Phonon dispersion studies in liquid Na–Cs alloy

Abstract

The Ashcroft empty-core model is used to derive the partial potentials of Na-Cs alloy through a pseudopotential approach. The potential functions are calculated at different concentrations of Cs. From the partial potentials an effective potential is computed. It is in general found that the mixed potential [Formula: see text] lies in between that of the pure metals, namely, [Formula: see text] and [Formula: see text]. The effective potential along with g(r) of the alloy is used to evaluate the longitudinal- and transverse-phonon frequencies in the momentum space through the use of Takeno and Goda's equations. It is found that longitudinal-phonon frequencies ωL(k) show collective excitations even at large values of k while the transverse phonons ωT(k) reach a constant value quickly. Further it is found that the first minimum in the ωL(k) curve appears to coincide with the first peak position in the total structure of the alloy. This is found to be true at all concentrations. Similar observations have been made by other researchers. As a typical illustration the elastic moduli, namely, C11 and C44 are evaluated by different methods for 50 at.% Cs. These methods involve the use of the first and second derivatives of the effective potential. The values calculated show a fair interconsistency proving the veracity of the derived potential function.