Preface ..................................................... IX
Symbols ..................................................... XV
1 Principles of X-ray Diffraction .............................. 1
1.1 The Basic Phenomenon .................................... 1
1.2 The θ/2θ Scan .......................................... 11
1.3 Intensity of Bragg Reflections ......................... 14
1.3.1 Atomic Form Factors ............................. 17
1.3.2 Structure Factor ................................ 19
1.3.3 Multiplicity .................................... 24
1.3.4 Geometry Factor ................................. 25
1.3.5 Preferred Orientation (Texture) ................. 25
1.3.6 Polarization Factor ............................. 26
1.3.7 Absorption Factor ............................... 26
1.3.8 Integration of the Interference Function ........ 29
1.4 Applications ........................................... 37
Exercises ................................................... 39
References .................................................. 41
2 Identification of Chemical Phases ........................... 43
2.1 Histogram-Based Techniques ............................. 43
2.2 Linear Attenuation Coefficient ......................... 55
2.3 Determination and Interpretation of the μt Product ..... 60
2.4 Analysis of Phase Mixtures ............................. 66
2.5 Amorphous Thin Films ................................... 70
2.6 Accurate Determination of Lattice Parameter ............ 74
2.7 Applications ........................................... 80
Exercises ................................................... 81
References .................................................. 83
3 Line Profile Analysis ....................................... 85
3.1 Model Functions and Peak Parameters .................... 86
3.2 Instrumental Line Profile .............................. 97
3.3 Deconvolution by Fourier Techniques ................... 101
3.4 Reflection Broadening by Small Crystallite Size
Only .................................................. 107
3.4.1 Scherrer Equation .............................. 108
3.4.2 Column Height Distribution ..................... 111
3.4.3 Crystallite Shapes Other Than Cubes ............ 112
3.4.4 Determination of the Column Height
Distribution Function .......................... 115
3.4.5 Determination of the Crystallite Size
Distribution Function .......................... 118
3.5 Concomitant Occurrence of Size and Strain
Broadening ............................................ 120
3.5.1 Analysis According to Williamson and Hall ...... 122
3.5.2 Method of Warren and Averbach .................. 126
3.5.3 Single-Line Analysis ........................... 129
3.5.4 Techniques of Whole-Pattern Fitting ............ 130
3.6 Applications .......................................... 134
Exercises .................................................. 136
References ................................................. 138
4 Crazing Incidence Configurations ........................... 143
4.1 Grazing Incidence X-ray Diffraction (GIXRD) ........... 148
4.2 Penetration Depth and Information Depth ............... 155
4.3 Depth-Dependent Properties ............................ 158
4.4 Refractive Index for X-rays ........................... 160
4.5 Total External Reflection and Critical Angle .......... 161
4.6 X-ray Reflectivity (XRR) .............................. 165
4.6.1 Reflectivity of a Substrate .................... 166
4.6.2 Reflectivity of a Single Layer ................. 168
4.6.3 Reflectivity of Multilayers and
Superlattices .................................. 171
4.7 Grazing Incidence Diffraction (GID) ................... 175
4.8 Applications .......................................... 177
Exercises .................................................. 179
References ................................................. 181
5 Texture and Preferred Orientation .......................... 183
5.1 Texture Factors ....................................... 188
5.2 Pole Figures .......................................... 191
5.3 Measurement of Pole Figures ........................... 195
5.4 Directions, Orientations and Inverse Pole Figures ..... 200
5.5 Fiber Textures or Layer Textures ...................... 204
5.5.1 Harmonic Method ................................ 204
5.5.2 Whole Pattern Techniques ....................... 207
5.5.3 Rocking Curves (ω Scans) ....................... 211
5.6 Biaxial and Fully General Textures .................... 216
5.6.1 Azimuthal Scans (ɸ Scans) ...................... 218
5.6.2 General Orientation Distribution ............... 220
5.6.3 Determination of Fully General Texture ......... 225
5.7 Depth Dependence of Thin-Film Textures ................ 228
5.8 Applications .......................................... 230
Exercises .................................................. 234
References ................................................. 235
6 Residual Stress Analysis ................................... 239
Mario Birkholz and Christoph Genzel
6.1 Ceiiinnosssttuv ....................................... 241
6.2 Fundamental Equation of XSA ........................... 246
6.3 Measurement of dΨ Distributions ....................... 249
6.4 Diffraction Elastic Constants (DECs) s1 and l/2s2 ..... 258
6.5 Grain Interaction Models .............................. 261
6.6 The Effect of Texture ................................. 265
6.7 Classification of Stresses ............................ 268
6.7.1 Classification by Dimension .................... 268
6.7.2 Residual Stresses in Multiphase Materials ...... 269
6.7.3 Origin of Residual Stresses: Extrinsic and
Intrinsic Stresses ............................. 271
6.8 Effect of Residual Stress Gradients ................... 273
6.8.1 General Considerations ......................... 273
6.8.2 The Biaxial Stress State ....................... 274
6.9 Detection of Residual Stress Gradients in Thin
Films ................................................. 276
6.9.1 Basic Relations ................................ 276
6.9.2 X-ray Penetration Depth for the General Case
of Asymmetric Diffraction ...................... 278
6.9.3 Special Methods for X-ray Stress Gradient
Analysis ....................................... 281
6.9.4 Grazing-Incidence Diffraction (GID) ............ 282
6.9.5 The Scattering Vector Method ................... 284
6.9.6 Realization of H Mode on a Four-Circle
Diffractometer ................................. 286
6.10 Applications .......................................... 289
Exercises .................................................. 291
References ................................................. 291
7 High-Resolution X-ray Diffraction .......................... 297
Mario Birkholz and Paul F. Fewster
7.1 Strain, Strain Relaxation and Composition in
Epitaxial Layers ...................................... 303
7.2 High-Resolution Rocking Curves ........................ 306
7.3 Mosaicity and Extinction .............................. 314
7.4 Dynamical Theory of Ewald and Extensions .............. 329
7.5 High-Resolution Rocking Curves and Profiles from
Layer Structures ...................................... 324
7.6 Reciprocal Space Mapping .............................. 332
7.7 Diffuse Scattering .................................... 337
7.8 Extensions to High-Resolution Diffraction ............. 338
Exercises .................................................. 339
References .................................................... 340
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