Dynamics of liquid Au from neutron Brillouin scattering and ab initio simulations: Analogies in the behavior of metallic and insulating liquids

We performed a neutron Brillouin scattering determination of the dynamic structure factor of liquid gold in the wave-vector range $6<Q<16$ nm${}^{-1}$. Despite the experimental difficulties due to the considerable neutron absorption and the high melting temperature of the sample, a non-negligible coherent signal could successfully be extracted and revealed the presence of underdamped ion density-fluctuation modes in the whole $Q$ range of the experiment. The quality of the data further enabled a significant comparison with the results of ab initio simulations for liquid gold. The agreement found between neutron and simulation data not only provides a necessary test of ab initio methods still limited to the use of few hundreds atoms, but also reasonably justifies a thorough analysis of the simulated dynamics in the extended $Q$ range that can be more comfortably accessed by calculations. A viscoelastic modeling of the simulated spectra proves to be appropriate and, surprisingly, the so-derived salient dynamic features of liquid gold show an overall $Q$ behavior globally similar to that already found for insulating liquids. The present and recent results on the collective properties of simple liquids thus lead us to embrace the concept that simple liquid metals and insulators, at the nanometer length scale, are dynamically much less different than expected.

Figure 1

Single-scattering intensity of the vanadium sample at $Q=6$ nm${}^{-1}$ (dots with error bars) and Gaussian fit curve (red line).

Figure 2

Neutron data (dots with error bars) at three experimental $Q$ values compared with the global fit curve (solid, red) obtained with the modeling summarized in Eqs. (3) and (4). The various components of Eq. (3), i.e., the coherent (green dash dots), incoherent (magenta dashes) and double scattering (blue dots) signals, are also shown.

Figure 3

Dynamic structure factor of gold at four $Q$ values of the NBS experiment. The experimental data (black dots with error bars) are broadened by the instrumental energy resolution. The corresponding fit by means of the GH model (red solid line) has been carried out taking detailed-balance asymmetry and resolution into account. The curve fit is the same as the green line in Fig. 2, although in different units.

Figure 4

Top panel: frequency (red dots with error bars) and damping (blue circles with error bars) of the acoustic modes of gold as a function of $Q$, as obtained from the GH fits of the experimental data. The hydrodynamic behaviors are also shown for both quantities: a solid red line for the frequency and a dotted blue parabola for the damping. Bottom panel: $Q$ dependence of the thermal damping GH parameter (symbols with error bars) compared with the corresponding hydrodynamic prescription (solid parabola).

Figure 5

Comparison between the dynamic structure factor of gold as obtained by means of ab initio simulations (black dashes) and by the GH modeling of the experimental data (red solid line) already reported in Fig. 3. The simulation spectra have been asymmetrized and convoluted with the experimental resolution function.

Figure 6

Dynamic structure factor of liquid gold as obtained by means of ab initio simulations (dots with error bars) at two example wave vectors. Fit results obtained by a GH (dashed green curve) and a VE (solid red line) modeling of the simulation data are compared.

Figure 7

Dispersion curve obtained from the VE fits of the simulated spectra (full circles with error bars). The red circles are the corresponding experimental results already shown in Fig. 4. The straight line is the linearized hydrodynamics prescription. Data are missing around the position of the main maximum in the static structure factor due to the instability of the fit results in such a wave-vector region (see text).

Figure 8

$Q$ dependence of the undamped frequency $\Omega \left(Q\right)$ (full circles with error bars) and the damping $z_{\mathrm{s}}$ (black circles with error bars) of the VE equivalent harmonic oscillator representing the collective excitations in liquid gold, obtained from the VE fit to the simulated spectra. The red circles and red squares are the corresponding experimental results already shown for $z_{\mathrm{s}}$ in Fig. 4.

Figure 9

Dispersion curves and their hydrodynamic asymptotes for different liquids as obtained by consistent VE analysis of available simulation data. The center-of-mass dynamics of acoustic excitations in liquid CO${}_2$ and CD${}_4$ is compared to that of liquid Au and Cd. In each frame the liquid under consideration is directly specified. The top-left frame is the same as Fig. 7. The plots regarding CO${}_2$ and CD${}_4$ where taken from Refs. 36 and 7, respectively.

Figure 10

Ratio of damping to frequency of acoustic excitations for the four liquids previously considered. Data for each system have been appositely scaled (see text) to the carbon dioxide values and plotted as a function of $Q/Q_p$. Note that Cd and Au have the same $Q_p$ value (26 nm${}^{-1}$), just as it happens for CD${}_4$ and CO${}_2$ (19 nm${}^{-1}$). Data for Au (red stars), Cd (green squares), CO${}_2$ (pink diamonds), and CD${}_4$ (blue dots) substantially follow the same curve. The dashed line shows the hydrodynamic behavior of $z_{\mathrm{s}}/{\omega }_{\mathrm{s}}$ for CO${}_2$.