X-Ray and Neutron Diffraction in Nonideal Crystals

1. Distribution of the Scattering Intensity. General Aspects.- 1.1 Diffraction Techniques for Analyzing Imperfections in Crystals.- 1.2 Kinematical Theory of Scattering.- 1.2.1 Dynamical and Kinematical Theories.- 1.2.2 X-Ray Scattering Intensity.- 1.2.3 Scattering Cross Section for Thermal Neutrons.- 1.2.4 Applicability Range for the Kinematic Theory.- 1.3 Scattering by Perfect Crystals of Finite Size.- 1.3.1 Intensity Distribution in Reciprocal Lattice Space: Form Function.- 1.3.2 Intensity Distribution in the Debye Diffraction Pattern.- 1.4 Scattering in Undistorted Crystals Containing Microscopic Cavities or Inclusions.- 1.5 Scattering by Crystals Containing Defects of Arbitrary Type. Classification of Defects.- 1.5.1 Analysis of Scattering by Imperfect Crystals.- 1.5.2 Scattering by Crystals with Randomly Distributed Defects.- 1.5.3 Classification of Defects.- 1.5.4 Diffuse Scattering by Crystals Containing First-Class Defects Under Weak Overlap of the Displacement Fields of Individual Defects.- 1.5.5 Approximation of Smoothly Varying Distortions.- 1.5.6 Scattering Intensity with Correlated Arrangement of Defects.- 1.6 Harmonic Analysis of the X-Ray Line Shapes.- 1.6.1 Fourier Coefficients for the Intensity Distributions of X-Ray Lines.- 1.6.2 Limiting Cases of Nondistorted and Large-Size Crystallites.- 1.6.3 Analysis of Crystallite Size and Distortions.- 2. Static Displacements in Crystals with Bounded Defects.- 2.1 Fluctuation Waves of Defects Concentration and Static Displacements.- 2.1.1 Symmetry of Defects.- 2.1.2 The Defect Distribution in Terms of Static Concentration Waves.- 2.1.3 Static Displacement Waves.- 2.2 Macroscopic Theory for the Static Displacement Waves.- 2.2.1 Long-Wavelength Fluctuation Waves and the Free Energy of the Anisotropic Elastic Continuum.- 2.2.2 Amplitudes of the Fluctuation Waves of Static Displacements.- 2.2.3 Fourier Components of the Static Displacements in the Continuum Description.- 2.2.4 Simplifications Introduced by Symmetry.- 2.2.5 Fluctuation Waves in Thin Films.- 2.3 Microscopic Theory for the Static Displacement Waves.- 2.3.1 Free Energy of Distorted Crystal with Bravais Lattice.- 2.3.2 Transition to the Long-Wave Approximation and the Related Force Constants.- 2.3.3 Crystals of Arbitrary Structure.- 2.4 Static Displacement Fields Around Bounded Defects.- 2.4.1 Atom Displacements Far from Defects.- 2.4.2 Atomic Displacements Near Defects, Green Functions and Mean Squares of Static Displacements.- 2.5 Static Distortions in Quasi-One-Dimensional and Quasi-Two-Dimensional Crystals.- 2.5.1 Discreteness of the Lattice and Spatial Dispersion.- 2.5.2 Static Distortion Fields of Defects in Strongly-Anisotropic Crystals.- 3. Positions and Intensities of Regular Reflection Peaks.- 3.1 Shift of X-Ray Lines in Imperfect Crystals and the Determination of Defect Concentrations.- 3.1.1 Influence of Defects on X-Ray Line Positions and Estimated Crystal Sizes.- 3.1.2 Studies of Vacancies in Crystals.- 3.1.3 Complexes in Solid Solutions and Their Effect on the Lattice Parameters.- 3.1.4 Dilation Effects Caused by Dislocation Loops.- 3.2 Regular Reflection Intensities in Perfect Crystals.- 3.2.1 Intensity Attenuation Factors.- 3.2.2 Debye-Waller Factor in Perfect Harmonic Crystals.- 3.2.3 Chain-Like and Layered Crystals.- 3.2.4 Effect of Anharmonicity on the Debye-Waller Factor.- 3.3 Effect of Static Displacements on Intensities of Regular Reflections.- 3.3.1 Debye-Waller Factor Due to Static Displacements.- 3.3.2 Effects in Crystals Containing Particles of a New Phase or Dislocation Loops.- 3.3.3 Layered and Chain-Like Crystals.- 3.3.4 Concentrated Solutions.- 3.3.5 Experimental Results on Regular Reflection Intensities in Imperfect Crystals.- 3.4 Effect of Thermal Vibrations in Imperfect Crystals.- 3.4.1 Crystals with Low Defect Concentrations.- 3.4.2 Concentrated Solutions.- 3.5 Debye-Waller Factors in Dynamical Diffraction Effects.- 3.5.1 Anomalous Transmission.- 3.5.2 X-Ray Fluorescence.- 3.5.3 Spatial Intensity Oscillations.- 3.5.4 Critical Potentials.- 4. Diffuse Scattering of X-Rays and Neutrons by Crystal Defects.- 4.1 Weakly Distorted Crystals.- 4.1.1 Scattering by Single Defects.- 4.1.2 Scattering Intensity Near Reciprocal Lattice Points: Symmetry of Defects and Force Dipole Tensors.- 4.1.3 Scattering Intensity Distribution at Large Distances from Reciprocal Lattice Points and Determination of the Defect Configuration and the Force Field.- 4.1.4 Diffuse Scattering and the Correlation in Defect Positions.- 4.1.5 Experiments on Scattering by Point Defects in Irradiated Crystals and Dilute Solutions.- 4.1.6 Scattering by Self-localized Electrons.- 4.1.7 Diffuse Scattering Representation in Various Experimental Techniques.- 4.2 Effects of Groups of Point Defects, New-Phase Particles, or Small-Radius Dislocation Loops.- 4.2.1 Scattering by Large Bounded Defects in Weakly Distorted Crystals.- 4.2.2 Diffuse Scattering by Weakly Distorted Crystals with Particles of a Second Phase and Ageing of Solutions.- 4.2.3 Diffuse Scattering by Small-Radius Dislocation Loops in Strained and Irradiated Materials.- 4.3 Intensity Distribution for Scattering by Strongly Distorted Crystals with Finite Defects.- 4.3.1 Change in Scattering Intensity Distribution with Increasing Defect Strength.- 4.3.2 Integrated Intensity from Strongly Distorted Crystals.- 4.3.3 Intensity Distribution in the Reciprocal Space.- 4.3.4 The Debye Diffraction Pattern.- 4.3.5 Experiments on Strongly Distorted Ageing Alloys and Irradiated Materials.- 4.3.6 Nonrandom Arrangement of Finite Defects.- 4.4 Strongly Anisotropic Crystals.- 4.4.1 Quasi-Two-Dimensional Crystals.- 4.4.2 Quasi-One-Dimensional Crystals.- 4.5 Effect of Finite Defects in Thin Films and Surface Layers on X-Ray Scattering.- 4.5.1 Scattering Intensity for Imperfect Finite Crystals.- 4.5.2 Diffuse Scattering by Defects in Thin Films.- 4.5.3 Broadening of Regular Reflection Peaks in Free Films with a Large Surface Area.- 4.5.4 Diffuse Scattering by Defects in a Thin Surface Layer.- 5. Scattering of X-Ray and Neutrons in Crystals with Dislocations.- 5.1 Broadening of Peaks by Randomly Distributed Defects of the Second Class.- 5.1.1 Linear Dislocations.- 5.1.2 Large-Radius Dislocation Loops.- 5.1.3 Dislocation Dipoles.- 5.1.4 Stacking Faults and Split Dislocations.- 5.2 Effect of Nonrandom Dislocation Arrangement on Scattering Intensity Distribution.- 5.2.1 Scattering by Crystals with Dislocation Walls and a Dislocation Description for the Effects Caused by Blocks and Cells.- 5.2.2 Correlation in the Uniform Dislocation Ensemble and in Crystals with Nonuniform Dislocation Arrangement.- 5.3 Diffraction Methods of Investigation of Dislocation Ensembles.- 5.3.1 Determination of Dislocation Density.- 5.3.2 Correlation and Inhomogeneity in Dislocation Arrangement.- 5.3.3 Dislocations in Narrow Small-Angle Walls (Boundaries) and Excess Dislocations of a Given Sign.- 5.3.4 Diffraction Techniques for Analyzing the Grain Boundaries.- Appendices.- A. Cumulant Expansion.- B. Equations for Amplitudes of Static Displacement Waves for Various Crystal and Defect Symmetries.- D. Mean Squares of Static Displacements in fee Crystals.- for Strongly Deformed Crystals Containing Limited-Size Defects.- F. Calculation of T(?) for Homogeneous Dislocation Ensemble.- References.