Crystal structure analysis: principles and practice
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Oxford
Oxford University Press
2009
|
| Edition: | 2. ed., 1. publ. |
| Series: | IUCr texts on crystallography
13 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 387 S. Ill., graph. Darst. |
| ISBN: | 9780199219469 9780199219476 |
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| 245 | 1 | 0 | |a Crystal structure analysis |b principles and practice |c Alexander J. Blake ... Ed. by William Clegg |
| 250 | |a 2. ed., 1. publ. | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2009 | |
| 300 | |a XVII, 387 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a IUCr texts on crystallography |v 13 | |
| 650 | 4 | |a X-ray crystallography | |
| 650 | 4 | |a Crystals |x Structure | |
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| 700 | 1 | |a Blake, Alexander J. |e Sonstige |4 oth | |
| 700 | 1 | |a Clegg, William |e Sonstige |4 oth | |
| 830 | 0 | |a IUCr texts on crystallography |v 13 |w (DE-604)BV002805877 |9 13 | |
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|---|---|
| adam_text | Contents
1
Introduction
to diffraction
1
1.1
Introduction
1
1.2
X-ray scattering from electrons
1
1.3
X-ray scattering from atoms
1
1.4
X-ray scattering from a unit cell
2
1.5
The effects of the crystal lattice
2
1.6
X-ray scattering from the crystal
3
1.7
The structure-factor equation
4
1.8
The electron-density equation
5
1.9
A mathematical relationship
6
1.10
Bragg slaw
6
1.11
Resolution
7
1.12
The phase problem
8
2
Introduction to symmetry and diffraction
9
2.1
The relationship between a crystal structure
and its diffraction pattern
9
2.2
Translation symmetry in crystalline solids
10
2.3
Symmetry of individual molecules, with
relevance to crystalline solids
12
2.4
Symmetry in the solid state
16
2.5
Diffraction and symmetry
18
2.6
Further points
20
Exercises
24
3
Crystal growth and evaluation
27
3.1
Introduction
27
3.2
Protect your crystals
27
3.3
Crystal growth
28
3.4
Survey of methods
28
3.4.1
Solution methods
28
3.4.2
Sublimation
33
3.4.3
Fluid-phase growth
33
3.4.4
Solid-state synthesis
34
3.4.5
General comments
34
χ
Contents
3.5 Evaluation 35
3.5.1
Microscopy
35
3.5.2
X-ray photography
36
3.5.3
Diffractometry
36
3.6
Crystal mounting
36
3.6.1
Standard procedures
36
3.6.2
Air-sensitive crystals
38
3.6.3
Crystal alignment
39
4
Space-group determination
41
4.1
Introduction
41
4.2
Prior knowledge and information other than from
diffraction
42
4.3
Metric symmetry and
Laue
symmetry
43
4.4
Unit cell contents
43
4.5
Systematic absences
44
4.6
The statistical distribution of intensities
47
4.7
Other points
48
4.8
A brief conducted tour of some entries in
International Tables for Crystallography, Volume A
50
Exercises
52
5
Background theory for data collection
53
5.1
Introduction
53
5.2
A step-wise theoretical journey through an
experiment
53
5.3
The geometry of X-ray diffraction
55
5.3.1
Real-space considerations: Bragg s law
55
5.3.2
Reciprocal-space considerations:
the
Ewald
sphere
56
5.4
Determining the unit cell: the indexing process
58
5.4.1
Indexing: a conceptual view
58
5.4.2
Indexing procedure
60
5.5
Relating diffractometer angles to
unit cell parameters: determination of the
orientation matrix
62
5.6
Data-collection procedures and strategies
64
5.6.1
Criteria for selecting which data to collect
64
5.6.2
How best to measure data: the need for
reflection scans
65
5.7
Extracting data intensities: data integration
and reduction
67
5.7.1
Background subtraction
67
5.7.2
Data integration
68
5.7.3
Crystal and geometric corrections to data
68
Exercises
72
6
Practical aspects of data collection
73
6.1
Introduction
73
Contents xi
6.2
Collecting data with area-detector
diffractometers
73
6.3
Experimental conditions
75
6.3.1
Radiation
75
6.3.2
Temperature
76
6.3.3
Pressure
77
6.3.4
Other conditions
77
6.4
Types of area detector
77
6.4.1
Multiwire proportional chamber (MWPC)
77
6.4.2
Phosphor coupled to a TV camera
78
6.4.3
Image plate (IP)
78
6.4.4
Charge-coupled device
(CCD)
78
6.5
Some characteristics of
CCD
area-detector systems
80
6.5.1
Spatial distortion
81
6.5.2
Non-uniform intensity response
81
6.5.3
Bad pixels
81
6.5.4
Dark current
81
6.6
Crystal screening
82
6.6.1
Unit cell and orientation matrix
determination
84
6.6.2
If indexing fails
86
6.6.3
Re-harvest the reflections
86
6.6.4
Still having problems?
87
6.6.5
After indexing
87
6.6.6
Check for known cells
87
6.6.7
Unit cell volume
88
6.7
Data collection
88
6.7.1
Intensity level
88
6.7.2
Mosaic spread
89
6.7.3
Crystal symmetry
89
6.7.4
Other considerations
90
Exercises
91
Practical aspects of data processing
93
7.1
Data reduction and correction
93
7.2
Integration input and output
93
7.3
Corrections
94
7.4
Output
95
7.5
A typical experiment?
95
7.6
Examples of more problematic cases
96
7.7
Twinning and area-detector data
98
7.8
Some other special cases (in brief)
99
Exercises
101
Fourier syntheses
103
8.1
Introduction
103
8.2
Forward and reverse Fourier transforms
104
8.3
Some mathematical and computing considerations
107
8.4
Uses of different kinds of Fourier syntheses
108
xii Contents
8.4.1
Patterson syntheses
8.4.2
E-maps
8.4.3
Full electron-density maps, using
(8.2)
or
(8.3)
as they stand
8.4.4
Difference syntheses
8.4.5
2F0
-
Fc syntheses
8.4.6
Other uses of difference syntheses
8.5
Weights in Fourier syntheses
8.6
Illustration in one dimension
8.6.1
Fc synthesis
8.6.2
Fo synthesis, as used in developing
a partial structure solution
8.6.3
Fo
—
Fc synthesis
8.6.4
Full Fo synthesis
Exercises
109
109
109
110
111
112
112
113
114
114
114
114
115
9
Patterson syntheses for structure determination
117
9.1
Introduction
117
9.2
What the Patterson synthesis means
118
9.3
Finding heavy atoms from a Patterson map
121
9.3.1
One heavy atom in the asymmetric
unit of
PÏ
121
9.3.2
One heavy atom in the asymmetric
unit of i^/c
122
9.3.3
One heavy atom in the asymmetric
unit of
P2î
2^i
124
9.3.4
One heavy atom in the asymmetric
unit of Pbca
124
9.3.5
One heavy atom in the asymmetric
unit of P2i
125
9.3.6
Two heavy atoms in the asymmetric
unit of
PÏ
and other space groups
125
9.4
Patterson syntheses giving more than one possible
solution, and other problems
126
9.5
Patterson search methods
128
9.5.1
Rotation search
129
9.5.2
Translation search
129
Exercises
131
10
Direct methods of crystal-structure determination
133
10.1
Amplitudes and phases
133
10.2
The physical basis of direct methods
134
10.3
Constraints on the electron density
135
10.3.1
Discrete atoms
135
10.3.2
Non-negative electron density
136
10.3.3
Random atomic distribution
ІЗ7
10.3.4
Maximum value of
ƒ
p3(x)dV
139
Contents xiii
10.3.5
Equal atoms
139
10.3.6
Maximum entropy
140
10.3.7
Equal molecules and p(x)
=
const.
140
10.3.8
Structure invariants
140
10.3.9
Structure determination
141
10.3.10
Calculation of
E
values
142
10.3.11
Setting up phase relationships
142
10.3.12
Finding reflections for phase determination
142
10.3.13
Assignment of starting phases
144
10.3.14
Phase determination and refinement
144
10.3.15
Figures of merit
144
10.3.16
Interpretation of maps
145
10.3.17
Completion of the structure
146
Exercises
147
11
An introduction to maximum entropy
149
11.1
Entropy
149
11.2
Maximum entropy
150
11.2.1
Calculations with incomplete data
150
11.2.2
Forming images
152
11.2.3
Entropy and probability
152
11.3
Electron-density maps
153
155
155
156
158
158
160
162
164
165
167
13
Refinement of crystal structures
169
13.1
Equations
169
13.1.1
Bragg slaw
170
13.1.2
Structure factors from the continuous
electron density
170
13.1.3
Electron density from the structure
amplitude and phase
170
13.1.4
Structure factor from a parameterized
model
172
13.2
Reasons
f
or performing refinement
172
13.2.1
To improve phasing so that computed
electron density maps more closely
represent the actual electron density
172
13.2.2
To try to verify that the structure is correct
173
12
Least-squares fitting of parameters
12.1
Weighted mean
12.2
Linear regression
12.2.1
Variances and covariances
12.2.2
Restraints
12.2.3
Constraints
12.3
Non-linear least squares
12.4
Ill-conditioning
12.5
Computing time
Exercises
xiv Contents
13.2.3
To obtain the best values for the
parameters in the model
175
13.3
Data quality and limitations
175
13.3.1
Resolution
175
13.3.2
Completeness
176
13.3.3
Leverage
176
13.3.4
Weak reflections and systematic absences
176
13.3.5
Standard uncertainties
177
13.3.6
Systematic trends
177
13.4
Refinement fundamentals
177
13.4.1
w, the weight
178
13.4.2
Yi, the observations
178
13.4.3
Y2, the calculations
179
13.4.4
Issues
180
13.5
Refinement strategies
180
13.6
Under- and over-parameterization
182
13.6.1
Under-parameterization
182
13.6.2
Over-parameterization
183
13.7
Pseudo-symmetry, wrong space groups and Z
> 1
structures
183
13.8
Conclusion
184
Exercises
186
14
Analysis of extended inorganic structures
189
14.1
Introduction
189
14.2
Disorder
190
14.2.1
Site-occupancy disorder
191
14.2.2
Positional disorder
192
14.2.3
Limits of Bragg diffraction
193
14.3
Phase transitions
194
14.4
Structure validation
195
14.5
Case history
1 -
BiMg2VO6
196
14.6
Case history
2 -
Mo2P4Oi5
199
Exercises
203
15
The derivation of results
205
15.1
Introduction
205
15.2
Geometry calculations
205
15.2.1
Fractional and Cartesian co-ordinates
205
15.2.2
Bond distance and angle calculations
207
15.2.3
Dot products
208
15.2.4
Transforming co-ordinates
208
15.2.5
Standard uncertainties
209
15.2.6
Assessing significant differences
211
15.3
Least-squares planes and dihedral angles
211
15.3.1
Conformation of rings and other
molecular features
213
15.4
Hydrogen atoms and hydrogen bonding
213
Contents xv
15.5
Displacement parameters
214
15.5.1 ßs, ßs
and ¡Is
215
15.5.2
The equivalent
isotropie
displacement
parameter
215
15.5.3
Symmetry and anisotropic displacement
parameters
216
15.5.4
Models of thermal motion and geometrical
corrections: rigid-body motion
217
15.5.5
Atomic displacement parameters and
temperature
218
Exercises
219
16
Random and systematic errors
221
16.1
Random and systematic errors
221
16.2
Random errors and distributions
222
16.2.1
Measurement errors
222
16.2.2
Describing data
222
16.2.3
Theoretical distributions
225
16.2.4
Expectation values
227
16.2.5
The standard error on the mean
229
16.3
Taking averages
229
16.3.1
Testing for normality using a histogram
230
16.3.2
The y? test for normality
231
16.3.3
Averaging data when / .¿»l
232
16.4
Weighting schemes
232
16.4.1
Weights used in least-squares refinement
with single-crystal diffraction data
233
16.4.2
Robust-resistant weighting schemes and
outliers
234
16.4.3
Assessing weighting schemes
235
16.5
Analysis of the agreement between observed and
calculated data
238
16.5.1
R
factors
238
16.5.2
Significance testing
239
16.6
Estimated standard deviations and standard
uncertainties of structural parameters
240
16.6.1
Correlation and covariance
240
16.6.2
Uncertainty propagation
242
16.7
Systematic errors
242
16.7.1
Systematic errors in the data
243
16.7.2
Data thresholds
244
16.7.3
Errors and limitations of the model
244
16.7.4
Assessment of a structure determination
247
Exercises
250
17
Powder diffraction
251
17.1
Introduction to powder diffraction
251
17.2
Powder versus single-crystal diffraction
252
xvi Contents
17.3
Experimental
methods
254
17.4
Information
contained in a powder pattern
258
17.4.1
Phase identification
258
17.4.2
Quantitative analysis
259
17.4.3
Peak-shape information
260
17.4.4
Intensity
inf
ormation
261
17.5
Rietveld
refinement
261
17.6
Structure solution from powder diffraction data
264
17.7
Non-ambient studies
265
Exercises
268
18
Introduction to twinning
271
18.1
Introduction
271
18.2
A simple model for twinning
271
18.3
Twinning in crystals
272
18.4
Diffraction patterns from twinned crystals
274
18.5
Inversion, merohedral and pseudo-merohedral
twins
276
18.6
Derivation of twin laws
279
18.7
Non-merohedral twinning
280
18.8
The derivation of non-merohedral twin laws
282
18.9
Common signs of twinning
283
18.10
Examples
285
Exercises
296
19
The presentation of results
299
19.1
Introduction
299
19.2
Graphics
300
19.3
Graphics programs
300
19.4
Underlying concepts
301
19.5
Drawing styles
302
19.6
Creating three-dimensional illusions
306
19.7
The use of colour
307
19.8
Textual information in drawings
307
19.9
Some hints for effective drawings
308
19.10
Tables of results
309
19.11
The content of tables
310
19.11.1
Selected results
310
19.11.2
Redundant information
311
19.11.3
Additional entries
311
19.12
The format of tables
312
19.13
Hints on presentation
312
19.13.1
In research journals
312
19.13.2
In theses and reports
313
19.13.3
On posters
313
19.13.4
As oral presentations
313
19.13.5
On the web
314
19.14
Archiving of results
315
Contents xvii
20 The crystallographic
information file
(CIF)
319
20.1
Introduction
319
20.2
Basics
319
20.3
Uses of
CIF
321
20.4
Some properties of the
CIF
format
321
20.5
Some practicalities
323
20.5.1
Strings
323
20.5.2
Text
324
20.5.3
Checking the
CIF
325
21
Crystallographic databases
327
21.1
What is a database?
327
21.2
What types of search are possible?
327
21.3
What information can you get out?
328
21.4
What can you use databases for?
328
21.5
What are the limitations?
328
21.6
Short descriptions of crystallographic databases
328
22
X-ray and neutron sources
333
22.1
Introduction
333
22.2
Laboratory X-ray sources
333
22.3
Synchrotron X-ray sources
335
22.4
Neutron sources
339
A Appendix A: Useful mathematics and formulae
343
343
343
344
345
346
348
348
349
350
351
353
385
A.I
Introduction
A.2
Trigonometry
A.3
Complex numbers
A.4
Waves and structure factors
A.5
Vectors
A.6
Determinants
A.7
Matrices
A.8
Matrices in symmetry
A.9
Matrix inversion
A.10
Convolution
В
Appendix
Б:
Questions and answers
Index
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV035622961 |
| callnumber-first | Q - Science |
| callnumber-label | QD945 |
| callnumber-raw | QD945 |
| callnumber-search | QD945 |
| callnumber-sort | QD 3945 |
| callnumber-subject | QD - Chemistry |
| classification_rvk | UQ 5000 UQ 5100 VG 9900 |
| ctrlnum | (OCoLC)316424882 (DE-599)BVBBV035622961 |
| dewey-full | 548/.81 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 548 - Crystallography |
| dewey-raw | 548/.81 |
| dewey-search | 548/.81 |
| dewey-sort | 3548 281 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik |
| edition | 2. ed., 1. publ. |
| format | Book |
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| id | DE-604.BV035622961 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:41:48Z |
| institution | BVB |
| isbn | 9780199219469 9780199219476 |
| language | English |
| lccn | 2009011644 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017678064 |
| oclc_num | 316424882 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-19 DE-BY-UBM DE-11 DE-20 DE-355 DE-BY-UBR |
| owner_facet | DE-29T DE-703 DE-19 DE-BY-UBM DE-11 DE-20 DE-355 DE-BY-UBR |
| physical | XVII, 387 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Oxford University Press |
| record_format | marc |
| series | IUCr texts on crystallography |
| series2 | IUCr texts on crystallography |
| spelling | Crystal structure analysis principles and practice Alexander J. Blake ... Ed. by William Clegg 2. ed., 1. publ. Oxford Oxford University Press 2009 XVII, 387 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier IUCr texts on crystallography 13 X-ray crystallography Crystals Structure Kristallstrukturanalyse (DE-588)4137204-9 gnd rswk-swf Röntgenstrukturanalyse (DE-588)4137203-7 gnd rswk-swf Röntgenstrukturanalyse (DE-588)4137203-7 s DE-604 Kristallstrukturanalyse (DE-588)4137204-9 s Blake, Alexander J. Sonstige oth Clegg, William Sonstige oth IUCr texts on crystallography 13 (DE-604)BV002805877 13 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017678064&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Crystal structure analysis principles and practice IUCr texts on crystallography X-ray crystallography Crystals Structure Kristallstrukturanalyse (DE-588)4137204-9 gnd Röntgenstrukturanalyse (DE-588)4137203-7 gnd |
| subject_GND | (DE-588)4137204-9 (DE-588)4137203-7 |
| title | Crystal structure analysis principles and practice |
| title_auth | Crystal structure analysis principles and practice |
| title_exact_search | Crystal structure analysis principles and practice |
| title_full | Crystal structure analysis principles and practice Alexander J. Blake ... Ed. by William Clegg |
| title_fullStr | Crystal structure analysis principles and practice Alexander J. Blake ... Ed. by William Clegg |
| title_full_unstemmed | Crystal structure analysis principles and practice Alexander J. Blake ... Ed. by William Clegg |
| title_short | Crystal structure analysis |
| title_sort | crystal structure analysis principles and practice |
| title_sub | principles and practice |
| topic | X-ray crystallography Crystals Structure Kristallstrukturanalyse (DE-588)4137204-9 gnd Röntgenstrukturanalyse (DE-588)4137203-7 gnd |
| topic_facet | X-ray crystallography Crystals Structure Kristallstrukturanalyse Röntgenstrukturanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017678064&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002805877 |
| work_keys_str_mv | AT blakealexanderj crystalstructureanalysisprinciplesandpractice AT cleggwilliam crystalstructureanalysisprinciplesandpractice |