High-Precision Shock Wave Measurements of Deuterium: Evaluation of Exchange-Correlation Functionals at the Molecular-to-Atomic Transition

We present shock compression data for deuterium through the molecular-to-atomic transition along the principal Hugoniot with unprecedented precision, enabling discrimination between subtle differences in first-principle theoretical predictions. These observations, supported through reshock measurements, provide tight constraints in a regime directly relevant to planetary interiors. Our findings are in best agreement with density functional theory; however, no one exchange-correlation functional describes well both the onset of dissociation and the maximum compression along the Hugoniot.

Figure 1

Representative experimental data, in this case from VISAR. Gray line: aluminum flyer plate velocity. Cyan (blue) line: $\alpha$-quartz (deuterium) shock velocity. The inset shows a schematic of the experimental configuration; note the dimensions are not to scale.

Figure 2

Deuterium $U_s-u_p$ Hugoniot. Chemical picture models: red line, Sesame72 [30]; blue line, Kerley03 [31]. FT-DFT: magenta line, Lenosky et al. [33]; black line, PW91 [32, 34] corrected for ${\rho }_0$ of $0.167\mathrm{g}/{\mathrm{cm}}^3$; dark gray circles, PBE, this work; light gray circles, optB86b, this work; green line, green circles, vdW-DF1, this work; green triangle, vdW-DF1 with elevated $T_e$, this work; orange line, orange circles, vdW-DF2, this work. QMC: purple squares, Tubman et al. [14]. Data: black circles, gas gun [2]; red diamonds, plate impact with aluminum standard [6], reanalyzed using the recent aluminum release model [35] (weighted averages of up to seven individual experiments); cyan diamonds, plate impact with $\alpha$-quartz standard, this work. Dashed black line, extrapolation of the weighted least-squares linear fit to the gas-gun data [2]; dashed cyan line, weighted least-squares piecewise fit to the experimental data shown here. The lower panel plots $\mathrm{\Delta }{U}_s$ relative to the fit to the gas-gun data (dashed black line).

Figure 3

Deuterium $P$-density compression Hugoniot (all relative to ${\rho }_0=0.167\mathrm{g}/{\mathrm{cm}}^3)$. Lines and symbols are as in Fig. 2. Note that the $x$ and $y$ scales of the inset match the main figure.

Figure 4

Deuterium reshock experimental observables: $U_s^Q$ vs $U_s^{\mathrm{D}}$. Lines and symbols are as in Fig. 2. Note that the $x$ and $y$ scales of the inset match the main figure.

Figure 5

Ratio of the increase in $P$ upon reshock to first shock pressure ($\mathrm{\Delta }P/P_1$) as a function of $P_1$ for reshock from an $\alpha$-quartz anvil. Lines and symbols are as in Fig. 2. The dashed black line is the PW91 result shifted $\sim 3\mathrm{GPa}$ to higher $P$. Note that the $x$ and $y$ scales of the inset match the main figure.