Effect of ionic disorder on the principal shock Hugoniot

The effect of ionic disorder on the principal Hugoniot is investigated using multiple scattering theory to very high pressure (Gbar). Calculations using molecular dynamics to simulate ionic disorder are compared to those with a fixed crystal lattice, for both carbon and aluminum. For the range of conditions considered here we find that ionic disorder has a relatively minor influence. It is most important at the onset of shell ionization and we find that, at higher pressures, the subtle effect of the ionic environment is overwhelmed by the larger number of ionized electrons with higher thermal energies.

Figure 1

Time variation of pressure for aluminum at 1 eV and 2.7 g/${\mathrm{cm}}^3$. The pressure fluctuates over molecular-dynamics time steps (blue line). The average pressure is shown by the red horizontal line and the gray area covers one standard deviation from this mean value. For this case, the time step is 2.2 fs and we calculate the pressure at every 50th time step.

Figure 2

Effect of the correlation radius on the pressure for aluminum plasmas at conditions close to points on the principal Hugoniot. Each panel corresponds to a different temperature and density. Each line corresponds to a different molecular-dynamics snapshot. The percent change in the pressure is relative to the value at the largest correlation radius shown. Note that the correlation radius is in units of ion-sphere radii for each case.

Figure 3

Aluminum Hugoniot with experimental data [44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59]. Shown are results from the present model with molecular-dynamics configurations (MST MD), the present model with an fcc lattice (MST fcc), the Tartarus average atom model [15], and the FPEOS of Militzer and co-workers [27, 60]. The “No MS” calculation is a simplified model described in the text. The two set of stars correspond to the temperatures labeled on the plot. Note that the initial density was taken to be 2.7 g/${\mathrm{cm}}^3$.

Figure 4

Aluminum Hugoniot focused on the region of ionization of the $n=2$ shell. Shown are results from the present multiple scattering calculation with an fcc lattice (MST fcc), the present model with molecular-dynamics configurations (MST MD), and the FPEOS of Militzer and co-workers [27, 60]. The points labeled “Elk” and “VASP” are our own calculations of a Hugoniot point at 50.1 eV using the elk [64] and vasp [65, 66, 67] codes, where an fcc lattice has been assumed. The black stars show the effect of reducing the MST internal energy in steps of $1E_H$ (right to left stars, starting at $1E_H$).

Figure 5

Diamond Hugoniot with experimental data [70, 71, 72, 73, 74, 75, 76, 77]. Shown are results from the present MST calculation with an assumed diamond structure (MST Diamond), the present model with molecular-dynamics configurations (MST MD), the FPEOS model [27], and the Tartarus average atom model [15]. Note that the initial density was taken to be 3.52 g/${\mathrm{cm}}^3$.

Figure 6

Density of states for diamond at a temperature of 0.5 eV. The vasp and elk calculations (present work) are compared to MST calculations. The MST calculation with eight extra expansion centers noticeably improves agreement with the vasp and elk results, compared to the calculation with zero extra centers.

Figure 7

Average ionization along principal Hugoniot from the Tartarus average atom model.

Figure 8

Pressure along the 13.5-g/${\mathrm{cm}}^3$ isochore. Despite having relatively small influence on the Hugoniot curve, the effect of ionic disorder can be significant. Note that the vertical lines on the MST MD results show plus or minus one standard deviation (see Fig. 2).