Main

The phase diagram of liquid water is shown in Fig. 1a. If kept at low temperature, HDA can be recovered to ambient pressure, and upon heating transforms to a lower-density amorphous (LDA) form. Further heating results in what appears to be step-like increase in heat capacity at 129 ± 1 K (this resembles a glass transition) and recrystallization into ice I at 160 K9,10,11. Compressing LDA results in transformation back to HDA at 2 kbar. Above the glass transition, a deeply supercooled liquid water has been postulated9,12. Two deeply supercooled liquid forms corresponding to the HDA and LDA solid forms are postulated, a high-density liquid (HDL) and a low-density liquid (LDL), with a clearly demarcated transformation between the two. This transition curve has been extended into ‘no man’s land’, a region of the water phase diagram where only crystalline ice has been found (although recently it has been observed that rapid compression into no man’s land may result in short-lived forms of amorphous ice13). Ultimately, the concept of a second critical point in water was hypothesized and the search for experimental confirmation is currently a field of active research2. This hypothesis is challenged by the fact that bulk liquid water cooled slowly from a higher temperature crystallizes homogenously, and that amorphous forms warmed from a lower temperature also crystallize2. In addition to HDA and LDA, very-high-density amorphous (VHDA) ice has also been experimentally observed upon temperature annealing HDA under high pressure14. Analysis of X-ray radial distribution functions and Raman data measured during the transition from VHDA to LDA indicate that the local structure of LDA trends towards ice I and that of VHDA towards ice VI8,15.

Fig. 1: Phase diagrams of crystalline ice and liquid and amorphous water.
figure 1

a, Possible relationships between pressure-amorphized ice, deeply supercooled liquid water and supercooled liquid water. The transformation between crystalline ice and HDA occurs near 1.0 GPa at 100 K. In the region above about 145 K, no amorphous or liquid forms occur, and the first crystalline form is probably ice IX. The glass transitions between LDA and LDL and between HDA and HDL occur around 130 K (HDL and LDL are the deeply supercooled liquid forms). Only crystalline forms of bulk ice are observed in the pink-shaded area (no man’s land), and the proposed second critical point is located within this region. b, Phase diagram of crystalline phases of ice in the relevant pressure ranges. The phase boundary lines indicate historical approximations of where transformations are thought to occur. The horizontal arrow represents the pressure–temperature path taken.

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Each amorphous ice form is thought to exist in its own local minimum of the overall energy landscape, with attempts made to identify the amorphous form with the lowest relative local energy minima that would represent the kinetically most stable form of amorphous ice16. Although HDA re-crystallization has also been observed17,18, the impossibility of keeping HDA isostatic and observing re-crystallization has prompted changes to the thermal conditions that effectively move the sample into other regions of the phase diagram. Our study differs from previous work in that we observe directly the lowest-energy crystal forms occurring at the conditions of HDA formation.

Above 10 kbar, the crystalline structure of ice comprises two sublattices. Each of these networks is bonded by an intra-network hydrogen-bonding arrangement with no inter-network hydrogen bonding. These forms consist of two interpenetrating networks. As such, each hydrogen-bonded network can retain a nearly ideal tetrahedral bonding arrangement while increasing the overall density to accommodate the applied pressure. These higher-temperature structures are proton-disordered and, upon cooling, should transition into energetically favoured proton-ordered structures. However, the nature of the hydrogen-bonded network means that molecular reorientations are cooperative, and as the molecular kinetics reduce upon cooling, the transformation becomes kinetically ‘frozen in’ and the ordered forms never form, with few exceptions, such as ice VIII. Doping these phases with an acid (or base) allows increased mobility upon cooling, and at least partial transformation to the ordered structure can occur. For example, doping ice V and XII with hydrochloric acid (HCl) results in ice XIII and ice XIV upon cooling. Cooling HCl-doped ice VI results in the formation of proton-ordered ice XV19,20. Both ice VI and ice XV are composed of two interpenetrating hydrogen-bonded networks. The interpenetrating nature of ice XV enables the molecules to be tetrahedrally bonded with minimal distortion of the tetrahedral angle; thus, this phase is probably the most stable ice structure in the pressure region from about 8 kbar to about 15 kbar, as indicated in the phase diagram of ice shown in Fig. 1b.

We therefore re-investigated this pressure region using a range of compression rates, with the goal of further characterizing the amorphization process and the resulting structures. A detailed outline of how each sample was prepared for this study is given in Methods. Figure 2a shows structural data collected before and after the compression of a pure sample of ice Ih at 100 K. The pressure was quickly and linearly ramped from ambient to 15 kbar at a rate of 8.7 bar s−1. The data show that the initial ‘as produced’ sample is ice Ih and has no other contaminant phases. Diffraction data collected after compression show the sample to be fully amorphized HDA ice, as in previous studies. Further compression of this sample led to the transformation to a form previously denoted as ice VII′ owing to its close structural relationship to ice VII21. We note that ice VII′ is formed from two interpenetrating sublattices and is proton-disordered.

Fig. 2: Diffraction data of amorphous and crystalline ice for increasing pressure at 100 K.
figure 2

a, Structure factor functions, S(Q), of crystalline ice Ih and HDA after fast compression (see text). b, Diffraction data for the series of crystalline phases observed after slow compression of the sample (see text). The final result was a mixture of remnant ice XV′ and ice VIII′. Vertical lines connecting datasets indicate that the hydraulic load on the sample was increased, but the sample pressure remained constant—an indication of a progressing phase transition. The main peaks of ice IX are marked by asterisks and those of ice XV by black circles. This crystalline sequence was observed in four independent datasets.

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Figure 2b shows diffraction data collected during the slow compression of a pure ice Ih sample at 100 K (see Extended Data Fig. 1 for the pressure–load curve). The initial diffraction pattern shows the sample as produced, again with no sign of contaminant phases. Initial tests indicated that one of the samples may have been contaminated with ice IX seeds (which formed upon cooling), so measures were taken to ensure that the samples used to collect the data presented in Fig. 2 were phase-pure (see Extended Data Figs. 2, 3). The pressure was increased from ambient to 2.0 kbar at the same compression rate (8.7 bar s−1) that had resulted in HDA in the previous run, but the pressure was maintained at 2 kbar and a second diffraction pattern was taken over the course of 1 h. Other than compression of the unit cell, no structural changes were observed at this point. The pressure was then increased at 8.7 bar s−1 to 3.0 kbar, where the sample was again held isobarically, and another diffraction pattern was collected for 1 h. In this dataset, the initial stages of the formation of ice IX were indicated by the appearance of the most intense diffraction peak of ice IX at 2.99 Å. During the next increase in hydraulic load on a Paris–Edinburgh press, it was noted that the position of the Bragg peaks did not shift and no change in the unit cell volume was observed—an indication that the sample was progressing through a phase transition and the transformation from ice Ih to ice IX continued. The sample fully transformed to ice IX by 7 kbar. Increasing the pressure above 10 kbar resulted in the formation of ice XV′, which was stable up to 30 kbar, when it transformed to ice VIII′. (We use prime notation to indicate that various studies report variable levels of proton ordering, while the overall crystal structure is similar to that of pure ice XV and ice VIII, so the degree of ordering may vary.) We observed this transformation sequence in four independent experimental runs, with the additional diffraction data, along with amorphization data plotted in d space, where d is the distance between lattice planes, and data comparing ice Ih, XV′ and VIII′ provided in Extended Data Figs. 2, 3 and 4, respectively.

An illustration of the stepwise transformation sequence for the formation of HDA and the high-pressure crystalline phases is shown in Fig. 3. It is important to note here that on slow pressurization the progression of the crystalline phases is as follows. First, an ordering transition to ice IX′ occurs and allows at least partial ordering of the water dipoles without forming an interpenetrating lattice. This is followed at higher pressure by the division of the single hydrogen-bonded network into the interpenetrating and ordered networks of ice XV′. If the stability field of ice IX′ is ‘stepped over’ by pressurizing rapidly and directly into the field of ice XV′, any resulting ordering is kinetically inhibited and the phase transformation is arrested, giving instead the highly disordered ice form known as HDA ice. Extended Data Fig. 5 shows data collected from the crystalline phases produced by rapid and slow compression.

Fig. 3: Amorphous and crystalline structural progression of ice when compressed at 100 K.
figure 3

a, Transformation of ice Ih when compressed slowly at 100 K (see text). At 3 kbar, ice Ih collapses to distorted, tetrahedrally bonded ice IX′, followed by the formation of ice XV′ above 10 kbar, and finally of ice VIII′ above 30 kbar. b, Transformation sequence observed upon fast compression at 100 K (see text). Formation of ice IX is not possible on the timescale that the sample is within its stability field, and once in the field of ice XV, the kinetics is too slow to simultaneously order the protons and form an interpenetrating structure, resulting in HDA ice followed by ice VII′.

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Mapping the sequence of equilibrium structures that are seen when avoiding HDA formation provides useful insight into the structural pathway leading to pressure-induced amorphous ice. Ice IX′ seems to be the key phase in this regard, in that it facilitates the transition between ice Ih and ice XV′, the equilibrium crystalline structure associated with HDA. Put differently, if ice IX is not given time to form, as is the case during rapid compression, proton ordering and interpenetration of the two sublattices to form ice XV cannot occur concurrently, and HDA inevitably results. This finding challenges the interpretation of the increase in heat capacity when heating HDA to 129 ± 1 K as evidence of a glass transition22. Instead, temperature annealing of amorphous ice, which is understood as a kinetically interrupted crystal-to-crystal transition, would result in the system structurally completing its unfinished transition and moving towards its more energetically favourable crystalline state at the given pressure and temperature—not to a dynamically free liquid state or a more relaxed glassy state16. Therefore, the idea of expanded HDA (or eHDA) needs to be re-evaluated.

Furthermore, by quickly recovering HDA through the stability field of ice IX′, the formation of LDA (after heating at ambient pressure) may be the kinetically inhibited result of interrupted crystallization of ice Ih. It may be that if HDA is slowly depressurized, with a substantial pause near 3 kbar, ice IX′ may form, followed by ice Ih, thus completing a cycle of stable crystalline phases.

This work experimentally confirms the conceptual framework that indicates that HDA could be a “derailed state along the ice I to ice IV pathway”4 (here we show that it is the pathway from ice I to ice XV) and confirms the postulation that the formation of HDA is a kinetic event and not a thermodynamic one5,23,24. Finally, the interpenetrating and non-interpenetrating nature of the underlying stable crystalline phases of ice may be the principal structural difference between LDA and VHDA. Given that earlier work hinted that the local structure of recovered VHDA and LDA is similar to crystalline forms of ice VI and ice I, respectively (ice VI is the proton-disordered form of ice XV), the full impact of these results can now be appreciated with the demonstration of the formation of the equilibrium crystalline structures under pressure and temperature conditions within the formation zone of HDA. The results imply that a connection between pressure-prepared amorphous ice and deeply supercooled water needs to be re-evaluated. Theoretical studies have also previously questioned the relationship between amorphous ices and liquid water25,26,27,28. Those studies used molecular dynamics simulations that implied ice-crystallite formation or nucleation, instead of a two-liquid equilibrium, and their results were limited by the timescales of these simulations—a constraint that is essentially removed in our experiment.

Methods

The sample-loading techniques that resulted in the formation of the crystalline phases and the amorphous form were identical and proceeded as follows. D2O (Sigma Aldrich, 99.99% deuterium) was placed in the lower hemisphere of a single-toroid soft-metal-encapsulated gasket. The gasket was made of a TiZr alloy with a null-scattering composition29. The sample and gasket were then placed above boiling liquid nitrogen until the sample froze. The upper portion of the gasket was then placed over the sample. The frozen sample filled the gasket volume completely. In one measurement the gasket contained a small lead pellet to act as a pressure marker. The gasket loaded with ice Ih was then placed between two toroidal cubic boron nitride anvils30 inside a VX5 Paris–Edinburgh press that was fitted inside a liquid nitrogen cryostat. The anvil’s binding rings were modified to include an integrated channel machined into the binding ring to facilitate circulation of liquid nitrogen, thus cooling the sample. A temperature-sensing diode was fixed to the anvil, 3 cm from the sample position. Tests with a second thermocouple embedded in lead and held at the sample position indicated a difference of less than 1 K between the two. A small load was quickly applied after the sample was placed between the anvils to seal the gasket and prevent sample evaporation once the cryostat was evacuated. The Paris–Edinburgh press was placed in the cryostat, which was quickly evacuated, and liquid nitrogen immediately began to flow through the system. The sample was cooled to 100 K over the course of about 30 min.

The SNAP instrument at the Spallation Neutron Source at Oak Ridge National Laboratory was configured in low-resolution mode to adequately capture the necessary momentum-transfer range to characterize the HDA form and facilitate the like-for-like comparison with the crystalline phases. Initial data were collected to verify the formation of ice Ih with no phase contamination before any pressure was applied. In the initial experiments a small fraction of the sample was observed to be ice IX, indicating that some pressure had been applied to the sample. The loading technique was then modified so that no pressure was applied to the sample when sealing the gasket. For each loading, a new D2O sample and gasket were used to avoid potential ice IX ‘seeds’ in the gasket (avoiding any possibility of the ice-memory effect occurring, as has been reported in clathrate hydrate nucleation31). Once it was confirmed that ice I was formed with no contaminant phase present, the sample was pressurized in one of two ways. First, the sample pressure was increased to 2 kbar and diffraction data were collected for 1 h. At this point, no ice IX′ was found. Then, the pressure was increased to 3 kbar, where we detected the initial formation of ice IX′. Each of these two datasets was measured for 1 h, and the sample pressure was increased into the pressure–temperature field of ice IX over the course of 2 h. This resulted in the formation of the crystalline series reported above. Second, the pressure was increased directly from near-ambient to 15 kbar in just under 30 min. The first dataset was then measured after this direct pressurization into the stability field of ice XV, without first holding the sample pressure in the stability field of ice IX as in the previous experiment. This resulted in the formation of HDA ice.