KNOWLEDGE AND UNDERSTANDING:
Understand the basic elements of crystalline structures and the characteristics of the solid state.
Understand the main properties of X-ray sources, and acquire the diffraction techniques for the characterization of chemical structures.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Acquire the ability to relate the three-dimensional structure and symmetry to the chemical and physical properties of molecules and crystalline materials.
Acquire the ability to collect and analyze diffraction spectra from powder samples and single crystals, and to use crystallographic databases.
Analyze diffraction data to obtain information on crystalline structures.

MAKING JUDGMENTS:
Acquire concepts and tools necessary for the description of the structural characteristics of crystalline solids.

COMMUNICATION SKILLS:
Learn how to produce images of crystalline structures using the software introduced during lessons and laboratory exercises, to highlight the main characteristics of three-dimensional structures.
Learn how to identify and explain the important relationships between structure and properties.

LEARNING SKILLS:
Read and understand articles on topics in structural chemistry and discuss critical issues.
Know and consult the principal databases related to the field of structural chemistry.

General Chemistry

Crystalline State: Differences between amorphous solids and crystalline structures (metals, ionic, covalent, and molecular crystals).
Symmetry in Molecules and Crystals: Study of symmetry elements/operations and notation systems (Schoenflies and Hermann-Mauguin). Analysis of crystallographic point groups, Laue groups, enantiomorphic classes, and polar classes and their impact on physical properties (Neuman principle) such as crystal morphology, piezoelectric and pyroelectric phenomena, and rotation of polarized light. Symmetry and cell parameter constraints, Bravais lattices, and unit cells: reduced, primitive, centered, and conventional. Space groups and the International Tables of Crystallography. Symmetry groups in one and two-dimensional spaces, line groups, floor groups, multi-dimensional space, and colored symmetry groups.
Inorganic Solids Structure: Representation of structural models. Geometric and topological aspects of sphere packing (2D and 3D), coordination interstices, and the polytype phenomenon. Organization and sharing of coordination polyhedra, Pauling's rules, and the taxonomy of polyhedra and period networks. Tessellation of 2D and 3D spaces.
Electromagnetic Waves and X-ray Sources: Introduction to X-ray sources (sealed tubes, rotating anodes, synchrotron radiation). Overview of synchrotron light properties (intensity, divergence, wavelength selection), insertion devices (wiggler), and detectors (IP, CCD, Pilatus).
Diffraction: Detailed analysis of diffraction theory, wave representation in the Argand diagram, Bragg's law, real and reciprocal lattice, and Ewald's sphere. Study of diffraction symmetry, Friedel's law, and systematic absences.
Data Analysis and Structural Determination: Data collection methods (Laue Method, Rotating Crystal Method). Reduction of diffraction data and solving the phase problem using the Patterson function, heavy atom method, and direct methods. Electron density maps, structural refinement, and the application of the least squares method, constraints, and restraints.
Practical Experience: Hands-on training in diffraction experiments at Elettra's XRD1 line, including crystal mounting, data collection, reduction of diffraction data, determination of cell and space group parameters, phase problem resolution, electron density map construction, and structure refinement.

Learning Outcomes
Graduates of this program will have:
• A comprehensive understanding of the structural characteristics of crystalline solids.
• Proficiency in the application of symmetry operations and notation systems in crystallography.
• Expertise in crystallographic data analysis and structural determination.
• Practical experience in modern diffraction techniques and the use of advanced crystallographic equipment, including the use of synchrotron radiation.

Giacovazzo et al., Fundamentals of Crystallography, International Union of Crystallography, Oxford University Press (2006).
Hypertext files (HTML) with interactive molecular models and lecture slides are available on the Moodle platform.

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. 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.

Lectures with PowerPoint slides and interactive sessions using the MOODLE platform to visualize crystal structures. Laboratory experiences in which each student familiarizes themselves with sample preparation for diffraction data collection from single crystals and with data analysis.

Links to free resources related to subjects covered in the lectures are available on the Moodle platform. Students are encouraged to consult volumes of the International Tables of Crystallography to deepen their knowledge of space groups and symmetry elements present in crystal structures.

The exam consists of an oral test with at least three questions concerning topics covered in the course. During the test, the student must demonstrate that they have acquired the basic concepts of structural chemistry, as well as the ability to link the various topics illustrated during the course. The student must also demonstrate that they can clearly present the acquired knowledge to show complete comprehension.

Lectures will not discuss subjects related to the Objectives of the 2030 agenda for sustainable development.