Fig. 1: Low-pressure bcc phase behaviour.

a Low-pressure phase diagram. The background colour corresponds to the classification shown in panel b. Blue and brown solid coexistence lines were computed from chemical-potential differences using thermodynamic integration (TI). Several points were benchmarked by direct-coexistence simulations at the points indicated. The dashed cyan line corresponds to points where the enthalpy and density are discontinuous along isobars (see Supplementary Fig. 1). The dashed orange line corresponds to the approximate point where the first secondary maximum in the O–H pair correlation function disappears. The thin magenta line gives an example TI route discussed in the main text (see panel d). b Mean frequency of proton displacement after 0.4 ps for MD simulations started from bcc ice at 40 GPa. Red corresponds to a symmetric unimodal distribution at small displacement (‘static ice’). Green corresponds to distributions with a mode at small displacement and a significant skewness to the right (‘ice VII (T)’). Yellow corresponds to a distribution with a mode at medium displacement and a skewness to the right (‘ice VII (R)’). Blue corresponds to a unimodal distribution at a large displacement. This classification of phases follows ref. 20. c Example discontinuity in the gradients of the chemical potentials for the phase transitions involving the liquid, VII′ and VII″ at 50 GPa. Grey lines are computed from upper and lower limits of the prediction interval at a 95% confidence level for integrands in thermodynamic integration; they are only visible for the VII′ line, since they are narrower than the line width for the remaining phases. d Change in chemical potential along the example TI route illustrated in panel a. The changeover in colour for ices VII/VII′/X is approximate and based on the classification of panel b.