Powder diffraction: theory and practice
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| Format: | Book |
| Language: | English |
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Cambridge
RSC Publ.
2009
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| Edition: | Repr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 582 S. Ill., graph. Darst. |
| ISBN: | 9780854042319 |
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| 245 | 1 | 0 | |a Powder diffraction |b theory and practice |c ed. by Robert E. Dinnebier ... |
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Record in the Search Index
| _version_ | 1804140852031782912 |
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| adam_text | Titel: Powder diffraction
Autor: Dinnebier, Robert E.
Jahr: 2009
Contents
Chapter 1 Principles of Powder Diffraction
Robert E. Dinnebier and Simon J. L. Billinge
1.1 Introduction 1
1.2 Fundamentals 1
1.3 Derivation of the Bragg Equation 3
1.4 The Bragg Equation in the Reciprocal Lattice 6
1.5 The Ewald Construction 11
1.6 Taking Derivatives of the Bragg Equation 15
1.7 Bragg s Law for Finite Size Crystallites 17
Bibliography 19
Chapter 2 Experimental Setups
Jeremy Karl Cocker oft and Andrew N. Fitch
2.1 Introduction 20
2.2 Sources of X-ray Radiation 21
2.2.1 Laboratory X-ray Sources 21
2.2.2 Synchrotron X-ray Sources 25
2.3 X-ray Optics 29
2.3.1 Filters 29
2.3.2 Monochromators 29
2.3.3 Mirrors 30
2.4 X-ray Detectors 31
2.4.1 Point Detectors 31
2.4.2 Linear Detectors 31
2.4.3 Area Detectors 32
2.4.4 Detector Calibration 33
2.5 Laboratory Instrumental Configurations 33
2.5.1 Reflection Geometry 33
2.5.2 Transmission Geometry 36
xjj Contents
2.6 Synchrotron Instrumental Configurations 37
2.6.1 Pre-sample Opties 37
2.6.2 Parallel-beam Instruments 38
2.6.3 Debye-Scherrer Geometry Instruments 40
2.7 Measurements 41
2.7.1 Sample Holders 41
2.7.2 Standard Samples 43
2.7.3 Data Acquisition 44
2.8 Energy Dispersive Powder X-ray Diffraction 45
2.9 Powder Neutron Diffraction 46
2.9.1 Properties of the Neutron 46
2.9.2 Sources of Neutrons 48
2.9.3 Detection of Neutrons 49
2.9.4 Monochromatic Techniques 50
2.9.5 Time-of-Flight Techniques 53
References 56
Chapter 3 The Intensity of a Bragg Reflection
R. B. Von Dreele and J. Rodríguez-Carvajal
Chapter 4
3.1 Introduction 58
3.2 Single Atom Scattering Theory 58
3.2.1 X-ray Scattering 58
3.2.2 Neutron Scattering 62
3.3 Scattering from a Crystal Lattice 63
3.3.1 Thermal Motion Effects 65
3.3.2 The Lorentz Factor 66
3.3.3 Scattering from a Modulated Crystal
Lattice 67
3.3.4 Neutron Magnetic Moment Scattering 71
3.4 Scattering from a Polycrystalline Powder 83
3.4.1 Friedel Pair Overlap 84
3.4.2 Reflection Multiplicity 84
3.4.3 Texture Effects 84
3.4.4 Absorption Effects 86
Acknowledgements 87
References 87
General Data Reduction
Rudolf Allmann
4.1 Introduction 89
4.2 Elimination of Fake Reflections (Outliers) 90
4.3 Fitting and Subtraction of Background 91
4.4 Data Smoothing 93
Contents
4.4.1 Smoothing by Sliding Polynomials
(Savitzky-Golay Method) 93
4.4.2 Digital Low Pass Filters 96
4.5 Koc2-Stripping 100
4.6 Peak Search Algorithms 105
4.6.1 Trend-oriented Peak Search 105
4.6.2 Peak Search by Second Derivatives 107
4.6.3 Peak Search with a Predefined
Peak Shape 110
4.7 Profile Fitting and Profile Shape Functions 111
4.8 Detection and Correction of Systematic Errors 119
4.8.1 External Standards 126
4.8.2 Internal Standards 127
4.8.3 Correction Together with the Refinement
of Lattice Constants 130
References 131
Chapter 5 The Profile of a Bragg Reflection for Extracting Intensities
Armel Le Bail
5.1 Introduction 134
5.2 Overview of Contributions to the Peak
Profile Function 135
5.3 Instrumental Aberrations 136
5.3.1 Largest Size Effect Ever Detected 13 7
5.3.2 Monte Carlo Ray-tracing 138
5.4 Sample Broadening 141
5.4.1 Crystallite Size 142
5.4.2 Lattice Strain 146
5.4.3 Anisotropie Sample Broadening: Faulting 148
5.5 Individual Peak Fitting and Line Profile Analysis 151
5.5.1 Peak Fitting for Intensity/Position Extraction -
With or without Cell Knowledge 152
5.5.2 Using Individual Peaks for Size/Distortion
Extraction 152
5.5.3 Further Approximations 152
5.6 Whole Powder Pattern Decomposition (WPPD) -
No Structure 153
5.6.1 No Cell Restraint 153
5.6.2 Cell-restrained Whole Powder Pattern
Decomposition 153
5.6.3 Main Applications of WPPD 156
5.7 Conclusions 158
References 159
xjv Contents
Chapter 6 Instrumental Contributions to the Line Profile in X-Ray
Powder Diffraction. Example of the Diffractometer with
Bragg-Brentano Geometry
Alexander Zuev
6.1 Introduction 166
6.2 Contributions to the Observed Profile 169
6.3 General Description of the Method 171
6.4 Basic Equations 173
6.4.1 Vector Equation of a Cone 173
6.4.2 Equation of a Conic 173
6.5 Diffractometer with Bragg-Brentano Geometry 175
6.5.1 Coordinate Systems for Bragg-Brentano
Geometry 175
6.5.2 Equation of a Conic in the Receiving Slit Plane
(Coordinate System CS) 176
6.5.3 Equation of a Conic in the Sample Surface Plane
(Coordinate System CS) 177
6.5.4 Case of the Degenerated Cone (20 = 90°) 177
6.5.5 Intersections of the Conic and Receiving Slit
Boundary 178
6.5.6 Angle Between Two Planes 178
6.6 Application of the Method 179
6.6.1 Some Illustrative Examples of the Conic
in the Receiving Slit Plane 179
6.6.2 Specific Instrumental Function 182
6.6.3 Total Instrumental Profile 192
6.7 About Misalignment, Soller Slits, Monochromator 194
6.7.1 Misalignment 194
6.7.2 Soller Slits 194
6.7.3 Monochromator 196
6.8 Plane Crystal Monochromator in the Diffracted
Beam 197
6.8.1 Setting of the Monochromator 197
6.8.2 Reflection Cones 198
6.8.3 Intersection of the Diffraction and Reflection
Conies in the Receiving Slit Plane 199
6.9 Effect of the Plane Monochromator on Instrumental
Function 200
6.9.1 Equatorial Aberration in the Presence
of the Monochromator 200
6.9.2 Axial Aberration in the Presence
of the Monochromator 201
6.9.3 Total Instrumental Function in the Presence
of the Monochromator 201
Contents xv
6.10 Conclusions 201
Acknowledgements 203
References 203
Chapter 7 Indexing and Space Group Determination
Angela Altomare, Carmelo Giacovazzo and Anna Moliterni
7.1 The Crystalline Lattice in Powder Diffraction 206
7.2 Indexing of a Powder Pattern 211
7.2.1 Introduction 211
7.2.2 Figures of Merit 213
7.2.3 Geometrical Ambiguities 214
7.2.4 Historical Indexing Programs 214
7.2.5 Evolved Indexing Programs 217
7.3 Space Group Determination 220
7.3.1 Introduction 220
7.3.2 The DASH Procedure 221
7.3.3 The EXPO2004 Procedure 222
References 225
Chapter 8 Crystal Structure Determination
Rocco Caliandro, Carmelo Giacovazzo and Rosanna Rizzi
.1 Introduction 227
.2 The Patterson Function 228
.3 Direci ; Methods 230
8.3.1 Scaling of the Observed Intensities
and Normalization of the Structure
Factors 232
8.3.2 Estimate of Structure Invariants 233
8.3.3 Tangent Formula 238
8.3.4 A Typical Direct Methods Procedure 239
8.3.5 Figure of Merit 239
8.3.6 Completion of the Crystal Structure
and Preliminary Refinement 240
8.3.7 Solving Crystal Structures from Powder
Neutron Data 242
.4 Direct-space Techniques 243
8.4.1 Grid Search Methods 245
8.4.2 Monte Carlo Methods 245
8.4.3 Simulated Annealing Techniques 249
8.4.4 Genetic Algorithm Techniques 252
8.4.5 Hybrid Approaches 254
8.4.6 Application to Real Structures 257
8.4.7 Crystal Structure Prediction 258
Contents
8.5 Conclusions and Outlook 260
Symbols and Notation 261
References 261
Chapter 9
Rietveld Refinement
R. B. Von Dreele
9.1 Introduction 266
9.2 Rietveld Theory 268
9.2.1 Least Squares 268
9.3 Constraints and Restraints 271
9.3.1 Introduction 271
9.3.2 Rigid Body Refinement 271
9.3.3 Rigid Body Refinement
ofFe[OP(C6H5)3]4Cl2FeCl4 274
9.3.4 Stereochemical Restraint Refinement 277
9.3.5 Protein Powder Refinements 279
Acknowledgement 280
References 280
Chapter 10 The Derivative Difference Minimization Method
Leonid A. Solovyov
10.1 Introduction 282
10.2 Derivative Difference Minimization Principle 283
10.3 DDM Decomposition Procedure 285
10.4 Results and Discussion 288
10.4.1 Tests on Simulated and Real Data 288
10.4.2 Applications of DDM 291
10.5 Conclusions 295
References 295
Chapter 11 Quantitative Phase Analysis
Ian C. Madsen and Nicola V. Y. Scarlett
11.1 Introduction 298
11.2 Phase Analysis 299
11.3 Mathematical Basis 300
11.3.1 Reference Intensity Ratio (RIR)
Methods 303
11.3.2 Rietveld-based Methods 304
11.4 Factors Limiting Accuracy 308
11.4.1 Particle Statistics 308
11.4.2 Preferred Orientation 310
Contents xvii
11.4.3 Microabsorption 312
11.4.4 Precision, Accuracy and the Calculation
of Error 314
11.5 Examples of QPA via Powder Diffraction 315
11.5.1 Application in Mineralogical Systems 315
11.5.2 Applications in Industrial Systems 322
11.6 Summary 326
Acknowledgements 326
Appendix A: Derivation of Errors in Rietveld-based
Quantitative Phase Analysis 327
Relative Phase Abundances 327
Absolute Phase Abundances 327
Amorphous Content 328
References 329
Chapter 12 Microstructural Properties: Texture and Macrostress
Effects
Nicolae C. Popa
12.1 Texture 332
12.1.1 The Orientation Distribution Function
and the Pole Distributions 332
12.1.2 Two Goals in Texture Analysis 335
12.1.3 Dollase-March Model 337
12.1.4 The Spherical Harmonics Approach 339
12.2 Macroscopic Strain and Stress 348
12.2.1 Elastic Strain and Stress in a Crystallite -
Mathematical Background 349
12.2.2 Strain and Stress in Polycrystalline Samples 352
12.2.3 Status of the Strain/Stress Analysis
by Diffraction 355
12.2.4 Strain/Stress in Isotropie Samples -
Classical Approximations 357
12.2.5 Hydrostatic Pressure in Isotropie
Polycrystals 363
12.2.6 The Macroscopic Strain/Stress by
Spherical Harmonics 365
References 373
Chapter 13 Microstructural Properties: Lattice Defects
and Domain Size Effects
Paolo Scardi
13.1 Introduction 376
13.2 Origin of Line Broadening 377
Contents
13.2.1 Size Broadening 377
13.2.2 Strain Broadening 381
13.2.3 Other Sources of Line Broadening 384
13.3 Traditional versus Innovative Methods 387
13.3.1 Integral Breadth Methods 387
13.3.2 Fourier Methods 389
13.3.3 Profile Fitting and Traditional LPA
Methods 394
13.3.4 Whole Powder Pattern Modelling 395
13.4 WPPM: Examples of Application 396
13.4.1 Heavily Deformed Metal Powders 396
13.4.2 Nanocrystalline Cerium Oxide Powder 402
Acknowledgements 405
List of Principal Symbols 405
Appendix: Fourier Transforms of Profile Components 407
Instrumental Profile (IP) 407
Domain Size (S) 407
Faulting (F) 408
Dislocations (D) 408
Anti-phase Domain Boundaries (APB) 410
Stoichiometry Fluctuation (C) 410
References 411
Chapter 14 Two-dimensional Diffraction Using Area Detectors
Bernd Hinrichsen, Robert E. Dinnebier and
Martin Jansen
14.1 Two-dimensional Detectors 414
14.1.1 CCD Detectors 415
14.1.2 Imaging Plate Detectors 416
14.1.3 Flat Panel Detectors 416
14.1.4 Hybrid Pixel Detectors 417
14.2 Diffraction Geometry 418
14.2.1 Resolution and FWHM in
Two-dimensional Diffraction 419
14.2.2 Diffraction Angle Transformation 422
14.2.3 Incident Angle and Ray Distance
Calculations 426
14.2.4 General Transformations 426
14.3 Intensity Corrections 429
14.3.1 Lorentz Corrections 430
14.3.2 Polarization Correction 434
14.3.3 Incident Angle Correction 435
References 437
Contents xix
Chapter 15 Powder Diffraction under Non-ambient Conditions
Poul Norby and Ulrich Schwarz
15.1 Introduction 439
15.2 In Situ Powder Diffraction 440
15.2.1 Techniques and Instrumentation 442
15.3 Powder Diffraction at High Pressure 450
15.3.1 Introduction 450
15.3.2 The Diamond Anvil Cell 451
15.3.3 Pressure Media 453
15.3.4 Diffraction Measurements 454
15.3.5 Pressure Measurement 457
15.3.6 Thermodynamic Considerations 459
Selected Reviews 461
In-situ diffraction 461
High-pressure Diffraction 461
References 462
Chapter 16 Local Structure from Total Scattering and Atomic Pair
Distribution Function (PDF) Analysis
Simon Billinge
16.1 Introduction 464
16.2 Theory 470
16.2.1 Single Component Systems 470
16.2.2 Multicomponent Systems 473
16.3 Experimental Methods 479
16.4 Structural Modeling 481
16.4.1 Model Independent Structural
Information from the PDF 481
16.4.2 Modeling the PDF 482
16.4.3 Modeling Total Scattering in Reciprocal
Space 485
16.4.4 Emerging Modeling Approaches 486
References 491
Chapter 17 Computer Software for Powder Diffraction
Lachlan M. D. Cranswick
17.1 Introduction 494
17.2 Finding and Testing Software 494
17.2.1 Locating New Software 494
17.2.2 Selecting Software 495
17.2.3 Re-locating Software on the Internet 495
xx Contents
17.3 Available Software 495
17.3.1 Third-party Diffractometer Control
Software 495
17.3.2 Phase Identification and Search-match
Software 496
17.3.3 Crystal Structure Databases 498
17.3.4 Powder Data Conversion 500
17.3.5 Structure Data Conversion
and Transformation 503
17.3.6 Powder Diffraction Pattern Viewing
and Processing 504
17.3.7 Peak Finding and Peak Profiling 510
17.3.8 Powder Indexing 510
17.3.9 Space Group Assignment 521
17.3.10 Space Group Information Software
and Databases 521
17.3.11 Unit Cell Refinement 522
17.3.12 Full Profile Fitting (Pawley, Le Bail) 523
17.3.13 Texture Analysis Software 528
17.3.14 Size Strain Analysis 528
17.3.15 Single Crystal Suites useful to Powder
Diffraction 530
17.3.16 Powder Diffraction Suites 531
17.3.17 Structure Solution Software Specifically
for Powder Diffraction 531
17.3.18 Structure Solution Using Single
Crystal Software 534
17.3.19 2D to 3D Molecular Model
Generation 534
17.3.20 Single Crystal Refinement Programs
and Helper Programs to Assist in
Building up the Structure 538
17.3.21 Rietveld Structure Refinement 541
17.3.22 Pair Distribution Function Software 541
17.3.23 Hydrogen Placement Using Single
Crystal and Ancillary Software 541
17.3.24 Free Standing Powder and Single
Crystal Fourier Map Generation and
Display Software 541
17.3.25 Quantitative Phase Analysis 548
17.3.26 Powder Pattern Calculation 548
17.3.27 Structure Validation 548
17.3.28 Crystallographic Structure Visualization:
During Structure Solution and
Refinement 554
Contents xxi
17.3.29 Visualization and Photo Realistic Rendering
of Crystal Structures 555
17.3.30 Miscellaneous Resources 562
Appendix 1: Internet links for Cited Software
and Resources 562
Subject Index 571
|
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| author_facet | Dinnebier, Robert E. |
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| indexdate | 2024-07-09T22:06:33Z |
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| language | English |
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| spelling | Powder diffraction theory and practice ed. by Robert E. Dinnebier ... Repr. Cambridge RSC Publ. 2009 XXI, 582 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Röntgenstrukturanalyse (DE-588)4137203-7 gnd rswk-swf Pulvermethode (DE-588)4176353-1 gnd rswk-swf Röntgendiffraktometrie (DE-588)4336833-5 gnd rswk-swf Röntgenstrukturanalyse (DE-588)4137203-7 s Röntgendiffraktometrie (DE-588)4336833-5 s Pulvermethode (DE-588)4176353-1 s DE-604 Dinnebier, Robert E. edt HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018733116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Powder diffraction theory and practice Röntgenstrukturanalyse (DE-588)4137203-7 gnd Pulvermethode (DE-588)4176353-1 gnd Röntgendiffraktometrie (DE-588)4336833-5 gnd |
| subject_GND | (DE-588)4137203-7 (DE-588)4176353-1 (DE-588)4336833-5 |
| title | Powder diffraction theory and practice |
| title_auth | Powder diffraction theory and practice |
| title_exact_search | Powder diffraction theory and practice |
| title_full | Powder diffraction theory and practice ed. by Robert E. Dinnebier ... |
| title_fullStr | Powder diffraction theory and practice ed. by Robert E. Dinnebier ... |
| title_full_unstemmed | Powder diffraction theory and practice ed. by Robert E. Dinnebier ... |
| title_short | Powder diffraction |
| title_sort | powder diffraction theory and practice |
| title_sub | theory and practice |
| topic | Röntgenstrukturanalyse (DE-588)4137203-7 gnd Pulvermethode (DE-588)4176353-1 gnd Röntgendiffraktometrie (DE-588)4336833-5 gnd |
| topic_facet | Röntgenstrukturanalyse Pulvermethode Röntgendiffraktometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018733116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dinnebierroberte powderdiffractiontheoryandpractice |