Syllabus
I. Crystal structure and symmetry. 1. History of crystallography and structure analysis. Translation periodicity of crystals. Plane and space lattices. Symmetry operations. Hermann-Mauguin symbols. Elementary cells. Notation of directions and planes. Transformation of axes and plane indices. Stereographic projection. Groups. 2. Point groups. Crystallographic systems. Laue classes. Bravais lattices. Reciprocal lattice. Brillouin zones. 3. Space groups. Equivalent positions. Matrix description of symmetry operations. Wyckoff notation. International tables of crystallography. Examples of simple structures. 4. Influence of crystal symmetry on properties of compounds. Tensors and anisotropy of macroscopic properties. Neumann principle. Voigt principle. Curie principle.
II. Diffraction theory. 1. Geometric principles of diffraction. Reciprocal lattice. Laue conditions. Ewald construction. 2. Interaction of X-rays with matter. Absorption of radiation in material. Plane and spherical wave. Thomson and Compton scattering. Scattering on atom and ensamble of atoms. Atomic scattering factor, anomalous dispersion and absorption. Introduction of structure factor. Electron density and Fourier transformation. Basic atributes of diffraction peaks (position, intensity, width, shape) in kinematic theory of diffraction. 3. Static and dynamic displacements, temperature factor. Coherence length of photon. Crystals of finite dimensions. 4. Dynamic theory of diffraction. Wave equation for periodic medium. Single wave and two wave approximation. Some experimental effects - Pendellösung, Borrmann effect. Wave field in the diffracting crystal. 5. Comparison of scattering by X-rays, neutrons and electrons.
III. Structure analysis by diffraction 1. X-ray sources, detectors and monochromators. 2. Single crystal methods. Film methods. Orientation of crystal by Laue method. Space group determination - diffraction symbol. Single crystal diffractometers. 3. Phase problem. Structure determination (Patterson function, heavy-atom method, isomorphous replacement, direct methods). Study of deformation electron density due to bonding. 4. Powder diffraction. Information in powder diffraction pattern and its evaluation. Different diffraction geometries. 5. Application of structure analysis in materials research: phase identification, phase analysis, texture, stress, strain, crystallite size.
IV. Kinematic theory of high-energy electrons. 1. Kinematic approximation. Elastic and inelastic scattering. Wavelength of electrons. Electron scattering in potential field. Fresnel zones method. Amplitude-phase diagram. Phase shift of scattered wave. Elastic scattering on atom, elementary cell, distorted and undistorted crystal. Deviation from the Bragg position. 2. Interpretation of high-energy electron diffraction. Diffraction pattern from a single crystal and polycrystal. Intensity distribution in reciprocal lattice. Dimensional and shape effect. Extinction length. Limitations of kinematic theory. Kikuchi lines.
V. Lattice defects analysis in electron microscopy. 1. Phase contrast in ideal crystal. Column approximation. Intensity of the direct and diffracted beam. Effective deviation from the Bragg position. Intensity of diffracted beam in distorted crystal. Contrast on dislocations, stacking faults and precipitates. Visibility and invisibility of lattice defects in electron microscope. Reflection (two-beam) position. 2. Construction and properties of electron microscope. Faults and properties of magnetic lens. Correction of faults. Resolution, depth of sharpness. Imaging and diffraction in transmission electron microscope. Bright and dark field. Diffraction from selected area.
Annotation
Basic course for pre-graduated students, mainly for the students of the solid state physics. The lectures cover the fundamentals of kinematic and dynamic diffraction theory, fundamentals of crystallography and basic principles of the X-ray structure analysis and its most frequent applications. A special attention is paid to the physical principles of interaction of radiation with matter and to the relationship between the structure of matter and its physical properties. The second part of the course is devoted to the transmission electron microscopy and electron diffraction.
The following topics are discussed: Thomson and Compton scattering, atomic scattering factor, structure factor, Bragg equation, atomic displacement and vibrations, crystal lattices, reciprocal space and reciprocal lattices, Friedel's law, Laue classes, space groups, symmetry operations and Laue conditions for diffraction. The applications illustrate the orientation of crystals, qualitative and quantitative phase analysis, measurement of lattice parameters and the basic methods of structure solution (Patterson function, heavy atom method and isomorphic substitution). It is recommended to combine this lecture with the exercises FPL035.