Hugoniot and release measurements in diamond shocked up to 26 Mbar

The equation of state (EOS) of carbon in its high-pressure solid and liquid phases is of interest to planetary astrophysics and inertial confinement fusion. Of particular interest are the high-pressure shock and release responses of diamond as these provide rigorous constraints on important paths through the EOS. This paper presents experimental Hugoniot and release data for both single-crystal diamond (SCD) and nanocrystalline diamond (NCD), which is comprised of nanometer-scale diamond grains and is $\sim 5\%$ less dense than SCD. We find that NCD has a stiffer Hugoniot than SCD that can be attributed to porosity. A Grüneisen parameter of $\sim 1$ was derived from the data, which suggests increased coordination in the high-pressure fluid carbon compared to ambient diamond.

Figure 1

(a) The nanocrystalline diamond (NCD) target design comprising a CH ablator, a quartz pusher and witness, an NCD sample, and a standard positioned to facilitate measurements of transit times. (b) Raw VISAR (velocity interferometer system for any reflector) data from an experiment using the target design in (a). (c) Extracted shock velocities from (b). The shock-velocity history in NCD (solid black) was inferred from the average shock velocity (dashed gray) and the observed shock-velocity history in the adjacent quartz witness (solid orange) using the nonsteady waves correction [36]. The shock-velocity profile in the CH standard (solid blue) is observed once the shock breaks out of the NCD.

Figure 2

Schematics of (a) planar cryogenic and (b) warm targets used in single-crystal (SCD) Hugoniot and release experiments. Targets had a CH ablator and one to three standards (liquid ${\mathrm{D}}_2$, CH, quartz, or ${\mathrm{SiO}}_2$ foam) on the rear side of the SCD.

Figure 3

Full-density $\left({\rho }_0=3.515\mathrm{g}{\mathrm{cm}}^{-3}\right)$ diamond Hugoniot data. SCD data from this work (red squares), SCD data from Hicks et al. [14] re-analyzed using the updated quartz EOS [26] (blue circles), and polycrystalline data from Knudson, Desjarlais, and Dolan [8] (orange triangles). The data are compared to Hugoniots modeled using diamond EOS tables (colored curves). Weighted linear fits to the $U_{\text{s}}-u_{\text{p}}$ SCD data (this work and Hicks et al. [14]) projected into the $P-\rho$ plane (black curves).

Figure 4

NCD $\left({\rho }_0=3.36\mathrm{g}/{\mathrm{cm}}^3\right)$ Hugoniot data (gray squares) from impedance matching with a quartz standard. (a) The shock velocity versus particle velocity data and (b) the pressure versus density data are compared to Hugoniots modeled using diamond EOS tables (colored curves) and a porous model (solid black curve) modeled using Eq.(8) with $\mathrm{\Gamma }=1.04$. The porous model using $\mathrm{\Gamma }=1.04\pm 0.1$ is shown by gray-shaded areas. The Hugoniot curves derived from the EOS tables were modeled using the initial density of $3.36\mathrm{g}{\mathrm{cm}}^{-3}$.

Figure 5

(a) The NCD and SCD Hugoniot fits were used to derive (b) the Grüneisen parameter for liquid carbon. The density-dependent $\mathrm{\Gamma }$ from this work is higher than predictions using LEOS 9061 (dashed red curve), LEOS 64 (dashed–dotted green curve), SESAME 7834 (dotted purple curve), and SESAME 7830 (dashed–dotted blue curve). The shaded areas correspond to $1\sigma$-uncertainty bands in the (a) NCD (purple) and SCD (yellow) fits and (b) $\mathrm{\Gamma }\left(\rho \right)$ (gray).

Figure 6

(a) SCD and (b) NCD release data compared to predictions using diamond EOS models and existing Hugoniot fits for the standards. Data points are shock velocities for diamond releasing into liquid ${\mathrm{D}}_2$ (blue triangles), ${\mathrm{SiO}}_2$ foam (green diamonds), CH (red squares), and quartz (orange circles). Curves are the predicted $U_{\text{s}}^{\text{C}}-U_{\text{s}}^{\text{Stan.}}$ relationships determined using LEOS 9061 (dashed red), SESAME 7830 (dashed-dotted blue), and Mie-Grüneisen equations of state (solid black) to model the diamond Hugoniot and release paths and existing Hugoniot fits for the standards: liquid ${\mathrm{D}}_2$ [29, 30], ${\mathrm{SiO}}_2$ foam [26, 28], CH [27], and quartz [25, 26]. Dotted portions of curves indicate that an extrapolation of the Hugoniot fit outside the standard's data range was used. The Mie-Grüneisen models for diamond used $\mathrm{\Gamma }=1.04$ and referenced a fit to the Hugoniot data from this work and Hicks et al. [14] for SCD (a) and the porous model for NCD (b). The top axes in (a) and (b) show the pressures on the Hugoniots used in the Mie-Grüneisen models that correspond to the diamond shock velocities on the bottom axes. The dashed vertical lines in (a) and (b) indicate the completion of melt on the SCD Hugoniot at 24.$4\left(\pm 0.4\right)$ $\mathrm{km}{\mathrm{s}}^{-1}$ [7]. For data to the left of the line, diamond released from the coexistence region. For data to the right of the line, diamond released from the liquid phase. Error bars in (a) are about the size of the markers.