Lattice Dynamics of hcp Metals Computed from an Optimum-Model Potential

In recent papers by Shaw and Harrison and by Shaw, the model potential due to Heine, Abarenkov, and Animalu has been reformulated and optimized. This optimum-model potential is employed to obtain energy-wave-number characteristics, from which the phonon dispersion relations for beryllium, magnesium, and zinc are computed. The results of these calculations are compared with experimental results for high-symmetry directions. The fit is unsatisfactory for Be, somewhat better for Mg, and fairly good for Zn. The nonlocal part of the optimum-model potential does not play a significant role for Be and Mg, but is quite important in the case of Zn. By using values higher than unity for $m^{*}$ (the effective mass of the electron, in a.u.), the fit to experimental results could be substantially improved in the case of Mg. On employing $m^{*}$ as an adjustable parameter, a remarkably good fit to the experimental data for Mg was achieved with $m^{*}=1.60\mathrm{}$.