X-ray absorption spectroscopy of iron at multimegabar pressures in laser shock experiments

Taking advantage of the new opportunities provided by x-ray free electron laser (FEL) sources when coupled to a long laser pulse as available at the Linear Coherent Light Source (LCLS), we have performed x-ray absorption near-edge spectroscopy (XANES) of laser shock compressed iron up to 420 GPa ($\pm 50$) and 10 800 K ($\pm 1390$). Visible diagnostics coupled with hydrodynamic simulations were used to infer the thermodynamical conditions along the Hugoniot and the release adiabat. A modification of the pre-edge feature at 7.12 keV in the XANES spectra is observed above pressures of 260 GPa along the Hugoniot. Comparing with ab initio calculations and with previous laser-heated diamond cell data, we propose that such changes in the XANES pre-edge could be a signature of molten iron. This interpretation then suggests that iron is molten at pressures and temperatures higher than 260 GPa ($\pm 29$) and 5680 K ($\pm 700$) along the principal Fe Hugoniot.

Figure 1

Two lasers are focused on the multilayer iron sample while the unfocused LCLS beam probes the compressed sample within femtosecond times scales. A first spectrometer measures the incident beam while two different spectrometers are detecting the transmitted beam allowing XANES measurements with two different methods. On the rear side of the target, optical diagnostics (VISAR and SOP) have been installed allowing the shot-to-shot measurement of the thermodynamical conditions when compared with hydrodynamical simulations.

Figure 2

A zoom of the multilayer target is displayed with images from the two VISAR and the SOP measurements obtained at intensities of $9\times {10}^{12} {\mathrm{W}/\mathrm{cm}}^2$. For such intensities, the backside CH layer metallizes and allows the measurements of the instantaneous shock velocity from the two VISARs. On the right, we show the corresponding instantaneous velocity from the two VISARS, overlaid with the shock velocity from hydrodynamic simulations to extract the pressure and the temperature. For lower intensity, we used the shock transit time from the two VISARS and the SOP detectors.

Figure 3

Single-shot pressure as a function of the temperature (black dots), calculated from the VISAR and the SOP measurements when coupled to hydrodynamic simulations. The Hugoniot curves of the SESAME 2140, SESAME 2150, BLF, and the ab initio EOS are shown as green lines. The new melting curve of iron by Anzellini et al. [4] is shown for reference. The averaging of a group of data for XANES extraction is also shown.

Figure 4

Calculated temperature and pressure profiles in iron from hydrodynamic simulations (code MULTI [31]) using three different EOS (SESAME 2150, BLF, and the ab initio EOS) and obtained for an intensity of $5\times {10}^{12} {\mathrm{W}/\mathrm{cm}}^2$.

Figure 5

(a) XANES spectra with error ranges arising from photon statistics measured at various conditions (colored lines) and compared to spectra recorded at ambient conditions on bcc iron prior to shot (black lines). Groups of samples labeled from 1 to 5 as shown in Fig. 3 corresponding, for the Si crystal spectrometer, to average values of (1) 11.25 g/cc-2780 K-130 GPa, (2) 12.45 g/cc-5680 K-260 GPa, (3) 13.5 g/cc-8120 K-380 GPa, (4) 13.8 g/cc-10 800 K-420 GPa, and (5) 6 g/cc-4180 K-12 GPa. (b) Corresponding spectra obtained with the quartz crystal.

Figure 6

(a) Ab initio calculated XANES spectra of liquid Fe (full lines), hcp, and bcc Fe (dotted lines) phases compared to solid bcc Fe at ambient conditions (AC) (black lines). XANES spectra are calculated at the same temperatures and pressures than of the experimental groups, labeled from 1 to 5 (see Fig. 3) with (1) 11.25 g/cc-2780 K-130 GPa, (2) 12.45 g/cc-5680 K-260 GPa, (3) 13.5 g/cc-8120 K-380 GPa, (4) 13.8 g/cc-10 800 K-420 GPa, and (5) 6 g/cc-4180 K-12 GPa. (b) Zoom of the pre-edge region of the calculated XANES spectra of bcc iron at ambient conditions AC (black line), solid hcp Fe at 130 GPa (blue line), and liquid Fe at 260 GPa (green line). (c) Experimental XANES spectra obtained with the Si crystal spectrometers diagnostic at the same conditions. (d) Experimental XANES spectra obtained with the quartz spectrometer at similar conditions.

Figure 7

Iron phase diagram: Our results (red open squares for solid hcp and red full square for liquid Fe) are compared with previous results and extrapolation obtained in the literature from diamond-anvil-cell compression [4, 6, 36], shock-waves experiments [8, 9, 10, 11, 12, 13], and ab initio simulations [1, 2, 3]. The ICB pressure of 330 GPa is shown with a dashed blue line.