Overlap interaction between spheroidal ions and the lattice dynamics of zinc and beryllium

A phenomenological model of lattice dynamics of hcp metals has been developed by assuming the ions to have a spheroidal shape with the axis of revolution parallel to the $c$ axis. Overlap of spheroidal ions causes a noncentral interaction between the first neighbors (as in beryllium). The model is derived from a force system consisting of this noncentral overlap interaction, as six-neighbor central pair potential, and an electron-ion interaction term. Application of this model to zinc and beryllium shows that the force parameters coupling neighbors beyond the second are rather small as compared to the parameters for the first two neighbors. The dispersion curves derived from the model present a good agreement with the experimental curves.