Comprehensive observation of hydrogen ordering in ice VI was conducted by dielectric experiments in the pressure range 0.88–2.2 GPa. Ice VI was initially obtained at room temperature and its dielectric properties were determined in both cooling and heating runs in the temperature range 100–150 K, using a newly developed pressure cell (see Methods). After the heating runs, the sample was subsequently heated to room temperature for annealing. Then, the sample was compressed again, and dielectric measurements were conducted at different pressures (Fig. 1).
Phase transitions from ice VI to its hydrogen-ordered phases were observed at around 120–130 K, along with sudden weakening of the dielectric response of ice VI with decreasing temperature (Fig. 2a and b). Hydrogen ordering of ice suppresses reorientation of water molecules which induces the dielectric response of ice2,19. We defined the disorder–order phase-transition temperatures from ice VI to its hydrogen-ordered phases as the starting temperature at which the slope (dI/dT; I: dielectric-loss peak intensity) changes (Fig. 2b). The slope of the obtained phase boundary, i.e. dT/dP, between ice VI and its hydrogen-ordered phases changes from negative to positive at around 1.6 GPa with increasing pressure (Fig. 1). Based on the Clausius–Clapeyron relationship, i.e. dT/dP = ∆V/∆S, this sign change for dT/dP strongly indicates that ice VI has two different hydrogen-ordered phases with opposite signs for ∆V, because ∆S < 0 generally holds for hydrogen ordering. Since the currently known hydrogen ordering from ice VI to ice XV shows a positive volume change (observed at the lower pressure, 0.4 GPa8), ice XV is in the lower pressure region and the hydrogen-ordered phase in the higher-pressure region is a new phase, ice XIX, which has a smaller volume than ice VI and also ice XV. The appearance of ice XIX is governed by the PV term in the Gibbs energy expression, because the volume contraction thermodynamically stabilises ice XIX compared to ice XV. In this context, the phase boundary between ice XV and ice XIX should have a slope rather than lie horizontally as suggested previously13,16, because ice XV has a larger volume than ice XIX (the supposed phase boundary in Fig. 1 is shown vertically to emphasise this point). It is noteworthy that the phase transition between ice VI and XIX showed hysteresis for the transition temperature (Supplementary Fig. 1). This first-order phase transition is consistent with the sudden change in dielectric properties between ice VI and ice XIX (Fig. 2).
Neutron diffraction experiments were conducted at 1.6 and 2.2 GPa to confirm whether ice XIX is a hydrogen-ordered crystalline phase distinct from ice XV. Both cooling and heating runs were conducted at each pressure in the temperature range 80–150 K.
A transition from ice VI to ice XIX was also observed in the neutron diffraction experiments, as appearance of new peaks due to symmetry lowering (Fig. 3a). Some of the new peaks, e.g. those at 2.20 Å and 2.26 Å (indicated by blue triangles in Fig. 3a), cannot be assigned to the unit cell of ice XV; instead, they can be assigned to an expanded √2 x √2 x 1 cell with respect to the unit cell of ice VI (the unit cell of ice XV has a 1 x 1 x1 cell with respect to that of ice VI). This is unambiguous evidence that the hydrogen-ordered phase found in the higher-pressure region is a crystalline phase distinct from ice XV, and that ice VI has two different types of hydrogen ordering. The reflection conditions show that the unit cell of ice XIX has a primitive lattice. The reduced unit cell parameters of ice XIX, a and c, corresponding to the unit cell of ice VI, are expanded and contracted, respectively, upon hydrogen ordering (Fig. 3b); this tendency was also observed at 2.2 GPa. A comparison of the temperature dependences of c/a at 1.6 and 2.2 GPa (Fig. 3c) showed that the phase-transition temperature at 2.2 GPa was at about 7 K higher than that at 1.6 GPa. This result is consistent with the phase boundary between ice VI and XIX obtained by the dielectric experiments. On the other hand, no significant volume change was observed in our neutron diffraction experiments, in contrast to the expected negative volume change (∆V < 0) upon hydrogen ordering, probably due to the small volume contraction.
For the structure analysis of ice XIX, we considered candidates of its space group based on the group–subgroup relationship between ice VI and XIX, in addition to the experimentally confirmed reflection conditions. There are 36 subgroups for the space group of ice VI, P42/nmc, considering the primitive unit cell of ice XIX. Among them, thirteen space groups, having \(h0l:h+l=2n\) and \(0kl:k+l=2n\) reflection conditions, can be excluded from the observed reflection conditions. We conducted Rietveld analyses using structural models with 18 space groups of the remaining candidates, except for the lower-symmetry space groups: Pc, P21, P2, P\(\stackrel{-}{1}\) and P1—this cut-off is based on indices of the subgroups of P42/nmc (see details in Supplementary information). Notably, we do not rule out the possibility that the actual crystal structure of ice XIX having one of these space groups, although sufficient refinement agreements were obtained for the 18 candidates from our neutron diffraction data. A structural model of each candidate was constructed using a partially ordered model adopted in an earlier study8. P\(\stackrel{-}{4}\) or Pcc2 structural models are the most plausible for the space group of ice XIX, based on the structure refinements. Considering the suggested space group of ice XV, P\(\stackrel{-}{1}\)14 or Pmmn8, centrosymmetry of hydrogen configurations is the most significance difference in hydrogen configuration between ice XIX and ice XV. In particular, Pcc2 suggests a pyroelectric structure as well as ice XI and its polar direction is along the c axis. Although further investigations, such as a single-crystal neutron diffraction experiment, are necessary to precisely determine the hydrogen configurations, centrosymmetry will be an intriguing point in structural studies of ice XV and XIX.
Past arguments for the second hydrogen-ordered phase of ice VI should be mentioned here 7,13,15−17. The existence of such a phase (β-XV13) was suggested by Gasser et al. in samples decompressed from above 1.45 GPa to ambient pressure using various measurements13. For example, differential scanning calorimetry (DSC) experiments show an endotherm peak which cannot be assigned to the known phase transition between ice VI and XV. Rosu-Finsen et al.15 reported detailed DSC experiments conducted at different heating rates and using different quenching/annealing procedures. Their DSC results clarified that the peak also appeared for quenched samples decompressed from 1.0 GPa, where ice XIX does not appear13,15,16, and its appearance/disappearance depends on the heating rate of the DSC experiment. Based on these results, they questioned the supposed existence of a second hydrogen-ordered phase13, and explained the observed DSC profiles by introducing the idea of the deep-glassy state of ice VI. Meanwhile, based on the high-pressure observations presented herein, we firmly confirmed the presence of second hydrogen-ordered phase of ice VI, ice XIX, as a crystalline phase distinct from ice XV. In our view on the past arguments, although the samples decompressed from the higher-pressure region should have undergone hydrogen ordering from ice VI to ice XIX, further investigation is necessary to confirm whether the samples retain the crystal structure of ice XIX at ambient pressure. This is because the idea of the deep-glassy state seems reasonable for the DSC results of their decompressed samples, and additionally on comparing our dielectric loss data to that measured under ambient pressure13, revival of reorientation dynamics, which should be immobilised upon hydrogen ordering2, was evidenced by a reappearance of dielectric loss in the decompressed samples13 (Supplementary Fig. 1b). This reactivated reorientation might partially break the long-range hydrogen order of ice XIX to obtain more stable configurations under lower pressure. It is necessary to ensure consistency among all the observed data, based on both the newly found ice XIX and the concept of the deep-glassy state.
This study first demonstrates the existence of multiple hydrogen-ordered phases for a hydrogen-disordered phase and clarifies the effectiveness of applying pressure to induce phase competition among the hydrogen-ordered phases. Based on previous theoretical studies8–11 and the currently known phase diagram of ice, the low-temperature region of the phase diagram (below approx. 150 K) is a frontier region for exploring undiscovered ways of hydrogen-ordering in ice, which would greatly change the phase diagram of ice. It is additionally noteworthy that the unit cell size of ice XIX allows many possible hydrogen-ordered configurations (1964 symmetry-independent configurations), such that an exhaustive theoretical analysis for the all configurations is difficult. However, such a wide variety of hydrogen-ordered configurations and their stability evaluations might be a good benchmark for modern theoretical trials toward modelling biochemical and environmental processes with large water molecules, such as using topological graph invariant theory20, combining oriented graph theory and density functional calculations, which can evaluate the energy stability of a large number of water-molecule arrangements. To the best of our knowledge, this is the first report in a hydrogen-bonded material for which different hydrogen-ordered configurations are realised depending on the pressure, although electric field is a known effective parameter to control ferro- and antiferroelectric structures of organic compounds21,22. This newly discovered coupling between hydrogen bond and pressure will extensively develop a new research field of the pressure-controllability of hydrogen-ordered configurations. Furthermore, by combining high-electric field with high-pressure, this multi-extreme condition is expected to provide more various types of hydrogen ordering and physical properties (e.g. (anti-)ferroelectricity) to hydrogen-bonded materials. Very recent technical development of neutron diffraction experiment23 will encourage such novel exploration in P-T-E phase diagram focusing on the multiplicity of hydrogen-ordered phases.