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Crystal Structure Analysis: Principles and Practice 2nd Revised edition [Minkštas viršelis]

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(, University of York, UK), Edited by (, Department of Chemistry, University of Newcastle upon Tyne), (, University of Nottingham, UK), (, University of Cambridge, UK), (, University of Edinburgh, UK), (, University of Durham, UK), (, Universi)
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This text focuses on the practical aspects of crystal structure analysis and provides the necessary conceptual framework for understanding and applying the technique. Many worked examples, problems with answers, and illustrations are included throughout to reinforce the material presented. Significantly updated from the first edition.

This text focuses on the practical aspects of crystal structure analysis, and provides the necessary conceptual framework for understanding and applying the technique. By choosing an approach that does not put too much emphasis on the mathematics involved, the book gives practical advice on topics such as growing crystals, solving and refining structures, and understanding and using the results. The technique described is a core experimental method in modern structural chemistry, and plays an ever more important role in the careers of graduate students, postdoctoral and academic staff in chemistry, and final-year undergraduates.
Much of the material of the first edition has been significantly updated and expanded, and some new topics have been added. The approach to several of the topics has changed, reflecting the book's new authorship, and recent developments in the subject.

Recenzijos

`Review from previous edition 'Graduate students, lecturers, and professionals in crystallography, solid state chemistry, condensed matter physics, structural biology, and materials science, will find the thrust of this book exciting ... Professionals in the field would be morally and professionally remiss if they failed to read, consult and discuss this volume with students and colleagues. Amongst several features contributing towards making the book an important acquisition are: comprehensive and up-to-date character; emphasis on practical aspects of the topic; inclusion of many worked examples and problems; and an abundance of illustrative material throughout.' ' Current Engineering Practice `'... perhaps the most comprehensive and easy to use introduction to fundamental theory and techniques of structure analysis by X-ray diffraction, to appear from the world's scientific and technical publishing to date. It will be an invaluable reference to X-ray crystallographers, practitioners of X-ray analysis and all those involved in materials characterization.'' Current Engineering Practice `'This textbook should definitely be considered for use in introductory courses in X-ray structure determination as it provides a good framework for course organization. The concise treatment of the material (all of small-molecule X-ray crystallography in 265 pages) will work well when supplemented with lectures and additional class discussions.'

' Acta Crystallographica `'The book is very well written, has an excellent organization of material and is filled with many illustrative examples of the subject matter.' ' Acta Crystallographica

Introduction to diffraction
1(8)
Introduction
1(1)
X-ray scattering from electrons
1(1)
X-ray scattering from atoms
1(1)
X-ray scattering from a unit cell
2(1)
The effects of the crystal lattice
2(1)
X-ray scattering from the crystal
3(1)
The structure-factor equation
4(1)
The electron-density equation
5(1)
A mathematical relationship
6(1)
Bragg's law
6(1)
Resolution
7(1)
The phase problem
8(1)
Introduction to symmetry and diffraction
9(18)
The relationship between a crystal structure and its diffraction pattern
9(1)
Translation symmetry in crystalline solids
10(2)
Symmetry of individual molecules, with relevance to crystalline solids
12(4)
Symmetry in the solid state
16(2)
Diffraction and symmetry
18(2)
Further points
20(7)
Exercises
24(3)
Crystal growth and evaluation
27(14)
Introduction
27(1)
Protect your crystals
27(1)
Crystal growth
28(1)
Survey of methods
28(7)
Solution methods
28(5)
Sublimation
33(1)
Fluid-phase growth
33(1)
Solid-state synthesis
34(1)
General comments
34(1)
Evaluation
35(1)
Microscopy
35(1)
X-ray photography
36(1)
Diffractometry
36(1)
Crystal mounting
36(5)
Standard procedures
36(2)
Air-sensitive crystals
38(1)
Crystal alignment
39(2)
Space-group determination
41(12)
Introduction
41(1)
Prior knowledge and information other than from diffraction
42(1)
Metric symmetry and Laue symmetry
43(1)
Unit cell contents
43(1)
Systematic absences
44(3)
The statistical distribution of intensities
47(1)
Other points
48(2)
A brief conducted tour of some entries in International Tables for Crystallography, Volume A
50(3)
Exercises
52(1)
Background theory for data collection
53(20)
Introduction
53(1)
A step-wise theoretical journey through an experiment
53(2)
The geometry of X-ray diffraction
55(3)
Real-space considerations: Bragg's law
55(1)
Reciprocal-space considerations: the Ewald sphere
56(2)
Determining the unit cell: the indexing process
58(4)
Indexing: a conceptual view
58(2)
Indexing procedure
60(2)
Relating diffractometer angles to unit cell parameters: determination of the orientation matrix
62(2)
Data-collection procedures and strategies
64(3)
Criteria for selecting which data to collect
64(1)
How best to measure data: the need for reflection scans
65(2)
Extracting data intensities: data integration and reduction
67(6)
Background subtraction
67(1)
Data integration
68(1)
Crystal and geometric corrections to data
68(4)
Exercises
72(1)
Practical aspects of data collection
73(20)
Introduction
73(1)
Collecting data with area-detector diffractometers
73(2)
Experimental conditions
75(2)
Radiation
75(1)
Temperature
76(1)
Pressure
77(1)
Other conditions
77(1)
Types of area detector
77(3)
Multiwire proportional chamber (MWPC)
77(1)
Phosphor coupled to a TV camera
78(1)
Image plate (IP)
78(1)
Charge-coupled device (CCD)
78(2)
Some characteristics of CCD area-detector systems
80(2)
Spatial distortion
81(1)
Non-uniform intensity response
81(1)
Bad pixels
81(1)
Dark current
81(1)
Crystal screening
82(6)
Unit cell and orientation matrix determination
84(2)
If indexing fails
86(1)
Re-harvest the reflections
86(1)
Still having problems?
87(1)
After indexing
87(1)
Check for known cells
87(1)
Unit cell volume
88(1)
Data collection
88(5)
Intensity level
88(1)
Mosaic spread
89(1)
Crystal symmetry
89(1)
Other considerations
90(1)
Exercises
91(2)
Practical aspects of data processing
93(10)
Data reduction and correction
93(1)
Integration input and output
93(1)
Corrections
94(1)
Output
95(1)
A typical experiment?
95(1)
Examples of more problematic cases
96(2)
Twinning and area-detector data
98(1)
Some other special cases (in brief)
99(4)
Exercises
101(2)
Fourier syntheses
103(14)
Introduction
103(1)
Forward and reverse Fourier transforms
104(3)
Some mathematical and computing considerations
107(1)
Uses of different kinds of Fourier syntheses
108(4)
Patterson syntheses
109(1)
E-maps
109(1)
Full electron-density maps, using (8.2) or (8.3) as they stand
109(1)
Difference syntheses
110(1)
2Fo - Fc syntheses
111(1)
Other uses of difference syntheses
112(1)
Weights in Fourier syntheses
112(1)
Illustration in one dimension
113(4)
Fc synthesis
114(1)
Fo synthesis, as used in developing a partial structure solution
114(1)
Fo - Fc synthesis
114(1)
Full Fo synthesis
114(1)
Exercises
115(2)
Patterson syntheses for structure determination
117(16)
Introduction
117(1)
What the Patterson synthesis means
118(3)
Finding heavy atoms from a Patterson map
121(5)
One heavy atom in the asymmetric unit of P1
121(1)
One heavy atom in the asymmetric unit of P21/c
122(2)
One heavy atom in the asymmetric unit of P212121
124(1)
One heavy atom in the asymmetric unit of Pbca
124(1)
One heavy atom in the asymmetric unit of P21
125(1)
Two heavy atoms in the asymmetric unit of P1 and other space groups
125(1)
Patterson syntheses giving more than one possible solution, and other problems
126(2)
Patterson search methods
128(5)
Rotation search
129(1)
Translation search
129(2)
Exercises
131(2)
Direct methods of crystal-structure determination
133(16)
Amplitudes and phases
133(1)
The physical basis of direct methods
134(1)
Constraints on the electron density
135(4)
Discrete atoms
135(1)
Non-negative electron density
136(1)
Random atomic distribution
137(2)
Maximum value of ι p3 (x)dV
139(1)
Equal atoms
139(1)
Maximum entropy
140(1)
Equal molecules and p(x) = const.
140(1)
Structure invariants
140(1)
Structure determination
141(1)
Calculation of E values
142(1)
Setting up phase relationships
142(1)
Finding reflections for phase determination
142(2)
Assignment of starting phases
144(1)
Phase determination and refinement
144(1)
Figures of merit
144(1)
Interpretation of maps
145(1)
Completion of the structure
146(3)
Exercises
147(2)
An introduction to maximum entropy
149(6)
Entropy
149(1)
Maximum entropy
150(3)
Calculations with incomplete data
150(2)
Forming images
152(1)
Entropy and probability
152(1)
Electron-density maps
153(2)
Least-squares fitting of parameters
155(14)
Weighted mean
155(1)
Linear regression
156(6)
Variances and covariances
158(1)
Restraints
158(2)
Constraints
160(2)
Non-linear least squares
162(2)
Ill-conditioning
164(1)
Computing time
165(4)
Exercises
167(2)
Refinement of crystal structures
169(20)
Equations
169(3)
Bragg's law
170(1)
Structure factors from the continuous electron density
170(1)
Electron density from the structure amplitude and phase
170(2)
Structure factor from a parameterized model
172(1)
Reasons for performing refinement
172(3)
To improve phasing so that computed electron density maps more closely represent the actual electron density
172(1)
To try to verify that the structure is `correct'
173(2)
To obtain the `best' values for the parameters in the model
175(1)
Data quality and limitations
175(2)
Resolution
175(1)
Completeness
176(1)
Leverage
176(1)
Weak reflections and systematic absences
176(1)
Standard uncertainties
177(1)
Systematic trends
177(1)
Refinement fundamentals
177(3)
w, the weight
178(1)
Y1, the observations
178(1)
Y2, the calculations
179(1)
Issues
180(1)
Refinement strategies
180(2)
Under- and over-parameterization
182(1)
Under-parameterization
182(1)
Over-parameterization
183(1)
Pseudo-symmetry, wrong space groups and Z' 1 structures
183(1)
Conclusion
184(5)
Exercises
186(3)
Analysis of extended inorganic structures
189(16)
Introduction
189(1)
Disorder
190(4)
Site-occupancy disorder
191(1)
Positional disorder
192(1)
Limits of Bragg diffraction
193(1)
Phase transitions
194(1)
Structure validation
195(1)
Case history 1 - BiMg2VO6
196(3)
Case history 2 - Mo2P4O15
199(6)
Exercises
203(2)
The derivation of results
205(16)
Introduction
205(1)
Geometry calculations
205(6)
Fractional and Cartesian co-ordinates
205(2)
Bond distance and angle calculations
207(1)
Dot products
208(1)
Transforming co-ordinates
208(1)
Standard uncertainties
209(2)
Assessing significant differences
211(1)
Least-squares planes and dihedral angles
211(2)
Conformation of rings and other molecular features
213(1)
Hydrogen atoms and hydrogen bonding
213(1)
Displacement parameters
214(7)
βs, Bs and Us
215(1)
`The equivalent isotropic displacement parameter'
215(1)
Symmetry and anisotropic displacement parameters
216(1)
Models of thermal motion and geometrical corrections: rigid-body motion
217(1)
Atomic displacement parameters and temperature
218(1)
Exercises
219(2)
Random and systematic errors
221(30)
Random and systematic errors
221(1)
Random errors and distributions
222(7)
Measurement errors
222(1)
Describing data
222(3)
Theoretical distributions
225(2)
Expectation values
227(2)
The standard error on the mean
229(1)
Taking averages
229(3)
Testing for normality using a histogram
230(1)
The X2 test for normality
231(1)
Averaging data when X2red»1
232(1)
Weighting schemes
232(6)
Weights used in least-squares refinement with single-crystal diffraction data
233(1)
Robust-resistant weighting schemes and outliers
234(1)
Assessing weighting schemes
235(3)
Analysis of the agreement between observed and calculated data
238(2)
R factors
238(1)
Significance testing
239(1)
Estimated standard deviations and standard uncertainties of structural parameters
240(2)
Correlation and covariance
240(2)
Uncertainty propagation
242(1)
Systematic errors
242(9)
Systematic errors in the data
243(1)
Data thresholds
244(1)
Errors and limitations of the model
244(3)
Assessment of a structure determination
247(3)
Exercises
250(1)
Powder diffraction
251(20)
Introduction to powder diffraction
251(1)
Powder versus single-crystal diffraction
252(2)
Experimental methods
254(4)
Information contained in a powder pattern
258(3)
Phase identification
258(1)
Quantitative analysis
259(1)
Peak-shape information
260(1)
Intensity information
261(1)
Rietveld refinement
261(3)
Structure solution from powder diffraction data
264(1)
Non-ambient studies
265(6)
Exercises
268(3)
Introduction to twinning
271(28)
Introduction
271(1)
A simple model for twinning
271(1)
Twinning in crystals
272(2)
Diffraction patterns from twinned crystals
274(2)
Inversion, merohedral and pseudo-merohedral twins
276(3)
Derivation of twin laws
279(1)
Non-merohedral twinning
280(2)
The derivation of non-merohedral twin laws
282(1)
Common signs of twinning
283(2)
Examples
285(14)
Exercises
296(3)
The presentation of results
299(20)
Introduction
299(1)
Graphics
300(1)
Graphics programs
300(1)
Underlying concepts
301(1)
Drawing styles
302(4)
Creating three-dimensional illusions
306(1)
The use of colour
307(1)
Textual information in drawings
307(1)
Some hints for effective drawings
308(1)
Tables of results
309(1)
The content of tables
310(2)
Selected results
310(1)
Redundant information
311(1)
Additional entries
311(1)
The format of tables
312(1)
Hints on presentation
312(3)
In research journals
312(1)
In theses and reports
313(1)
On posters
313(1)
As oral presentations
313(1)
On the web
314(1)
Archiving of results
315(4)
The crystallographic information file (CIF)
319(8)
Introduction
319(1)
Basics
319(2)
Uses of CIF
321(1)
Some properties of the CIF format
321(2)
Some practicalities
323(4)
Strings
323(1)
Text
324(1)
Checking the CIF
325(2)
Crystallographic databases
327(6)
What is a database?
327(1)
What types of search are possible?
327(1)
What information can you get out?
328(1)
What can you use databases for?
328(1)
What are the limitations?
328(1)
Short descriptions of crystallographic databases
328(5)
X-ray and neutron sources
333(10)
Introduction
333(1)
Laboratory X-ray sources
333(2)
Synchrotron X-ray sources
335(4)
Neutron sources
339(4)
Appendix A: Useful mathematics and formulae
343(10)
Introduction
343(1)
Trigonometry
343(1)
Complex numbers
344(1)
Waves and structure factors
345(1)
Vectors
346(2)
Determinants
348(1)
Matrices
348(1)
Matrices in symmetry
349(1)
Matrix inversion
350(1)
Convolution
351(2)
Appendix B: Questions and answers
353(32)
Index 385
William Clegg: Formerly Wissenschaftlicher Assistant at the University of Göttingen in Germany, two Joint Appointments at Daresbury Laboratory, Founding Joint Editor of Acta Crystallographica Section E, BCA Council Member, RSC Corday-Morgan Medal 1985.; Alexander J Blake: Formerly Research Fellow at the University of Edinburgh, previous Chairman of the BCA Chemical Crystallography Group, Deputy Editor of Acta Crystallographica Section C, Vice-President of the British Crystallographic Association, Scientific Director of the BCA CCG Intensive Course on X-ray Structural Analysis.

Jacqueline M Cole: Formerly Research Associate at the University of Kent and Junior Research Fellow at St Catherine's College Cambridge, BCA Chemical Crystallography Prize 2000, Franco-British Science Prize 2006, Brian Mercer Feasibility Award 2007, RSC SAC Silver Medal 2009.; John S O Evans: Formally Royal Commission for the Exhibition of 1851 Research Fellow at the Inorganic Chemistry Laboratories, Oxford, recipient of the RSC Meldola medal for contributions to solid state chemistry, former honorary secretary/treasurer of the BCA Physical Crystallography Group, chair of the ISIS crystallography panel, scientific co-director of the IoP Structural Condensed Matter Physics Group/BCA PCG residential school on powder diffraction.

Peter Main: Co-developer of MULTAN program for direct methods in crystallography.; Simon Parsons: Formerly Research Fellow at the University of Oxford and staff crystallographer at the University of Edinburgh, previous Chairman of the BCA Chemical Crystallography Group.; David J Watkin: Coordinator for the program system CRYSTALS, founder of the BCA Intensive Schools, former chairman of the IUCr Computing Commission.