Crystal Dynamics of Metallicβ−Snat 110°K

Abstract

The frequency/wave-vector phonon dispersion relation for all of the symmetry branches and some of the nonsymmetry branches with wave vectors along the [$0,0,\zeta$], [$1,0,\zeta$], [$\zeta ,0,0\mathrm{}$], and [$\zeta ,\zeta ,0\mathrm{}$] ($\Lambda ,V,\Sigma$, and $\Delta$) directions have been studied at 110°K using inelastic neutron scattering. In addition, selected portions of the [$\eta ,0,\zeta$] branches ($\eta =0.1, 0.2, 0.3 \mathrm{in} \mathrm{units} \mathrm{of} \frac{2\pi }{c}$) which are parallel to the $\Lambda$ and $V$ directions have been studied. The experimentally determined dispersion relation shows much detailed structure, with several sharp kinks. This structure precludes a description of the crystal dynamics of $\beta -\mathrm{S}\mathrm{n}$ in terms of a Bornvon Kármán model with forces extending to a limited number of shells of neighboring atoms. Although the structure in the dispersion relation is probably due to the strong electron-phonon interaction in $\beta -\mathrm{S}\mathrm{n}$, straightforward analysis in terms of Kohn anomalies is impossible because of the complex Fermi surface of $\beta -\mathrm{S}\mathrm{n}$. This suggests that the crystal dynamics of $\beta -\mathrm{S}\mathrm{n}$ can only be explained by a detailed calculation which takes the electronic band structure into account in a realistic manner.