Ab Initio Simulations for the Ion-Ion Structure Factor of Warm Dense Aluminum

We perform ab initio simulations based on finite-temperature density functional theory in order to determine the static and dynamic ion-ion structure factor in aluminum. We calculate the dynamic structure factor via the intermediate scattering function and extract the dispersion relation for the collective excitations. The results are compared with available experimental x-ray scattering data. Very good agreement is obtained for the liquid metal domain. In addition we perform simulations for warm dense aluminum in order to obtain the ion dynamics in this strongly correlated quantum regime. We determine the sound velocity for both liquid and warm dense aluminum which can be checked experimentally using narrow-bandwidth free electron laser radiation.

Figure 1

Second frequency moments for aluminum from DFT-MD simulations (lines) compared with the OCP values (crosses). Lower curve: 1023 K and $2.35\mathrm{g}/{\mathrm{cm}}^3$, upper curve: 40 600 K and $5.2\mathrm{g}/{\mathrm{cm}}^3$.

Figure 2

Static structure factor $S_{\mathrm{ii}}(k)$ at 1023 K and $2.35\mathrm{g}/{\mathrm{cm}}^3$ from x-ray diffraction experiments [22] (red dashed line) and DFT-MD simulation (black solid line).

Figure 3

Ion feature at 10 eV and $8.1\mathrm{g}/{\mathrm{cm}}^3$ from DFT-MD simulations (solid line) compared with the x-ray Thomson scattering data of Ma et al. [24] (dots).

Figure 4

DSF $S_{\mathrm{ii}}(\overrightarrow{k},\omega )$ at 1000 K and $2.3565\mathrm{g}/{\mathrm{cm}}^3$. Dashed lines: experimental data from x-ray scattering [28]. Solid lines with dots: DFT-MD of Alemany et al. [30]. Solid lines: present DFT-MD. The lower wave numbers always correspond to the present DFT-MD, while the upper ones correspond to Ref. [28] and [30]. Each set of curves is shifted by a constant offset of $0.5{\mathrm{PHz}}^{-1}$ with respect to the lower one.

Figure 5

DSF $S_{\mathrm{ii}}(\overrightarrow{k},\omega )$ at 3.5 eV and $5.2\mathrm{g}/{\mathrm{cm}}^3$ from DFT-MD simulation. The wave vectors at 3.5 and $7.3{\AA }^{-1}$ correspond to the positions of the peaks in the static structure factor.

Figure 6

Dispersion relation for ion acoustic modes. (a) Liquid aluminum at 1000 K and $2.3565\mathrm{g}/{\mathrm{cm}}^3$. (b) Warm dense aluminum at 40 600 K and $5.2\mathrm{g}/{\mathrm{cm}}^3$. Circles: dispersion relation from the positions of the side peaks of the DSF $S_{\mathrm{ii}}(\overrightarrow{k},\omega )$. Dots: dispersion relation of the peaks of the longitudinal current correlation function $J_{\mathit{l}}(\overrightarrow{k},\omega )$.