Extension of the Dispersion-Relation Measurements of Beryllium

Abstract

The phonon dispersion-relation data for beryllium have been extended for waves propagating in the [$01\overline{1}0$] and [$11\overline{2}0$] directions by recent neutron scattering measurements. Measurements were confined to phonons which have their polarization vectors aligned parallel to the hexagonal plane. Branches for the [$01\overline{1}0$] direction of wave propagation designated TO(∥) and TA(∥) have intercept frequencies at the zone boundary of 1.72 and 1.21, respectively, in units of ${10}^{13}$ ${\sec }^{-1\mathrm{}}$. Comparison is made between these data and latticedynamical models of Gupta and Dayal, Iyengar et al., and DeWames et al. The model of DeWames et al. gives the best agreement with the data but further improvements are desired. The Rosenstock sum Rule which has been applied to the dispersion-relation data for the symmetry directions indicates the presence of considerable nonelectrostatic or trace-variable forces. These forces are presumed to arise from the ion-core repulsion and the kinetic energy of the conduction electrons in beryllium.