Crystal Chemistry and Crystallography

A.Y. 2025/2026
6
Max ECTS
56
Overall hours
SSD
GEO/06
Language
English
Learning objectives
Knowledge and understanding, aimed at the description of crystalline matter, providing the skills to identify, describe and do research on the crystalline state of geological materials, with particular attention to the rules of distribution of cations and anions in crystallographic sites in the main rock-forming minerals.

Applied knowledge and understanding: the course provides the ability to recognize and appropriately describe periodicity and symmetry and to identify it through the support of morphological and basic diffraction studies, providing support to the Earth Science disciplines, which require knowledge of the properties of the crystalline state of geomaterials and the crystallographic control of the distribution of chemical elements.
Expected learning outcomes
Making autonomous judgements: The course delivers ability to face crystallographic problems through analysis and management of symmetry rules and how to recognize them through experimental observations. The student will be proficient on understanding and critically analyzing the experimental

results obtained through experiments aimed at recognize crystalline geomaterial from its symmetry and its crystal chemical formula, 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 crystallographic 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).
Single course

This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.

Course syllabus and organization

teaching not active in the academic year 2025-26

Lesson period
First semester
Course syllabus
A. Symmetry of crystals

Symmetry operations. Lattices. Point Groups and Symmetry Classes. Symmetry systems. Bravais Lattices. Space Groups (2D, 3D). International Tables. Reciprocal lattice.

B. X-ray scattering

Diffraction concept. Background. Bragg equation. Ewald's sphere. Symmetry in reciprocal space. Structure factor (scattering factor, temperature factor). Determination of the spatial group (systematic absences). Structural refinement.

C. Experimental Techniques

Brief illustration of diffraction by single crystal (X-rays, electrons and neutrons).

D. Crystalchemistry

Structure and morphology. Ionic raddi. Coordination polyhedra. Bond strength and bond-length. Bond valence and hydrogen bond. Structure types. Crystal-chemical formulas of rock-forming minerals.
Prerequisites for admission
Basic chemistry concept (chemical formulas, ionic radii, etc.). It is advisable to have appropriate training in matrix and vector calculus. Basic knowledge of complex numbers.
Teaching methods
Lectures and exercises (calculation exercises with the use of crystallographic programs) and visit to the X-ray diffraction and TEM laboratories.

Powerpoint slides downloadable in the myARIEL portal of the course
Teaching Resources
Giacovazzo C. et al. (2011) Fundamentals of crystallography. 3rd Edition. IUCr, Oxford Science Publications, Oxford. (chapters 1, 3 and 7)

Borchardt-Ott,W. (1995) Crystallography. Springer (ISBN 978-3-642-16451-4) (or 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.
GEO/06 - MINERALOGY - University credits: 6
Practicals: 24 hours
Lessons: 32 hours