Ab initio calculation of the miscibility diagram for mixtures of hydrogen and water

We calculate the miscibility gap in mixtures of hydrogen and water under high-temperature and high-pressure conditions as relevant for planetary interiors with density functional theory combined with classical molecular dynamics. In contrast to earlier calculations, we find a miscibility gap at temperatures below 1500–2000 K at pressures of up to 300 kbar, which extends the experimentally known immiscibility region by one order of magnitude in pressure. In contrast to extrapolated experimental demixing lines reaching to high temperatures, our results indicate a termination of the demixing region close to 2000 K. This finding profoundly impacts the understanding of the interiors of ice-giant planets such as Neptune and Uranus by supporting a partially demixed interior, including a density discontinuity near 2000 K, which corresponds to planetary radii of 0.85–0.95 in Uranus and Neptune. Additionally, our findings are relevant for thermal evolution models of Earth that aim to explain the formation of superreducing mineral associations.

Figure 1

Free enthalpy of mixing $\mathrm{\Delta }g$ as function of the water fraction $x{\mathrm{H}}_2\mathrm{O}$ for 1000 K and 120 kbar. Results from classical nuclear motion using the ideal molecular entropy: gray stars. Results calculated with the CCI method are shown in red, specifically: using the classical nuclear motion as red diamonds, by including the NQC as red triangles. The double-tangent constructions are depicted as dotted lines. The dashed-dotted line quantifies the size of the free enthalpy salient (concave section) $\mathrm{\Delta }\tilde{g}(p,T)$ [see Eq. (4)].

Figure 2

Free enthalpy of mixing $\mathrm{\Delta }g$ for different $p\text{−}T$ conditions. (a)–(c) show $\mathrm{\Delta }g$ for $T=1000$, 1500, and 2000 K, respectively. Our raw data are shown by colored triangles. The solid lines are Redlich-Kister fits [39]. The dashed lines represent the double-tangent constructions.

Figure 3

Results for $\mathrm{\Delta }\tilde{g}(p,T)$ at 1000 K (blue), 1500 K (red), and 2000 K (black). The solid lines represent the corresponding fit from Eq. (5), which has a linear pressure dependence.

Figure 4

$T\text{−}p$ diagram with all conditions for which we calculated $\mathrm{\Delta }g$ (green triangles). The green demixing line $T_d\left(p\right)$ shows the lowest pressure and highest temperatures where demixing occurs according to the condition $\mathrm{\Delta }\tilde{g}(p,T)=0$ [see Eq. (5)]. For comparison we show GEMC results of Bergermann et al. [29] (red circles), experiments by Bali et al. [23] (blue line), experiments by Seward and Franck [22] (purple diamonds), and experiments by Vlasov et al. [24] (cyan line). The melting line of water is shown in dark red [58]. Predicted $T\text{−}p$ profiles along Uranus' and Neptune's radius are shown by solid and dashed lines, respectively: Scheibe et al. [17] (black) and Nettelmann et al. [12] (model N1: gray). We also added Earth's Archean geotherms as given by Mareschal and Jaupart [59] (orange shaded area). The inset shows the low-pressure region in more detail.