This course is part of the programme
Doctoral study programme Physics

Objectives and competences

The primary goal of this course is to give students the theoretical and practical knowledge in crystallography and X-ray diffraction methods needed for the characterization of the structure of different crystalline materials.




-Symmetry in crystals (crystal lattice, unit cell, symmetry elements and operations, point and space groups, crystal structure)
-X-ray diffraction in crystals (crystal planes, Muller indices, interference of scattered waves, Bragg condition, reciprocal lattice, diffraction characteristics of the polycrystalline materials)
-Determination and optimization of the crystal structure (structure factor, phase problem, Fourier transform (FT), optimization of the structural model, database)
-X-ray powder diffraction (powder diffractometer, powder pattern, qualitative and quantitative analysis, Rietveld analysis)
-Other diffraction methods (neutron diffraction, electron diffraction. synchrotron radiation and diffraction)
-Structural characteristics of crystals (ionic, covalent and metallic crystals, close packing, errors in crystals)

Intended learning outcomes

Knowledge and understanding:

Students learn the principles of symmetry in crystals, diffraction and diffraction methods, with emphasis on X-ray powder diffraction. They learn how to use X-ray diffraction methods, theoretically the preparation of the sample and performing the measurement, and practically about the analysis and interpretation of the results. In practical projects students gain knowledge how to use the specialized software for diffraction analysis. With practical work on examples from research practice they learn the evaluation and interpretation of XRD data.


  • V.K. Pecharsky in P.Y. Zavalij: Fundamentals of Powder Diffraction and Structural Characterization of Materials, Springer, New York, 2005. E-version
  • W. Clegg, Crystal Structure Determination, Oxford University Press, Oxford, 1998.
  • C. Hammond, The Basics of Crystallography and Diffraction, Third Edition, Oxford University Press, Oxford, 2009.Catalogue E-version
  • C. Giacovazzo, H. L. Monaco, G. Artioli, D. Viterbo, M. Milanesio, G. Ferraris, G. Gilli, P. Gilli, G. Zanotti and M. Catti, Fundamentals of Crystallography, Third Edition, Oxford University Press, Oxford, 2011. Catalogue E-version
  • N. Zabukovec Logar, tutorials in Slovene language on the web:
  • X'Pert HighScore Plus tutorial - PANalytical on the web:
  • TOPAS ACADEMIC tutorial on the web E-version


Written exam / Seminar presentation of selected topics for professors and students /Short individual project prepared in written form (qualitative and quantitative analysis of the X-ray powder pattern of unknown sample and crystal structure determination from single-crystal X-ray data). (40/30/30)

Lecturer's references

Full professor of Chemistry at the University of Nova Gorica.