PHON: A program to calculate phonons using the small displacement method Original Research Article

The program phon calculates force constant matrices and phonon frequencies in crystals. From the frequencies it also calculates various thermodynamic quantities, like the Helmholtz free energy, the entropy, the specific heat and the internal energy of the harmonic crystal. The procedure is based on the small displacement method, and can be used in combination with any program capable to calculate forces on the atoms of the crystal. In order to examine the usability of the method, I present here two examples: metallic Al and insulating MgO. The phonons of these two materials are calculated using density functional theory. The small displacement method results are compared with those obtained using the linear response method. In the case of Al the method provides accurate phonon frequencies everywhere in the Brillouin Zone (BZ). In the case of MgO the longitudinal branch of the optical phonons near the centre of the BZ is incorrectly described as degenerate with the two transverse branches, because the non-analytical part of the dynamical matrix is ignored here; however, thermodynamic properties like the Helmholtz free are essentially unaffected.