Two-dimensional X-ray Diffraction (eBook)

Bob B. He, PhD, is Director of Innovation and Business Development XRD² at Bruker AXS-an industry leader in X-ray diffraction instrumentation and solutions (formally Siemens AXS). Dr. He holds 17 U.S. patents and two R&D 100 awards in XRD instrumentation. In recognition of his contribution to the XRD community, he has been recently awarded ICDD Fellow. He earned his doctorate in materials science from Virginia Tech.

Preface xiii

1. Introduction 1

1.1 X-Ray Technology, a Brief History, 1

1.2 Geometry of Crystals, 2

1.3 Principles of X-Ray Diffraction, 11

1.4 Reciprocal Space and Diffraction, 13

1.5 Two-Dimensional X-Ray Diffraction, 19

References, 26

2. Geometry and Fundamentals 29

2.1 Introduction, 29

2.2 Diffraction Space and Laboratory Coordinates, 31

2.3 Detector Space and Detector Geometry, 35

2.4 Sample Space and Goniometer Geometry, 46

2.5 Transformation from Diffraction Space to Sample Space, 50

2.6 Reciprocal Space, 52

2.7 Summary, 53

References, 55

3. X-Ray Source and Optics 57

3.2 X-Ray Optics, 63

References, 85

4. X-Ray Detectors 87

4.1 History of X-Ray Detection Technology, 87

4.2 Point Detectors in Conventional Diffractometers, 89

4.3 Characteristics of Point Detectors, 92

4.4 Line Detectors, 100

4.5 Characteristics of Area Detectors, 107

4.6 Types of Area Detectors, 119

References, 137

5. Goniometer and Sample Stages 141

5.1 Goniometer and Sample Position, 141

5.2 Goniometer Accuracy, 145

5.3 Sample Alignment and Visualization Systems, 149

5.4 Environment Stages, 151

References, 155

6. Data Treatment 157

6.1 Introduction, 157

6.2 Non-Uniform Response Correction, 157

6.3 Spatial Correction, 161

6.4 Detector Position Accuracy and Calibration, 166

6.5 Frame Integration, 177

6.6 Multiple Frame Merge, 186

6.7 Scanning 2D Pattern, 194

6.8 Lorentz, Polarization, and Absorption Corrections, 197

References, 208

7. Phase Identification 211

7.1 Introduction, 211

7.2 Relative Intensity, 212

7.3 Geometry and Resolution, 216

7.4 Sampling Statistics, 221

7.5 Preferred Orientation Effect, 227

References, 233

8. Texture Analysis 235

8.1 Introduction, 235

8.2 Pole Density and Pole-Figure, 236

8.3 Fundamental Equations, 238

8.4 Data Collection Strategy, 242

8.5 Texture Data Process, 251

8.6 Orientation Distribution Function, 256

8.7 Fiber Texture, 261

8.8 Polymer Texture, 264

8.9 Other Advantages of XRD2 for Texture, 268

References, 269

9. Stress Measurement 271

9.1 Introduction, 271

9.2 Principle of X-ray Stress Analysis, 280

9.3 Theory of Stress Analysis with XRD2, 292

9.4 Process of Stress Measurement with XRD2, 307

9.5 Experimental Examples, 325

A9.1 Calculate Principal Stresses, 349

A9.2 Calculate the direction cosines for principal stresses (Eigenvectors), 350

References, 353

10. Small Angle X-ray Scattering 357

10.1 Introduction, 357

10.2 2D SAXS Systems, 361

10.3 Applications Examples, 367

10.4 Some Innovations in 2D SAXS, 370

References, 374

11. Combinatorial Screening 379

11.1 Introduction, 379

11.2 XRD2 Systems for High Throughput Screening, 380

11.3 Combined Screening with XRD2 and Raman, 390

Reference, 393

12. Miscellaneous Applications 395

12.1 Percent Crystallinity, 395

12.2 Crystal Size, 402

12.3 Retained Austenite, 412

12.4 Crystal Orientation, 414

12.5 Thin Film Analysis, 418

Reference, 429

13. Innovation and Future Development 433

13.1 Introduction, 433

13.2 Scanning Line Detector for XRD2, 434

13.3 Three-Dimensional Detector, 438

13.4 Pixel Direct Diffraction Analysis, 441

13.5 High Resolution Two-Dimensional X-Ray Diffractometer, 444

References, 451

Appendix A. Values of Commonly Used Parameters 453

Appendix B. Symbols 459

Index 465