Crystallography and Laboratory
A.Y. 2024/2025
Learning objectives
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.
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).
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
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
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.
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 physics of wave phenomena. Basic knowledge of complex numbers, Fourier transform and convolutions of mathematical functions.
Teaching methods
Lectures and exercises (calculation exercises or with the use of crystallographic and structural refinement programs) and visit to the X-ray diffraction and TEM laboratories.
Powerpoint slides downloadable in the myARIEL portal of the course
https://myariel.unimi.it/course/view.php?id=4194
Attendance is strongly recommended
Powerpoint slides downloadable in the myARIEL portal of the course
https://myariel.unimi.it/course/view.php?id=4194
Attendance is strongly recommended
Teaching Resources
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)
Borchardt-Ott,W. (1995) Crystallography. Springer (ISBN 978-3-642-16451-4) (o r the 2nd edition 2011)
Borchardt-Ott,W. (1995) Crystallography. Springer (ISBN 978-3-642-16451-4) (o r the 2nd edition 2011)
Assessment methods and Criteria
Examinations to verify knowledge consists 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 the solution of type exercises (student must bring a scientific calculator to the test), with contents and difficulties similar to those faced in the exercises; the oral discussion, starting from the contents of the written test, focuses on all the topics covered in the course.
The results (in thirty) of the written test are communicated on the same day of the test and it is possible to view the corrections of the test. The result is not averaged with the evaluation of the oral exam. The vote (recorded in thirty) is that obtained in the oral exam.
The results (in thirty) of the written test are communicated on the same day of the test and it is possible to view the corrections of the test. The result is not averaged with the evaluation of the oral exam. The vote (recorded in thirty) is that obtained in the oral exam.
GEO/06 - MINERALOGY - University credits: 9
Practicals: 36 hours
Lessons: 48 hours
Lessons: 48 hours
Professors:
Camara Artigas Fernando, Voltolini Marco
Educational website(s)
Professor(s)
Reception:
9:00 - 10:00 AM
23 Botticelli st., first floor