry
500
6.1
Procedures for completing a partial model
502
6.1.1
Weights for Fourier syntheses
502
6.1.2
Syntheses for completing a partial model
503
References
504
Contents
xvii
7
Inorganic and mineral crystals
512
Giovanni Ferraris
512
513
513
515
516
517
518
518
519
521
525
525
528
530
533
535
536
537
539
540
540
542
544
546
546
546
547
551
559
560
561
563
564
565
566
570
571
571
572
573
575
576
7.1
Introduction
7.2
Bonding aspects
7.2.1
Chemical bond and solid-state properties
7.2.2
Melting
7.2.3
Cleavage
7.2.4
Structure and morphology
7.2.5
Morphology and optical properties
7.2.6
Representing crystal structures
7.2.7
The ionic radii
7.2.8
Packing of spheres
7.2.9
Coordination polyhedra
7.2.10
Interstitial sites in hep and ccp
7.2.11
Ionic radii and coordination polyhedra
7.2.12
Electrostatic bond strength and Pauling s rales
7.2.13
Bond strength vs. bond length
7.2.14
The charge distribution (CD) method
7.2.15
Applications of CD and ECoN
7.2.16
Bond valence and hydrogen bond
7.2.17
Bond valence and hydrates
7.2.18
Bond strength of the O.
..
О
hydrogen bond
7.2.19
Polymorphism
7.2.20
Solid solutions
7.2.21
Solid solutions, order/disorder and crystal-chemical
formula
7.3
Structure types
7.3.1
Closest- and close-packing structure types
7.3.2
Packing spheres only
7.3.3
Filling tetrahedral sites
7.3.4
Filling octahedral sites
7.3.5
Filling octahedral and tetrahedral sites
7.3.6
More cp structures
7.4
Structures with complex anions
7.4.1
Orthosilicates
7.4.2
Disilicates and ring silicates
7.4.3
Chain silicates (inosilicates)
7.4.4
Layered silicates (phyllosilicates)
7.4.5
Tectosilicates
7.4.6
More structures of technological interest
7.5
Modular structures
7.5.1
Polytypism
7.5.2
Modelling the structure of
OD polytypes
7.5.3
Identification of long-period polytypes
7.5.4
Poiysomatic series
xviii
Contents
7.5.5
Modelling structures of polysomes
577
7.5.6
Modulated structures
581
7.6
Real structures
582
7.6.1
Symmetry domains
582
7.6.2
Unmixing phenomena
585
References
586
8
Molecules and molecular crystals
592
Gastone Gilli and
Paola Gilli
8.1
Chemistry and X-ray crystallography
592
8.1.1
Crystal and molecular structure
592
8.1.2
The growth of structural information
594
8.2
The nature of molecular crystals
595
8.2.1
Intermolecular forces
595
8.2.2
Thermodynamics of molecular crystals
616
8.2.3
Free and lattice energy of a crystal from atom-atom
potentials
619
8.2.4
Polymorphism
622
8.2.5
The prediction of crystal structures
623
8.3
Elements of classical stereochemistry
627
8.3.1
Structure: constitution, configuration, and
conformation
627
8.3.2
Isomerism
629
8.3.3
Ring conformations
634
8.4
Molecular structure and chemical bond
642
8.4.1
Introduction
642
8.4.2
Quantum-mechanical methods
643
8.4.3
Qualitative bonding theories
645
8.4.4
The VSEPR theory
647
8.4.5
The VB theory
649
8.4.6
Molecular mechanics (MM)
651
8.4.7
Molecular mechanics, force fields, and molecular
simulation (MS)
654
8.5
Molecular hermeneutics: the interpretation of molecular
structures
657
8.5.1
Correlation methods in structural analysis
657
8.5.2
Some three-centre-four-electron linear systems
659
8.5.3
Nucleophilic addition to organometallic compounds
661
8.5.4
Nucleophilic addition to the carbonyl group
662
8.5.5
Conformational rearrangements by structure-correlation
methods
664
8.5.6
Evidence for resonance-assisted
Н
-bond
(RAHB)
by structure-correlation methods
669
References
673
Contents
xix
Protein crystallography
685
Giuseppe Zanotti
9.1
Introduction
685
9.2
Biological macromolecules
687
9.2.1
Globular proteins
687
9.2.2
Protein folding: general rales
688
9.2.3
Levels of organization of proteins: secondary
structure
689
9.2.4
Representation of the polypeptide chain conformation
692
9.2.5
Higher levels of organization: tertiary and quaternary
structure, domains and subunits
692
9.2.6
The influence of the medium
694
9.2.7
Groups other than
amino
acids
695
9.2.8
Protein classification
695
9.2.9
Nucleic acids
696
9.3
Protein crystals
696
9.3.1
Principles of protein crystallization
697
9.3.2
Crystallization methods
699
9.3.3
Testing the conditions: factorial approaches
700
9.3.4
Membrane proteins
701
9.3.5
The solvent content of protein crystals
701
9.3.6
Cryotechniques
705
9.3.7
Preparation of isomorphous heavy-atom derivatives
706
9.3.8
How isomorphous are isomorphous derivatives?
707
9.4
The solution of the phase problem
708
9.4.1
The isomorphous replacement method
708
9.4.2
The determination of heavy-atom positions
709
9.4.3
The single isomorphous replacement (SIR) method
710
9.4.4
The classical solution of the problem of phase ambiguity:
the MIR technique
712
9.4.5
Anomalous scattering: a complementary (or alternative)
approach to the solution of the phase problem
713
9.4.6
The optimal choice of wavelength and the multiple
anomalous dispersion (MAD) technique
715
9.4.7
The use of anomalous scattering in the identification
of ionic species bound to a protein
718
9.4.8
The use of anomalous scattering in the determination of the
absolute configuration of the
macromolecule
718
9.4.9
The treatment of errors
719
9.4.10
The refinement of heavy-atom parameters
723
9.4.11
Maximum-likelihood and Bayesian estimates: an alternative
approach in phase refinement
725
9.4.12
Picking up minor heavy-atom sites: the difference-Fourier
synthesis
727
9.4.13
Density modification: how to solve the phase ambiguity
and improve the electron-density map
727
XX
Contents
9.4.14 Rotation and
translation
functions and the molecular
replacement method
733
9.4.15
The first step in molecular replacement:
the rotation function
734
9.4.16
The rotation matrix
С
and the choice of variables
737
9.4.17
Translation functions
738
9.4.18
Self-rotation and self-translation functions: improving the
electron-density maps
740
9.4.19
Practical hints in molecular replacement
740
9.4.20 Ab initio
methods in macromolecular crystallography
742
9.5
The interpretation of the electron-density maps and the
refinement of the model
745
9.5.1
The interpretation of the electron-density maps
745
9.5.2
Interactive computer graphics and model building
746
9.5.3
The refinement of the structure
747
9.5.4
Constrained versus restrained least squares
749
9.5.5
Restrained and constrained least squares
752
9.5.6
Crystallographic refinement by molecular dynamics
753
9.5.7
The strategy of the refinement of protein structures
754
9.5.8
R
factor and
Rţ^:
structure validation
756
9.5.9
Thermal parameters, disorder and TLS refinement
757
9.5.10
The organization of solvent
761
9.5.11
The influence of crystal packing
761
9.5.12
Dynamical studies: time-resolved crystallography
762
Appendices
763
9.A Some formulae for isomorphous replacement and
anomalous dispersion
763
9.B Translation functions
764
9.C Conventions and symbols for
amino
acids and peptides
766
9.D Software programs available for macromolecular crystallography
calculations
767
References
769
10
Physical properties of crystals: phenomenology
and modelling
776
Michele Catti
10.1
Introduction
776
10.2
Crystal anisotropy and tensors
777
10.2.1
Tensorial
quantities
778
10.2.2
Symmetry of
tensorial
properties
780
10.3
Overview of physical properties
782
10.4
Electrical properties of crystals
783
10.4.1
Pyroelectricity and ferroelectricity
784
10.4.2
Dielectric impermeability and optical properties
785
10.5
Elastic properties of crystals
787
10.5.1
Crystal strain
788
Contents
xxi
10.5.2
Inner deformation
790
10.5.3
Stress tensor
792
10.5.4
Elasticity tensor
793
10.5.5
Examples and applications
797
10.6
Piezoelectricity
797
10.6.1
Symmetry properties of the piezoelectric tensor
800
10.7
Modelling of structural and elastic behaviour
802
10.7.1
Atomistic potential functions
802
10.7.2
Athermal equation of state
804
10.7.3
Elastic constants
805
10.8
Crystal defects
807
10.9
Experimental methods
808
10.10
Planar defects
810
10.11
Line defects: dislocations
814
10.11.1
The Burgers circuit
815
10.11.2
X-ray topography of dislocations
817
10.11.3
Energy of a dislocation
818
10.11.4
Motion and interaction of dislocations
819
10.11.5
Partial dislocations
820
10.11.6
Small-angle grain boundaries
821
10.12
Point defects
822
10.13
Thermal distribution of defects
823
10.14
Diffusion
824
10.15
Ionic conductivity
825
Appendices
826
10.
A.I Properties of second-rank tensors
826
10.A.2 Eigenvalues and eigenvectors
827
10.A.3 Representation surfaces and their properties
828
References
829
Index
831
|
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| id | DE-604.BV037327017 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:22:09Z |
| institution | BVB |
| isbn | 9780199573653 9780199573660 |
| language | English |
| lccn | 2010043821 |
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| series | International Union of Crystallography texts on crystallography |
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| spelling | Introduzione alla cristallografia moderna Fundamentals of crystallography ed. by C. Giacovazzo 3. ed. Oxford [u.a.] Oxford Univ. Press 2011 XXI, 842 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier International Union of Crystallography texts on crystallography 15 Oxford science publications Hier auch später erschienene, unveränderte Nachdrucke Kristallographie (DE-588)4033217-2 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Kristallographie (DE-588)4033217-2 s DE-604 Giacovazzo, Carmelo Sonstige oth International Union of Crystallography texts on crystallography 15 (DE-604)BV002805877 15 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022481048&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fundamentals of crystallography International Union of Crystallography texts on crystallography Kristallographie (DE-588)4033217-2 gnd |
| subject_GND | (DE-588)4033217-2 (DE-588)4143413-4 |
| title | Fundamentals of crystallography |
| title_alt | Introduzione alla cristallografia moderna |
| title_auth | Fundamentals of crystallography |
| title_exact_search | Fundamentals of crystallography |
| title_full | Fundamentals of crystallography ed. by C. Giacovazzo |
| title_fullStr | Fundamentals of crystallography ed. by C. Giacovazzo |
| title_full_unstemmed | Fundamentals of crystallography ed. by C. Giacovazzo |
| title_short | Fundamentals of crystallography |
| title_sort | fundamentals of crystallography |
| topic | Kristallographie (DE-588)4033217-2 gnd |
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