Last Modified 15 May 2001
A Brief Description of How One Calculates Phonon Frequencies For Several Structures:
This is a collection of files describing our work in using the NRL Tight-Binding Method to calculate phonon frequencies as a function of wave-vector using the frozen phonon approximation. The procedures can also be applied to the calculation of phonon frequencies by other methods, such as first-principles total energy calculations or via embedded-atom potentials.
This is not a tutorial on the frozen phonon approximation, though many details of the process will probably show up in the notes. Basically, we calculate the total energy as a function of the amplitude of a ``frozen'' phonon wave in a solid, calculate the curvature of the energy as a function of the wave amplitude, and determine the normal mode frequency from the curvature.
Since we are finding total energies in a periodic solid by a band structure technique our phonon wave vectors must ``fit'' into the solid, i.e., the displaced atoms must still form a supercell. For computational simplicity we'll restrict ourselves to supercells containing no more that sixteen primitive cells. This should still provide a rather good sampling of the Brillouin zone and enable us to compute a phonon density of states (PDOS).
Supercells, phonon polarizations, and the resulting space group operations are derived from the ISOTROPY package developed by Prof. Harold Stokes of BYU. In some cases we have shifted the origin and orientation of the lattice so that it is in agreement with the ``standard'' form used in the International Tables for Crystallography. These tables are duplicated on-line at the Bilbao Crystallographic Server.
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