Experimental evidence for the existence of a second partially-ordered phase of ice VI

Ice exhibits extraordinary structural variety in its polymorphic structures. The existence of a new form of diversity in ice polymorphism has recently been debated in both experimental and theoretical studies, questioning whether hydrogen-disordered ice can transform into multiple hydrogen-ordered phases, contrary to the known one-to-one correspondence between disordered ice and its ordered phase. Here, we report a high-pressure phase, ice XIX, which is a second hydrogen-partially-ordered phase of ice VI. We demonstrate that disordered ice undergoes different manners of hydrogen ordering, which are thermodynamically controlled by pressure in the case of ice VI. Such multiplicity can appear in all disordered ice, and it widely provides a research approach to deepen our knowledge, for example of the crucial issues of ice: the centrosymmetry of hydrogen-ordered configurations and potentially induced (anti-)ferroelectricity. Ultimately, this research opens up the possibility of completing the phase diagram of ice.

authors observation of no volume change from diffraction) up to the last data point at 2.2 GPa at which, clearly, the transition temperature changes. However, could not the change of the 2.2 GPa data point be related to the approach to an ice VIII boundary?
In summary, on this point, although I don't claim my interpretation is more valid than the authors, I believe it illustrates a weakness in their volume argument and the location of the transition. In particular, the data should be presented with a serious analysis of systematic and random errors that could affect the transition temperatures extracted in this way. The proposal of a transition and, especially, the volume change have to be critically judged in light of this.
I then wanted to comment on the neutron data. The measurements were conducted along isobars at 1.6 and 2.2 GPa. c/a data are shown at both pressures, but the diffraction data are only shown at 1.6 GPa. The authors point to the appearance of weak, but to me unambiguous, peaks that appear in the diffraction pattern following a reduction of c/a ratio. This is quite convincing evidence of an ordering transition. As the new peaks are unindexed on ice VX, it does suggest that a new phase has been formed. I would have liked to see the data at 2.2 GPa and it's not clear why this doesn't appear in either the main manuscript or the supplementary material. It would surely be important to show that the same peaks were observed as at 1.6 GPa? I would also have been interested to see data at the same temperature, but lower pressure: the absence of these new peaks would strengthen the evidence for the location of the phase transition. This would be helpful especially as the DLPI data for the D2O sample seems less clear than for H2O. I noted that in the neutron data, the new peaks appear between 108 and 115 K, but this seems to be cooler than the transition temperatures given by the DLPI. I wondered if this was an isotope effect (the D2O DLPI data seem less reliable than the H2O so hard to say), or whether it might also be an effect of cooling rate?
The authors conducted a quite thorough investigation of possible model fits to the neutron data and this is perhaps the most valuable work in the paper. I noticed that the consistent misfits of the peak width at ~1.81 Å seem to be due to a large, Lorentzian-like broadening of the measured peak. Since such a peak-shape is often associated with particle-size effects, I wondered if this could be due to finite domain sizes of the ordered phase. In this case, they would be quite directional as only this peak is affected. Maybe this is worth further comment.
Lastly, on the refinements, there were several places where it was mentioned that the refinements were "conducted several times for each model" and the subsequent χ2 values "averaged values over several refinement results". This seemed an unusual process to me, as I would expect a given model to converge to the exact same structure when refined to the same data. If it is true that the model converges to different local minima upon successive refinement cycles, it implies to me that something may be wrong and parameters in the refinement are unstable. I would wish the authors to comment further on this and to reassure me that the data are not being 'over fitted' with more parameters than available data points. In the case that data are being over fitted, the selection of a model, on the basis of it giving the lowest χ2 may not be robust. It would have been helpful in the review to have had a cif file and a secondary check on the model would have been whether sensible O-D bondlengths were obtained (coordinates are given, but I'm afraid I didn't have time to enter all of these manually). Also, were these freely refined or were constraints used?
Beyond the discussions above, I had several minor further queries, listed here: line 90: "the phase boundary between ice XV and XIX should have a slope rather than lie horizontally as suggested previously". I found this confusing as the phase diagram the authors use has pressure on the x-axis and temperature on the y-axis. In this case, the transition between XV and XIX should be approximately vertical not horizontal? line 156 and 162 attempt to reconcile DSC measurements on recovered samples, interpreted in terms of a "deep-glassy state of ice VI" with their observation of a new, ordered, crystalline phase. The authors seem to suggest that their ordered phase may disorder upon pressure lowering. This, to me, seemed a little counter intuitive: even if hydrogen mobility increases as pressure reduces, where would the additional energy come from to disorder the dipoles, which are already in an lower energy ordered state? The authors should provide some further justification for their explanation.
line 183 mentions "large water molecules" what does this refer to? Aren't all water molecules the same size?
Supplementary line 99: From the description of the pressure measurement, via ruby fluorescence, it seemed quite plausible to me that there would be a systematic deviation between ruby pressure and sample pressure, due to pressure gradients and that the ruby lies at one end of the sample. Given that the uncertainty in transition pressures of a few kbars would have a significant effect on the drawing of phase boundaries, did the authors attempt to quantify this and (if necessary) apply a correction?
Reviewer #2 (Remarks to the Author): For the first time, a new hydrogen-ordered ice-phase has been described which shows a different hydrogen-ordering as compared to the already known hydrogen-ordered phase (ice XV) relating to the same known hydrogen-disorders phase (ice VI). The discovery, however, of such a phase belongs to Gasser et al., having reported on a beta-ice XV in 2018.
However, here is shown the first, unambiguous, structural evidence (by neutron diffraction) of such a phase.
Beside this, the paper presents a new technical development of a pressure cell allowing dielectric measurements.
Dielelectric measurements delivered the first hints for a second, high-pressure form XIX in the phase boundary region of ice VI, XV and XIX. I fully back these results.
Then, neutron powder diffraction (avoiding formation of single crystals by a well-chosen pressuretemperature path) shall establish the experimental basis of an unambiguous structure analysis, showing a different hydrogen (well, deuterium) order as compared to ice XV. Structure solution was performed using group-subgroup relationships to find the potential ordering models to be tested. Out of the 18 possible subgroups, five were able to explain the observed diffraction patterns, and two of them have been retained as possible structure models.
Here comes my criticism: The selection was seemingly been done by comparison of chi2 values as a criterion for the goodness of fit. The differences are not dramatic, as the supplementary figure 4 shows on the five best candidates. The final two candidates have been selected from these two only on the numerical chi2 argumentation. This is, unfortunately, not satisfying, although I must admit that one has barely any other choice. All structure models seem to explain all observed peaks (except the retained Pcc2 one, where the peak at about d=2.28AA seems not to be explained ...). There's no further indication that the finally selected models are truly the good ones.
On the other side, the structure of XV is not unambiguous neither --and it (seems to have) has different possibly symmetries as compared to ice XIX (not only the two retained models, also the five best ones, even the 18 considerable ones). This shall be valid as structural proof for ice XIX being of different structure as compared to ice XV, thus, a new phase.
So this work does NOT reveal the structure of ice XIX, it just confirms anew phase by conclusive dielectric measurements involving a new technical device development and structure analysis on neutron powder diffraction. The structure remains clearly unknown, but it seems to be clearly different from any potential ice XV structure. This discovery is sufficiently important to be published in a science journal read by many communities (geosciences, physics, physical chemistry, crystallography...), but it remains somehow unsatisfying. I know how difficult it is to get better quality neutron diffraction data from high pressure devices, and how difficult it will be to get even a single crystal, therefore I cannot ask the authors for much additional information to be incorporated right now.
Despite my concerns, I suggest the paper for publication. I do not insist on rephrasing, although some phrasing could have been clearer (especially to avoid the final deception at the end, when the interested reader does not find the expected unambiguous structure solution).

Reviewer #3 (Remarks to the Author):
This paper reports on experiments on H2O ice in the range 0.88-2 GPa and low temperatures using dielectric and neutron diffraction methods, and claims the discovery of a new hydrogen-ordered form of ice VI referred to as ice XIX. With ice XV, this would be the second H-ordered form of ice VI, and a counter-example of the presently observed bijective relation between H-disordered and Hordered phases. Ice XIX is located in the same P-T region as a previously reported variant of ice XV denoted beta-XV [Ref. 13]. Compared to this previous work in which ice samples were obtained at high pressures and then characterized on pressure-quenched samples, the present authors performed in situ studies. My general opinion is that although the experimental data appear solid and point to a different structure of ice than ice XV, the present work does not constitute a major progress from what was already known from the previous study cited above which would justify its publication in Nat. Comm. I also believe that before claiming a new phase of ice and assigning a Roman numeral to it, its structure should be firmly established, which could not be achieved in the present study. In addition, I find that the discussion of the dielectric data is poor compared to the rather exhaustive analysis of the neutron data. Detailed comments are given below: -The quantitative analysis of dielectric data is poor: only the shift of the loss peak intensity with T is reported. What about the relaxation time and related activation energy which can be inferred from the peak frequency ? There is an apparent change of slope sign at 1.6 GPa (from negative to positive) in the loss peak intensity vs T evolution in the ice VI domain ( Fig. 2b and Fig. S2), which is not commented at all. Dielectric data on non-doped H2O is reported in SM but not mentioned in main text and are barely commented, although clear differences with the data on doped ice are apparent. How do the authors explain these differences ? -In figure S1a, the authors report the loss peak intensity from 124 K to 150K. However from Figure S1b the peak at 124 K is clearly not in the measured frequency window, how did the authors obtained its intensity ? It would also be useful to the readers if the authors gave the complete set of dielectric data they measured at each pressure in the SM.
-The authors define the disorder-order phase transition as the temperature at which the slope of the loss peak intensity changes. What is the physical basis for this definition ? Similarly, the author state that the transition is first order, however both dielectric signals and lattice parameters appear to change continuously over a temperature range of ~10 K, which at first-sight is not compatible with a first-order process. It is possible that the continuous character arises from the coexistence of the two phases and kinetics of the transition but this has to be discussed.
-Comparison with the data on beta-XV phase reported by Gasser et al [Ref. 13] is absent. How do the authors's dielectric data compare with those reported in this work? Do the authors think that their ice XIX is the same as Gasser et al's ice beta-XV, and if not why ? Did they try to recover samples of ice XIX at room pressure and characterize them as in Ref. 13 ? -There are little discussion on kinetic effects in the experiments, which are known to be very important in the low T regime of the present experiments. In particular, the cooling rate in dielectric experiments is not specified. Did the authors perform measurements at different cooling rates ?
-The data is presented as isobaric scans. Can the authors explain how pressure was kept constant upon varying temperature ?
-The authors say that they did not consider the 5 lowest symmetry space group in their neutron powder refinement as "sufficient refinement agreements" were obtained for the other 18. They should specify what they mean by sufficient agreement, preferably in a quantitative manner.
-The authors say "centrosymmetry of hydrogen configurations is the most significance difference in hydrogen configuration between ice XIX and ice XV". But they found that P-4 is one of the most plausible space group of ice XIX, which to my understanding is a centrosymmetric group.
-As a minor comment, I find the title expression "new diversity form of ice polymorphism" rather odd and unclear. I had to read the abstract to understand its meaning. I suggest to remove it or find a better one. #Reviewer 1 We appreciate Referee 1's helpful comments. Firstly, we will mention the modifications regarding the phase boundary between ice VI and its hydrogen-ordered phases, ice XV and XIX. This would be the main concern of Reviewer 1, as commented below:

In summary, on this point, although I don't claim my interpretation is more valid than the authors, I believe it illustrates a weakness in their volume argument and the location of the transition. In particular, the data should be presented with a serious analysis of systematic and random errors that could affect the transition temperatures extracted in this way. The proposal of a transition and, especially, the volume change have to be critically judged in light of this.
We reconsidered the definition of the phase transition temperatures, which was previously defined as the intersection of two straight lines fitted to the temperature dependence of dielectric loss peak intensity (DLPI) derived from ice VI and its hydrogen-ordered phases in the original submission. As indicated by Reviewer 1, the previous definition includes arbitrariness depending on how the two fitting regions are divided, we reanalyzed the temperature dependence of DLPI by the least arbitrariness, as shown from the following paragraph. Additionally, concerning the lower temperature region in which hydrogen ordering occurs, there is uncertainty for the previously employed linear approximation due to insufficient data points (this was also indicated by Reviewer 1). In the new definition, the DLPI of ice VI is assumed to be linearly dependent on temperature, and the phase transition temperature is redefined as the temperature at which the DLPI starts to deviate from the linearity. This deviation is caused by the hydrogen-ordering of ice VI as mentioned in our original manuscript. The following is the procedure for determining the deviation, taking the case of 1.9 GPa as an example. The raw DLPI data in the cooling run at 1.9 GPa are shown below (Figure 1-1; in this letter, we named figures by Figure "reviewer comment number-sequential number").

Figure 1-1| Temperature dependence of dielectric loss peak intensity (DLPI) of
HCl-doped ice VI and its hydrogen-ordered phase (ice XIX) at 1.9 GPa upon cooling 1. First, it is obvious that the hydrogen ordering transitions occurred above 122 K in the cooling run. From this temperature, the DLPI data were obtained at several temperature points. In the case of the cooling run, {122, 124, 126, 128, 130, and 132} were selected. Hereafter, the number of selected temperature points is denoted by N.
2. Let us consider a temperature set selected in the same manner of step 1. We represent an element of the temperature set by Ti, where i takes from 1 to N and Ti < Ti+1. Linear fitting is conducted for the DLPI data, { ! , ⋯ , "#$ }, obtained in the temperature range from Ti to the highest temperature of the measurement (Tmax; Tmax was 150 K at 1.9 GPa). The fitted DLPI data are denoted by & ' ! , ⋯ , ' "#$ (.

3.
We calculate the residual sum of squares (RSS) between the observed { ! , ⋯ , "#$ } and the fitted & ' ! , ⋯ , ' "#$ (, and then the RSS is normalized by the number of the DLPI data, { ! , ⋯ , "#$ }. Hereafter, the normalized RSS is denoted by ! . Let us consider that we decrease i from N (corresponding to a decrease of temperature Ti). When the hydrogen ordering happens, the normalized RSS should become large compared to that obtained above transition temperature due to the deviation from the linearity. This behavior can be shown in the following figure at around 126 K in the cooling run ( Figure 1-2).

Figure 1-2|
Temperature dependence of normalized RSS in the cooling run at 1.9 GPa 4. Finally, to judge the phase transition temperature, we evaluate ! !%& ⁄ (i takes from 1 to N-1). The figure below shows the temperature dependence of the ratio ! !%& ⁄ obtained at various pressures (Figure 1-3). In this figure, the values of the ratio are nearly 1 in higher temperature region where ice VI is stable. This is because fitting residuals of ! and !%& take similar values owing to good linearity between DLPI and measured temperature. Based on the results, Figure 1-4 shows the phase diagram of ice VI and its hydrogen-ordered phases, determined using the ratio ! !%& ⁄ of 1.5, 2, and 3 of as criteria values for the phase transition (Figure 1-4). The transition temperature is determined by (Ti + Ti+1)/2, whose ! !%& ⁄ is first above the criteria with decreasing of Ti from N. The displayed error bars show the temperature range from Ti to Ti+1. The three phase diagrams are only slightly different, and the main feature of the negative/positive dT/dP slope of ice VI and XV/XIX phase boundaries is common to all criteria. The relatively low transition temperature at 2.0 GPa might be caused by supercooling, which is a feature of first-order phase transition. In this study, the ratio, 2, was chosen as the criterion, because the criterion of 1.5 is occasionally too strict for the ratio obtained before the transition temperature; for example in the data of 1.6 GPa, the ratio is 1.42 and 1.37 at 122.5 and 125 K, respectively (Figure 1-3). If the criterion is too strict, the phase transition temperature would be overestimated. In addition, the ratio, 3.0, may underestimate the transition temperature considering such as the case of 1.7 and 2.0 GPa (see Figure 1-3). In the phase diagrams, the provisional phase boundary between ice XV and XIX is denoted between two pressures where the transition temperature increases (decreases) (2016)), although we have no explanation for the isotope effect.  Figure 2b, we previously showed the temperature dependence of DLPI obtained at 1.3 GPa, but the data are not shown in the modified figure due to the small number of data points compared to other pressures. The analysis of the phase transition temperature from ice VI to its hydrogen-ordered phases was added in Supplementary material.

Figure 1|
Representative experimental paths of dielectric and neutron diffraction experiments described in the phase diagram of ice obtained herein.

Figure 2| Temperature dependence of dielectric properties of HCl-doped ice VI and its hydrogen-ordered phases.
Hereafter, based on the above discussion, we reply Referee 1's comments in order. Fig 1 and  In the modified determination of the transition temperatures, the coloring was changed between 1.5 and 1.6 GPa from which the transition temperature increases with increasing pressure. Additionally, in this revision, we have added a new figure to supplementary material regarding the temperature dependences of relaxation times following the advice from Reviewer 3. This figure would also resolve the concern that "the 1.6 GPa point this appears to artificially lower the transition temperature". As known in other hydrogen ordering of ice, such as from ice Ih to XI, the relaxation time becomes longer accompanied with the phase transition due to the suppression of molecular reorientation. We observed this phenomenon in the case of ice VI (see the below Figure 1-5). In the figure, the phase transition from ice VI to ice XIX can be seen more obviously than our DLPI result. Also, the phase transition observed at 1.6 GPa occurs more firmly at the lowest temperature than at the higher pressures. It is noted that the relaxation time reflects the hydrogen ordering at a slightly lower temperature than DLPI. This could be related to the difference in the degree of domain growth of the ordered phase to change relaxation time and DLPI. On the other hand, it is difficult to determine the phase transition between ice VI and XV from the temperature dependence of relaxation time due to its slight change accompanied by the hydrogen ordering. This is the reason why we did not use the data of relaxation times for the phase-boundary analysis. We added the analysis of dielectric relaxation to Supplementary Material (content 1).  As suggested by Referee 1, we added the neutron diffraction patterns obtained at 2.2 GPa in supplementary material as shown below (Figure 1-6). The diffraction patterns also show obvious change along with the hydrogen ordering, which occurs at a higher temperature compared to the diffraction pattern obtained at 1.6 GPa. Two important new peaks were observed at around 2.2 Å (indicated by blue ticks), which is the evidence that ice XIX has a distinct crystal structure. It should be mentioned that ice VIII (indicated by a black tick) coexists under the pressure. Since ice VIII already appears from 150 K and the existence of ice VIII would not affect the Gibbs's energy of ice VI and XIX (in other words, their transition temperature), it would be reasonable to consider that the higher transition temperature at 2.2 GPa is a consequence of the positive dT/dP slope.

I noted that in the neutron data, the new peaks appear between 108 and 115 K, but this seems to be cooler than the transition temperatures given by the DLPI. I wondered if this was an isotope effect (the D2O DLPI data seem less reliable than the H2O so hard to say), or whether it might also be an effect of cooling rate?
The difference in sensitivity of the measurements for hydrogen-ordering would cause the indicated gap. To observe hydrogen-ordering from appearance of neutron diffraction peakss, larger domain growth may be needed, whereas lattice parameter or dielectric measurements are much more sensitive to the hydrogen-ordering. The phase boundary derived from the temperature dependence of lattice parameter (Fig. 3b in the main manuscript) shows consistent phase transition temperature at around 118 K with that obtained from the DLPI data (Figure 1-4), meanwhile significant intensity change cannot be observed in the diffraction patterns even at 115 K. Similar phenomena are observed in the case of ice VII-VIII phase transition (Komatsu et al., PNAS, 117, 6356-6361 (2020)).

1.6
The authors conducted a quite thorough investigation of possible model fits to the neutron data and this is perhaps the most valuable work in the paper. I noticed that the consistent misfits of the peak width at ~1.81 Å seem to be due to a large, Lorentzian-like broadening of the measured peak. Since such a peak-shape is often associated with particle-size effects, I wondered if this could be due to finite domain sizes of the ordered phase. In this case, they would be quite directional as only this peak is affected. Maybe this is worth further comment.
We agree that the peak broadening was caused by particle-size effects (this point was mentioned in Methods of our original manuscript). Although the peak at ~1.81 Å seems to have a strong peak broadening, this degree of broadening can be also seen in other new peaks. The reason for the apparently significant broadening of the peak at ~1.81 Å would be just its strong intensity as compared to the other new peaks.
1.7 Lastly, on the refinements, there were several places where it was mentioned that the refinements were "conducted several times for each model" and the subsequent χ2 values "averaged values over several refinement results". This seemed an unusual ··process to me, as I would expect a given model to converge to the exact same structure when refined to the same data.
We changed the sentence "conducted several times for each model" to a more direct one shown in the following to avoid the doubt as indicated by Reviewer 1.
In structure analysis of ice XIX of Methods and also a part of the caption in Supplementary Fig. 6 (the following modification is about the caption of Supplementary  Fig. 6 as a representative example): Before) Structure refinements were conducted several times for each model to confirm their reproducibility; these results are plotted in this figure.
↓ (The underlined part was changed.) After) In the first step of structure refinements, the cite occupancies of hydrogen atoms were fitted one by one, and subsequently fitted together as variables. Since the first step has arbitrariness in its fitting order (e.g. α→β→··· and β→α→···), we conducted structure refinements in several ways for each model by changing the fitting order cyclically, such as α→β→··· and β→γ→···. However, the fitting results are almost independent of the order. We appreciate this indication and changed the sentence as shown below.
Before) In this context, the phase boundary between ice XV and ice XIX should have a slope rather than lie horizontally as suggested previously, because ice XV has a larger volume than ice XIX (the supposed phase boundary in Fig. 1 is shown vertically to emphasise this point).

↓ (The underlined part was changed.)
After) In this context, the phase boundary between ice XV and XIX would be close to a vertical unlike horizontal suggested in the previous study if their entropy difference is enough small, because ice XV has a larger volume than ice XIX (the supposed phase boundary in Fig. 1 is shown vertically to emphasise this point). Thermal fluctuation might suppress the long-range order of ice XIX, but in the experimental time scale, the fluctuation is not enough to cause a phase transition from ice XIX to more stable hydrogen-ordered phase of ice VI under ambient pressure. In this context, the suppression would cause an amorphous-like structure rather than a disordered state. This amorphization is well known in decompressed samples to ambient pressure as a phase transition from a high-pressure phase to an amorphous phase.
1.11 The authors should provide some further justification for their explanation. line 183 mentions "large water molecules" what does this refer to? Aren't all water molecules the same size?
Thank you so much for the suggestion; "large water molecules" was corrected to "a large number of water molecules". We deem that the pressure correction is not necessary. Although we have not confirmed pressure gradient in our developed cell, piston-cylinder apparatus would only have enough small pressure gradient compared to its general achievable pressure, about 2 GPa, unless samples are compressed/decompressed at low temperature, such as 77 K. It is noted that in our dielectric measurements every compression was conducted at room temperature. In addition, even if there is a pressure gradient, the ruby is always set at the same position, as shown in the cell assembly (Supplementary Figure 10). The pressure discrepancy between sample and ruby, if any, becomes only offset of our pressure estimation. This would not affect our main claims that ice VI has two types of hydrogen ordering depending on pressure and the hydrogen-ordered phases show opposite volume change each other in the phase transition from ice VI. #Reviewer 2 We appreciate Reviewer 2's positive response, and completely agree his/her indication for our structure refinements of the new hydrogen-ordered ice XIX. As indicated by Reviewer 2, it would be difficult to determine the crystal structure of the new phase from powder neutron diffraction, and we would be happier if the crystal structure is strictly solved using single crystal samples overcoming its experimental difficulties. Also, we hope that the new hydrogen-ordering phenomena and our new technical device development inspires many studies in the wide-ranging fields e.g., geosciences, physics, physical chemistry, crystallography, and so on.
#Reviewer 3 3.1 My general opinion is that although the experimental data appear solid and point to a different structure of ice than ice XV, the present work does not constitute a major progress from what was already known from the previous study cited above which would justify its publication in Nat. Comm.
For the first time, we have established the presence and nature of a new hydrogen-ordered ice which shows a different hydrogen-ordering as compared to the already known hydrogen-ordered phase (ice XV). Although the existence of the new hydrogen-ordered phase is supposed by Gasser et al. as β-XV, no direct evidence has been obtained thus far. Here we show the first, unambiguous, structural evidence for the new phase (ice XIX) by in-situ neutron diffraction under high-pressure. In addition, our high-pressure dielectric measurement clarifies that the hitherto unknown phase diagram of ice VI and its hydrogen-ordered phases which should be essential information for our deep understanding of the intriguing hydrogen-ordering of ice VI. The new phase diagram of ice will directly inspire many studies in the wide-ranging fields, e.g., geosciences, physics, and physical chemistry. It is also stressed the point that our newly developed high-pressure cell for the dielectric measurements would be a powerful tool for further investigation of the various hydrogen-ordering of ice in detail as with this study.
3.2 In addition, I find that the discussion of the dielectric data is poor compared to the rather exhaustive analysis of the neutron data. Detailed comments are given below: We added a more detailed analysis for dielectric measurements as shown below.

The quantitative analysis of dielectric data is poor: only the shift of the loss peak intensity with T is reported. What about the relaxation time and related activation energy which can be inferred from the peak frequency ?
We added the analysis of dielectric relaxation in Supplementary Material (content 1) which is shown in the below Figure 3-1 (we here named figures by Figure "reviewer comment number-sequential number"). As known in other hydrogen ordering of ice, the relaxation time becomes longer when the phase transition occurs. This is due to the suppression of molecular reorientation. We observed this behavior in the phase transition between ice VI and XIX (Figure 3-1). Activation energy of HCl-doped ice VI and DCl-doped deuterated ice VI is about 0.2 eV, which is a consistent value with that of other HCl/DCl-doped and also KOH/KOD-doped disordered ice, such as ice V and Ih (Koster et al., Phys. Rev. B 94, 184306 (2016); Kawada, J. Phys. Soc. Jpn. 58, 295-300 (1989)). On the other hand, the phase transition between ice VI/XV and DCl-doped ice VI/XIX show a relatively small change in their relaxation times. The previous dielectric study on ice V and Ih reported a similar isotope effect in their hydrogen (heavy hydrogen) ordering. Although the reason for this difference is not yet clear, Kawada (1989) indicated that the degree of hydrogen/heavy hydrogen ordering would be related to the difference. As with the isotope effect, the difference in the degree of hydrogen-ordering might also be the reason for the relatively small change in the relaxation time of the phase transition from ice VI to ice XV compared to that between ice VI and XIX. Figure  3-2 shows the temperature dependence of dielectric loss peak intensity obtained in cooling and heating runs at 0.88 and 2.2 GPa, where ice XV and XIX are stable, respectively. It can be seen that the hydrogen ordering of ice XV happens in a wider temperature region (~20 K) compared to that of ice XIX (~5 K). These results are consistent with the supposed difference in the degree of hydrogen-ordering between ice XV and XIX. The difference would be due in part to the height of the activation barrier of hydrogen ordering and energy difference between ice VI and the hydrogen-ordered phases. However, we need further investigation for such discussion.
Figure 3-2| Temperature dependence of dielectric loss peak intensity obtained in cooling and heating runs at 0.88 and 2.2 GPa, where ice XV and XIX is stable, respectively. At 2.2 GPa, data measured below 124 K (upon cooling) and 130 K (upon heating) are not shown here, because the dielectric response of ice XIX almost disappeared in the temperature region.

3.4
There is an apparent change of slope sign at 1.6 GPa (from negative to positive) in the loss peak intensity vs T evolution in the ice VI domain (Fig. 2b and Fig. S2), which is not commented at all.
As shown in the left side of Figure 3-3, the temperature shift of dielectric loss peak was obtained in two different high-pressure runs conducted at 1.9 GPa, where their samples were changed. These data show no reproducibility of the indicated tendency, such that we did not mention anything about that. It is stressed the point that the different samples of ice VI show the consistent temperature dependence of relaxation times and phase transition temperature to ice XIX each other (see the right side of the figure).

Figure 3-3|
Comparison of a temperature shift of dielectric loss peak of ice VI (left side) and temperature dependence of relaxation time of ice VI and XIX (right side) obtained in two different high-pressure runs conducted at 1.9 GPa, where their samples were changed.

Dielectric data on non-doped H2O is reported in SM but not mentioned in main text
and are barely commented, although clear differences with the data on doped ice are apparent. How do the authors explain these differences ?
It is reasonable that pure ice and HCl-doped ice exhibit different dielectric responses, because the chemical dopant locally breaks the ice rules by which the molecular reorientation can be activated. This activation causes clear differences in terms of the dielectric responsibility of ice. Quantitatively, pure ice VI has higher activation energy for the molecular reorientation, ~0.5 eV (measured at 1.1 GPa in Johari et al., 61, 4292-4300 (1974)), compared to that of the HCl-doped ice VI, ~0.2 eV (Figure 3-1). We added this explanation in Supplementary Material.
3.6 In figure S1a, the authors report the loss peak intensity from 124 K to 150K. However from Figure S1b the peak at 124 K is clearly not in the measured frequency window, how did the authors obtained its intensity ? It would also be useful to the readers if the authors gave the complete set of dielectric data they measured at each pressure in the SM.
The raw data and fitted curves of the dielectric constant and loss are shown below in Figure 3-4, in which loss tangent is also displayed for reference. Although, as indicated by Reviewer 3, the dielectric loss peak is unclear in the temperature, we conducted its model fitting by also referring other dielectric properties, dielectric constant and loss tangent. We added the measured data of dielectric properties of ice VI and its hydrogen-ordered phases. 3.7 The authors define the disorder-order phase transition as the temperature at which the slope of the loss peak intensity changes. What is the physical basis for this definition ?
Also, related to the next comment: Similarly, the author state that the transition is first order, however both dielectric signals and lattice parameters appear to change continuously over a temperature range of ~10 K, which at first-sight is not compatible with a first-order process. It is possible that the continuous character arises from the coexistence of the two phases and kinetics of the transition but this has to be discussed.
First, the temperature hysteresis along with phase transition between ice VI and XIX (Supplementary Figure 1) is the evidence that the phase transition is first order. The indicated (apparent) continuous change is caused by the coexistence of the disorder/order phases. It is expected that first-order phase transition shows a sudden change in physical properties of samples; for example, dielectric properties and lattice parameters are expected to be changed in the case of hydrogen ordering of ice. In the dielectric measurements, we use dielectric loss to analyze the phase transition because the peak is easy to be traced to its temperature change. Although dielectric constant is generally used in disorder/order phase transition of dielectrics, the intensity of both physical quantities, dielectric constant and loss, is mainly changed by static dielectric constant ' based on the Debye dispersion model. Therefore, the dielectric loss peak intensity is also appropriate for the evaluation of the phase transition.  (2018)). We compared our dielectric loss data obtained at 1.9 GPa with the data reported by Gasser et al. (2018). There is an apparent difference between them (see Figure 3-5) in the temperature region below about 108 and 124 K, where the samples are in the hydrogen-ordered state, respectively. The difference might reflect the revival of molecular reorientation, which should be immobilized upon hydrogen ordering, in the decompressed sample. Taking account of the "deep-glassy state" suggested by Rosu-Finsen et al. (Chem. Sci. 10, 515-523 (2019)), we consider that it is non-trivial that ice XIX and the decompressed sample are the same ones, although we do not have neutron diffraction data of such decompressed samples to confirm that.  We agree that the systematic study for the kinetics effects on the hydrogen ordering of ice VI is important, but in this study, we did not conduct such experiments because our main purpose is to obtain direct evidence for the existence of the second hydrogen-ordered phase of ice VI. All dielectric measurements in this study were conducted using the same cooling rate 2 K/h.

3.10
The data is presented as isobaric scans. Can the authors explain how pressure was kept constant upon varying temperature?
We did not keep the pressure constant. The figures below plot sample pressures determined in dielectric and neutron diffraction measurements at 1.9 and 1.6 GPa, respectively. The sample pressure slightly changed with decreasing (increasing) temperature.

Figure 3-6|
Representative temperature-dependence of sample pressure in dielectric (a) and neutron diffraction (b) measurements at 1.9 and 1.6 GPa, respectively.
We mentioned the sample-pressure change in dielectric measurements in Methods as following: It is noted that sample pressure is slightly changed by decreasing (increasing) temperature at most about 0.1 GPa in the measured temperature region. The shown pressure of the dielectric data corresponds to that measured at around phase-transition temperature. In the neutron diffraction measurement, the sample pressure also changed about 0.1 GPa in the measured temperature range, and the shown pressure was determined in the same manner as the dielectric measurement.

3.11
The authors say that they did not consider the 5 lowest symmetry space group in their neutron powder refinement as "sufficient refinement agreements" were obtained for the other 18. They should specify what they mean by sufficient agreement, preferably in a quantitative manner.
We agree that the sentence "sufficient refinement agreements" is not an appropriate representation and modified it as shown below.
Before) 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, P1 / 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.
After) We conducted Rietveld analyses using structural models with 18 space groups of the remaining candidates, except for Pc, P21, P2, P 1 / and P1, which are the lower-symmetry space groups of P4 / , Pca21, Pcc2, P21/a and P21/c selected as the best candidates for ice XIX based on their fitting ( values. Since the best candidates show close ( (between 5.3 and 6.0 as shown in Supplementary Fig. 8) and they can explain all observed new peaks of ice XIX (see Supplementary Fig. 9), the lower-symmetry space groups were not considered here. Notably, we do not rule out the possibility that the actual crystal structure of ice XIX having one of the lower-symmetry space groups.
Along with this modification, we added a new figure in Supplementary Material (Supplementary Figure 9) which shows finally fitted lines for the experimentally obtained neutron diffraction patterns of ice XIX using the P4 / and Pcc2 structure model.

Supplementary Figure 9|
Neutron diffraction patterns collected at 1.6 GPa and 80 K (black dots) and finally fitted lines (coloured by red) using the most plausible structure models for ice XIX, P4 / (a) and Pcc2 (b). The black ticks represent all the peak positions expected from the unit cells of ice XIX. The blue lines show residuals between the observed and simulated diffraction patterns.
3.12 The authors say "centrosymmetry of hydrogen configurations is the most significance difference in hydrogen configuration between ice XIX and ice XV". But they found that P-4 is one of the most plausible space group of ice XIX, which to my understanding is a centrosymmetric group.
Although 4 / does not have polar direction (Reviewer 3 perhaps imply this point), no centrosymmetry exists in the space group.
3.13 As a minor comment, I find the title expression "new diversity form of ice polymorphism" rather odd and unclear. I had to read the abstract to understand its meaning. I suggest to remove it or find a better one.
We agree to this comment and changed the title to "Ice XIX: Discovery of second hydrogen ordered phase of ice VI".