Evidence for out-of-equilibrium states in warm dense matter probed by x-ray Thomson scattering

A recent and unexpected discrepancy between ab initio simulations and the interpretation of a laser shock experiment on aluminum, probed by x-ray Thomson scattering (XRTS), is addressed. The ion-ion structure factor deduced from the XRTS elastic peak (ion feature) is only compatible with a strongly coupled out-of-equilibrium state. Orbital free molecular dynamics simulations with ions colder than the electrons are employed to interpret the experiment. The relevance of decoupled temperatures for ions and electrons is discussed. The possibility that it mimics a transient, or metastable, out-of-equilibrium state after melting is also suggested.

Figure 1

Ion-ion static factor computed within HNC-Y-SRR formulation and optimized to fit data [8, 9] (red solid line) compared with the OCP result at $\Gamma =55$ (black solid line). Diamonds are obtained with an equilibrium OF simulation at $T_e=T_i=10$ eV; filled circles are nonequilibrium OF simulation with $T_i=2$ eV, $T_e=10$ eV.

Figure 2

Atomic form factor (AFF) for aluminum at 8.1 ${\mathrm{g}/\mathrm{cm}}^3$ and $T_e=10$ eV. Black circles are Hubbell's tabulated results [25]. The (blue) solid line is the full TF atomic form factor, the dashed line is the ion form factor $f_i\left(k\right)$, and the dot-dashed line is the screening term $q\left(k\right)$. The same symbols in red show Souza's results [11]. Triangles are the atomic form factor deduced from Fig. 2 of [9]. The gray area shows the region where the maximum in ion feature occurs.

Figure 3

Circles with error bars are the experimental data of Ma et al. [8]. The dashed line (blue) and dot-dashed line (blue) are the ion feature computed from an equilibrium simulation $T_i=T_e=10$ eV with present OF and Rüter's OB simulations [10], respectively. The nonequilibrium OF simulation results, 8.1 ${\mathrm{g}/\mathrm{cm}}^3,T_i=2$ eV, and $T_e=10$ eV are represented by the gray (brown) area using Ma form factor (highest limit) or Thomas-Fermi atomic form factor (lowest limit). Note that the $x$ axis is logarithmic to emphasize the region around 4 Å${}^{-1}$.