Materials Physics on an Atomistic Scale 2

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.

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.

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

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