DENSITY OF STATES OF SOME SIMPLE EXCITATIONS IN SOLIDS

The density of states of the spectrum E(k)=E0-E1 Σ {δ}ei(kδ) which occurs for different types of elementary excitations in solids, when only next neighbour interactions are taken into account (with Δ being the next neighbour lattice vectors), were computed and are investigated and tabulated for the cubic space groups. Its singularities are discussed with regard to a paper of van Hove [5]. As is detailed in the paper, using the standard approximation of these functions for the calculation of thermodynamic observables proves to be justified only for very low temperatures. In order to facilitate their application for calculations in case of higher temperatures, the exact densities of states are approximated by elementary functions with a relative error of less than 1 per 1000. © 1969.