Experimental study of the polyamorphism of water . II . The isobaric transitions between HDA and VHDA at intermediate and high pressures

Since the first report of very-high density amorphous ice (VHDA) in 2001 [T. Loerting et al., Phys. Chem. Chem. Phys. 3, 5355-5357 (2001)], the status of VHDA as a distinct amorphous ice has been debated. We here study VHDA and its relation to expanded high density amorphous ice (eHDA) on the basis of isobaric heating experiments. VHDA was heated at 0.1 ≤ p ≤ 0.7 GPa, and eHDA was heated at 1.1 ≤ p ≤ 1.6 GPa to achieve interconversion. The behavior upon heating is monitored using in situ volumetry as well as ex situ X-ray diffraction and differential scanning calorimetry. We do not observe a sharp transition for any of the isobaric experiments. Instead, a continuous expansion (VHDA) or densification (eHDA) marks the interconversion. This suggests that a continuum of states exists between VHDA and HDA, at least in the temperature range studied here. This further suggests that VHDA is the most relaxed amorphous ice at high pressures and eHDA is the most relaxed amorphous ice at intermediate pressures. It remains unclear whether or not HDA and VHDA experience a sharp transition upon isothermal compression/decompression at low temperature.


I. INTRODUCTION
Water, the molecule of life, is ubiquitous in nature and yet bears astonishing properties.3][4][5] It is further suspected that those two liquids have amorphous counterparts, namely, high-density amorphous ice (HDA) and low-density amorphous ice (LDA), 6,7 both of which were first reported by Mishima et al. 8,9 Hence, the existence of distinct amorphous forms, a phenomenon called polyamorphism, hints at the existence of distinct liquids.Since the third amorphous ice form called very high-density amorphous ice (VHDA) was reported in 2001, 10 naturally the question arose whether water could even form three distinct liquids.Although being highlighted about a decade ago, 3,11 the status of VHDA is still an open question.
In attempting to answer this question, one has to clarify whether VHDA is a truly distinct polyamorph or not.Since we devoted a fair share of the Introduction in Paper I 12 to the general discussion of polyamorphism, we are not going to dwell on this any further here.We simply state that if VHDA is a distinct polyamorph it has to share a first-order-like transition a) Present address: Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 5, I-00185 Roma, Italy.b) Author to whom correspondence should be addressed: thomas.loerting@uibk.ac.at with other amorphous ices.Given that studies of VHDA both during isobaric heating at low pressures [12][13][14][15][16] and isothermal decompression at T ≥ 125 K 17,18 showed that VHDA transforms to HDA before it transforms to LDA, the key question on the status of VHDA boils down to the clarification of the HDA-VHDA relation.

A. The relation of HDA and VHDA
VHDA is usually produced by heating HDA at pressures exceeding 0.8 GPa. 10 HDA itself is produced by pressure induced amorphisation (PIA), i.e., compressing hexagonal ice at 77 K to pressures above 1.0 GPa. 8 This HDA obtained from PIA is commonly referred to as unannealed HDA (uHDA). 19t is contrasted with relaxed HDA forms exhibiting lower density than uHDA, called expanded HDA (eHDA).Routes to eHDA are isobaric heating of uHDA at pressures below 0.5 GPa 19,20 or decompression of VHDA at 140 K to pressures below 0.4 GPa. 17 Based on its high thermal stability at ambient pressure, [19][20][21] eHDA is regarded as a highly relaxed form of HDA.
The preparation of VHDA involves a transformation from uHDA. 10 This transformation involves a sudden, but small change in density, and hence it is hard to characterize the nature of the transition.A kink in the density versus pressure curve was reported around 0.8 GPa indicating a possible, albeit very small discontinuity. 22Even if there is no, or only a very small, discontinuity in density, there is a clear difference in ∂ ρ/∂p, which for VHDA is smaller (0.10 g cm 3 GPa 1 ) than for HDA (0.21 g cm 3 GPa 1 ). 22Further evidence for a jump-like transformation from HDA to VHDA was provided by ex situ Raman-spectroscopy, 22 a possible maximum in the relaxation dynamics 23 and corresponding glass-to-liquid transition temperatures. 23,24Most prominently two density jumps were found during isothermal compression of LDA at 125 K. 25 The first jump at 0.45 GPa corresponds to the LDA → HDA transition and the second one at 0.95 GPa was assigned to the HDA → VHDA transition. 25Based on ambient pressure structures, it was argued 11 that those two transitions should be similar since the coordination number (defined to 3.3 Å) changes from four (LDA) to five (HDA) to six (VHDA). 26,27n the other hand, there are a number of studies, in which a jump-like transformation from HDA to VHDA could not be identified.Mishima 28 used similar high-pressure annealing as Loerting et al., 10 but stated that all states found were variations of a single polyamorph, i.e., HDA.This is supported by a more recent study reporting no kink in the density versus pressure curve at ≈0.8 GPa, implying also a smooth change in compressibility. 29In addition, the HDA → VHDA density step reported at 125 K 25 was not found in a volumetric study by Mishima 30 utilizing a similar path but much higher compression rates, or upon compression of LDA at 100 K. 25 Furthermore, an in situ Raman spectroscopy study of the isothermal compression of LDA at 135 K by Yoshimura et al. does not report a HDA → VHDA transition. 31Since Loerting et al. 25 reported that the lower the compression rate is, the sharper the step is.Mishima's rate of 0.6 GPa min 1 30 might have been too high to see this step.Yoshimura et al. 31 did not report a step presumably since they are lacking measurements in the relevant pressure range and/or since they worked at higher temperature.Still, different results were also obtained for LDA II , a relaxed form of LDA (cf.Ref. 32 for details on LDA II ).When LDA II is compressed at 125 K, no second step, corresponding to a HDA → VHDA transition, is found. 3314]16 Finally, results from high-pressure scattering experiments 34,35 and spectroscopy 29 also point toward VHDA and HDA becoming increasingly similar at increasing pressure.
7][38] While a first-order-like HDA → VHDA transition was reported in LiCl-H 2 O, it could not be identified in NaCl-H 2 O. Also in numerical studies, the results are ambiguous.5][46][47][48][49] Besides, the results of Refs.42 and 43 were criticized 50 for their treatment of long-range interactions.

B. Aim of this work
If one assumes the existence of a binodal separating VHDA and HDA, it should be located around a pressure of 0.8 GPa based on studies favouring a separation.This hypothesis is schematically depicted in Fig. 1(a).As recently suggested by us, this hypothesis involves a low-lying critical point above which the distinction between HDA and VHDA disappears. 23ccording to this scheme, HDA should be thermodynamically more stable at lower pressures and VHDA at higher pressures.The other parts show the experimental paths taken to test for the occurrence of stability limits: Part (b) shows the VHDA-path: hexagonal ice is compressed at 77 K and subsequently heated at 1.1 GPa.Upon reaching 160 K, the sample is quenched to 77 K and brought to 0.1 ≤ p ≤ 0.7 GPa.At the final pressure, the sample is heated again and then quench-recovered to 77 K and 1 bar.Parts (c) and (d) show the eHDA path: hexagonal ice is compressed at 77 K and subsequently heated at 1.1 GPa.Upon reaching 160 K, the sample is cooled to 140 K and decompressed.Upon reaching 0.1 GPa, the sample is quenched to 77 K.The sample is then recompressed to 1.1 ≤ p ≤ 1.6 GPa where it is heated again to 160 K and quench-recovered to 77 K and 1 bar.
However, because of kinetic limitations at 77 K, HDA can be compressed to pressures beyond 0.8 GPa without transforming to VHDA 8,10 and VHDA can be recovered to ambient pressure without transforming to HDA. 10,18 Similar kinetic hindrance is observed for the HDA-LDA case, where a large hysteresis is present. 30Besides the binodal, however, limits of stability have to exist at which the amorphous ices inevitably experience a polyamorphic transition.Again, those limits were charted for the LDA-HDA case and sharp first-orderlike transitions were found. 9,12,17,20,21,30,32,51We here aim to investigate the possible existence of such stability limits for the HDA-VHDA case.To this end, we study both the behavior of VHDA during isobaric heating at 0.1 ≤ p ≤ 0.7 GPa (i.e., in the metastability domain of HDA) to look for signs of a VHDA → eHDA transition and the isobaric heating behavior of eHDA at 1.1 ≤ p ≤ 1.6 GPa (i.e., in the metastability domain of VHDA) to look for signs of an eHDA → VHDA transition.The isobaric heating steps are monitored by in situ volumetry and the samples are further characterized ex situ using powder X-ray diffraction (XRD) and differential scanning calorimetry (DSC).

II. EXPERIMENTAL DETAILS
In order to produce the different samples, 500 µl of pure water was pipetted into a preformed indium container (m ≈ 320 mg) at 77 K. Indium serves as a low-temperature lubricant, a technique pioneered by Mishima et al. 8 The samples were then put in a high-pressure cell of 8 mm bore diameter, and the cell was subsequently placed in a material testing machine (Zwick model BZ100/TL3S; for details on our apparatus, see Ref. 52).The pressure was raised to 1.0 GPa at 77 K to push the air out of the sample, reduced to 0.02 GPa and subsequently raised again to 1.5-1.7 GPa with 0.14 GPa min 1 .During the last step, the ice sample transforms to uHDA via PIA.The pressure was subsequently reduced to 1.1 GPa.Then the samples were heated isobarically with 3 K min 1 to 160 K to produce VHDA.After reaching 160 K, two different paths were taken: the VHDA-path [cf.For the VHDA-path, the samples were quenched with liquid N 2 after reaching 160 K and decompressed at 77 K to 0.1 ≤ p ≤ 0.7 GPa with a rate of 0.14 GPa min 1 .After reaching the desired pressure, the VHDA samples were heated with 3 K min 1 to temperatures between 98 and 167 K and quenched with liquid N 2 thereafter.This step serves the purpose of investigating the VHDA → eHDA transformation.After the quench procedure, the samples were brought back to ambient pressure with a rate of 0.14 GPa min 1 , pushed out of the pressure cell, stored at 77 K, and characterized by x-ray diffraction (XRD) and differential scanning calorimetry (DSC).Additionally one VHDA sample was completely decompressed at 77 K without heating at lower pressure.This sample serves as the VHDA reference here.
For the eHDA-path, the samples were cooled at 1.1 GPa to 140 K. Then the samples were isothermally decompressed to 0.1 GPa with 0.02 GPa min 1 and quenched with liquid N 2 upon reaching 0.1 GPa.This results in eHDA. 17The samples were then recompressed to pressures between 1.1 and 1.6 GPa at 77 K, where eHDA was heated isobarically with 3 K min 1 to 160 K.This step serves the purpose of investigating the eHDA → VHDA transformation.After reaching 160 K, the samples were quenched and recovered and characterized as explained for the VHDA path.Additionally, one eHDA sample was completely decompressed after quench at 0.1 GPa without recompression and heating at high pressure.This sample serves as the eHDA reference here.
During all high-pressure steps, in situ dilatometry was performed by recording the piston displacement.The piston displacement curves were converted to change of volume curves assuming constant cell diameter and correcting for the apparatus behavior by subtracting a blind experiment.For the blind experiment, we perform the same steps as for the real experiment, leaving only the water out.Thus, we are able to record the behavior of the apparatus and the indium along the studied paths (cf.Ref. 53).
For the purpose of recording X-ray diffractograms, the samples were first divided into two or three pieces and each piece was powdered and measured separately.Hence, two or three diffractograms were recorded per sample.Division and powdering were performed in liquid N 2 .The powder was cold-loaded onto a precooled (≈80 K) nickel-plated copper sample holder in flat geometry.The low-temperature chamber by Anton-Paar (TTK 450) holding the sample holder is then closed and pumped to approximately 10 2 mbar.We used a Siemens D 5000 diffractometer equipped with a Cu-Kα x-ray source (λ = 1.541Å) to record the diffractograms at ≈80 K from 2θ = 10 • (K = 0.71 Å 1 ) to 2θ = 54 • (K = 3.70 Å 1 ) using a step width of 0.02 • and acquisition time of 1 s per step.The phase composition of crystalline samples containing more than one polymorph was determined using PowderCell (version 2.4, BAM, Bundesanstalt für Materialforschung und -prüfung, Berlin, Germany).The relevant structural data were taken from Refs.54-63 for several ice polymorphs and from Ref. 64 for our nickel-plated copper sample holder.
For the purpose of recording DSC heating scans, small parts of the sample were put in DSC-crucibles at 77 K.The crucibles were placed into the 93 K pre-thermostated DSCinstrument (Perkin-Elmer DSC 8000).Thermograms were recorded in two subsequent scans with a heating rate of 10 K min 1 : A first scan from 93 to 233 K to record the latent heat of the irreversible transformation(s) and a second scan from 93 to 293 K.The second scan serves as baseline for the first scan and is used to calculate the sample mass from the melting endotherm of hexagonal ice.

A. Analysis of the volume curves
The volume curves of the isobaric heating experiments with VHDA samples at different pressures in the metastability domain of HDA are shown in Fig. 2(a).The starting points of the curves include the volume change during decompression, i.e., the curves show V m (T )−V VHDA m (77 K, 1.1 GPa).For example, for the 0.1 GPa curve in Fig. 2(a), the starting point at 0.8 cm 3 mol 1 implies that VHDA expands by 0.8 cm 3 mol 1 upon decompression from 1.1 GPa to 0.1 GPa.
All curves show that heating results in an expansion of the VHDA samples.The expansion always consists of two stages: (i) a non-linear stage at low temperatures and (ii) a sharp step at higher temperatures marking the crystallization of the sample.The shape of the volume curves suggests that the samples relax in a continuous fashion toward higher molar volume before this relaxation is terminated by crystallization.
It is further evident that the lower the pressure is, the more non-linear expansion is seen.This is not surprising since VHDA is a relaxed amorphous ice at 1.1 GPa, but not at other pressures.Lowering the pressure and heating the sample yield relaxation toward lower density, i.e., expansion.The further the deviation from 1.1 GPa, the more expansion is expected.
This line of reasoning explains also a difference to uHDA.While the VHDA samples expand at all pressures studied here, uHDA is known to expand during isobaric heating below 0.35 GPa, 29,65 but it compacts at higher pressures. 29In other words, the initial density of uHDA at p < 0.35 GPa is lower than the density in the relaxed state, whereas the initial density of VHDA is always higher than the density in the relaxed state at all pressures ≤0.7 GPa.

B. XRD and DSC analysis
To characterize the states that appear when VHDA is heated isobarically, the experiments corresponding to the lines in Fig. 2  respectively.In addition, XRD scans (middle panel) and DSC scans (right panel) are shown, where each scan has the same colour code as the symbols and is connected by the horizontal dashed line with the symbols.
From X-ray diffractograms, amorphous samples are easily distinguished from crystalline samples since they lack sharp reflexes and only show broad halo peaks.Our criterion for the state of relaxation in amorphous samples is the location of the maximum of the first halo peak (2θ max ).
In DSC scans, high density amorphous ice (VHDA or HDA) shows two exotherms: 20,21,28,66,67 (i) the amorphousamorphous transition to LDA and (ii) the crystallization of LDA to cubic ice.By contrast, high-pressure crystalline ices show only one exotherm, [68][69][70][71][72] namely, the polymorphic transition to stacking-disordered cubic ice. 73,74Our criterion for the state of relaxation in amorphous samples is the onset temperature of the first exotherm, which we denote T e here.
FIG. 5. Analogous to Fig. 3 for heating of VHDA at 0.6 and 0.7 GPa.The green point belongs to the experiment at 0.6 GPa and the purple to the experiment at 0.7 GPa as indicated by the arrows.The black diffractograms at the bottom of (b) are calculated diffractograms of ice IV, ice XII and the sample holder.Having set the stage for a proper understanding of the XRD and DSC data, we now turn to the interpretation.The XRD measurements corresponding to samples quenched before the sharp volume step show a fully amorphous diffraction pattern [see part (b) of Figs.3-5], where the halo peak shifts to lower angles upon heating.This shift is summarized for the whole pressure range (0.10-0.70 GPa) in Fig. 6(a).At 0.10 GPa, the shift amounts to 3.0 • and decreases to 0.5 • at 0.5 GPa.At 0.6 and 0.7 GPa, practically no shift occurs prior to crystallization.This is consistent with the volume changes in Fig. 2(a): at 0.10 GPa, a volume change of 2.8 cm 3 mol 1 takes place prior to crystallization, which shrinks to 0.4 cm 3 mol 1 at 0.50 GPa.For 0.70 GPa, no more than 0.1 cm 3 mol 1 expansion takes place.
Also, the results from our DSC scans agree with these findings.The samples quenched before crystallization show two exothermic peaks indicative of the amorphous nature of the samples.We summarize all corresponding onset temperatures T e in Fig. 6(b).For 0.10 GPa, T e shifts by 5 K, whereas for 0.50-0.70GPa a shift of 2 K is observed.As we showed in a previous study, such a shift indicates relaxation. 20Again, the samples heated at low pressures show a significant amount of relaxation, whereas barely any relaxation is visible at higher pressures.
The dashed lines in Figs.6(a) and 6(b) indicate reference measurements for VHDA, eHDA, and LDA.Clearly, VHDA progresses toward the eHDA reference state upon heating.At 0.1 GPa, the eHDA reference state is reached when VHDA is heated to ≈140 K, as judged both from XRD [Fig.6(a)] and DSC [Fig.6(b)].This indicates that VHDA samples that have been decompressed at 140 K to 0.1 GPa and VHDA samples that have been decompressed at 77 K to 0.1 GPa and then heated to 140 K are at the same state.Hence, this is a case of path independence, which is a sign for equilibration in the amorphous state.This corroborates our earlier results on the nature of the transition to LDA at 4 MPa. 12he relaxation is also noted from the peak area of the first exotherm in Fig. 3(c), which reflects the heat associated with the polyamorphic transition.In VHDA itself, we here find a heat of 637 J mol 1 , in agreement with the value 640 ± 10 J mol 1 reported by Winkel. 33 This reduces to 462 ± 41 J mol 1 after heating at 0.1 GPa.That is, the enthalpy associated with relaxation amounts to ≈175 J mol 1 .
To judge whether path-independence occurs also at other pressures studied here, we also compare our isobaric experiments with the isothermal results of Winkel et al. 17,21 in Figs.6(c DSC to study the states that occur during decompression of VHDA at 140 K.Hence, if our results for samples heated to 140 K coincide with the data points from Refs. 17 and 21, path independence is confirmed.First, we note that the data point after heating VHDA at 0.1 GPa to 140 K coincides with Winkel et al.'s data, confirming the above found path independence.After heating at 0.25 GPa to 141 K, the XRD data point comes very close to Winkel et al.'s [cf.Fig. 6(c)] suggesting path-independence, whereas the DSC point does not [cf.Fig. 6(d)].For all higher pressures, heating to significantly higher temperatures was necessary to match Winkel et al.'s data both in XRD and DSC.Thus, path-independence is not the case at p > 0.25 GPa.Hence, metastable equilibrium is definitely reached at 140 K and 0.1 GPa, it is close at 140 K and 0.25 GPa, and it is not reached at higher pressures, consistent with previous results. 12,21hat is, the isobaric heating of VHDA at 0.1 ≤ p ≤ 0.7 GPa results in a continuous relaxation followed by crystallization.The characterizations employed indicate that the relaxation yields states varying continuously from VHDA at high pressures to eHDA at low pressures, consistent with similar isothermal experiments 17,18 as well as isobaric experiments at 1 bar 13,14,16 and 4 MPa. 12The crystallization behavior will be discussed in Sec.V.

A. Analysis of the volume curves
The volume curves of the isobaric heating experiments of eHDA in the metastability domain of VHDA are shown in Fig. 2(b).The reference for these volume curves is an eHDA sample at 0.1 GPa.The starting points of the curves reflect the volume change incurred upon compressing eHDA at 77 K, i.e., the curves show V m (T )−V eHDA m (77 K, 0.1 GPa).All curves show that the samples densify during heating.This densification progresses in a continuous fashion, indicating that only a relaxation takes place.We stopped the heating prior to the crystallization temperature T X , and so no sharp steps are seen [by contrast to Fig. 2(a)].A notable exception occurred in one experiment at 1.3 GPa, where a sharp step upon reaching 160 K was observed, marking the crystallization of the sample.This experiment is discussed in the supplementary material.

B. XRD and DSC analysis
For the eHDA experiments, no samples were quenched in the smooth densification step.Therefore, all characterizations performed yield only information about the state reached after heating to 160 K. Figure 7 is designed in analogy to Figs. 3-5 Both the XRD and DSC measurements show that all samples are mainly amorphous after the heating procedure, although crystalline traces were found.Figures 8(a  The heat of the polyamorphic transition recorded in DSC after the isobaric heating is 703 ± 47 J mol 1 for 1.3 GPa and 719 ± 56 J mol 1 for 1.6 GPa.These values are slightly higher as the one found for our VHDA reference sample (637 J mol 1 ) and the value reported by Winkel 33 (640 ± 10 J mol 1 ), both of which were prepared at 1.1 GPa.This indicates that at higher pressure denser VHDA forms, which shows higher transition enthalpies to LDA.
That is, isobaric heating of eHDA at 1.1 ≤ p ≤ 1.6 GPa to 160 K leads to a continuous densification in all cases.As apparent from the XRD and DSC characterizations, the heating produces states that are VHDA or close to it.

A. VHDA
As discussed in Sec.III, the heating of VHDA at 0.1 ≤ p ≤ 0.7 GPa always terminates in a sharp volume step indicating the crystallization of the sample.If we take the temperature of the volume step as the crystallization temperature of VHDA, we find that VHDA crystallises at significantly higher temperatures than uHDA.][77] The assignment of the sharp step to a crystallization event is corroborated from out XRD and DSC data.After the sharp step at 0.10 GPa [Fig.3(a)], the XRD scan shows sharp Bragg peaks [Fig.3(b)] and the DSC scan shows only a single exotherm [Fig.3(c)].In the supplementary material, we show the phase composition after crystallization, which is consistent with the idea that both eHDA 75,76 and VHDA 77 differ from uHDA in that in the latter nanocrystalline remnants are present.

B. eHDA
Only one out of nine samples shows a volume step before 160 K, but still XRD measurements show traces of ice XII.At 1.1 GPa, no measurement out of six performed (two per sample) was free of crystalline reflexes, and at 1.3 GPa only one out of six and at 1.6 GPa five out of seven contained no crystalline reflexes.The sheer occurrence of crystalline traces at 160 K is surprising, when considering the known crystallization temperatures at these pressures (cf.Fig. 9).This finding may be explained by the very recent study of Tonauer et al., 78 who demonstrated the presence of nanocrystalline domains in eHDA produced by decompression to 0.1 GPa.According to this work, nanocrystalline domains form upon compression from LDA-nanodomains, which themselves appear in the eHDA preparation step at ≤0.10 GPa at 140 K.Since our eHDA samples were prepared that way, they presumably contain crystalline traces that continuously grow from nanocrystalline domains. 78

VI. SUMMARY AND CONCLUSION
We studied the behavior of VHDA and eHDA by in situ volumetry upon isobaric heating at 0.1 ≤ p ≤ 0.7 GPa and 1.1 ≤ p ≤ 1.6 GPa, respectively, in search of sharp limits of stability.No such sharp limit was observed in any of the experiments reported here, but instead a continuous relaxation process followed by a sharp crystallization.For VHDA a pronounced volume relaxation takes place at lower pressures, which proceeds through a continuum of states in between VHDA and eHDA.In addition, the transformation from eHDA to VHDA at high pressures appears as a continuous densification, and all isobaric transformations studied here are clearly less sharp than the isobaric eHDA → LDA transition. 12,20,21[28][29][30][33][34][35][36] This suggests that there is a continuum of states between VHDA and HDA at least in the temperature range studied here, i.e., at T ≥ 77 K.At such temperatures, eHDA and VHDA can be regarded as two extreme cases of HDA.0][21] Nevertheless, the possible maximum in T g 23,24 and the second density jump upon isothermal compression of LDA at 125 K 25 still demand an explanation.We suggest that sufficiently slow isothermal experiments in the pressure range of interest (≈0.8 GPa) might reveal a first-order-like transition between HDA and VHDA, similar to the experiment reported previously at 125 K. 25 Future work will be required to check this suggestion and to verify or falsify the existence of the binodal shown in Fig. 1(a).
Irrespective of the answer to this question, the practical importance of VHDA is without a doubt.77]79 If however uHDA is annealed at high pressure, VHDA is obtained 10 and VHDA is most likely fully amorphous. 13,14,29,77,79If this fully amorphous VHDA is subsequently decompressed at 140 K to obtain eHDA, 17 the fully amorphous nature is inherited by eHDA. 75,76Besides the fully amorphous nature, VHDA (and eHDA at low p) show a higher crystallization temperature than uHDA (cf.Fig. 9), extending the field of possible experiments in unknown parts of the no-man's land, possibly into regions where the amorphous ice turns into an ultraviscous liquid. 6Hence, we conclude that VHDA is the proper amorphous ice to be studied at pressures above 0.8 GPa.

SUPPLEMENTARY MATERIAL
See supplementary material for a more detailed discussion of the crystallization events observed in this study as well as for a brief discussion on DSC onset temperatures.

FIG. 1 .
FIG. 1.(a) Schematic phase diagram indicating a possible critical point ending a binodal (dotted line) separating HDA and VHDA.The corresponding limits of stability (solid lines) are also shown.The dashed lines are the approximate location of the glass-to-liquid transition T g based on Ref. 24.The other parts show the experimental paths taken to test for the occurrence of stability limits: Part (b)shows the VHDA-path: hexagonal ice is compressed at 77 K and subsequently heated at 1.1 GPa.Upon reaching 160 K, the sample is quenched to 77 K and brought to 0.1 ≤ p ≤ 0.7 GPa.At the final pressure, the sample is heated again and then quench-recovered to 77 K and 1 bar.Parts (c) and (d) show the eHDA path: hexagonal ice is compressed at 77 K and subsequently heated at 1.1 GPa.Upon reaching 160 K, the sample is cooled to 140 K and decompressed.Upon reaching 0.1 GPa, the sample is quenched to 77 K.The sample is then recompressed to 1.1 ≤ p ≤ 1.6 GPa where it is heated again to 160 K and quench-recovered to 77 K and 1 bar.

FIG. 2 .
FIG. 2. In situ volumetry of the isobaric heating of VHDA (a) and eHDA (b) at different pressures.V VHDA,0 m FIG. 3. XRD and DSC analysis of intermediate states of the isobaric heating of VHDA at 0.1 and 0.25 GPa.(a) shows the volume change and the squares mark temperatures of quench-recovery.The corresponding diffractograms and calorigrams after quench-recovery are shown in (b) and (c), respectively.In (b), the dotted grey line at 24.0 • (1.69 Å 1 ) marks the position of the first diffraction maximum for LDA according to Refs.80 and 32.The dotted grey lines at 29.7 • (2.09 Å 1 ) and at 32.4 • (2.26 Å 1 ) mark the position of the first diffraction maximum of the eHDA and VHDA references, respectively.The black diffractograms at the bottom of (b) are calculated diffractograms of ice I c , ice IX/III and the sample holder.In (c), the dotted grey lines at 130, 136, and 166 K mark the onset temperature of the VHDA → LDA, eHDA → LDA, and LDA → I c transition, respectively.

FIG. 4 .
FIG.4.Analogous to Fig.3for heating of VHDA at 0.35 and 0.50 GPa.The black diffractograms at the bottom of (b) are calculated diffractograms of ice IX/III, ice V, ice IV and the sample holder.

124509- 6 P
. H. Handle and T. Loerting J. Chem.Phys.148, 124509 (2018) FIG. 6. Summary of the ex situ XRD and DSC results after the isobaric heating of VHDA.Part (a) shows the average positions of the first diffraction maximum as found in XRD as a function of the respective maximum T in the isobaric heating step.Part (b) shows the average DSC transition temperature T e of the high-density amorphous ice as a function of the respective maximum T in the isobaric heating step.The dotted grey lines mark the values of the VHDA and eHDA reference samples, as well as the values for LDA.Solid lines are guide to the eye.Parts (c) and (d) show only data points after heating VHDA to ≈140 K as a function of pressure.Here also values obtained from isothermal decompression of VHDA at 140 K from Refs. 17 and 21 are shown for comparison.Please note we corrected the data of Ref. 21 to match the onset temperatures of LDA crystallization (see the supplementary material).
. The volume curves from Fig. 2(b) are reproduced (left panel), and the XRD scans (middle panel) and the DSC scans (right panel) are shown in the same colour code and are connected by dashed horizontal lines.
FIG. 7. XRD and DSC-analysis of initial and final states of the isobaric heating of eHDA at high pressures.(a) shows the volume change of the complete transition.The corresponding diffractograms and calorigrams after quench-recovery are shown in (b) and (c), respectively.In (b), the dotted grey line at 24.0 • (1.69 Å 1 ) marks the position of the first diffraction maximum for LDA according to Refs.80 and 32.The dotted grey lines at 29.7 • (2.09 Å 1 ) and at 32.4 • (2.26 Å 1 ) mark the position of the first diffraction maximum of the eHDA and VHDA references, respectively.The black diffractograms at the bottom of (b) are calculated diffractograms of ice XII and the sample holder.In (c), the dotted grey lines at 130, 136, and 166 K mark the onset temperature of the VHDA → LDA, eHDA → LDA, and LDA → I c transition, respectively.

FIG. 8 .
FIG. 8. Summary of the ex situ XRD and DSC results after the isobaric heating of eHDA to 160 K. Part (a) shows the average positions of the first diffraction maximum as found in XRD after heating and part (b) shows the average DSC transition temperature T e of the highdensity amorphous after heating.At each pressure, three different samples were studied.The dotted grey lines mark the values of the VHDA and eHDA reference samples, as well as the values for LDA.

FIG. 9 .
FIG. 9. Phase diagram of water based on Refs. 1, 58, 81, and 82 highlighting the liquid and high-density amorphous phase.For HDA and VHDA, the crystallization temperatures found in this work are compared with data from the literature. 29,30,68,75-77The dashed red line indicates the temperature where we find crystalline traces after heating eHDA.