Introduction to X-Ray Powder Diffractometry

$Introduction to X-Ray Powder Diffractometry by Jenkins, Ron; Snyder, Robert, 9780471513391$

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ISBN: 9780471513391 | 0471513393
Cover: Hardcover
Copyright: 7/12/1996

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Introduction to X-ray Powder Diffractometry, a collaboration between two internationally known and respected experts in the field, provides invaluable guidance to anyone using X-ray powder diffractometers and diffractometry in materials science, ceramics, the pharmaceutical industry, and elsewhere.

PREFACE

xvii

(2)

CUMULATIVE LISTING OF VOLUMES IN SERIES

xix

CHAPTER 1. CHARACTERISTICS OF X-RADIATION

(22)

1.1. Early Development of X-ray Diffraction

(1)

1.2. Origin of X-radiation

(1)

1.3. Continuous Radiation

(2)

1.4. Characteristic Radiation

(9)

1.4.1. The Photoelectric Effect

(1)

1.4.2. The Auger Effect

(2)

1.4.3. Fluorescent Yield

(1)

1.4.4. Selection Rules

(4)

1.4.5. Nondiagram Lines

(1)

1.4.6. Practical Form of the Copper K Spectrum

(2)

1.5. Scattering of X-rays

(2)

1.5.1. Coherent Scatter

(1)

1.5.2. Compton Scatter

(1)

1.6. Absorption of X-rays

(3)

1.7. Safety Considerations

(2)

References

(2)

CHAPTER 2. THE CRYSTALLINE STATE

(24)

2.1. Introduction to the Crystalline State

(3)

2.2. Crystallographic Symmetry

(9)

2.2.1. Point Groups and Crystal Systems

(2)

2.2.2. The Unit Cell and Bravais Lattices

(1)

2.2.3. Reduced Cells

(3)

2.2.4. Space Groups

(1)

2.3. Space Group Notation

(6)

2.3.1. The Triclinic or Anorthic Crystal System

(1)

2.3.2. The Monoclinic Crystal System

(2)

2.3.3. The Orthorhombic Crystal System

(1)

2.3.4. The Tetragonal Crystal System

(1)

2.3.5. The Hexagonal and Trigonal Crystal Systems

(1)

2.3.6. The Cubic Crystal System

(1)

2.3.7. Equivalent Positions

(1)

2.3.8. Special Positions and Site Multiplicity

(1)

2.4. Space Group Theory

(2)

2.5. Crystallographic Planes and Miller Indices

(1)

References

(3)

CHAPTER 3. DIFFRACTION THEORY

(50)

3.1. Diffraction of X-rays

(2)

3.2. The Reciprocal Lattice

(5)

3.3. The Ewald Sphere of Reflection

(3)

3.4. Origin of the Diffraction Pattern

(3)

3.4.1. Single Crystal Diffraction

(1)

3.4.2. The Powder Diffraction Pattern

(2)

3.5. The Location of Diffraction Peaks

(4)

3.6. Intensity of Diffraction Peaks

(11)

3.6.1. Electron Scattering

(1)

3.6.2. The Atomic Scattering Factor

(2)

3.6.3. Anomalous Scattering

(1)

3.6.4. Thermal Motion

(2)

3.6.5. Scattering of X-rays by a Crystal: The Structure Factor

(5)

3.7. The Calculated Diffraction Pattern

(7)

3.7.1. Factors Affecting the Relative Intensity of Bragg Reflections

(4)

3.7.2. The Intensity Equation

(2)

3.8. Calculation of the Powder Diffraction Pattern of KCI

(3)

3.9. Anisotropic Distortions of the Diffraction Pattern

(9)

3.9.1. Preferred Orientation

(4)

3.9.2. Crystallite Size

(2)

3.9.3. Residual Stress and Strain

(3)

References

(3)

CHAPTER 4. SOURCES FOR THE GENERATION OF X-RADIATION

(24)

4.1. Components of the X-ray Source

(1)

4.2. The Line-Voltage Supply

(1)

4.3. The High-Voltage Generator

(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

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Introduction to X-Ray Powder Diffractometry

Summary

Author Biography

Table of Contents

Supplemental Materials