Navigating at Will on the Water Phase Diagram

Despite the simplicity of its molecular unit, water is a challenging system because of its uniquely rich polymorphism and predicted but yet unconfirmed features. Introducing a novel space of generalized coordinates that capture changes in the topology of the interatomic network, we are able to systematically track transitions among liquid, amorphous, and crystalline forms throughout the whole phase diagram of water, including the nucleation of crystals above and below the melting point. Our approach, based on molecular dynamics and enhanced sampling or free energy calculation techniques, is not specific to water and could be applied to very different structural phase transitions, paving the way towards the prediction of kinetic routes connecting polymorphic structures in a range of materials.

Figure 1

(a) The $\mathrm{TIP}4\mathrm{P}/2005$ water phase diagram [40] is shown in grey, and phase transitions between (meta)stable phases (blue labels) simulated with metadynamics are indicated with red arrows. Dashed green lines represent variations of the (P,T) conditions of the system within a phase, performed with unbiased molecular dynamics simulations. (b) Two-dimensional map reproducing distances between PIV vectors defined in Eq. (1). The map axes are defined within an arbitrary rotation.

Figure 2

(a) Sequence of snapshots ($\alpha$, $\beta$, $\gamma$, $\delta$, $\epsilon$) of the umbrella sampling simulation describing the progressive crystallization of LDA water into Ice I. Molecules in icelike environment, with an average local tetrahedral bond order parameter [17] of oxygen higher than 0.7, are shown in blue (in the box only). Snapshot $\gamma$ shows the Ice I nucleus at its critical size (saddle point in the free-energy profile). Snapshot $\epsilon$ shows stacking disordered ice I, with Ic cubic regions separated by Ih hexagonal layers (green lines). (b) Free-energy profile along the LDA–Ice I transformation pathway ($T=240\mathrm{K}$, $P=1\mathrm{bar}$) obtained via the weighted histogram analysis method applied to umbrella sampling trajectories. (c) Comparison of the free-energy profiles, projected along the $s$ coordinate, for the crystallization transitions LDA–Ice I at $T=240\mathrm{K}$ and $P=1\mathrm{bar}$ and liquid–Ice I at $T=260\mathrm{K}$ and $P=1\mathrm{bar}$. The free energy minima of each simulation are arbitrarily set to zero ($N$ is the number of water molecules, here 800).

Figure 3

(a) Free-energy profiles projected along the path collective variable $s$ for the Ice I–HDA transformation at different thermodynamic conditions: $T=100\mathrm{K}$ and $P=10\mathrm{kbar}$ (black), $T=120\mathrm{K}$ and $P=10\mathrm{kbar}$ (red), $T=100\mathrm{K}$ and $P=12\mathrm{kbar}$ (blue). The free energy of HDA ice is arbitrarily set to zero. The inset shows the position of the three transformations in the phase diagram: at $T=100\mathrm{K}$ and $P=10\mathrm{kbar}$ Ice I is metastable [see Fig. 1] and separated from HDA ice by a barrier. (b) Sequence of snapshots ($\alpha$, $\beta$, $\gamma$) along the amorphization process at $T=100\mathrm{K}$ and $P=10\mathrm{kbar}$. They are taken from the umbrella sampling trajectories and their position along the $s$ coordinate is shown in panel (a).

Figure 4

(a) Snapshots representing the oxygen atoms of the system in four different configurations: VHDA, Ice VII-P (plastic phase), Ice VII, and Ice $\mathsf{Y}$. All these structures are visited by the system while simulating the VHDA–Ice VII transformation at $T=300\mathrm{K}$ and $P=50\mathrm{kbar}$ via metadynamics. (b) Oxygen–oxygen radial distribution functions as a function of the number of metadynamics simulation steps, for the stable configurations shown in panel (a). The color code is consistent with panel (a). (c) Free energy landscape at $T=300\mathrm{K}$ and $P=50\mathrm{kbar}$ in the $\{s,z\}$ space obtained from umbrella sampling simulations. Equilibrated Ice VII and Ice $\mathsf{Y}$ are used to define the path collective variables. The simulation box includes $N=360$ water molecules.