Elastic and inelastic scattering in electron diffraction and imaging

목차 (Table of Contents)

• CONTENTS
• Part I Diffraction and Imaging of Elastically Scattered Electrons
• 1. Basic Kinematic Electron Diffraction
• 1.1. Wave Properties of Electrons = 3
• 1.2. Plane Wave = 4
• 1.3. Single-Atom Scattering = 5
• 1.4. Mott Formula = 6
• 1.5. Kinematic Electron Diffraction in Thin Crystals = 8
• 1.6. Reciprocal Space = 11
• 1.7. Bragg's Law = 12
• 1.8. Abbe's Imaging Theory = 16
• 1.9. Some Mathematical Operations = 18
• 1.9.1. Fourier Transformation = 18
• 1.9.2. Convolution Calculation = 18
• 1.9.3. Dirac Delta Function = 20
• 2. Dynamic Elastic Electron Scattering I: Bloch Wave Theory
• 2.1. Relativistic Corrections in Single-Electron Scattering Theory = 23
• 2.2. Bethe Theory = 25
• 2.2.1. Basic Equations = 25
• 2.2.2. Characteristics of Bloch Waves = 28
• 2.2.3. Orthonormal Relationship of Bloch Waves = 29
• 2.2.4. Bethe Theory and Band Structure Theory = 30
• 2.3. Two-Beam Theory = 31
• 2.4. Dispersion Surfaces = 35
• 2.5. Aplications in CBED = 37
• 2.6. Critical Voltage Effect = 40
• 2.7. Diffraction of Layered Materials = 42
• 2.8. HOLZ Reflections = 44
• 2.9. Real-Space Bloch Wave Theory of ZOLZ Reflections = 44
• 2.9.1. Projected Potential Approximation = 45
• 2.9.2. ZOLZ Reflections = 45
• 2.9.3. Effects of HOLZ Reflections = 47
• 2.10. Diffraction Contrast Images of Imperfect Crystals = 47
• 2.10.1. Potential of Imperfect Crystals = 49
• 2.10.2. Modified Bloch Wave Theory = 50
• 2.10.3. Column Approximation = 50
• 2.10.4. Howic-Whelan Equation = 51
• 2.10.5. $$\alpha$$ Coefficient Method = 54
• 2.11. Weak-Beam Imaging = 54
• 2.12. Absorption Effect in Dynamical Calculations = 59
• 2.13. Summary = 60
• 3. Dynamic Elastic Electron Scattering II: Multislice Theory
• 3.1. Physical Optics Approach = 61
• 3.1.1. Phase Object Approximation = 62
• 3.1.2. Huygens' Principle = 63
• 3.1.3. Multislice Theory = 65
• 3.2. Quantum Mechanical Basis of Multislice Theory = 65
• 3.2.1. Inclined Incident Beam Case = 65
• 3.2.2. Multislice Solution of the Schr$$\ddot o$$dinger Equation = 65
• 3.3. Simulations of HRTEM Images and Electron Microdiffraction Patterns = 70
• 3.4. Calculations of HOLZ Reflections = 74
• 3.5. Improved Multislice Approaches = 75
• 3.5.1. Modified Multislice Theory for ZOLZ Reflections = 75
• 3.5.2. Modified Multislice Theory for HOLZ Reflections = 77
• 3.6. Effects of a Magnetic Field = 80
• 3.7. Summary = 81
• 4. Dynamic Elastic Electron Scattering III: Other Approaches
• 4.1. Scattering Matrix Theory = 83
• 4.2. Green's Function Theory = 85
• 4.3. Semireciprocal Space Method = 87
• 4.4. Scattering Operator in Electron Diffraction = 88
• 4.5. Diffraction in Imperfect Crystals = 90
• 4.6. Equivalence among Various Theories = 91
• 4.7. Comparing of Bloch Wave and Multislice Theories = 94
• 5. Diffraction and Imaging of Reflected High-Energy Electrons from Bulk Crystal Surfaces
• 5.1. Geometry of RHEED = 97
• 5.2. Bloch Wave Theory = 100
• 5.3. Parallel-to-Surface Multislice Theories = 106
• 5.3.1. Method I = 107
• 5.3.2. Method II = 112
• 5.4. Perpendicular-to-Surface Multislice Theory = 116
• 5.5. Electron Reflection Process in RHEED = 118
• 5.6. Thermal Diffuse Scattering in RHEED = 123
• 5.7. Summary = 126
• Part II DIFFRACTION AND IMAGING OF INELASTICALLY SCATTERED ELECTRONS
• 6. Inelastic Excitations and Absorption Effect in Electron Diffraction
• 6.1. Kikuchi Patterns = 129
• 6.1.1. Formation of Kikuchi Lines = 131
• 6.1.2. Inelastic Excitations in Crystals = 132
• 6.1.3. Bremsstrahlung = 135
• 6.1.4. Electron Compton Scattering = 136
• 6.2. Yoshioka's Equations for Inelastically Scattered Electrons = 137
• 6.2.1. Basic Equations = 137
• 6.2.2. Incoherence and Coherence of Inelastically Scattered Electrons = 139
• 6.2.3. Conservation of Intensity = 140
• 6.2.4. Absorption Phenomenon = 141
• 6.3. Effects of Inelastic Excitations on an Elastic Wave = 141
• 6.3.1. Mixed Dynamic Form Factor = 142
• 6.3.2. Absorption Potential―Reciprocal-Space Description = 144
• 6.3.3. Absorption Potential―Real-Space Description = 145
• 6.3.4. Interpretating the Imaginary Potential = 146
• 6.3.5. Effect of Inelastic Absorption in Quantilative Electron Microscopy = 148
• 6.3.6. Virtual Inelastic Scattering = 149
• 6.4. Inelastic-Scattering Process I: Phonon Excitation = 150
• 6.4.l. Phonons in Crystals = 150
• 6.4.2. Perturbation Effect of Atomic Vibrations on Crystal Potential = 153
• 6.4.3. Electron-Phonon Interactions = 155
• 6.4.4. Phonon Dispersion Surfaces = 157
• 6.4.5. Debye-Waller Factor = 159
• 6.4.6. Mixed Dynamic Form Factor for Multiphonon Excitations = 160
• 6.4.7. Absorption Potential = 164
• 6.5. Inelastic-Scattering Process II: Valence Excitation = 167
• 6.5.1. Dielectric Response Theory of Valence Excitations = 167
• 6.5.2. Mean Free Path and Absorption Potential = 169
• 6.5.3. Interface and Surface Excitations = 170
• 6.5.4. The Mixed Dynamic Form Factor and Generalized Dielectric Function = 175
• 6.6. Inelastic-Scattering Process III: Atomic Inner Shell Excitation = 176
• 6.6.1. Excitation Matrix = 177
• 6.6.2. Absorption Potential = 178
• 6.7. Diffraction and Channeling Effects in X-Ray and Auger Electron Emissions = 180
• 6.7.1. Localization in Atomic Inner Shell Excitation = 180
• 6.7.2. Delocalization in Electron Impact Ionization in Crystals = 181
• 6.8. Minimum Momentum Transfer in Inelastic Scattering = 185
• 6.8.1. Conservation of Energy = 185
• 6.8.2. Conservation of Momentum = 185
• 6.9. Summary = 187
• 7. Semiclassical Theory of Thermal Diffuse Scattering
• 7.1. Frozen Lattice Model = 189
• 7.2. Two-Beam TDS Theory = 192
• 7.3. Total Absorption Coefficient = 196
• 7.4. Many-Beam TDS Theory = 198
• 7.5. Multiphonon Excitations = 200
• 7.6. Evaluating the Debye-Waller Factor = 207
• 7.7. Coherent Length in Thermal Diffuse Scattering = 208
• 7.8. Diffuse Scattering of Imperfect Crystals = 212
• 7.8.1. Huang Scattering = 212
• 7.8.2. Diffuse Scattering Produced by Point Defects = 213
• 7.9. Summary = 216
• 8. Dynamic Inelastic Electron Scattering I. Bloch Wave Theory
• 8.1.Solution of Yoshioka's Equations = 217
• 8.2. Iterative Method = 220
• 8.3. Diffraction of Single Inelastically Scattered Elections = 221
• 8.4. Theory of Kikuchi Patterns = 224
• 8.5. Diffraction of Double Inelastically Scattered Electrons = 226
• 8.6. Coherent Double Inelastic Scattering under Delta Function Localization Approximation = 231
• 8.7. Diffraction Contrast Images of Inelastically Scattered Electrons = 234
• 8.7.1. Images of Stacking Faults = 235
• 8.7.2. Solution of Yoshioka's Equations for Imperfect Crystals = 236
• 8.7.3. Diffraction Contrast Imaging of Single Inelastically Scattered Electrons = 238
• 8.8. Summary = 239
• 9. Reciprocity in Electron Diffraction and Imaging
• 9.1. Reciprocity Theorem for Elastically Scattered Electrons = 241
• 9.2. Equivalence of TEM and STEM = 243
• 9.3. Reciprocity Theorem for Inelastically Scattered Electrons = 247
• 9.4. Summary = 250
• 10. Dynamic Inelastic Electron Scattering II: Green's Function Theory
• 10.1. Generalized Reciprocity Theorem = 251
• 10.2. Fourier Transform of Green's Function = 253
• 10.3. First-Order TDS = 255
• 10.4. Atomic Inner Shell Single Inelastic Excitation = 257
• 10.5. Double Inelastic Electron Scattering = 258
• 10.6. Summary = 263
• 11. Dynamic Inelastic Electron Scattering III: Multislice Theory
• 11.1. Multislice Solution of Yoshioka's Equations = 265
• 11.2. Conservation of Total Electrons = 271
• 11.3. First-Order Results = 272
• 11.4. Special Cases of Only One Excited Slate = 273
• 11.4.1. Valence-Loss Scattering = 274
• 11.4.2. Thermal Diffuse Scattering = 275
• 11.5. Imaging with TDS Electrons in STEM = 278
• 11.5.1. ImageFormation = 278
• 11.5.2. Contribution of Bragg-Reflected Electrons = 281
• 11.5.3. Contribution of TDS Electrons = 281
• 11.5.4. Effects of Multiphonon and Multiple Phonon Scattering = 285
• 11.5.5. Effects of Coherent TDS = 286
• 11.5.6. Detection Geometry and Coherence in HAADF-STEM Imaging = 293
• 11.6. Imaging with TDS Electrons in TEM = 294
• 11.6.1. Image Formation = 294
• 11.6.2. Incoherent Imaging Theory = 296
• 11.7. Effect of Phase Correlation Between Atom Vibrations in TDS Electron Imaging = 298
• 11.8. Effect of Huang Scattering in Composition-Sensitive Imaging = 299
• 11.9. Resolution of an Incoherent Image = 303
• 11.10. Real-Space Multislice Theory of TDS = 305
• 11.10.1. Basic Equations = 305
• 11.10.2. Atomic-Number-Sensitive Imaging in STEM―the Exact Theory = 307
• 11.10.3. Multislice Calculation of Dynamic Scattering Operator $$O_p$$ = 312
• 11.10.4. Atomic-Number-Sensitive Imaging in TEM―the Exact Theory = 314
• 11.10.5. Dislocation Contrast Due to Huang Scattering = 315
• 11.11. Summary = 320
• 12. Dynamic Inelastic Electron Scattering IV: Modified Multislice Theory
• 12.1. General Theory = 321
• 12.2. Single Inclastic Scattering = 323
• 12.3. Equivalence with Multislice Theory = 325
• 12.4. Absorption function = 327
• 12.5. Localized Inelastic Scattering = 328
• 12.6. Diffraction of TDS Electrons―Semiclassical Approach = 329
• 12.6.1. Basic Equations = 329
• 12.6.2. Streaks in TDS Electron Diffraction Patterns = 332
• 12.7. Diffraction of Phonon-Scattered Electrons―Quantum Mechanical Approach = 336
• 12.7.1. Fundamental Treatment = 337
• 12.7.2. Diffraction Patterns of Phonon-Scattered Electrons = 339
• 12.7.3. Directions of TDS Streaks = 341
• 12.8. Equivalence of Frozen Lattice Model and Phonon Excitation Theories for TDS = 349
• 12.9. Diffraction of Atomic Inner Shell Scattered Electrons = 351
• 12.10. Summary = 354
• 13. Inelastic Scattering in High-Resolution Transmission Electron Imaging
• 13.1. Contribution of Valence Loss Electrons = 356
• 13.1.1. Diffraction of Valence Loss Electrons = 356
• 13.1.2. Energy-Filtered HRTEM Images of Valence Loss Electrons = 358
• 13.1.3. Approaching the Completely Delocalized Scattering Model = 359
• 13.1.4. Perturbation Theory for Calculating $$\Psi$$ = 361
• 13.1.5. Effect of Surface Plasmon Excitation = 362
• 13.1.6. Energy-Filtered Inelastic Images of Interfaces = 364
• 13.2. Contribution of Phonon-Scattered Electrons = 367
• 13.3. TDS in High-Resolution Off-Axis Electron Holography = 370
• 13.3.1. Electron Holography with Time-Dependent Perturbation = 370
• 13.3.2. Multislice Calculation of 〈$$\Phi$$〉 = 373
• 13.3.3. Inelastic Scattering in Electron Holography = 375
• 13.4. Summary = 375
• 14. Multiple Inelastic Electron Scattering
• 14.1. Transport Equation Theory = 377
• 14.1.1. Energy Distribution of Plural Inelastically Scattered Electrons = 378
• 14.1.2. Angular Distribution of Plural Inelastically Scattered Electrons = 380
• 14.2. Improved Theories = 383
• 14.3. Density Matrix Theory of Electron Diffraction = 385
• 14.3.1. Kinetic Equation of Multiple Inelastic Electron Scattering = 386
• 14.3.2. Absorption Effect in Calculating Green's Function = 388
• 14.3.3. Delocalized Multiple Inelastic Scattering = 391
• 14.4. A Modified Multislice Theory = 393
• 14.4.1. Double Inelastic Scattering = 393
• 14.4.2. Function = 397
• 14.4.3. Multiple Scattering Theory = 397
• 14.4.4. Multiple Phonon Scattering in HAADF-STEM Imaging = 399
• 14.5. Summary = 401
• 15. Inelastic Excitation of Crystals in Thermal Equilibrium with the Environment
• 15.1. Basic Equations = 403
• 15.2. Electron Images and Diffraction Patterns = 406
• 15.3. Solution to a Fluctuating Component = 406
• 15.4. Contributions of Fluctuating Components to Electron Diffraction Pattern and Image = 408
• 15.5. Nonfluctuating Inelastic Components = 410
• 15.6. Absorption Effect for Elastic Waves = 412
• 15.7. Applications in Phonon Scattering = 412
• APPENDIXES
• A. Physical Constants, Electron Wavelengths, and Wave Numbers = 419
• B. Properties of Fourier Transforms = 421
• B.1. Identities = 422
• C. Some Properties of Dirac Delta Functions = 423
• C.1. Defining Relationships and Normalization Conditions = 423
• C.2. Useful Representations of the Delta Function = 423
• D. Integral Form of the Schr$$\ddot o$$dinger Equation = 427
• E. Some Useful Mathematical Relations = 431
• References = 433
• Index = 443