05-MCM-CR Crystallography

Representative Johannes Birkenstock

Learning Contents:

Fundamentals of Crystallography for all aspects of materials and mineral science
- properties of crystals
- crystals and periodicity
- symmetry of crystals and crystal properties
- basics of crystal chemistry and crystal physics
- crystal structure models
- crystal structure determination
- space-group theory
- group-subgroup relationships
- transformations in crystallography
- calculation of interatomic distances and angles

X-ray diffraction - fundamentals and methods
- diffraction and scattering phenomena
- diffraction and periodicity
- diffraction in direct and reciprocal space
- powder diffraction methods
- methods for powder diffraction data analyses
- calculation of powder diffraction patterns
- Rietveld analysis of powder diffraction patterns - understanding, evaluation and application

Learning Outcomes, Targeted Competencies:

Students will understand the specific properties of crystals and be able to describe them with crystallographic tools. X-ray diffraction methods and up-to-date methods for X-ray diffraction data analysis will be understood in detail and the students will be able to apply the latter. Specifically the following skills will be achieved:
- knowledge in crystallography will be the prerequisitefor the understanding of 3-dimensional crystal structures
- knowledge in symmetry relationships and laws will be the prerequisite for understanding crystal properties
- training in X-ray diffraction methods will enable students to identify minerals and crystalline compounds, and to determine atomic positions in crystals.

Prior Knowledge:


Course Type 1: Lecture, Exercise (L+E) 2.0 SWS ( 28.0 h)

Course Type 2: Lecture, Exercise (L+E) 3.0 SWS ( 42.0 h)

Tutorial(s): -


70.0 h presence time
70.0 h self-study
40.0 h exam workload

180 h total workload

Exam Type:

combination exam


exam elements: 1
SL: 1

100 % written exam
0 % assignment


Borchardt-Ott, W. (2012): Crystallography. An Introduction. Springer.
Hammond, C. (2009): The Basics of Crystallography and Diffraction. Oxford University Press.
Hoffmann, F. (2020): Introduction to Crystallography. Springer.
Giacovazzo, C. (2011): Fundamentals of crystallography. IUCr.
X-ray diffraction:
1. Rietveld´s initial papers
- Rietveld (1967), Acta Cryst. 22, 151-152
- Rietveld (1969), J. Appl. Cryst. 2, 65-71.
2. Some introductory articles to the Rietveld method
- Albinatti, Willis (1982), J. Appl. Cryst., 15, 361-374.
- Mc Cusker et al. (1999), J. Appl. Cryst., 32, 36-50.
3. Comprehensive Rietveld book
- Young (ed.) (1995), The Rietveld method, IUCr Monographs on Crystallography 5, 298 S.