dynamical-matrix-matlab

A 200-line MATLAB code for calculating the dynamical matrix using the Tersoff potential

Features

• This is a pedagogical code for teaching some basics of harmonic lattice dynamics.
  • Forces and force constants are calculated by using finite difference from the Tersoff empirical potential.
  • The dynamical matrix at the Gamma point is constructed from the force constants and the phonon density of states (DOS) is calculated from the eigenvalues of the dynamical matrix.
  • Nowadays no one would calculate the phonon DOS in this way, but I believe this code has pedagogical value. It can also serve as a starting point for building a phonon NEGF (nonequilibrium Green's function) code. I will publish such a code later.

File organizations

• There are two scripts:

  • test_F.m
  • test_D.m

• The "test_F.m" script calls the "find_r", "find_neighbor", and "find_F" functions.

• The "test_D.m" script calls the "find_r", "find_neighbor", and "find_D" functions.

• Both the "find_F" and "find_D" functions call the "find_E" function.

Unit system

• I use the following basic units:

  • Length: Angstrom
  • Mass: amu (atomic mass unit)
  • Energy: eV

• Other units are then derived.

Running the examples

• Run the "test_F.m" script to test whether the force on each atom is zero. This takes about one second.

• Run the "test_D" script to get a phonon DOS plot. This takes about one minute.

Contact

• Zheyong Fan: brucenju(at)gmail.com