Water and the many phases of ice display a plethora of complex physical properties and phase relationships1,2,3,4 that are of paramount importance in a range of settings including processes in Earth’s hydrosphere, the geology of icy moons, industry and even the evolution of life. Well-known examples include the unusual behaviour of supercooled water2, the emergent ferroelectric ordering in ice films4 and the fact that the ‘ordinary’ ice Ih floats on water. We report the intriguing observation that ice II, one of the high-pressure phases of ice, disappears in a selective fashion from water’s phase diagram following the addition of small amounts of ammonium fluoride. This finding exposes the strict topologically constrained nature of the ice II hydrogen-bond network, which is not found for the competing phases. In analogy to the behaviour of frustrated magnets5, the presence of the exceptional ice II is argued to have a wider impact on water’s phase diagram, potentially explaining its general tendency to display anomalous behaviour. Furthermore, the impurity-induced disappearance of ice II raises the prospect that specific dopants may not only be able to suppress certain phases but also induce the formation of new phases of ice in future studies.
Whenever water freezes at a given pressure, hydrogen-disordered phases of ice, which display orientational disorder of the hydrogen-bonded water molecules3,6,7,, crystallize. The corresponding hydrogen-ordered counterparts exhibit long-range orientational order and form on cooling as required by the third law of thermodynamics8,9,10. The one notable exception, which displays a fundamentally different behaviour compared to the other ice phases, is ice II whose region of stability dominates the phase diagram in the pressure range up to 1 GPa (Fig. 1a). Ice II remains hydrogen-ordered up to temperatures 6 °C below the melting point11,12, whereupon it undergoes phase transitions to the hydrogen-disordered ices Ih, III, V or VI rather than to its own hydrogen-disordered counterpart. Recent computational studies have shown that the phase transition from ice II to the hypothetical hydrogen-disordered ice IId would take place only at temperatures well within the stability region of the liquid, highlighting a strong resilience of ice II towards hydrogen disordering13,14.
Here, we test the response of water’s phase diagram with respect to a specific disturbance, the addition of small amounts of ammonium fluoride (NH4F). While NH4F is well known to mix with the ‘ordinary’ ice Ih across a large composition range15,16 and has been shown to incorporate into clathrate hydrates17,18, the mixing of NH4F with high-pressure phases of ice has not been previously investigated. The local hydrogen-bonding environment of ice is, in principle, well adapted for incorporating NH4+ and F– ions in terms of the length, strength and number of hydrogen bonds19. Yet, a major chemical difference between H2O, NH4+ and F– lies in the different numbers of hydrogen bonds they can donate or accept. Consequently, as shown schematically in Fig. 1b, the replacement of a H2O molecule in ice with NH4+ or F– requires the reorientations of two neighbouring water molecules.
Remarkably, the presence of small amounts of NH4F leads to the disappearance of the hydrogen-ordered ice II from water’s phase diagram and the hydrogen-disordered ices III and V are found instead (Fig. 1c). Ice II appears to be incompatible with NH4F, whereas the other phases of ice can incorporate the impurity, which leads to a shift of the onset of melting towards lower temperatures. Unlike for pure ice, the melting of the two-component solid solutions is expected to take place over a temperature range. Figure 2a shows neutron diffraction data for D2O ice with 2.5 mol% ND4F collected at 0.3 GPa with argon gas as the pressure medium. The doped ice III, which exists instead of ice II in the phase diagram of pure ice, is present on heating from 200 K to its final melting point at ~255 K. Due to the high argon pressure, argon clathrate hydrate forms in the temperature range of melting.
On lowering the mole percentage of NH4F, the ice III persists down to 0.5 mol% at 0.3 GPa. Figure 1d shows the volume changes of metastable ice Ih/NH4F solid solutions recorded on isobaric heating at 0.3 GPa. Below 0.5 mol%, the ice III ‘plateau’ drops towards the ‘basin’ of denser ice II that must form when approaching pure ice. The appearance of ice II at 0.25 mol% ND4F was investigated with neutron diffraction at 0.3 GPa. Figure 2b shows that a metastable stage of ice III is first observed at 200 K. On heating to 235 K, the ice III transforms to ~80 weight percent (w%) ice II while ~20 w% of ice III remains. The metastable nature of the initial ice III is demonstrated by cooling back to 180 K during which the weight fraction of ice II increases gradually. As observed for pure ice II, it persists up to 245 K on subsequent heating, where transformation to ice III and finally melting are observed.
Ice II appears at a nominal mole percentage of 0.25 mol% ND4F, yet the actual solubility of ND4F in ice II is much smaller. As has been shown for solid solutions of ice Ih and NH4F, the lattice constants are sensitive indicators for the amount of NH4F mixed into the ice, which leads to subtle contractions of the lattice constants19. The a lattice parameter of D2O ice III with 2.5 mol% ND4F determined from the neutron diffraction data is 6.66015 ± 0.00007 Å at 0.3 GPa and 200 K. The corresponding value for the metastable ice III with 0.25 mol% ND4F is 0.100 ± 0.001% greater at the same pressure and temperature. After transforming the 0.25 mol% ND4F sample to ice II on heating and cooling back to 200 K, the a lattice parameter of the ~10 w% ice III is within error the same as observed for the 2.5 mol% sample. This means that the vast majority of ND4F is located within the ice III and that the solubility of ND4F in ice II is very small. This is also illustrated by the fact that the neutron diffraction data of the ice II in the 0.25 mol% sample is consistent with pure and fully hydrogen-ordered ice II (see Supplementary Section 2).
The exclusion of ND4F from the growing ice II crystals indicates that this process is governed by the underlying thermodynamics and that a high free-energy cost is associated with the incorporation of ND4F into ice II. Density functional theory calculations show that the local substitution energies of NH4F into ices IId and III are very similar (see Supplementary Section 3). Consequently, the different responses of ices II and III to NH4F must be due to differences in the characteristics of their hydrogen-bonded networks.
The inability of the hydrogen-ordered ice II to incorporate ammonium fluoride suggests that its configurational manifold is ‘topologically constrained’. This means that the ice rules in ice II are strictly enforced, and that thermally excited ionic (H3O+ and OH–) and Bjerrum defects (O···O and O–H···H–O) are completely absent, which is consistent with dielectric spectroscopy measurements20. Its topologically constrained nature therefore clearly distinguishes ice II from the competing phases in the phase diagram. Similar to topologically constrained manifolds in ferroelectrics21, spin ice22,23 and biomembranes24, the ice-rule manifold of ice II exhibits the remarkable property of zero entropy and a fully ordered hydrogen structure at relatively high temperatures12, despite the availability of a vast number of hydrogen-disordered states.
Figure 3a shows schematically the problem associated with the incorporation of F– and NH4+ ions at random into the topologically constrained ice II manifold. With no ionic and Bjerrum defects available to screen them, the dopants enter the constrained manifold of ice-rule states as topological defects25. This can be rationalized by constructing a flux of hydrogen-displacement vectors in a manner analogous to spin-ice mapping26 and is most easily visualized for the two-dimensional square ice and if the orientational order is considered to be ferroelectric (Fig. 3a). The flux lines of hydrogen displacement are then parallel in the hydrogen-ordered state. Following NH4F doping, the flux lines must connect two dopant sites and they are expected to be strongly entangled and interwoven in three-dimensional ice structures. The dopants therefore act as topological defects in the hydrogen-displacement flux, charge-like sources and sinks of flux27 that disrupt the orientational order of the water molecules over long distances along a system of flux tubes between the NH4+ and F– defects. The enthalpy cost per ion then scales at least as ~x–1/3, where x is the dopant fraction, and low-level doping comes at a high free-energy cost per ion. This does not apply to the competing ices Ih, III, V and VI because of the absence of orientational order and the availability of Bjerrum defects to screen the topological charges.
The formation of closely bound NH4+–F– pairs would of course reduce the energy of the randomly doped system illustrated in Fig. 3a, but it turns out that on the topologically constrained ice-rules manifold of ice II, this cannot eliminate flux tubes of significant length. In either scenario, the overall result is a significant increase in free energy per dopant ion, sufficient to preclude the absorption of NH4F into the ice II structure. Full details of the statistical mechanics and the topology of the ice II network as well as experimental arguments against defect pairing are presented in Supplementary Section 4.
The corresponding thermodynamics are illustrated in Fig. 3b, which shows schematic free-energy versus temperature curves. The stable phase is the one with the lowest Gibbs free energy and the slopes of the curves reflect the entropy, S, according to (∂G/∂T)p = –S. Ice II suffers a substantial free-energy increase in the presence of NH4F arising from the long-range disruption of its periodic order. This raises its free energy towards the hydrogen-disordered ice IId, which is metastable at all temperatures and therefore absent from the phase diagram.
The topologically constrained nature of ice II clearly distinguishes it from the neighbouring phases in the phase diagram and we argue that the ice II anomaly has a wider impact on the water phase diagram. Generally speaking, the higher the entropy of a solid the greater its thermal stability with respect to competing phases (through G = H – TS). Although ice II is energetically very stable, its lack of configurational entropy means that it eventually becomes thermally unstable above a certain temperature with respect to more disordered phases (Fig. 3b). Assigning ice II an interaction-energy scale of –kθ per water molecule relative to its competing phases means that the temperature range of existence of the competing phases, the hydrogen-disordered ices Ih, III, V and VI as well as the liquid, is anomalously broadened towards low temperature, T < θ. As in the case of frustrated magnets such as pyrochlore spin ices or kagome spin liquids5, the persistence of disordered states down to temperatures lower than the mean-field ordering temperature To ~ θ implies that the disordered degrees of freedom in these phases are much more strongly correlated than they would be if they occurred only above To. In a sense, the disordered phases are energetically drawn towards the topologically constrained ice II state. Yet, the ice II order is precluded by its cost in entropy, at least on extended length scales. The consequence is a host of anomalous properties and phase transitions in the disordered solid and liquid states, as has been widely documented1,2,3,4. Therefore, the constrained topology of ice II not only determines its own special character but it may also provide a deeply rooted explanation for the existence of a host of anomalous condensed states that compete for stability in water’s phase diagram.
The doping-induced disappearance of ice II also provides a remarkable example of the impact an impurity can have on the appearance of the phase diagram of ice. Knowledge of such effects is obviously important whenever ice coexists with other materials in nature. It also raises the exciting prospect of instead of removing phases from the phase diagram to potentially favouring the formation of new phases of ice in the presence of specific dopants. Ammonium fluoride doping is expected to induce hydrogen disorder in all of the hydrogen-ordered phases of ice. The fully hydrogen-ordered phases should be most responsive due to their inabilities in screening the topological charges. In addition to ice II, we therefore predict the fully hydrogen-ordered ice VIII28 to undergo substantial free-energy increases in the presence of small amounts of ammonium fluoride. This makes its large region of stability above ~2 GPa particularly promising for finding new phases in future studies.
Ammonium fluoride (99.99% trace metal basis) and D2O (99.9% D) were purchased from Sigma Aldrich. Deuterated ammonium fluoride was prepared by dissolving NH4F in an excess of D2O and completely evaporating the D2O under nitrogen three times. All ammonium fluoride solutions were prepared and stored in polyethylene containers. The ice samples were prepared by quickly pipetting the aqueous solutions into an indium cup inside a piston–cylinder set-up precooled with liquid nitrogen. This was followed by isobaric heating or compression experiments using a 30-tonne hydraulic press. Changes in sample volume were detected using a GT5000RA-L25 positional transducer from RDP Electronics. After preparation of the high-pressure phases, some of the samples were quenched under pressure with liquid nitrogen and recovered at ambient pressure. X-ray powder diffraction was performed using a custom-made sample holder with Kapton windows mounted on a Stoe Stadi-P transmission diffractometer with Cu radiation at 40 kV, 30 mA, monochromated by a Ge 111 crystal. Data were collected using a Mythen 1 K linear detector and the temperature of the sample was controlled with an Oxford Instruments CryojetHT. For in situ pressure neutron diffraction measurements on the PEARL beamline30 at the ISIS facility, ground ice samples were transferred under liquid nitrogen into tubular TiZr cans, which were pressure-sealed and mounted inside a cryostat on the beamline. The pressure acting on the samples was generated with a gas-compressor set-up using argon gas as the pressure medium.
The neutron diffraction data shown in Fig. 2 and Supplementary Fig. 3 can be accessed at https://data.isis.stfc.ac.uk/doi/investigation/64414858. All other data are available from the corresponding author upon request.
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We thank the Royal Society (UF150665) and the Leverhulme Trust (RPG-2014-04) for funding, the ISIS facility for granting access to the PEARL instrument, C. Ridley for help with the PEARL pressure equipment, M. Vickers for help with the X-ray measurements, J. K. Cockcroft for access to the Cryojet, and S. L. Price, A. K. Soper and P. A. McClarty for helpful discussions. We also acknowledge the use of the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk) through the Materials Chemistry Consortium via EPSRC grant no. EP/L000202 and the EPSRC-funded Centre for Doctoral Training in Advanced Characterisation of Materials for a studentship (EP/L015277/1).