Learning outcomes of the course unit
to introduce the student to the theoretical and experimental knowledge of the main diffraction techniques and to their crystallographic applicationsto the determination(solution and refinement) ofthe crystal structure.
basic knowledge of crystal symmetry
Course contents summary
The Dirac deltafunction ; the lattice function; the Fourier transform and its application; the Fourier transform of a lattice function; convolutions; convolutions involving lattice functions; Fourier transformand convolutions
X-ray scattering; Thomsonand Compton scattering ; interference of scattered waves; diffracton by a crystal;the atomic scattering factor; the temperature factor; the structure factor; symmetry in the reciprocal lattice; Friedel law; phase restrictions; systematic absences; diffraction intensities; the Lorentz-polarization factor; the transmission factor; dynamical aspectsi: primaryand secondary extinctions, anomalous scattering and dispersion, Bijvoet pairs
Experimental aspects of X-ray diffraction
X-ray generation; conventional sources; sinchrotron ligth; single crystal diffractometer; powder diffraction; powder diffractometer
Structure solution and refinement
The Fourier synthesis and the phase problem in crystallography: sultution by trial and error; the Patterson function and its application in the structure solution; direct methods in crystallography; Wilson's stathisticsand normalized structure factos; the Sayre equation, structure invariant and semi-invariants; probabilistic extimation of the invariant triplets; the tangent formula della tangente; phasing procedure; least squares refinement of the structureaffinamento strutturale con tecniche di minimi quadrati; Rietveld refinement of powder data.
Theneutron-matter interaction; elastic and inelastic scattering ; the neutron scattering factor; magnetic scattering ; neutron sources; neutron vs. X-ray diffraction.
Kinematic theory of electron diffraction; the electronscattering factor; dynamical diffraction; the transmission electron microscope; HREM; electron crystallography.
Practice: instrumentation, data collaction, structure solution and refinement
Fundamentals of crystallography, C. Giacovazzo, H.L. Monaco, D. Viterbo, F. Scordari, G. Gilli, G. Zanotti, M. Catti, Eited by C. Giacovazzo, International Union of Cristallography, Oxford Science Publication
ISBN 0 19 855578 4
class and exercise
Assessment methods and criteria