brucefan1983 / MATLADY

A MATlab toolkit for LAttice DYnamics calculations based on empirical potentials

MATLADY

A MATlab toolkit for LAttice DYnamics calculations based on empirical potentials

Features

• This is a pedagogical code for teaching some basics of lattice dynamics.
  • Force constants are calculated by using finite difference from empirical potentials.
  • The dynamical matrices at a given set of k-points are constructed from the force constants.
  • From the eigenvalues and eigenvectors of the dynamics matrices, one can calculate many physical quantities.
  • In the very first version, the code can only calculate the phonon dispersion for systems described by the Tersoff potential.
  • I plan to enrich the features little by little.

File organizations

• Some scripts for testing:

  • test_Si.m: calculate the phonon dispersion of bulk silicon using the Tersoff-1989 potential;
  • test_graphene.m: calculate the phonon dispersion of 2D graphene using the Tersoff-2010 potential (with some modifications).

• The testing scripts call

  • the function "find_r" to build up the real space super cell;
  • the function "find_k" to build up the reciprocal space;
  • the driver function "matlady" to do the major calculations;
  • the "plot_dispersion" function to plot the phonon dispersion.

• The "matlady" function calls

  • the "find_neighbor" function to construct one neighbor list for force calculations and one for building up the dynamical matrix;
  • the "find_phi_all" function to calculate all the force constants that are needed;
    • the "find_phi_all" function calls the "find_phi_one" function
    • the "find_phi_one" function calls the "find_E" function
    • the "find_E" function calls the "find_E_tersoff" function
  • the "find_nu" function to construct the dynamical matrix and to calculate the phonon spectrum.

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_Si.m" script to get the phonon dispersion for bulk silicon. This takes less than one second.

• Run the "test_graphene.m" script to get the phonon dispersion for 2D graphene. This takes less than one second.

Contact

• Zheyong Fan: brucenju(at)gmail.com