Dispersion effects and real atomic vibrations of impure crystals studied based on interatomic effective potential

Abstract

The dispersion effects and real atomic vibrations of crystals containing doping atoms have been studied using the interatomic effective potential which includes the many-body effects based on the contributions of nearest neighbors of the host and doping atoms. The analytical expressions are derived for the dispersion relations describing the dispersion effects consisting of the acoustic and optic branches, forbidden zone, as well as for the amplitude and phase shift of the real atomic vibrations of impure crystals. The Morse potential is assumed to describe the single-pair atomic interaction. The interrupts of wave propagation caused by doping atoms and the changes of thermodynamic properties due to the real atomic vibrations, as well as the areas of localization of forbidden zones and doping atoms have been specified. The numerical results for Fe doped by atoms of W calculated by the present theory using the interatomic effective potential are found to be in good agreement with experiment obtained from the measured Morse potential parameters and quite different from those of its inverse doping process (W doped by atoms of Fe), while they are the same if the single-pair potential is used.