Introduction to Crystallography

This module gives an introduction to the description and properties of crystalline solids. First, the geometrical and mathematical basics of the description of crystals are introduced, for example the representation and application of symmetry properties and space groups. Then, based on the atomic structure of crystals, their crystal chemistry and structure are discussed. In addition, typical deviations from the ideal crystal structure are discussed, e.g. defects and disorder but also structural changes at phase transitions. Experimental methods for determining the real structure of crystals like X-ray and neutron diffraction are an essential tool in solid state physics and chemistry. Therefore, they will be discussed in detail in this module. Both the advantages and limits of the different methods for different applications are considered, as well as the resulting requirements for the samples. Finally, the relationships between macroscopic physical properties and crystalline structure and symmetry properties respectively via tensor calculations will be shown.

After successful completion of the module the students are able to:

1. read and explain the basic structural properties of different crystal structures based on their space groups;
2. name possible methods for the growth of crystalline solids and their impact on the real structures;
3. understand and explain the physical aspects of certain examination methods, in particular the physical interaction between the samples and the probe;
4. reproduce and explain the technical implementation of various experimental methods;
5. select and outline a suitable method of analysis for structural determination depending on the crystallographic topic to deal with;
6. bring the required properties of a sample into line with the chosen method;
7. explain the fundamental coupling between given structure symmetries and certain physical properties.

No preconditions in addition to the requirements for the Master’s program in Physics.

Learning and Teaching Methods

The module consists of a lecture which includes a projector presentation, in which both PowerPoint slides for graphic illustration and text writing with digital ink are used. This mixture does not only allow a quicker overview of facts and experiments but also an adaptation of the lecture pace to the speed of the students. Selected smaller "homework" with a direct in-depth reference to the lecture material will be discussed during the following lecture date. The time frame of the lecture allows a lot of interaction and the answering of questions during the presentations. The resulting scientific discussions actively involve the students.

The interplay of slide presentation for overview and details as well as text writing and discussion time to found basic knowledge, as well as an optional laboratory tour, allows the students to acquire the specific skills formulated above in relation to the crystallography and crystallographic methods for structure determination.

Blackboard and powerpoint presentation, complementary literature, internet

1. Borchardt-Ott, W: Kristallographie: Eine Einführung für Studierende der Naturwissenschaften (2018)
2. Kleber, W. et al.: Einführung in die Kristallographie (2010)
3. Massa, W.: Kristallstrukturbestimmng (2009)

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• name different space groups and their geometric properties.
• discuss the physical mechanisms underlying the concept of diffractometry.
• explain the main differences between powder and single-crystal samples when choosing suitable test methods.
• outline the concrete technical implementation of a method for structure determination by means of diffraction, as discussed in the lecture.