Knowledge and understanding, built also on the basis-level three-year degree, to achieve the ability to describe crystalline matter and undertake its study by diffraction techniques, enabling to identify, describe and perform research on the crystalline state of geological materials. Applying knowledge and understanding The course provides the ability to properly recognize and describe periodicity and symmetry and to identify it through diffraction analysis, thus providing support to Earth Sciences disciplines, that require knowledge of the properties of the crystalline nature of geomaterials.
Expected learning outcomes
Making judgements The course delivers ability to face crystallographic problems through analysis and management of the complexity of processes underlying radiation-matter interaction. The student will be proficient on understanding and critically analysing the experimental results obtained through diffraction experiments, as well as the assessment of accuracy/reliability of experimental data. Communication skills The course will deliver the knowledge of international terminology, including symbolism and English jargon, enabling universal communication of problems and phenomena related to the symmetry of materials and its study by diffraction techniques. The student will be qualified to propagate the crystallographic knowledge outreach in a wide range of contexts. Learning skills The student will be able to outspread the acquired knowledge allowing him to cope independently in crystallographic research, both in geological contexts and with synthetic inorganic materials (mineralogical proxies).
Lesson period: Second semester
(In case of multiple editions, please check the period, as it may vary)
A. Symmetry of crystals Symmetry operations. Lattices. Point Groups and Symmetry Classes. Symmetry systems. Bravais Lattices. Space Groups (2D, 3D). Group theory. International Tables. Matrix representation of symmetry operators. Reciprocal lattice. B. X-ray scattering Diffraction concept. Background. Radiation-matter interaction: coherent and incoherent scattering; absorption and fluorescence. Scattering, scattering factor. Temperature factor. Structure factor. Bragg equation. Ewald's sphere. Symmetry in reciprocal space. Determination of the spatial group (systematic absences). Dynamic theory of diffraction. Fourier Synthesis and methods to retrieve the phase. Completion of the structure. Structural refinement. C. Experimental Techniques X-ray sources: conventional, synchrotron facilities. Filters, monochromators, collimators and detectors. Single Crystal Diffraction. Powder diffraction. Electron diffraction. Neutron diffraction.
Prerequisites for admission
It is advisable to have appropriate training in matrix and vector calculus and wave physics.
Frontal lessons and exercises (calculation exercises or with the use of crystallographic calculation programs and structural refinement) and visit to the diffraction laboratories.
Giacovazzo C. et al. (2011) Fundamentals of crystallography. 3rd Edition. IUCr, Oxford Science Publications, Oxford. (chapters 1, 3 and 5 + some aspects covered in 6) Powerpoint slides downloadable in the ARIEL portal of the course https://fcamaracl.ariel.ctu.unimi.it/v5/home/Default.aspx
Assessement methods and criteria
The verification takes place through an exam consisting of a written test and an oral test (discussion), both mandatory: The written test aims to ascertain the basic knowledge acquired during the theoretical lessons and laboratory exercises through (a) the solution of type exercises, with contents and difficulties similar to those faced in the exercises, (b) a multiple choice test. The oral discussion, starting from the contents of the written test, focuses on all the topics covered in the course.