Equation of state, ionic structure, and phase diagram of warm dense krypton

Extensive quantum molecular dynamics (QMD) simulations are performed to determine the equation of state, sound velocity, and phase diagram of middle-$Z$ krypton in a warm dense regime where the pressure (P) is up to 300 GPa and the temperature is up to 60 kK. The shock wave experimental data are used to validate the present theoretical models. It is found that, within the regime of the current density ($\rho$) and temperature ($T$), sound velocity can effectively discriminate differences between different theoretical models, and therefore it is more suitable as a benchmark to verify the practicability of models. The QMD-simulated results of the ionic structures and electronic properties imply the occurrence of two kinds of phase transitions, including transition from a solidlike to fluid state and that from an insulator to conductive fluid in this T-P regime. The calculated electrical conductivities confirm that the metallization transition occurs at about 60 GPa and 17.5 kK along the principal Hugoniot. With the help of simulation results and experimental data, a comprehensive phase diagram for krypton is constructed by using the solid-fluid and insulator-metal fluid phase boundaries, which fills the gap of the experimental work [Proc. Natl. Acad. Sci. USA 112, 7925 (2015)]. These results will provide an instructive basis for the experimental investigations of rare gases over a wide T-P range.

Figure 1

Hugoniot curve for fluid krypton: our QMD-PBE results are compared with the shock compression experiment [21], QMD results with standard and improved AM05 XC functional [22], and five chemical models (SFVT [34], LEOS 360, LEOS Y360 [22], SESAME 5180, and SESAME 5181 [35]). The SFVT model with the consideration of dissociation is shown by the magenta dotted line. The inset gives the temperature as a function of the pressure along the principal Hugoniot.

Figure 2

The bulk sound velocity as a function of the density and pressure, respectively, from our QMD-PBE simulation, chemical models (SFVT, SESAME 5180 and SESAME 5181 [35]), and experiment results [21], along the principal Hugoniot.

Figure 3

The PDF of dense krypton along three isochores with densities of (a) 2.617 $\mathrm{g}/{\mathrm{cm}}^3$, (b) 5.328 $\mathrm{g}/{\mathrm{cm}}^3$, and (c) 8.00 $\mathrm{g}/{\mathrm{cm}}^3$ at different temperatures. The first peaks of the PDF are arranged from high to low along the direction of the blue dashed-line arrow.

Figure 4

Electronic density of state of dense krypton by using the PBE [(a), (c), and (e)] and HSE06 [(b), (d), and (f)] XC functional with densities of 2.617, 5.328, and 8.00 $\mathrm{g}/{\mathrm{cm}}^3$. The band gaps of dense krypton at 1 kK are marked, and the Fermi energy is shifted to zero.

Figure 5

Band gap of krypton at an initial fluid point, compared with QMD results along 1000 and 2500 K isotherms calculated by the PBE and the HSE06 functionals with $7\times 7\times 7k$-points; the theoretical results for the fcc solid krypton at 0 K calculated with $21\times 21\times 21k$-points and the first-principles calculation by Kwon et al. [13].

Figure 6

The density dependence of the dc conductivity (squares) for krypton at 2.5 kK (red), 5kK (orange), 10 kK (green), 27 kK (cyan), 37 kK (magenta), 48 kK (violet), and 60 kK (navy blue) computed with the PBE functional, compared with the experimental result of Glukhodedov et al. [21] and Veeser et al. [48]. The pink region around the Mott [49] minimum metallic conductivity is used to determine the density of metallization. The orange solid line represents our calculated dc conductivity along the principal Hugoniot.

Figure 7

Phase diagrams of krypton from the calculated (squares) and experimental (sphere) data [21]. The insulating fluid is defined as $\sigma <2\times {10}^4\mathrm{S}/\mathrm{m}$ and conducting fluid as $\sigma >{10}^5\mathrm{S}/\mathrm{m}$. The squares refer to the conductivity along seven isochores of 2.617, 4.119, 5.328, 6.56, 8.0, and $9.0{\mathrm{g}/\mathrm{cm}}^3$, the circles represent the dc conductivity along the principal Hugoniot, and the value of conductivity is shown by color with the color bar. The melting curve of solid krypton [14, 15] is also used to define phase boundaries between the solid phase and fluid phase.