Equation of state, phonons, and lattice stability of ultrafast warm dense matter

Using the two-temperature model for ultrafast matter (UFM), we compare the equation of state, pair-distribution functions $g\left(r\right)$, and phonons using the neutral pseudoatom (NPA) model with results from density functional theory (DFT) codes and molecular dynamics (MD) simulations for Al, Li, and Na. The NPA approach uses state-dependent first-principles pseudopotentials from an “all-electron” DFT calculation with finite-$T$ exchange-correlation functional (XCF). It provides pair potentials, structure factors, the “bound” and “free” states, as well as a mean ionization $\overline{Z}$ unambiguously. These are not easily accessible via DFT+MD calculations which become prohibitive for $T/T_F$ exceeding $\sim 0.6$, where $T_F$ is the Fermi temperature. Hence, both DFT+MD and NPA methods can be compared up to $\sim 8\mathrm{eV}$, while higher $T$ can be addressed via the NPA. The high-$T_e$ phonon calculations raise the question of UFM lattice stability and surface ablation in thin UFM samples. The ablation forces in a UFM slab are used to define an “ablation time” competing with phonon formation times in thin UFM samples. Excellent agreement for all properties is found between NPA and standard DFT codes, even for Li where a strongly nonlocal pseudopotential is used in DFT codes. The need to use pseudopotentials appropriate to the ionization state $\overline{Z}$ is emphasized. The effect of finite-$T$ XCF is illustrated via its effect on the pressure and the electron-density distribution at a nucleus.

Figure 1

Two-temperature ion-ion pair potentials for electrons at three different temperatures and ions at $T_i=0.026\mathrm{eV}$ (300 K), for (a) Al, (b) Li, and (c) Na.

Figure 2

Quasiequilibrium phonon spectra at $T_e=6\mathrm{eV}$ obtained with NPA and with abinit for (a) Al, (b) Li, and (c) Na. The NPA equilibrium phonon spectra at 300 K are shown to illustrate the effect of increasing $T_e$ (dashed lines).

Figure 3

Quasiequilibrium pressures obtained with the NPA (lines), abinit (circles), and vasp (triangles) for Al, Li, and Na.

Figure 4

Total pressure of the solids as a function of the lattice parameter of the crystal relative to the room-temperature value $a_0$ for (a) Al, (b) Li, and (c) Na.

Figure 5

The NPA free-electron density $n_f\left(r\right)$ for ${\mathrm{Al}}^{3+}$ at density $\rho =2.7{\mathrm{g}/\mathrm{cm}}^3$, with $T_e=8\mathrm{eV}$ and $T_i=0.026\mathrm{eV}$, calculated using XC at finite $T$ and at $T=0$. The inset shows the density for larger $r/r_{\text{WS}}$.

Figure 6

Comparison between the pressure of Al in the UFM regime computed via the NPA model with the finite-$T{F}_{\text{XC}}$ and with the zero-$T{F}_{\text{XC}}$.

Figure 7

Comparison between the pressure computed with the NPA (line) and with abinit (circles) when heating is applied to the valence electron of Na only or to all electrons (nine electrons in the abinit simulations).

Figure 8

The Li-Li NPA-MHNC pair distribution function $g\left(r\right)$ at 2000 K (0.173 eV), $\rho =0.85{\mathrm{g}/\mathrm{cm}}^3$, compared with the $g\left(r\right)$ of Ref. [54].

Figure 9

Comparison of the NPA isochoric pressures for the UFM system and the equilibrium liquid system. Inset: comparison of the NPA pressures in the low-$T$ regime where DFT+MD is practical.