Ethane-xenon mixtures under shock conditions

Mixtures of light elements with heavy elements are important in inertial confinement fusion. We explore the physics of molecular scale mixing through a validation study of equation of state (EOS) properties. Density functional theory molecular dynamics (DFT-MD) at elevated temperature and pressure is used to obtain the thermodynamic state properties of pure xenon, ethane, and various compressed mixture compositions along their principal Hugoniots. To validate these simulations, we have performed shock compression experiments using the Sandia Z-Machine. A bond tracking analysis correlates the sharp rise in the Hugoniot curve with the completion of dissociation in ethane. The DFT-based simulation results compare well with the experimental data along the principal Hugoniots and are used to provide insight into the dissociation and temperature along the Hugoniots as a function of mixture composition. Interestingly, we find that the compression ratio for complete dissociation is similar for several compositions suggesting a limiting compression for C-C bonded systems.

Figure 1

Snapshot of the liquid ethane reference state nuclear positions within a supercell at density $\rho =0.571$ $\mathrm{g}/{\mathrm{cm}}^3$ at 163 K from a DFT-MD AM05 calculation. C atoms are brown and H atoms are white.

Figure 2

Same as Fig. 1, but now including Xe with mass ratio $x=0.19$ and density $\rho =1.676$ $\mathrm{g}/{\mathrm{cm}}^3$. Xe atoms are gray.

Figure 3

Target cell configuration for the ethane and the Xe-ethane mixture shock compression experiments.

Figure 4

Experimental measurements: quartz shock velocity ($U_S^{\text{Quartz}}$) vs sample shock velocity ($U_S$). The data for the pure Xe is from Ref. [11]. The lines are linear fits to the data. The slope uncertainty and the sum of the orthogonal distance from the fit are listed on the figure.

Figure 5

Hugoniot data from the Z experiments and the DFT simulations for the pure ethane, mass mixture, molar mixture, and pure Xe. All DFT data start from a reference state density for the system at $T=163$ K and 0 bar pressure. The initial states for the experimental data are listed in Tables 4, 5, 6 Error bars for the experimental data are on the order of the symbol unless indicated otherwise.

Figure 6

Reshock data in $\rho -P$ space for ethane and Xe-ethane mixtures. The symbols are chosen so that the principal Hugoniot state and reshock state have corresponding symbols.

Figure 7

DFT Hugoniot calculations in $P-T$ space. The $P-T$ slope increases after complete dissociation of the ethane.

Figure 8

The percent of total atoms in the system that are in each molecule type. The Xe atom percentage is not shown. Trace refers to all possible C-C and C-H combinations excluding ${\mathrm{C}}_2{\mathrm{H}}_6$. Juxtaposed on the plot is the DFT Hugoniot (dashed line). Complete dissociation is observed by 1.9 $\mathrm{g}/{\mathrm{cm}}^3$.

Figure 9

Decomposition of the 50/50 mass mixture (${\rho }_0=0.96$ $\mathrm{g}/{\mathrm{cm}}^3$, $x=0.50$) along the Hugoniot. The dashed line indicates the DFT calculated Hugoniot.

Figure 10

Decomposition of the 50/50 molar mixture (${\rho }_0=1.676$ $\mathrm{g}/{\mathrm{cm}}^3$, $x=0.19$) along the Hugoniot. The dashed line indicates the DFT calculated Hugoniot.