Crystal Dynamics of Sodium at 90°K

Abstract

The frequency/wave vector dispersion relations for the lattice vibrations of sodium have been measured by neutron spectrometry along the symmetric lines [$00\zeta$], [$\zeta \zeta 0$], [$\zeta \zeta \zeta$], [$\frac{1}{2}\frac{1}{2}\zeta$], and [$\zeta \zeta 1$] and at several nonsymmetric points in the reduced zone. The measurements were made at 90°K using the triple-axis crystal spectrometer in the constant Q mode of operation. The results can be qualitatively described by a first- and second-neighbor force model but detailed analysis shows that fourth- and fifth-neighbor forces are probably significant. The calculated force constants for fifth neighbors are about 1 or 2% of those for first neighbors. Discontinuities in the slopes of the dispersion curves due to the Fermi surface (the Kohn effect) were not observed.