Shock-induced polymorphic transitions of $\mathrm{Pb}{\mathrm{F}}_2$ up to 1 TPa and their implications for the universal behavior of shocked $A{X}_2$ compounds

Hugoniot data for $\mathrm{Pb}{\mathrm{F}}_2$ single crystals were measured for pressures up to 1 TPa through gas gun and laser shock experiments. Experimental results show that $\mathrm{Pb}{\mathrm{F}}_2$ transforms to a less compressible phase at 29 GPa and possibly melts at 57 GPa. Quantum molecular-dynamics simulations were also performed to calculated the liquid Hugoniot for $\mathrm{Pb}{\mathrm{F}}_2$. The simulated results are in good agreement with the experimental results, supporting the high-pressure phase is liquid. The current study, combined with previous studies on $\mathrm{Ti}{\mathrm{O}}_2, \mathrm{Si}{\mathrm{O}}_2$, and $\mathrm{Ca}{\mathrm{F}}_2$, suggests that for $A{X}_2$ compounds, decreasing of Hugoniot slope can be taken as an indication of melting, and the Hugoniot slope approaches 1.2 at ultrahigh pressure.

Figure 1

Experimental configurations and typical results: (a) inclined-mirror method (No. 3), (b) DISAR method (No. 6), and (c) laser shock (No. 12).

Figure 2

Shock velocity $\left(U_S\right)$-particle velocity $\left(U_p\right)$ relation for $\mathrm{Pb}{\mathrm{F}}_2$. $c_b$ is the bulk sound velocity, and $c_{l100}$ and $c_{l111}$ are the longitudinal sound velocities along the $\langle 100\rangle$ and $\langle 111\rangle$ directions, respectively. The solid lines are linear fittings to the Hugoniot data.

Figure 3

Hugoniot compression curve of $\mathrm{Pb}{\mathrm{F}}_2$ with static compression data (Ref. [7]).

Figure 4

Comparing Hugoniot curve with calculated elastic response and static compression data of $\beta \text{−}\mathrm{Pb}{\mathrm{F}}_2$ (Ref. [39]). The dotted line is a third-order Birch-Murnaghan fitting to the static compression data.

Figure 5

Hugoniot curve of $\mathrm{Pb}{\mathrm{F}}_2$ with QMD results. The blue and green lines are calculated 0–K (Ref. [6]) and experimentally determined 300 K (Ref. [7]) isotherms of the ${\mathrm{Ni}}_2\mathrm{In}$ type and γ-phase $\mathrm{Pb}{\mathrm{F}}_2$, respectively. The black line is the Hugoniot compression curve.

Figure 6

Hugoniot data of $\mathrm{Pb}{\mathrm{F}}_2$ in liquid-phase region. The dashed line is the result of fitting to Eq. (2).

Figure 7

$U_s\text{−}{U}_p$ Hugoniot of specific $A{X}_2$ compounds. The dashed-dotted line is the UHFM $\left(U_s=5.8+1.2U_p\right)$. The dashed lines are linear fittings to the Hugoniot of $\mathrm{Ti}{\mathrm{O}}_2$ and $\mathrm{Pb}{\mathrm{F}}_2$ with $S$ fixed at 1.2 for $U_p>7\mathrm{km}/\mathrm{s}$ and ∼4 km/s, respectively. The small arrows indicate where melting occurs.

Figure 8

x–t diagram illustrating wave interactions in the IM experiments.