Model for the Lattice Dynamics of Metals and Its Application to Sodium

Abstract

A simple lattice dynamical model for metals is presented. A body‐centered cubic lattice of ion cores interacting with nearest and next‐nearest neighbors imbedded in a uniform background of electron gas is considered. A secular equation determining the frequencies of normal modes of vibration is derived. This equation contains three force constants which can be written in terms of elastic constants. The dispersion relations are presented for propagation vectors in the [100], [110], and [111] directions. Comparison is made in the case of sodium with the experimental curves obtained from neutron spectrometry and also with theoretical calculations of Toya. Our model is found to give a satisfactory description of the lattice dynamics of sodium.