Student projects

• Update the information about this course on the HTU server
• Calculate the molecular orbitals of ethylene, butadiene, and benzene.
• Upload a video to YouTube (<10 minutes) that explains some topic in the course outline.
• Upload a video to YouTube that explains how to use a piece of laboratory equipment in the physics building related to this course.
  • x-ray diffractometer
  • atomic force microscope
  • Low energy electron diffraction
  • etc.
• Upload a video to YouTube that explains how to solve an old exam question.
• Replace the flash audio player with a html5 audio player on the website.
• Implement the triclinic crystal system in the Brillouin zone applet.
• Make a web page that specifies the symmetry points and lines of a Brillouin zone like the one for fcc.
  • Triclinic
  • Simple Monoclinic
  • Base centered Monoclinic
  • Simple Orthorhombic
  • Base centered Orthorhombic
  • Face centered Orthorhombic
  • Body centered Orthorhombic
  • Simple Tetragonal
  • Body centered Tetragonal
  • Trigonal
• Write a program that calculates the structure factors for a 2D crystal with two atoms per unit cell. Assume the electron densities can be approximated by Gaussians.
• Construct the empty lattice approximation for photons for one of the Bravais lattices not already calculated. See: Empty lattice approximation for photons.
• Write a program that will plot the phonon dispersion curves in any direction in k-space.
• Add a column to the table of phonon properties.
• Check if the exam questions could really be solved if you only know what is listed in the "For the exam" sections. For the molecules part of the course, the "For the exam" section can be found here.
• Digitize the phonon density of states for some material (make a table of data from a plot) so we can make plots of the phonon density of states like we have for the electron density of states. This will allow us to make buttons to calculate the phonon properties of some materials like the buttons at the bottom of this page.
• Add rows for the Gibbs energy $G=U-TS+pV$, the enthalpy $H=U+pV$ and the specific heat at constant volume $C_p=\frac{dH}{dT}$ to the table of thermodynamic properties for free electrons.
• In the plane wave method, the Schrödinger equation is rewritten as a set of algebraic equations. These algebraic equations (the central equations) can be expressed as a matrix. For electrons moving through a potential given by the molecular orbital Hamiltonian, the diagonal elements of this matrix are $M_{ii}=\frac{\hbar^2}{2m}\left( \vec{k}+\vec{G}_i \right)^2$and the off-diagonal elements are $M_{ij}=-Ze^2/\left(V\epsilon_0 \left( \vec{G}_i+\vec{G}_j \right)^2\right)$. A student already wrote Matlab scripts fcc_plane_wave.m, fcc_plane_wave_script.m to solve for the eigen values of this matrix. Write a file to that describes what this script does and plot the output for some fcc crystals.
• Add a column to the table of band structures calculated by tight binding http://lamp.tu-graz.ac.at/~hadley/ss1/bands/tbtable/tbtable.html.
• Compare the electron dispersion relation for a one-dimensional chain of finite potential wells in the tight binding model with the exact results from the Kronig-Penney model.
• Calculate the electron density of states in the tight binding model for one of the cases where the dispersion relation has been calculated. See: http://lamp.tu-graz.ac.at/~hadley/ss1/bands/tbtable/tbtable.html. You should provide a page that can be used to plot and tabulate the density of states like this one: http://lamp.tu-graz.ac.at/~hadley/ss1/bands/tbtable/simple_cubic_dos.html.

The video below is a summary of a presentation given by Roland Resel at the e-learning session of the meeting of the International Union of Crystallography in Madrid, August 2011. It explains the idea of using student projects to generate e-learning material.