New diversity form of ice polymorphism: Discovery of second hydrogen ordered phase of ice VI

More than 20 crystalline and amorphous phases have been reported for ice so far. This extraordinary polymorphism of ice arises from the geometric flexibility of hydrogen bonds and hydrogen ordering, and makes ice a unique presence with its universality in the wide fields of material and earth and planetary science. A prominent unsolved question concerning the diversity is whether a hydrogen-disordered phase of ice transforms into only one hydrogen-ordered phase, as inferred from the current phase diagram of ice, although its possible hydrogen configurations have close energies. Recent experiments on a high-pressure hydrogen-disordered phase, ice VI, revealed an unknown hydrogen-ordered form ($\beta$-XV) besides the known ordered phase, ice XV, which would be a counterexample of the question. However, due to lack of experimental evidence, it has not been clarified whether $\beta$-XV is a distinct crystalline phase. Herein we report a second hydrogen-ordered phase for ice VI, ice XIX, unambiguously demonstrated by neutron diffraction measurements. The phase boundary between ice VI and ice XIX shows that ice VI contracts upon the hydrogen ordering, which thermodynamically stabilizes ice XIX in higher-pressure region than ice XV because of its smaller volume than ice XV. The pressure-driven phase competition between hydrogen-ordered phases, also theoretically suggested in other ice polymorphs, can induce hydrogen ordering of ice in different manners. Thus, this study demonstrates a hitherto undiscovered polymorphism of ice.

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 ice 14,15 . 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 GPa 4 ), 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 previously 8,11 , 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 (Extended data 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 × √2 × 1 cell with respect to the unit cell of ice VI (the unit cell of ice XV has a 1 × 1 × 1 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, P4 2 /nmc, considering the primitive unit cell of ice XIX. Among them, thirteen space groups, having ℎ0 : ℎ + = 2 and 0 : + = 2 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, P2 1 , P2, P1 ̅ and P1-this cut-off is based on indices of the subgroups of P4 2 /nmc (see details in Supplementary). 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 study 4 . P4 ̅ 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, P1 ̅ 9 or Pmmn 4 , 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 3,8,10-12 .
The existence of such a phase (β-XV 8 ) in decompressed samples from above 1.45 GPa was first suggested by Gasser et al. using various measurements at ambient pressure 8 . For example, differential scanning calorimetry (DSC) gave an unassignable endotherm peak from the known phase transition between ice VI and XV. Rosu-Finsen et al. 10 reported further detailed DSC experiments conducted under ambient pressure at different cooling/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 did not appear 8,10,11 , and its appearance/disappearance depends on the heating rate used in the DSC experiment. Based on these results, they questioned the supposed existence of a second hydrogen-ordered phase 8 , and suggested another scenario by introducing the idea of the deep-glassy state of ice VI to interpret the observed DSC profiles. Based on the in-situ observations presented herein, we firmly confirmed the presence of a second hydrogen-ordered phase of ice VI under high pressure, and named it ice XIX, as a crystalline phase distinct from ice XV. In our view for the past arguments, although the decompressed samples in the higher-pressure region should undergo hydrogen ordering from ice VI to ice XIX before decompression, it is necessary to investigate whether the decompressed samples retain the crystal structure of ice XIX as well as its crystallinity. This is because the idea of the deep-glassy state seems reasonable based on the DSC profiles of their decompressed samples, and on comparing our in-situ dielectric loss data to that measured under ambient pressure 8 , revival of reorientation dynamics, which should be immobilised upon hydrogen ordering 15 , was evidenced by a reappearance of dielectric loss of the decompressed samples under ambient pressure 8 (see also Extended Data Fig. 1b). This reactivated reorientation might partially break the long-range hydrogen order of ice XIX to obtain more stable configurations under lower pressure. Further investigation 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 studies 4-7,16 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 theory 17 , 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 also the first report of 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 hydrogen-bonded ferroelectrics 18,19 . This newly discovered coupling between hydrogen bond and pressure will extensively develop a new research field focusing on the pressure-controllability of hydrogen-ordered configurations, which potentially include significant physical properties, e.g.
piezo-and (anti)ferro-electric, using established techniques of neutron diffraction experiments.

Figure 1| Representative experimental paths of dielectric and neutron diffraction experiments described in the phase diagram of ice obtained herein. Dielectric experiments of ice VI and its
hydrogen-ordered phases were conducted at 0.88-2.2 GPa. HCl (99.9%, Wako) was introduced as a dopant (concentration: 10 -2 M) to accelerate the hydrogen ordering of ice VI 20 . The measured temperature was in the range 100-150 K and changed at a rate of 2 K/h. Neutron diffraction experiments of DCl-doped D 2 O (concentration: 10 -2 M) were conducted using a more complicated path to ensure that the sample was a fine powder through solid-solid phase transitions, i.e., ice III→ice V→ice VI. Sample diffraction was collected at 1.6 and 2.2 GPa, and the temperature range was 80-150 K. Temperature was changed at a rate of 6 K/h. Diffraction patterns were collected using new samples in each run at different pressures to confirm reproducibility. Phase boundaries among ice VI, ice XV, and ice XIX are described by black solid lines, based on dielectric experiments (red and blue squares correspond to phase transition temperatures from ice VI to ice XV and XIX, respectively). The dotted line shows the provisional phase boundary between ice XV and ice XIX (see main text).

Figure 2| Temperature dependence of dielectric properties of HCl-doped ice VI and its
hydrogen-ordered phases. a, Dielectric constant and dielectric loss of HCl-doped ice VI and its hydrogen-ordered phase (ice XIX) obtained at 1.9 GPa upon cooling. The measured frequency was from 3 mHz to 2 MHz. b, Temperature dependence of dielectric loss peak intensity of HCl-doped ice VI and its hydrogen-ordered phases obtained in the pressure range 0.88-2.2 GPa upon cooling (black diamonds). Each peak intensity of dielectric loss was estimated using a model fitting the corresponding dielectric loss spectrum based on the Debye dielectric-relaxation equation (polydispersion type). Under each pressure, peak intensities were normalised by that obtained at the highest temperature. Each plot was shifted by 0.7 with increasing pressure for clarity. The grey lines were separately fitted for the data of loss peak intensity originating from ice VI and its hydrogen-ordered phases at each pressure. The phase-transition temperature was defined by an intersection of the two grey lines. The black arrows indicate the phase transition temperature at each pressure.

Dielectric measurements
We conducted in-situ dielectric measurements under high pressure using a newly developed cell assembly. One of the most notable features of our development is that along with measuring the dielectric properties of the sample, the sample pressure can be simultaneously estimated using the ruby fluorescence method. This feature allows us to closely investigate the phase structure of ice in terms of its hydrogen ordering. The cell assembly is based on a piston-cylinder-type high-pressure apparatus (see details of the cell assembly in Supplementary Information)

Neutron diffraction measurements
The neutron diffraction measurements were conducted at PLANET beamline 11 at the Materials and Life Science Experimental Facility of J-PARC, Ibaraki, Japan 21 . DCl-doped D 2 O sample was used as a starting material (DCl concentration: 10 -2 M), and ice VI was prepared through solid-solid phase transitions, ice III→V→VI, to obtain a fine powder sample (Fig. 1). Pressure and temperature were controlled by using a Mito-system 22 , and the pressure was estimated from the lattice parameter of Pb, which was added to the sample as a pressure marker 23 .

Structure analysis of ice XIX
Initial candidates of ice XIX were determined based on the group-subgroup relationship between ice VI and XIX, using the SUBGROUPS program opened on the Bilbao crystallographic server 24-26 . The structural models for the 18 space group candidates were constructed based on the partially hydrogen-ordered model adopted in a previous study 4 . Hydrogen occupancies and atomic coordinates were the fitting parameters obeying the ice rule in this model (details of the 18 structural models are given in Supplementary Information). Structure refinements were conducted for the neutron diffraction patterns corrected at 1.6 GPa and 80 K using all the structure models employing the Rietveld method (program: GSAS with EXPGUI 27,28 ). We used the initial structural parameters with the ice VI structural model, based on the neutron diffraction pattern obtained at 1.6 GPa and 80 K. It was noted that site occupancies of hydrogen atoms were initially considered fitting parameters in the refinements with fixed atomic positions of hydrogen. χ 2 values of the structure models are plotted in Extended Data Fig. 3, where numerical values are shown only for five candidates with χ 2 < 9. For each structural model, Rietveld refinements were performed several times to confirm their reproducibility. The space group P4 ̅ was deemed the most plausible candidate in this step. Extended Data Fig. 4 shows fitted lines using the five possible structural models (red-coloured) for the neutron diffraction pattern obtained at 1.6 GPa and 80 K (black lines). It should be mentioned that an observed Bragg peak, marked by a black tick at 1.82 Å, shows broadening compared to the simulated ones. This peak is derived from the new hydrogen-ordered phase. Generally, peak broadening arises from two factors, insufficient crystallite size and/or microstrain in the crystal, consistent with the partially hydrogen-ordered state of ice XIX. Structure refinements, including atomic positions of hydrogen, were conducted for the five candidates (Extended Data Fig. 5); the fitted results obtained employing only hydrogen occupancies as fitting parameters (Extended Data Fig. 4) were subsequently used for these refinements. χ 2 values of P4 ̅ and Pcc2 were comparable considering the dispersion of their refinement results, and those structural models were considered the most plausible for ice XIX. Atomic fractional coordinates for ice XIX using the two models are shown in Extended Data Tables 1 and 2, where lattice parameters have also been refined. Figure 1| Comparison of the phase transition in cooling and heating runs at 1.9

Extended data
GPa. a, Each peak intensity of dielectric loss is normalised by that obtained at the highest temperature in each run. At temperatures lower than the lowest temperature points shown in the figure, the dielectric response of ice XIX almost disappeared in the measured frequency region; thus, the peak intensity in that region is not shown here. Each of the cooling and heating results corresponds to the data shown in Fig. 2a (main text) and this Extended Data Fig. 1b, respectively. b, Dielectric constant and dielectric loss of HCl-doped ice VI and its hydrogen-ordered phase (ice XIX) obtained at 1.9 GPa upon heating. The measured frequency ranged from 3 mHz to 2 MHz. Figure 2| Temperature dependence of dielectric loss peak intensity of DCl-doped D 2 O ice VI and its hydrogen ordered phases obtained from 1.1 to 2.0 GPa. Peak intensities are normalised by that obtained at the highest temperature in each pressure run. Each plot was shifted by 0.5 with increasing measured pressure for clarity. The black diamonds represent obtained data. The grey lines were separately fitted to the data of loss peak intensity originating from ice VI and its hydrogen-ordered phases at each pressure (Fitted lines for 1.3 GPa are not shown due to its ambiguous change in the slope). The black arrow indicates the phase transition temperature at each pressure.

Extended data
Extended data Figure  Extended Data Table 1| Atomic fractional coordinates for ice XIX using P4 ̅ (tetragonal) structure model (lattice parameters: = = 8.61941(7) and = 5.59297 (8)  The dielectric response in the lower frequency region (below 10 Hz at 240 K) is derived from the DC electric conductivity of the sample. Temperature dependence of dielectric constants and loss shows that the frequency dispersion derived from the molecular rotation (10 3 Hz at 240 K) shifts to lower frequency with decreasing temperature. This means that the dynamics of molecular rotation becomes slowdown with decreasing temperature. As the most important point shown in Supplementary Figure   2, the dielectric response of non-doped ice VI almost disappears at 160 K in the measured frequency range due to the slowdown of the molecular-rotation dynamics. No dielectric response was shown at the hydrogen-ordering temperature of ice VI observed in HCl-doped sample (at ~130 K).

Supplementary Methods: Details of the 18 candidates
Supplementary Figure 3 shows definitions of site labels of hydrogen atoms for the 18 structure models. Corresponded site occupancies of the hydrogen atom sites are represented by one or a few variables, denoted by Greek letters (Supplementary Table 1), which are actually fitting parameters for the Rietveld refinements using hydrogen site occupancies.

Supplementary Note: the criterion of "higher and lower symmetry" space group
We only took account of 18 candidates of "higher symmetry" space groups for the structure analysis of ice XIX as mentioned in the main text. Considering two structure models, whose space groups are related by group-subgroup relationship, the subgroup structure model generally shows better agreement with the experimental data comparing with the structure model of its parent space group.
Hence we set a criterion of "lower symmetry" space groups disregarded in this study based on a quantitative index, Group-Subgroup index. We consider a space group, represented by G. G is an infinite group due to its translation symmetry. Its translation operations make normal subgroup, H, of the space group, G. A coset of G by H, denoted by G/H, makes a quotient group. G/H is composed of finite elements and the number of elements is called order of G/H, represented by |G/H|. For example, let us take P1 as an example space group of a crystal structure, S. When we choose a minimum unit cell of the S, T(P1) is defined by all translation operations corresponding to the unit cell. Then, |P1/T(P1)| = 1 holds. Hereafter, we consider a case that S is the crystal structure of ice VI. In the case of the space group of ice VI, P4 2 /nmc, |P4 2 /nmc/T(P4 2 /nmc)| is 16. When the unit cell of ice VI is expanded to √2 × √2 × 1, the cell volume becomes two times larger. We represent corresponded translation operations as √2×√2×1 (P4 2 /nmc). Then an order |P4 2 /nmc/ √2×√2×1 (P4 2 /nmc)| is 32. The Group-Subgroup index, s, is defined as follows: where H is a subgroup of P4 2 /nmc. For example in a case, H = P1 ̅ , Group-Subgroup index, s, is 16.
Because, P1 ̅ /T(P1 ̅ ) includes two elements; one is for trivial equivalent symmetry and the other one is about inversion symmetry. In this study, we ignored five space groups, Pc, P2 1 , P2 and P1 ̅ and P1, and this means that we only considered space groups, whose Group-Subgroup indexes are less than 8 from their sufficient refinement agreements for the neutron diffraction patterns. Space groups with