Phase Diagram and Electrical Conductivity of High Energy-Density Water from Density Functional Theory

The electrical conductivity and structure of water between $2000–70000\mathrm{K}$ and $0.1–3.7\mathrm{g}/{\mathrm{cm}}^3$ is studied by finite temperature density functional theory (DFT). Proton conduction is investigated quantitatively by analyzing diffusion, the pair-correlation function, and Wannier center locations, while the electronic conduction is calculated in the Kubo-Greenwood formalism. The conductivity formulation is valid across three phase transitions (molecular liquid, ionic liquid, superionic, electronic liquid). Above 100 GPa the superionic phase directly borders an electronically conducting fluid, not an insulating ionic fluid, as previously concluded. For simulations of high energy-density systems to be quantitative, we conclude that finite temperature DFT should be employed.

Figure 1

Theoretical phase diagram for water in the HEDP regime, each point represents a DFT-MD simulation. Molecular liquid—no dissociation of ${\mathrm{H}}_2\mathrm{O}$ (yellow). Insulating ionic liquid—dissociation of ${\mathrm{H}}_2\mathrm{O}$ and a gap in the electronic structure (gray). Superionic—very small O diffusion coefficient and gap in the electronic structure (blue). Electronically conducting ionic fluid—dissociation of ${\mathrm{H}}_2\mathrm{O}$, no gap in the electronic structure (red). The dashed lines are guides to the eye. The transition from superionic phase to the conducting fluid shows little hysteresis in the phase change, as can be inferred from the dense sampling in that region.

Figure 2

Snapshots of the structure (oxygen atoms are white, hydrogen atoms red) at $T=4000\mathrm{K}$ and $\rho =2.5\mathrm{g}/{\mathrm{cm}}^3$. Superimposed is a constant-electron-density surface (gold) projected from the HO state. Using the true temperature induces a shift from $S$ to $P$ character, changing the structure from being localized to spanning the cell, enabling conduction. The shift takes 20–100 fs to appear after changing the electronic temperature from $T_e=1000\mathrm{K}$ to $T_e=4000\mathrm{K}$. The left snapshot is taken from this transition period, the right snapshot after the system is in equilibrium at $T_e=4000\mathrm{K}$.

Figure 3

Upper: electronic conductivity (filled symbols and full lines) and ionic conductivity (open symbols and dashed lines) of water as a function of density for different temperatures: 70  (blue star), 44 (dark red triangles), 22 (black diamonds), 10 (red squares), 8 (magenta stars), 6 (turquiose triangles), 4 (blue squares), and 2 kK (black triangles). The sharp drops in conductivity for 4000 and 6000 K at 2.5 and $3.2\mathrm{g}/{\mathrm{cm}}^3$, respectively, corresponds to entering the superionic phase (see Fig. 1.) Lower: Ionic conductivity, as calculated for ${\mathrm{D}}_2\mathrm{O}$ and scaled by 1.3 to compare to ${\mathrm{H}}_2\mathrm{O}$ experiments. 2000 K from Eq. (1) (black triangles) and using the full hydrogen diffusion (black stars). 4000 K from Eq. (1) (blue squares) and using the full hydrogen diffusion (blue diamonds). Experimental data single shock at approximately 2000 K [5] (black circles) and multiple shock data between 2000 and 6000 K [6] (blue circles).