Educational Program

Structural Chemistry. Characteristics of amorphous solids and the crystalline state (metals, ionic, covalent, and molecular structures). 
Elements and operations of symmetry (direct and indirect congruence). Elements and operations of point symmetry. Schoenflies and Hermann-Mauguin notations. Matrix representation of symmetry operations. Diagrams in the Cartesian plane and symbols of symmetry elements used in the International Tables of Crystallography. Proper and improper rotation axes (roto-inversion and roto-reflection). Notation of the point symmetry elements. 
Crystallographic point groups, crystalline systems, Laue groups, enantiomorphic classes, and polar classes. Symmetry classes and physical properties. The Neuman principle. Crystal morphology. The piezoelectric and the pyroelectric phenomena. Rotation of polarized light and symmetry of diffraction.
Symmetry with translation in crystals (screw axes and glide planes). Constraints imposed on cell parameters by symmetry elements. Crystal lattice and unit cells: reduced, primitive, centered, and conventional cells. Bravais lattices. Niggli matrix. Frequency of Bravais cells. The space groups. International Tables of Crystallography. 
Symmetry groups in one and two-dimensional spaces. Line groups and floor groups. Multi-dimensional space and colored symmetry groups. Unconventional primitive cells.
Structure of inorganic solids. Representation of structural models: sticks; ball and sticks, thermal ellipsoids; coordination polyhedra; space fill.
Geometric and topological aspects: various types of sphere packing (2D and 3D packing), coordination interstices, and the polytype phenomenon.
Organization of polyhedra, sharing of faces and sides of coordination polyhedra, and Pauling's rules. 
Taxonomy of polyhedra and period networks. 
Tessellation of 2D and 3D space. Reference structures.
Electromagnetic waves. Hard and soft X-rays. X-ray sources: sealed X-ray tubes; rotating anode; synchrotron. Synchrotron radiation. Advantages of synchrotron light: intensity (brightness); divergence; white light; wavelength selection. Scheme of a synchrotron. Emission spectrum. Insertion Devices: Wiggler. Front-end. Monochromators and mirrors. Detectors: IP, CCD and Pilatus. Diffractometers.
Diffraction theory. Waves in the Argand diagram. Condition of reflection. Bragg's law. Real lattice and reciprocal lattice. Ewald's sphere. Origin and phase in the Argand diagram. Systematic absences. Diffraction symmetry. Friedel's law. 
Mounting of crystals. Data collection methods: Laue Method and Rotating Crystal Method. Optimization of experimental variables.
Data reduction. The main methods of solving the phase problem. The Patterson function and the heavy atom method. Direct methods. The triplet relations. The anomalous dispersion. From Friedel's pairs to Bijvoet's pairs. Types of electron density maps. Limit of resolution and quality of electron density maps. Construction of the model and interpretation of the maps. Structural refinement. Least squares method. Constraints and restraints.
Practical experience of diffraction experiments at Elettra's  XRD1 line. Crystal mounting and data collection. Reduction of diffraction determination of cell and space group parameters, resolution of the phase problem with the heavy atom method, electron density maps, and structure refinement.