Learning objectives
<br />The aim of the course is to achieve a good understanding of X-ray and neutron diffraction and scattering techniques, and of their main applications to the condensed matter physics.
Prerequisites
<br />Good working knowledge of advanced calculus: functions of two or more variables, differential equations, functions of complex variables, Fourier transforms.<br />Good working knowledge of classical mechanics, electricity and magnetism, quantum mechanics.
Course unit content
<br />Introduction to X-ray diffraction<br />X rays: waves and photons, scattering from an electron, from an atom, from a molecule, Compton scattering, absorption, reflection refraction, coherence, magnetic interactions, X-ray sources, laboratory instrumentation, synchrotron radiation, collimation, spectral prperties, wigglers and undulators.<br />Kinematic theory of X-ray diffraction<br />Scattering from a crystal lattice, Bragg and Laue equations, Ewald sphere, the structure factor of the unit cell, lattice vibrations, Debye-Waller factor, integrated intensity.<br />Refraction and reflection of X rays<br />Index of refraction and absorption, Snell's law and Fresnel equations, reflection from an homogeneous layer with finite thickness, from a multilayer, rough surfaces and interfaces..<br />Dynamic theory of X-ray diffraction<br />Reflection and transmission from few atomic layers, Darwin theory, Darwin reflectivity curve, width of the Darwin curve, integrated intensity, standing waves.<br />X-ray absorption<br />Photoelectric absorption, scattering and absorption cross sections, X-ray absorption from a single atom, EXAFS, theoretical framework and examples, X-ray dicroism, resonant scattering.<br />Introduction to neutron scattering <br />Neutron properties and complementarities between neutrons and X-rays, neutron production, reactors, spallation sources, neutron transport, guides, neutron selection: monochromators and choppers, neutron detectors, instrumentation: diffractometers, small angle scattering instruments and reflectometers, spectrometers at continuous sources: TAS & TOF, spectrometers at pulsed sources, high resolution spectrometers.. <br />Neutron scattering theory<br />Scattering cross-sections, the dynamic structure factor, coherent and incoherent scattering, scattering functions and correlation functions, energy spectrum accessible to neutrons and atomic motions that can be probed.<br />Neutron diffraction<br />diffraction from crystal structures, diffraction from disordered systems, small angle scattering, form factor, structure factor, contrast variation..<br />Inelastic and quasielastic neutron scattering<br />Inelastic scattering, normal modes, one-phonon cross section, measure of the dispersion curves, incoherent scattering and incoherent approximation, vibrational spectroscopy, correlation functions and intermediate scattering functions, examples of diffusive motions.<br />Magnetic neutron scattering<br />Magnetic interactions of neutrons with electrons, magnetic cross section and form factor, diffraction from magnetically ordered systems, polarised neutrons, inelastic neutron scattering.
Bibliography
<br />Neutron and Synchrotron Radiation for Condensed Matter Studies, Vol I, (Springer-Verlag & Les Editions de Physique) <br />X-ray diffraction, B.E. Warren (1990 - Dover Publ.) <br />The Optical Principles of the Diffraction of X-rays, R.W. James (1982 - Ox Bow Press) <br />Introduction to the Theory of Thermal Neutron Scattering, G.L. Squires, (1978 - Cambridge Univ. Press,) <br />Neutrons and Solid State Physics, L. Dobrzynski, K. Blinowski (1994 – Ellis Horwood) <br />Neutron Scattering Methods of Experimental Physics, Vol. 23A,(1986 - Academic Press, New York)<br />
Teaching methods
<br />Teaching:<br />Theoretical lectures and practical exercises<br />Evaluation:<br />Oral exam
