X-Ray and Neutron Diffraction in Nonideal Crystals

Mikhail Alexandrovich Krivoglaz died unexpectedly when he was preparing the English edition of his two-volume monograph on diffraction and diffuse scatter­ ing of X-rays and neutrons in imperfect crystals. His death was a heavy blow to all who knew him, who had worked with him and to the world science community as a whole. The application of the diffraction techniques for the study of imperfections of crystal structures was the major field of Krivoglaz' work throughout his career in science. He started working in the field in the mid-fifties and since then made fundamental contributions to the theory of real crystals. His results have largely determined the current level of knowledge in this field for more than thirty years. Until the very last days of his life, Krivoglaz continued active studies in the physics of diffraction effects in real crystals. His interest in the theory aided in the explanation of the rapidly advancing experimental studies. The milestones marking important stages of his work were the first mono­ graph on the theory of X-ray and neutron scattering in real crystals which was published in Russian in 1967 (a revised English edition in 1969), and the two­ volume monograph published in Russian in 1983-84 (this edition is the revised translation of the latter).

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.