Materials Physics on an Atomistic Scale 1

This module is concerned with the arrangement and movement of atoms in solids. As these aspects determine to a large part the macroscopic properties of matter, their microscopical understanding is fundamental to, e.g., the tuning of materials for technological applications.

The following topics pertaining to the static arrangement of atoms in solids will be treated in detail:

• symmetries - point groups, space groups, Bravais lattices, positions within the unit cell
• crystal structures - elementary systems and compounds
• point defects
• aspects of order - short-range and long-range order
• statistics and thermodynamics - fundamental models for predicting observables from microscopic parameters
• phases and phase diagrams

For all the above points both a general description of the relevant concepts as well as a motivation by microscopic models will be given, but also a quantitative discussion of their realization in typical systems.

A continuation of the module is PH2219 in the following semester.

Upon successful completion of the module, students are able to:

• list the main crystal structures and analyze them with respect to their symmetries
• understand and predict which structure a given system will assume
• to apply the concepts relevant for describing point defects and to understand their behaviour
• to apply simple statistical and thermodynamical models
• to read phase diagrams and to deduce thermodynamic aspects, as well as to predict the phase diagrams resulting from given microscopic parameters
• to have a feeling for the typical values of the physical quantities relevant for the atomic scale, such as distances and energies, and to understand their consequences

Generally, this module intends to bring the students to a point where they can rationalize the results of theoretical or experimental investigations of pertinent aspects from the point of view of the present state of science, and thus to prepare them for original research.

No preconditions exceeding the admission requirements for the master degree program.

The module consists of a lecture. The learning content is presented by blackboard writing and verbal lecturing, with a detailed discussion of the treated phenomena. Here active contributions from the students (comprehension questions) are invited. To consolidate the content, private study of the provided lecture script is indicated.

Black board or beamer presentation. A lecture script will be provided, outlining the essential contents, but not superceding the detailed discussions given in the lecture.

Fundaments of solid-state physics:

• N.W. Ashcroft & N.D. Mermin: Solid State Physics, De Gruyter Oldenbourg, (2012)
• H. Ibach, H. Lüth: Festkörperphysik, Springer-Verlag, (2009)
• Ch. Kittel: Introduction to Solid State Physics, Wiley, (2018)
• R. Gross & A. Marx: Festkörperphysik, De Gruyter, (2018)
• U. Rössler: Solid State Theory: An Introduction, Springer-Verlag, (2009)

Statistical physics:

• F. Schwabl: Statistische Mechanik, Springer-Verlag, (2006)

classical metal physics:

• G. Gottstein: Physikalische Grundlagen der Metallkunde, Springer-Verlag, (2007)
• P. Haasen: Physikalische Metallkunde, Springer-Verlag, (2013)

classical solid-state chemistry:

• J. Maier: Festkörper - Fehler und Funktion, Springer-Verlag, (2000)

atomic aspects of solids:

• M.T. Dove: Structure and Dynamics: An Atomic View of Materials, Oxford University Press, (2003)

specialized aspects:

• W. Borchardt-Ott & H. Sowa: Kristallographie. Eine Einführung für Naturwissenschaftler, Springer Spektrum, (2013)
• R.J.D. Tilley: Defects in Solids, John Wiley & Sons, (2008)

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 discussions of the relevant concepts as well as typical realizations in solids.

For example an assignment in the exam might be:

• sketching and discussing of fundamental crystal structures, their symmetries, prototypical examples
• temperature dependence of point defect concentrations, explaining the concepts of formation energies and entropies
• discussing short-range order, defining the Warren-Cowley parameters
• explaining phase diagrams

In the exam no learning aids are permitted.