Lattice-Dynamic Calculation for Alkali Metals

Abstract

We present a model calculation of lattice dynamics for alkali metals. The lattice potential consists of the electrostatic energy and the screened electron-ion interaction. The screened potential is formed by linearly screening a Heine-Abarenkov-type ion potential, and the Hartree dielectric function is modified to include approximately exchange and correlation effects. The model parameters are determined according to the experimental elastic constants. Expressions for elastic constants are derived by taking the long-wave limit of the secular equation. From our results in lattice dynamics, we find that the shear waves are dominated by the electrostatic potential, but for the longitudinal waves the contributions from both potentials are comparable and opposite in size. The agreement between the calculated and the observed dispersion curves is good for Na and K where neutron-scattering data are available. We have also calculated the effective ion-ion potential for the alkali metals. All of these potentials exhibit a minimum near the equilibrium position and some long-range oscillations caused by electron-ion interaction.