Diffraction Physics (eBook)

Front Cover 1
Diffraction Physics 4
Copyright Page 5
Contents 8
Preface to the first edition 6
Preface to the second edition 7
Preface to the third edition 7
SECTION I: PHYSICAL OPTICS 18
Chapter 1. Fresnel and Fraunhofer diffraction 20
1.1. Introduction 20
1.2. Wave equations and waves 22
1.3. Superposition and coherence 25
1.4. Huygen' s principle 28
1.5. Scattering theory approach 30
1.6. Reciprocity 33
1.7. Fresnel diffraction 33
1.8. Fraunhofer diffraction 38
Problems 41
Chapter 2. Fourier transform and convolutions 42
2.1. Preliminaries 42
2.2. Fourier transforms: general 47
2.3. Fourier transforms and diffraction: examples 52
Problems 65
Chapter 3. Imaging and diffraction 68
3.1. Wave theory of imaging 68
3.2. Abbe theory 72
3.3. Small angle approximation 73
3.4. Phase contrast 76
3.5. Holography 80
3.6. Multi-component systems 84
3.7. Partial coherence 86
Problems 89
SECTION II: KINEMATICAL DIFFRACTION 92
Chapter 4. Radiations and their scattering by matter 94
4.1. X-rays 94
4.2. Electrons 98
4.3. Neutrons 105
Problems 109
Chapter 5. Scattering from assemblies of atoms 110
5.1. The kinematical approximation 110
5.2. Real and reciprocal space 112
5.3. The generalized Patterson function 115
5.4. Examples of correlation functions 118
5.5. Correlation in space and time 121
5.6. Diffraction geometry and intensities 130
5.7. Practical considerations 132
5.8. Sections and projections 136
Problems 138
Chapter 6. Diffraction from crystals 140
6.1. Ideal crystals 140
6.2. Diffraction geometry 143
6.3. Crystal structure analysis 148
6.4. Structure analysis methods 151
6.5. Neutron diffraction structure analysis 155
6.6. Electron diffraction structure analysis 158
Problems 159
Chapter 7. Diffraction from imperfect crystals 162
7.1. Formulation of the diffraction problem 162
7.2. Patterson function approach 164
7.3. Deviations from an average lattice 167
7.4. Imperfect crystals with no average lattice 174
Problems 180
SECTION III: DYNAMICAL SCATTERING 182
Chapter 8. Diffraction by perfect crystals 184
8.1. Multiple coherent scattering 184
8.2. Theoretical approaches 185
8.3. Bethe theory 187
8.4. Two-beam approximation 192
8.5. The Laue (transmission) case 195
8.6. Bethe potentials 199
8.7. The Bragg case 201
Chapter 9. Dynamical diffraction effects 206
9.1. Thickness fringes, rocking curves-electron diffraction 206
9.2. Dynamical effects of X-ray and neutron diffraction 216
9.3. Borrmann effect 222
Problems 224
Chapter 10. Extension to many beams 226
10.1. Dynamical n-beam diffraction 226
10.2. Extension of Bethe theory - transmission 228
10.3. The Darwin-type approach 237
10.4. Special cases - beam reduction 239
10.5. Computing methods 241
10.6. Column approximation 244
Problems 246
Chapter 11. Multi-slice approaches 248
11.1. Propagation of electrons in crystals 248
11.2. Multiple-scattering series 254
11.3. General double-summation solution 257
11.4. Computing methods 260
11.5. Intensities from non-periodic objects 265
11.6. Real-space formulations 267
Problem 271
SECTION IV: APPLICATIONS TO SELECTED TOPICS 272
Chapter 12. Diffuse scattering and absorption effects 274
12.1. Thermal diffuse scattering 274
12.2. Static atom displacements 279
12.3. Electron excitations 286
12.4. Dynamical effects in diffuse scattering 291
12.5. Absorption effects 296
Chapter 13. Electron microscope imaging 304
13.1. Electron microscopes 304
13.2. Image formation 309
13.3. Contrast for thin specimens 311
13.4. The imaging of crystals 318
13.5. Image contrast in STEM 330
13.6. Electron holography 335
13.7. Combining high-resolution imaging with diffraction 343
Problems 345
Chapter 14. K-line patterns and channelling 346
14.1. Kossel lines 346
14.2. Kikuchi lines 352
14.3. External sources of divergent radiation 356
14.4. Information from K-line patterns 358
14.5. Channelling 360
14.6. Secondary radiations 363
Chapter 15. Application of dynamical effects in single crystals 366
15.1. Dependence of dynamical effects on crystal parameters 366
15.2. X-ray interferometry 366
15.3. n–beam and 2-beam dynamical diffraction 368
15.4. Accurate determinations of structure amplitudes 371
15.5. The determination of crystal symmetries 380
15.6. Coherent convergent-beam electron diffraction 384
Chapter 16. Mosaic crystals and polycrystalline materials 386
16.1. General 386
16.2. Mosaic crystals 387
16.3. Polycrystalline material 391
Chapter 17. Ordering of atoms in crystals 402
17.1. The nature and description of disordered states 402
17.2. Order parameters 404
17.3. Patterson function 406
17.4. Size effects 407
17.5. Kinematical diffraction 409
17.6. Relationship with ordering energies 417
17.7. Dynamical scattering from disordered crystals 418
17.8. Out-of-phase domains 422
Problems 427
Chapter 18. Extended defects 428
18.1. Introduction 428
18.2. Stacking faults-statistical, kinematical theory 429
18.3. Dynamical diffraction by stacking faults 439
18.4. Dislocations 441
Chapter 19. Diffraction from surfaces 450
19.1. Introduction 450
19.2. Surface imaging and diffraction with electrons 452
19.3. Reflection from surfaces: grazing incidence 457
19.4. Reflection at normal incidence: LEED 468
19.5. Diffraction of emitted electrons 470
References 474
Index 494