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Tables of Contents for Introduction to X-Ray Powder Diffractometry
Chapter/Section Title
Page #
Page Count
PREFACE
xvii
2
CUMULATIVE LISTING OF VOLUMES IN SERIES
xix
 
CHAPTER 1. CHARACTERISTICS OF X-RADIATION
1
22
1.1. Early Development of X-ray Diffraction
1
1
1.2. Origin of X-radiation
2
1
1.3. Continuous Radiation
3
2
1.4. Characteristic Radiation
5
9
1.4.1. The Photoelectric Effect
5
1
1.4.2. The Auger Effect
5
2
1.4.3. Fluorescent Yield
7
1
1.4.4. Selection Rules
7
4
1.4.5. Nondiagram Lines
11
1
1.4.6. Practical Form of the Copper K Spectrum
12
2
1.5. Scattering of X-rays
14
2
1.5.1. Coherent Scatter
15
1
1.5.2. Compton Scatter
15
1
1.6. Absorption of X-rays
16
3
1.7. Safety Considerations
19
2
References
21
2
CHAPTER 2. THE CRYSTALLINE STATE
23
24
2.1. Introduction to the Crystalline State
23
3
2.2. Crystallographic Symmetry
26
9
2.2.1. Point Groups and Crystal Systems
28
2
2.2.2. The Unit Cell and Bravais Lattices
30
1
2.2.3. Reduced Cells
31
3
2.2.4. Space Groups
34
1
2.3. Space Group Notation
35
6
2.3.1. The Triclinic or Anorthic Crystal System
35
1
2.3.2. The Monoclinic Crystal System
35
2
2.3.3. The Orthorhombic Crystal System
37
1
2.3.4. The Tetragonal Crystal System
37
1
2.3.5. The Hexagonal and Trigonal Crystal Systems
38
1
2.3.6. The Cubic Crystal System
38
1
2.3.7. Equivalent Positions
39
1
2.3.8. Special Positions and Site Multiplicity
40
1
2.4. Space Group Theory
41
2
2.5. Crystallographic Planes and Miller Indices
43
1
References
44
3
CHAPTER 3. DIFFRACTION THEORY
47
50
3.1. Diffraction of X-rays
47
2
3.2. The Reciprocal Lattice
49
5
3.3. The Ewald Sphere of Reflection
54
3
3.4. Origin of the Diffraction Pattern
57
3
3.4.1. Single Crystal Diffraction
57
1
3.4.2. The Powder Diffraction Pattern
58
2
3.5. The Location of Diffraction Peaks
60
4
3.6. Intensity of Diffraction Peaks
64
11
3.6.1. Electron Scattering
64
1
3.6.2. The Atomic Scattering Factor
65
2
3.6.3. Anomalous Scattering
67
1
3.6.4. Thermal Motion
68
2
3.6.5. Scattering of X-rays by a Crystal: The Structure Factor
70
5
3.7. The Calculated Diffraction Pattern
75
7
3.7.1. Factors Affecting the Relative Intensity of Bragg Reflections
76
4
3.7.2. The Intensity Equation
80
2
3.8. Calculation of the Powder Diffraction Pattern of KCI
82
3
3.9. Anisotropic Distortions of the Diffraction Pattern
85
9
3.9.1. Preferred Orientation
85
4
3.9.2. Crystallite Size
89
2
3.9.3. Residual Stress and Strain
91
3
References
94
3
CHAPTER 4. SOURCES FOR THE GENERATION OF X-RADIATION
97
24
4.1. Components of the X-ray Source
97
1
4.2. The Line-Voltage Supply
98
1
4.3. The High-Voltage Generator
99
6
4.3.1. Selection of Operating Conditions
102
2
4.3.2. Source Stability
104
1
4.4. The Sealed X-ray Tube
105
9
4.4.1. Typical X-ray Tube Configuration
106
3
4.4.2. Specific Loading
109
4
4.4.3. Care of the X-ray Tube
113
1
4.5. Effective Line Width
114
2
4.6. Spectral Contamination
116
2
4.6.1. X-ray Tube Life
117
1
4.7. The Rotating Anode X-ray Tube
118
2
References
120
1
CHAPTER 5. DETECTORS AND DETECTION ELECTRONICS
121
30
5.1. X-ray Detectors
121
1
5.2. Desired Properties of an X-ray Detector
122
5
5.2.1. Quantum-Counting Efficiency
122
1
5.2.2. Linearity
123
2
5.2.3. Energy Proportionality
125
1
5.2.4. Resolution
126
1
5.3. Types of Detector
127
9
5.3.1. The Gas Proportional Counter
128
2
5.3.2. Position-Sensitive Detectors
130
1
5.3.3. The Scintillation Detector
131
1
5.3.4. The Si(Li) Detector
132
3
5.3.5. Other X-ray Detectors
135
1
5.4. Pulse Height Selection
136
2
5.5. Counting Circuits
138
2
5.5.1. The Ratemeter
139
1
5.6. Counting Statistics
140
2
5.7. Two-Dimensional Detectors
142
6
References
148
3
CHAPTER 6. PRODUCTION OF MONOCHROMATIC RADIATION
151
22
6.1. Introduction
151
2
6.2. Angular Dispersion
153
1
6.3. Makeup of a Diffractogram
154
4
6.3.1. Additional Lines in the Diffractogram
155
2
6.3.2. Reduction of Background
157
1
6.4. The Beta-Filter
158
4
6.4.1. Thickness of the Beta-Filter
159
1
6.4.2. Use of Pulse Height Selection to Supplement the Beta-Filter
160
2
6.4.3. Placement of the Beta-Filter
162
1
6.5. The Proportional Detector and Pulse Height Selection
162
1
6.6. Use of Solid State Detectors
163
1
6.7. Use of Monochromators
164
6
6.7.1. The Diffracted-Beam Monochromator
167
3
6.7.2. The Primary-Beam Monochromator
170
1
6.8. Comparison of Monochromatization Methods
170
2
References
172
1
CHAPTER 7. INSTRUMENTS FOR THE MEASUREMENT OF POWDER PATTERNS
173
32
7.1. Camera Methods
173
5
7.1.1. The Debye-Scherrer/Hull Method
173
1
7.1.2. The Gandolfi Camera
174
3
7.1.3. The Guinier Camera
177
1
7.2. The Powder Diffractometer
178
2
7.3. The Seemann-Bohlin Diffractometer
180
1
7.4. The Bragg-Brentano Diffractometer
180
7
7.5. Systematic Aberrations
187
8
7.5.1. The Axial-Divergence Error
187
4
7.5.2. The Flat-Specimen Error
191
2
7.5.3. Error Due to Specimen Transparency
193
1
7.5.4. Error Due to Specimen Displacement
194
1
7.6. Selection of Goniometer Slits
195
7
7.6.1. Effect of Receiving Slit Width
195
2
7.6.2. Effect of the Divergence Slit
197
5
References
202
3
CHAPTER 8. ALIGNMENT AND MAINTENANCE OF POWDER DIFFRACTOMETERS
205
26
8.1. Principles of Alignment
205
11
8.1.1. The Rough xyz Alignment
206
2
8.1.2. Setting the Takeoff Angle
208
2
8.1.3. Setting the Mechanical Zero
210
2
8.1.4. Setting the 2:1
212
1
8.1.5. Aligning of the Divergence Slit
213
1
8.1.6. Tuning of the Monochromator
214
2
8.2. Routine Alignment Checks
216
6
8.3. Evaluation of the Quality of Alignment
222
4
8.4. Troubleshooting
226
3
References
229
2
CHAPTER 9. SPECIMEN PREPARATION
231
30
9.1. General Considerations
231
2
9.2. Compositional Variations Between Sample and Specimen
233
1
9.3. Absorption Problems
234
1
9.4. Problems in Obtaining a Random Specimen
235
9
9.4.1. Particle Inhomogeneity
235
1
9.4.2. Crystal Habit and Preferred Orientation
236
4
9.4.3. Particle Statistics
240
4
9.5. Particle Separation and Size Reduction Methods
244
1
9.6. Specimen Preparation Procedures
244
10
9.6.1. Use of Standard Mounts
246
1
9.6.2. Back and Side Loading
247
2
9.6.3. Top Loading
249
1
9.6.4. The Zero Background Holder Method
249
2
9.6.5. Spray-Drying
251
2
9.6.6. Use of Aerosols
253
1
9.7. Measurement of the Prepared Specimen
254
4
9.7.1. Specimen Displacement
254
1
9.7.2. Mechanical Methods for Randomizing
255
2
9.7.3. Handling of Small Samples
257
1
9.7.4. Special Samples
257
1
References
258
3
CHAPTER 10. ACQUISITION OF DIFFRACTION DATA
261
26
10.1. Introduction
261
1
10.2. Steps in Data Acquisition
261
3
10.3. Typical Data Quality
264
1
10.4. Selection of the d-Spacing Range of the Pattern
265
5
10.4.1. Choice of the 20 Range
266
1
10.4.2. Choice of Wavelength
266
4
10.5. Manual Powder Diffractometers
270
4
10.5.1. Synchronous Scanning
270
1
10.5.2. Use of Ratemeters
270
2
10.5.3. Step Scanning
272
2
10.6. Automated Powder Diffractometers
274
7
10.6.1. Step Scanning with the Computer
277
2
10.6.2. Choice of Step Width
279
1
10.6.3. Open-Loop and Absolute Encoders
280
1
10.7. Use of Calibration Standards
281
4
10.7.1. External 20 Standards
282
1
10.7.2. Internal 20 and d-Spacing Standards
283
1
10.7.3. Quantitative Analysis Standards
283
1
10.7.4. Sensitivity Standards
284
1
10.7.5. Line Profile Standards
285
1
References
285
2
CHAPTER 11. REDUCTION OF DATA FROM AUTOMATED POWDER DIFFRACTOMETERS
287
32
11.1. Data Reduction Procedures
287
1
11.2. Range of Experimental Data to Be Treated
287
4
11.2.1. Computer Reduction of Data
288
3
11.3. Steps in Data Treatment
291
14
11.3.1. Use of Data Smoothing
292
5
11.3.2. Background Subtraction
297
2
11.3.3. Treatment of the Alpha(2)
299
1
11.3.4. Peak Location Methods
300
5
11.4. Conversion Errors
305
3
11.5. Calibration Methods
308
2
11.5.1. 20 Correction Using an External Standard
308
1
11.5.2. 20 and d-Spacing Correction Using an Internal Standard
309
1
11.5.3. Sensitivity Correction Using an External Intensity Standard
309
1
11.6. Evaluation of Data Quality
310
7
11.6.1. Use of Figures of Merit
310
2
11.6.2. Use of Figures of Merit for Instrument Performance Evaluation
312
1
11.6.3. Use of Figures of Merit for Data Quality Evaluation
313
3
11.6.4. Use of Figures of Merit in Indexing of Powder Patterns
316
1
References
317
2
CHAPTER 12. QUALITATIVE ANALYSIS
319
36
12.1. Phase Identification by X-ray Diffraction
319
4
12.1.1. Quality of Experiment Data
322
1
12.2. Databases
323
6
12.2.1. The Powder Diffraction File
324
2
12.2.2. The Crystal Data File
326
1
12.2.3. The Elemental and Interplanar Spacing Index (EISI)
327
1
12.2.4. The Metals and Alloys Index
328
1
12.3. Media on Which ICDD Databases Are Supplied
329
3
12.3.1. Historical Evolution of Database Media
329
1
12.3.2. Computer-Readable Products
330
1
12.3.3. The CD-ROM System
331
1
12.4. Manual Search/Matching Methods
332
12
12.4.1. The Alphabetic Method
333
2
12.4.2. The Hanawalt Search Method
335
4
12.4.3. The Fink Search Method
339
5
12.5. Limitations with the Use of Paper Search Manuals
344
1
12.6. Boolean Search Methods
345
2
12.7. Fully Automated Search Methods
347
3
12.7.1. First-Generation Programs
347
1
12.7.2. Second-Generation Search/Match Algorithms
348
1
12.7.3. Commercial Search/Match Programs
348
1
12.7.4. Third-Generation Search/Match Algorithms
349
1
12.8. Effectiveness of Search/Matching Using the Computer
350
1
References
351
4
CHAPTER 13. QUANTITATIVE ANALYSIS
355
34
13.1. Historical Development of Quantitative Phase Analysis
355
1
13.2. Measurement of Line Intensities
356
5
13.3. Foundation of Quantitative Phase Analysis
361
1
13.4. The Absorption-Diffraction Method
362
7
13.4.1. Use of Klug's Equation
365
2
13.4.2. Use of Measured Mass Attenuation Coefficients
367
1
13.4.3. Use of Mass Attenuation Coefficients Derived from Elemental Chemistry
368
1
13.5. Method of Standard Additions
369
1
13.6. The Internal Standard Method of Quantitative Analysis
370
6
13.6.1. I/I(corundum) and the Reference Intensity Ratio Method
372
1
13.6.2. The Generalized Reference Intensity Ratio
372
1
13.6.3. Quantitative Analysis with RIRs
373
1
13.6.4. The Normalized RIR Method
373
1
13.6.5. Constrained XRD Phase Analysis: Generalized Internal Standard Method
374
2
13.7. Quantitative Phase Analysis Using Crystal Structure Constraints
376
2
13.8. Quantitative Methods Based on Use of the Total Pattern
378
6
13.8.1. The Rietveld Method
378
5
13.8.2. Full-Pattern Fitting with Experimental Patterns
383
1
13.9. Detection of Low Concentrations
384
2
References
386
3
APPENDIX A: COMMON X-RAY WAVELENGTHS
389
1
APPENDIX B: MASS ATTENUATION COEFFICIENTS
390
1
APPENDIX C: ATOMIC WEIGHTS AND DENSITIES
391
1
APPENDIX D: CRYSTALLOGRAPHIC CLASSIFICATION OF THE 230 SPACE GROUPS
392
5
INDEX
397