Consistent wide-range equation of state of silicon by a unified first-principles method

Using a unified method of the extended first-principles molecular dynamics, we report a wide-range (density $\rho =2.329–18.632$ $\mathrm{g}/{\mathrm{cm}}^3$, temperature $T=1.00\times {10}^4–1.29\times {10}^8$ K) equation of state (EOS) and principal Hugoniot of silicon, which agree well with experimental results, and then evaluate the precision of the results of first-principles calculations and a universal database. Moreover, we investigate the effects of finite-temperature exchange-correlation functionals and emphasize their importance and necessity in the warm dense matter regime, although it vanishes in the nondegenerate and fully degenerate limits. Finally, we show the ionic radial distribution function and density of electronic states to study the evolution of warm dense Si towards the classic plasma limit along its principal Hugoniot. The established standard theoretical EOS table of Si provides a benchmark for the development of high-precision first-principles methods and may improve radiation-hydrodynamics simulations of inertial confinement fusion and deepen the understanding of high-energy-density physics.

Figure 1

Principal Hugoniot curve of Si calculated using the ext-FPMD method, compared with results from theoretical calculations and experimental measurements, including the combination of the KSMD and PIMC methods [41], the combination of the KSMD and OFMD methods [42, 43], QEOS, SESAME-3810, and shock experiments by Pavlovskii [25], Gust and Royce [26], Goto et al. [27], and Henderson et al. [29].

Figure 2

Calculated EOS points of Si using the ext-FPMD method (red stars with dashed lines) compared with the KSMD (black circles) and PIMC (blue squares) methods [41], where (a) shows the energy differences $\mathrm{\Delta }E=E-E_0$ and (b) shows pressure $P$. Energy differences in (a) and pressures in (b) at different $\eta$ are multiplied by corresponding coefficients for a better display.

Figure 3

Relative deviations of (a) the energy difference $\mathrm{\Delta }E=E-E_0$ and (b) pressure $P$ using the FTXC-KSDT and FTXC-GDSMFB functionals, taking the ZTXC-LDA functional as a reference.

Figure 4

Principal Hugoniots of Si using different types of exchange-correlation functionals, including ZTXC-GGA, ZTXC-LDA, FTXC-KSDT, and FTXC-GDSMFB. The inset shows a close-up near the maximum compression ratio.

Figure 5

Radial distribution functions of Si ions at fourfold density and various temperatures, calculated using the ext-FPMD method (solid red lines) and the PIMC method (blue dashed lines).

Figure 6

Density of electronic states of Si at fourfold density and various temperatures, calculated using the ext-FPMD method.