Rigorous Statistical Thermodynamical Model For Lattice Dynamics In Alloys

We propose another approach to overcome the difficulties of previous ab initio methods used to study lattice dynamics in disordered systems, such as alloys. Group III nitrides and arsenides are used as prototypical systems to validate the developed methodology. The phonon behaviors of ternary alloys, for specific concentrations, are calculated with a methodology based on the ab initio calculations of dynamics of the respective nitrides' and arsenides' bulks. The generalized phonons' behavior of long wavelengths for ternary alloys were simulated employing the generalized quasichemical approximation method to account for the inherent statistical disorder of the system. The model describes the evolution of optical phonons to the F point as a function of molar fraction for zinc blende ternary alloys for III arsenides and III nitrides for any arbitrary compositions. We have found that the obtained results are in good agreement with experimental data taken from Raman and IR measurements available in the literature.