High Frequency Dynamics in a Monatomic Glass

The high frequency dynamics of glassy selenium has been studied by inelastic x-ray scattering at beam line BL35XU (SPring-8). The high quality of the data allows one to pinpoint the existence of a dispersing acoustic mode for wave vectors ($Q$) of $1.5<Q<12.5{\mathrm{n}\mathrm{m}}^{-1}$, helping to clarify a previous contradiction between experimental and numerical results. The sound velocity shows a positive dispersion, exceeding the hydrodynamic value by $\approx 10\%$ at $Q<3.5{\mathrm{n}\mathrm{m}}^{-1}$. The $Q^2$ dependence of the sound attenuation $\Gamma (Q)$, reported for other glasses, is found to be the low-$Q$ limit of a more general $\Gamma (Q)\propto \Omega (Q{)}^2$ law, which applies also to the higher $Q$ region, where $\Omega (Q)\propto Q$ no longer holds.

Figure 1

IXS spectra of glassy selenium (open dots) measured for several momentum transfers, as indicated by the labels (${\mathrm{n}\mathrm{m}}^{-1}$). Also reported are the instrument resolution (dotted line) and the best fit line shape according to the model discussed in the text (solid line).

Figure 2

Relevant parameters obtained by fitting the IXS measurements. (a) Maximum of the longitudinal current correlation function (open dots) and the hydrodynamic dispersion [6] (dotted line). (b) Apparent sound velocity, $\Omega (Q)/Q$ (open dots), molecular dynamics results [8] (solid dots), and the hydrodynamic value (dotted line). (c) Sound attenuation (open dots) with the best $Q^2$ fit: $\Gamma =0.15Q^2$ with $\Gamma$ and $Q$ expressed in meV and ${\mathrm{n}\mathrm{m}}^{-1}$, respectively (dotted line). (d) Nonergodicity parameter as obtained from the $\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}/\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}$ ratio.

Figure 3

Comparison between the IXS results (open dots and error bar) and previous INS measurements from Ref. 10. Also reported is the best fit to the INS data (solid line).

Figure 4

Sound damping vs square of the excitation frequency. The quadratic dependence on the wave vector $Q^2$ shown in Fig. 2c turns out to be the low $Q$ limit of the more general dependence shown here.