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Materials Physics on an Atomistic Scale 2

Module PH2219

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2017

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2022SS 2021SS 2020SS 2019SS 2018SS 2017SS 2015

Basic Information

PH2219 is a semester module in German or English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for condensed matter physics
  • Specific catalogue of special courses for Applied and Engineering Physics
  • Complementary catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for Biophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 40 h 5 CP

Responsible coordinator of the module PH2219 in the version of SS 2017 was Michael Leitner.

Content, Learning Outcome and Preconditions


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.

Going beyond the coverage of an introductory Solid State Physics course and continuing the previous semester's course Materials Physics on an Atomistic Scale 1, here aspects of the oscillatory and diffusive dynamics in solids will be treated in detail:

  • classical equations of motion -- harmonic approximation, consequence of translational symmetry, normal modes
  • dispersions -- the Brillouin zone and special points, Born-von Karman model, consequences of point symmetries
  • phonon densities of states -- van Hove singularities, vibrational thermodynamics, Einstein and Debye models
  • effects beyond this setting -- anharmonicities, disorder
  • fundamental concepts of diffusion -- random walk theory, connection to the diffusion equation, its solutions
  • solid-state diffusion -- historical overview, transition state theory, Arrhenius behaviour, correlation functions, encounter model
  • diffusion mechanisms -- in elementary systems and compounds

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.

Learning Outcome

Upon successful completion of the module, students are able to

  • solve the equations of motion of atoms in a general crystal according to classical mechanics
  • find their way about the Brillouin zones of the important Bravais lattices
  • reproduce typical dispersion relations as well as recognize deviations from these typical cases
  • use the Born-von Karman approach to model measured phonon frequencies
  • understand the effect of symmetries on the normal modes
  • understand how the dispersions lead to features of the density of states (i.e., van Hove singularities)
  • employ model as well as actual phonon densities of states to compute thermodynamic quantities pertaining to vibrations
  • understand how deviations from the ideal case lead to a broadening of the phonon dispersion
  • derive the diffusion equation from the microscopic random walk
  • apply the concepts of jump diffusion
  • understand the characteristics of the possible diffusion mechanisms and thus, e.g., predict the effect of variations in compostion on the diffusivity

Generally, this modul 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. Having participated in the course PH2218: Materials Physics on an Atomistic Scale 1 is beneficial, but no hard requirement.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Materials Physics on an Atomistic Scale 2 Leitner, M. Wed, 10:00–12:00, PH-Cont. C.3201
and singular or moved dates

Learning and Teaching Methods

blackboard writing and verbal lecturing with detailed discussion of the treated phenomena as well as active contributions from students (comprehension questions), private study of the provided lecture script


A lecture script will be provided, outlining the essential contents, but not superseding the detailed discussions given in the lecture.


Fundaments of solid-state physics:

  • N. W. Ashcroft, N. D. Mermin: Solid State Physics
  • H. Ibach, H. Lüth: Festkörperphysik
  • Ch. Kittel: Introduction to Solid State Physics
  • R. Gross, A. Marx: Festkörperphysik
  • U. Rössler: Solid State Theory: An Introduction

Statistical physics:

  • F. Schwabl: Statistische Mechanik

classical metal physics:

  • G. Gottstein: Physikalische Grundlagen der Metallkunde
  • P. Haasen: Physikalische Metallkunde

classical solid-state chemistry:

  • J. Maier: Festkörper - Fehler und Funktion

atomic aspects of solids:

  • M. T. Dove: Structure and Dynamics: An Atomic View of Materials

specialized aspects:

  • W. Borchardt-Ott: Crystallography. An Introduction
  • B. Fultz: Phase Transitions in Materials
  • D. A. Porter, K. E. Easterling: Transformations in Metals and Alloys
  • R. J. D. Tilley: Defects in Solids
  • A. M. Kosevich: The Crystal Lattice. Phonons, Solitons, Dislocations, Superlattices

Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

Exam Repetition

The exam may be repeated at the end of the semester.

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