Computation of phonon dispersion relations using numerical method

A method to measure the phonon dispersion of a crystal based on molecular dynamics simulation is proposed and implemented as an extension to an open source classical molecular dynamics simulation code LAMMPS. In the proposed method, the dynamical matrix is constructed by observing the displacements of atoms during molecular dynamics simulation, making use of the fluctuation–dissipation theory. Atoms in solids make ceaseless vibrations about their equilibrium positions, and a collective vibration forms a wave of allowed wavelength and amplitude. The quantum of such lattice vibration is called the phonon, and the so-called lattice dynamics is the field of study to find the normal modes of these vibrations. In other words, lattice dynamics examines the relationship between the frequencies of phonons and the wave vectors, i.e., the phonon dispersion. The evaluation of the phonon dispersion requires the construction of the dynamical matrix. In atomic scale modelling, the dynamical matrices are usually constructed by deriving the derivatives of the force field employed, which cannot account for the effect of temperature on phonons, with an exception of the tedious quasi-harmonic procedure.

کلیدواژه ها:

first brillouin zone ، phonon spectrum ، numerical analysis ، dynamical matrix