Phase Diagram of a Deep Potential Water Model

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice ${\mathrm{VII}}^{\prime \prime }$ and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments.

Figure 1

Phase diagram of water. (${\mathrm{a}}_1$) DP model (red solid lines) and experiment (gray solid lines) for $T<420\mathrm{K}$. Black letters indicate phases that are stable in experiment and model. Ice III and XV (stable in experiment but metastable in model) are gray. Experimental coexistence lines are from Ref. [57] (melting curves), and from Refs. [9, 58, 59] (solid-solid curves). The gray triangle indicates the postulated Ih-II-XI TP [59]. The two dashed lines indicate the experimentally observed transitions $\mathrm{Ih}\to \mathrm{XI}$ and $\mathrm{X}\mathrm{I}\to \mathrm{Ih}$ [8]. The gray solid circle and square denote the VI-VIII-XV and the II-VI-XV TPs, respectively [3]. (${\mathrm{a}}_2$) Phase diagram at high $T$ and $P$. The experimental melting lines are from Ref. [60] and Ref. [13]. The VII-${\mathrm{VII}}^{\prime \prime }$-F TP is from Ref. [13]. (b) Phase diagram of $\mathrm{TIP}4\mathrm{P}/2005$ water [61].

Figure 2

Two-step melting of ice VII along the $P=30\mathrm{GPa}$ isobar, showing a solid-solid (VII-${\mathrm{VII}}^{\prime \prime }$) followed by a solid fluid (${\mathrm{VII}}^{\prime \prime }$-F) transition. (a) H (blue open square) and O (red solid square) diffusion coefficients as a function of temperature. (b) Enthalpy as a function of temperature. The estimated temperatures of solid-solid and solid-fluid transitions are indicated by the black arrows.

Figure 3

Phase diagram in the superionic region. SF and SS indicate ${\mathrm{VII}}^{\prime \prime }$-F solid-fluid and VII-${\mathrm{VII}}^{\prime \prime }$ solid-solid phase transitions, respectively. Solid and dashed lines indicate the SF and SS coexistence lines according to this work (red) and an earlier AIMD simulation (green). The solid green line is an upper bound for the melting $T$.