05-MCM-1-P3 Crystallography

Representative: Reinhard X. Fischer


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

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 Outcome

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 geometrical crystallography will be the prerequisite for 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.


Previous knowledge in crystallography and X-ray diffraction is not required, yet a general understanding of fundamental physical and chemical concepts. The classes will start from most fundamental ideas and rapidly proceed to up-to-date topics.


180 hours / 6 CP
Introduction to crystallography
• time for lectures and excercises (2 SWS x 14 weeks) 28 h
• time for preparation and post processing 38 h
• time for exams and preparation 24 h

X-ray diffraction & Rietveld analyis
• time for lectures and excercises (3 SWS x 14 weeks) 42 h
• time for preparation and post processing 30 h
• time for exams and preparation 18 h


module exam (combined marks):

written exam80 %
written report20 %


Putnis - Introduction to Mineral Sciences
Kleber, Bautsch, Bohm - Einführung in die Kristallographie
Giacovazzo et al. - Fundamentals of Crystallography

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.