Phonon dispersion in metals

Abstract

A simple lattice dynamical model for metals is proposed. A body-centered cubic lattice of ion cores imbedded in a responding background of electron gas is considered. The total potential energy of the lattice is evaluated as sum of a Coulombic part due to the ion-ion, ion-electron and electron-electron interactions and a non-Coulombic short range part due to ion-ion exchange repulsion and Van der Waals attraction. A secular equation determining the frequencies of the normal modes of vibration is derived. The dispersion relations are presented for propagation vectors in the [100], [110], [111] directions. Comparison is made in the case of sodium with experimental data obtained from neutron spectrometry. An appendix deals with series termination errors in certain lattice sums entering in Coulomb coupling coefficients.