Diffraction Physics

Cover......Page 1
Title page......Page 3
Date-line......Page 4
Preface to the first edition......Page 5
Preface to the third edition......Page 6
CONTENTS......Page 7
Section I - PHYSICAL OPTICS......Page 17
1.1. Introduction......Page 19
1.2.1. Wave functions......Page 21
1.2.2. Electromagnetic waves......Page 22
1.2.3. Particle waves......Page 23
1.3.1. Superposition......Page 24
1.3.2. Independent point sources......Page 25
1.4.1. Kirchhoff\'s formulation......Page 27
1.4.2. Application of the Kirchhoff formula......Page 28
1.5.1. Integral form of wave equation......Page 29
1.5.2. Born series......Page 30
1.7.1. Small angle approximation......Page 32
1.7.2. Fresnel integrals......Page 33
1.7.3. Periodic objects - \"Fourier images\"......Page 35
1.8. Fraunhofer diffraction......Page 37
Problems......Page 40
2.1.1. Delta-functions and discontinuities......Page 41
2.1.2. Convolutions......Page 42
2.1.3. Examples of convolutions......Page 43
2.2.1. Definitions......Page 46
2.2.2. Properties of Fourier transforms......Page 47
2.2.3. Multiplication and convolution......Page 49
2.2.4. Space and time......Page 50
2.3.2. A plane wave: the inverse of 2.3.1......Page 51
2.3.4. Slit function......Page 52
2.3.6. Straight edge......Page 53
2.3.7. Rectangular aperture......Page 54
2.3.9. Two very narrow slits......Page 55
2.3.11. Finite wave train......Page 56
2.3.12. Periodic array of narrow slits......Page 58
2.3.14. Diffraction grating: thin slits......Page 59
2.3.15. Diffraction grating: general......Page 60
2.3.16. Gaussian function......Page 61
2.3.17. Row of circular holes......Page 62
2.3.18. Complementary objects-Babinet\'s principle......Page 63
Problems......Page 64
3.1.1. Coherent wave optics......Page 67
3.1.2. Incoherent wave imaging......Page 70
3.2. Abbe theory......Page 71
3.3. Small angle approximation......Page 72
3.4.1. Phase and amplitude objects......Page 75
3.4.2. Out-of-focus contrast......Page 76
3.4.4. Zernike phase contrast......Page 78
3.5. Holography......Page 79
3.6. Multi-component systems......Page 83
3.7. Partial coherence......Page 85
Problems......Page 88
Section II - KINEMATICAL DIFFRACTION......Page 91
4.1.1. X-ray sources......Page 93
4.1.2. Scattering by electrons......Page 94
4.1.3. Scattering by atoms......Page 96
4.2.1. Sources of electrons......Page 97
4.2.2. Atom scattering amplitudes......Page 98
4.2.3. Phase object approximation......Page 100
4.2.4. Failure of first Born approximation......Page 101
4.2.5. \"Absorption\" effects......Page 102
4.3.1. Atomic scattering factors......Page 104
4.3.2. Nuclear spin scattering......Page 105
4.3.3. Isotopic disorder......Page 106
4.3.4. Thermal and magnetic scattering......Page 107
Problems......Page 108
5.1. The kinematical approximation......Page 109
5.2.1. Reciprocal space distribution......Page 111
5.2.2. The reciprocal lattice......Page 112
5.2.3. Friedel\'s law and the phase problem......Page 113
5.3. The generalized Patterson function......Page 114
5.4.1. Finite volume limitations......Page 117
5.4.2. Finite crystals......Page 118
5.5.1. Four-dimensional Patterson......Page 120
5.5.2. Special cases......Page 121
5.5.3. Ideal monatomic gas or liquid......Page 122
5.5.4. Real monatomic gases and liquids......Page 125
5.5.5. The hydrogen atom......Page 128
5.6. Diffraction geometry and intensities......Page 129
5.7.1. Finite sources and detectors......Page 131
5.7.2. Wavelength spread......Page 133
5.7.3. Integrated intensities......Page 134
5.8. Sections and projections......Page 135
Problems......Page 137
6.1. Ideal crystals......Page 139
6.2.1. Laue and Bragg diffraction conditions......Page 142
6.2.2. Shape transforms......Page 143
6.2.3. Special cases for electron diffraction......Page 144
6.3.1. The phase problem......Page 147
6.3.2. Supplementary information......Page 149
6.4.1. Trial and error......Page 150
6.4.3. Heavy-atom & isomorphous replacement methods......Page 151
6.4.4. Direct methods......Page 152
6.5.1. Nuclear scattering......Page 154
6.5.2. Magnetic scattering......Page 155
6.6. Electron diffraction structure analysis......Page 157
Problems......Page 158
7.1.1. Types of defects......Page 161
7.1.2. General diffraction formulation......Page 162
7.2.1. Patterson with average periodic structure......Page 163
7.2.2. Patterson with no average structure......Page 165
7.3.1. Random vacancies: no relaxation......Page 166
7.3.2. Clustered vacancies......Page 168
7.3.3. Lattice relaxation......Page 170
7.3.4. Thermal vibrations - Einstein model......Page 172
7.4.1. Uneven separation of lattice planes......Page 173
7.4.2. Disordered orientations......Page 176
Problems......Page 179
Section III - DYNAMICAL SCATTERING......Page 181
8.1. Multiple coherent scattering......Page 183
8.2. Theoretical approaches......Page 184
8.3.1. The dispersion equations......Page 186
8.3.2. Solutions of the equations......Page 188
8.3.3. Boundary conditions......Page 189
8.4.1. Bloch waves and dispersion surfaces......Page 191
8.4.2. Conduction electrons-energy representation......Page 193
8.5.1. Electron diffraction for a thin crystal......Page 194
8.5.2. Small angle approximation......Page 197
8.6. Bethe potentials......Page 198
8.7. The Bragg case......Page 200
9.1.2. Real space picture......Page 205
9.1.4. Extinction contours......Page 207
9.1.5. Convergent beam diffraction......Page 209
9.1.6. Diffraction and imaging of crystal wedges......Page 211
9.1.7. Absorption effects for wedges......Page 213
9.2.1. Techniques for X-ray diffraction......Page 215
9.2.2. Energy flow......Page 218
9.2.3. Dispersion surface picture......Page 219
9.2.4. Neutron diffraction......Page 220
9.3. Borrmann effect......Page 221
Problems......Page 223
10.1. Dynamical $n$-beam diffraction......Page 225
10.2.1. Matrix formulation......Page 227
10.2.2. Small angle approximation......Page 229
10.2.3. Bloch waves and boundary conditions......Page 230
10.2.4. The scattering matrix......Page 232
10.2.5. Derivation of the two-beam approximation......Page 234
10.3. The Darwin-type approach......Page 236
10.4. Special cases - beam reduction......Page 238
10.5. Computing methods......Page 240
10.6. Column approximation......Page 243
Problems......Page 245
11.1.1. Transmission through thin slices......Page 247
11.1.2. Three-dimensional objects......Page 249
11.1.3. Diffraction by a crystal......Page 250
11.1.4. General expression; excitation errors......Page 252
11.2.1. Zero-order scattering......Page 253
11.2.3. Multiple scattering......Page 254
11.3.1. General series solution......Page 256
11.3.2. Phase grating approximation......Page 257
11.4.1. \"Slice method\" calculations......Page 259
11.4.2. Steps in a computation......Page 261
11.4.3. Possible errors......Page 262
11.4.4. Consistency tests......Page 263
11.5. Intensities from non-periodic objects......Page 264
11.6.1. High-energy approximation......Page 266
11.6.2. Useful approximations......Page 268
11.6.3. A real-space basis for computing......Page 269
Problem......Page 270
Section IV - APPLICATIONS TO SELECTED TOPICS......Page 271
12.1.1. Phonons and vibrational waves......Page 273
12.1.2. Scattering for a longitudinal wave......Page 274
12.1.3. Diffuse scattering component......Page 275
12.1.4. Dispersion curves......Page 277
12.2.1. Relaxation around point defects......Page 278
12.2.2. Diffraction intensities for displaced atoms......Page 279
12.2.3. The Bragg peaks......Page 281
12.2.4. The diffuse scattering......Page 282
12.3.1. Inelastic X-ray scattering......Page 285
12.3.2. Electron excitation by electrons-plasmons......Page 286
12.3.3. Single-electron excitations......Page 288
12.4.1. Scattering and re-scattering......Page 290
12.4.2. Coherent and incoherent scattering......Page 292
12.4.3. Analysis of diffuse scattering......Page 294
12.5.1. The nature of absorption parameters......Page 295
12.5.2. Absorption of X-rays and neutrons......Page 296
12.5.3. \"Absorption\" for electrons......Page 297
12.5.4. Absorption due to thermal vibrations......Page 298
12.5.5. Absorption from electron excitations......Page 300
12.5.6. Values of absorption coefficients......Page 301
13.1.1. Conventional transmission e. m.......Page 303
13.1.2. Scanning transmission electron microscopes......Page 305
13.2. Image formation......Page 308
13.3.1. Phase-object approximation......Page 310
13.3.2. Weak-phase object approximation......Page 312
13.3.3. Failure of weak-phase object approximation......Page 315
13.3.4. Dark-field images......Page 316
13.4.1. Imaging of thin crystals; structure images......Page 317
13.4.2. Calculation of images of crystals: envelope......Page 321
13.4.3. Imaging of crystals - inelastic scattering......Page 323
13.4.4. Lattice fringe imaging......Page 325
13.4.5. Crystal imaging without lattice resolution......Page 328
13.5.1. STEM imaging of thin crystals......Page 329
13.5.2. STEM imaging of thicker crystals......Page 333
13.6. Electron holography......Page 334
13.7. Combining high-resolution imaging with diffraction......Page 342
Problems......Page 344
14.1.1. Geometry of Kossel lines......Page 345
14.1.2. Dynamical theory of Kossel intensities......Page 346
14.1.3. Kossel lines with limited resolution......Page 348
14.2. Kikuchi lines......Page 351
14.3. External sources of divergent radiation......Page 355
14.4. Information from K-line patterns......Page 357
14.5. Channelling......Page 359
14.6. Secondary radiations......Page 362
15.2. X-ray interferometry......Page 365
15.3. $n$-beam and 2-beam dynamical diffraction......Page 367
15.4. Accurate determinations of structure amplitudes......Page 370
15.4.1. Measurements of thickness fringes......Page 371
15.4.2. Structure amplitudes from rocking curves......Page 373
15.4.3. Convergent beam electron diffraction method......Page 374
15.4.4. The use of critical voltages......Page 375
15.4.5. Intersecting K-lines......Page 378
15.5. The determination of crystal symmetries......Page 379
15.6. Coherent convergent-beam electron diffraction......Page 383
16.1. General......Page 385
16.2.2. Kinematical integrated intensities......Page 386
16.2.3. Extinction effects......Page 388
16.3.1. Idealized models......Page 390
16.3.3. Line profile analysis......Page 393
16.3.4. Rietveld refinements......Page 395
16.3.5. Dynamical diffraction intensities......Page 396
16.3.6. $n$-beam diffraction effects......Page 399
17.1. The nature and description of disordered states......Page 401
17.2.1. Short-range order......Page 403
17.3. Patterson function......Page 405
17.4. Size effects......Page 406
17.5.1. Diffraction with ordering only......Page 408
17.5.2. Diffraction with ordering and size effects......Page 411
17.6. Relationship with ordering energies......Page 416
17.7.1. Dynamical effects in diffuse scattering......Page 417
17.7.2. Calculations of diffuse scattering......Page 418
17.7.3. Strong scattering, multi-atom correlations......Page 419
17.7.4. High resolution imaging disordered crystals......Page 420
17.8.1. Ordered out-of-phase superlattices......Page 421
17.8.2. Out-of-phase domains in disordered alloys......Page 423
17.8.3. Modulated structures......Page 424
Problems......Page 426
18.1. Introduction......Page 427
18.2.1. Patterson method for a simple case......Page 428
18.2.2. A general treatment......Page 430
18.2.3. Faults in close-packed structures......Page 436
18.3. Dynamical diffraction by stacking faults......Page 438
18.4.1. Diffraction effects......Page 440
18.4.2. The imaging of dislocations......Page 442
18.4.4. $n$-beam diffraction effects......Page 443
19.1. Introduction......Page 449
19.2.1. Phase-contrast imaging......Page 451
19.2.2. Crystal terminations and superlattices......Page 452
19.2.3. Structure analysis of surface superlattices......Page 454
19.2.4. Crystal profile imaging......Page 455
19.3.1. Kinematical approximation: x-rays, neutrons......Page 456
19.3.2. Standing wave techniques......Page 459
19.3.3. RHEED and REM......Page 460
19.4. Reflection at normal incidence: LEED......Page 467
19.5. Diffraction of emitted electrons......Page 469
References......Page 473
Index......Page 493