Learning outcomes of the course unit
the goal is to give to the students a good knowledge of the diffraction techniques and the possibility to approach the structure solution and refinement on the basis of diffraction data
Course contents summary
Dirac delta function, lattice function, Fourier transform (FT) and its applications, FT of a lattice function, function convolution, periodic function: convolution with a lattice function, FT of a convolution
X-ray scattering, scattering Thomson and Compton, interference of scattered waves and diffraction, diffraction from a infinite crystal, diffraction from a finite crystal, atomic scattering factor, temperature factor, structure factore, symmetry in the reciprocal space, Friedel’s law, phase restrictions, systematic absences, diffraction intensity, Lorentz’s factor, polarization, transmission factor, dynamical aspects: primary and secondary extinction, anamalous scattering, Bijvoet’s pairs.
Experimental aspects of X-ray diffraction
Generation of X-rays, conventional sources, sincrotron radiation, single crystal diffractometer, powder diffraction, powder diffractometer.
Methods for structure solution and refinement
Fourier synthesis and “the phase problem” in crystallography, trial and error methods, Patterson function (PF), symmetry of the PF, PF application in structure solution, direct methods in crystallography, Wilson’s statistics and normalized structure factors, Sayre’s equation, structure invariants and semi-invariants, probabilistic estimation of the invariant triplets, the tangent formula, phasing the reflections in direct methods, least-squares refinement of the structure, Rietveld refinement of powder data.
neutron-matter interaction, elastic and inelastic scattering, nuclear scattering factor, magnetic scattering, neutron sources, diffraction geometry in pulsed sources, use of neutron diffraction and comparison with X-ray diffraction
Kinematic theory of electron diffraction, electron scattering factor, outlines of dynamic diffraction theory, the transmission electron microscope (TEM), direct access to real and reciprocal space, high resolution TEM, comparison of electron, neutro and X-ray diffraction
C. Giacovazzo et al., Fundamentals of crystallography, IUCr, Oxford Science Publications,1992