Phases of ice

The phases of ice are all the possible

The accepted

This tetrahedral bonding angle of the water molecule essentially accounts for the unusually low density of the crystal lattice – it is beneficial for the lattice to be arranged with tetrahedral angles even though there is an energy penalty in the increased volume of the crystal lattice. As a result, the large hexagonal rings leave almost enough room for another water molecule to exist inside. This gives naturally occurring ice its rare property of being less dense than its liquid form. The tetrahedral-angled hydrogen-bonded hexagonal rings are also the mechanism that causes liquid water to be densest at 4 °C. Close to 0 °C, tiny hexagonal ice I_h-like lattices form in liquid water, with greater frequency closer to 0 °C. This effect decreases the density of the water, causing it to be densest at 4 °C when the structures form infrequently.

In the most common form of ice, ice I_h, the crystal structure is characterized by the oxygen atoms forming

Amorphous ices have the property of suppressing long-range density fluctuations and are, therefore, nearly hyperuniform.^[9] Despite the epithet "ice", classification analysis utilizing neural networks has shown that amorphous ices are glasses.^[10]

Pressure-dependent states

Ice from a theorized superionic water may possess two crystalline structures. At pressures in excess of 500,000 bars (7,300,000 psi) such superionic ice would take on a

Ice, water, and

The latent

The transition entropy from ice XIV to ice XII is estimated to be 60% of Pauling entropy based on DSC measurements.[20] The formation of ice XIV from ice XII is more favoured at high pressure.^[21]

When medium-density amorphous ice is compressed, released and then heated, it releases a large amount of heat energy, unlike other water ices which return to their normal form after getting similar treatment.^[22]

Hydrogen disorder

The hydrogen atoms in the crystal lattice lie very nearly along the hydrogen bonds, and in such a way that each water molecule is preserved. This means that each oxygen atom in the lattice has two hydrogens adjacent to it: at about 101 pm along the 275 pm length of the bond for ice Ih. The crystal lattice allows a substantial amount of disorder in the positions of the hydrogen atoms frozen into the structure as it cools to absolute zero. As a result, the crystal structure contains some residual entropy inherent to the lattice and determined by the number of possible configurations of hydrogen positions that can be formed while still maintaining the requirement for each oxygen atom to have only two hydrogens in closest proximity, and each H-bond joining two oxygen atoms having only one hydrogen atom.^[23] This residual entropy S₀ is equal to 3.4±0.1 J mol⁻¹ K⁻¹ ${\displaystyle =R\ln(1.50\pm 0.02)}$.^[24]

Calculations

There are various ways of approximating this number from first principles. The following is the one used by Linus Pauling.^[25][26]

Suppose there are a given number N of water molecules in an ice lattice. To compute its residual entropy, we need to count the number of configurations that the lattice can assume. The oxygen atoms are fixed at the lattice points, but the hydrogen atoms are located on the lattice edges. The problem is to pick one end of each lattice edge for the hydrogen to bond to, in a way that still makes sure each oxygen atom is bond to two hydrogen atoms.

The oxygen atoms can be divided into two sets in a checkerboard pattern, shown in the picture as black and white balls. Focus attention on the oxygen atoms in one set: there are N/2 of them. Each has four hydrogen bonds, with two hydrogens close to it and two far away. This means there are ${\textstyle {\tbinom {4}{2}}=6}$ allowed configurations of hydrogens for this oxygen atom (see Binomial coefficient). Thus, there are 6^N/2 configurations that satisfy these N/2 atoms. But now, consider the remaining N/2 oxygen atoms: in general they won't be satisfied (i.e., they will not have precisely two hydrogen atoms near them). For each of those, there are 2⁴ = 16 possible placements of the hydrogen atoms along their hydrogen bonds, of which 6 are allowed. So, naively, we would expect the total number of configurations to be

$${\displaystyle 6^{N/2}(6/16)^{N/2}=(3/2)^{N}.}$$

Using Boltzmann's entropy formula, we conclude that

$${\displaystyle S_{0}=k\ln(3/2)^{N}=nR\ln(3/2),}$$

${\displaystyle R\ln(3/2)=3.37\mathrm {J} \cdot \mathrm {mol} ^{-1}\mathrm {K} ^{-1}}$

The same answer can be found in another way. First orient each water molecule randomly in each of the 6 possible configurations, then check that each lattice edge contains exactly one hydrogen atom. Assuming that the lattice edges are independent, then the probability that a single edge contains exactly one hydrogen atom is 1/2, and since there are 2N edges in total, we obtain a total configuration count ${\displaystyle 6^{N}\times (1/2)^{2N}=(3/2)^{N}}$, as before.

Refinements

This estimate is 'naive', as it assumes the six out of 16 hydrogen configurations for oxygen atoms in the second set can be independently chosen, which is false. More complex methods can be employed to better approximate the exact number of possible configurations, and achieve results closer to measured values. Nagle (1966) used a series summation to obtain ${\displaystyle R\ln(1.50685\pm 0.00015)}$.^[27]

As an illustrative example of refinement, consider the following way to refine the second estimation method given above. According to it, six water molecules in a hexagonal ring would allow ${\displaystyle 6^{6}\times (1/2)^{6}=729}$ configurations. However, by explicit enumeration, there are actually 730 configurations. Now in the lattice, each oxygen atom participates in 12 hexagonal rings, so there are 2N rings in total for N oxygen atoms, or 2 rings for each oxygen atom, giving a refined result of ${\displaystyle R\ln(1.5\times (730/729)^{2})=R\ln(1.504)}$.^[28]

Known phases

These phases are named according to the Bridgman nomenclature. The majority have only been created in the laboratory at different temperatures and pressures.^[29]

History of research

Ice II

The properties of ice II were first described and recorded by

As ice II is completely hydrogen ordered, the presence of its disordered counterpart is a great matter of interest. Shephard et al.[80] investigated the phase boundaries of NH₄F-doped ices because NH₄F has been reported to be a hydrogen disordering reagent. However, adding 2.5 mol% of NH₄F resulted in the disappearance of ice II instead of the formation of a disordered ice II. According to the DFC calculation by Nakamura et al.,^[81] the phase boundary between ice II and its disordered counterpart is estimated to be in the stability region of liquid water.

Ice IV

1981 research by Engelhardt and Kamb elucidated crystal structure of ice IV through a low-temperature single-crystal X-ray diffraction, describing it as a rhombohedral unit cell with a space group of R-3c.

The disordered nature of Ice IV was confirmed by neutron powder diffraction studies by Lobban (1998) [86] and Klotz et al. (2003).^[87] In addition, the entropy difference between ice VI (disordered phase) and ice IV is very small, according to Bridgman's measurement.^[88]

Several organic nucleating reagents had been proposed to selectively crystallize ice IV from liquid water,

Search for a hydrogen-ordered counterpart

The ordered counterpart of Ice IV has never been reported yet. 2011 research by Salzmann's group reported more detailed DSC data where the endothermic feature becomes larger as the sample is quench-recovered at higher pressure. They proposed three scenarios to explain the experimental results: weak hydrogen-ordering, orientational glass transition, and mechanical distortions.^[91] reported the DSC thermograms of HCl-doped ice IV finding an endothermic feature at about 120 K. Ten years later, Rosu-Finsen and Salzmann (2021) ^[92]

Ice XI

Ice XI is the hydrogen-ordered form of the ordinary form of ice. The total internal energy of ice XI is about one sixth lower than ice I_h, so in principle it should naturally form when ice I_h is cooled to below 72 K. The low temperature required to achieve this transition is correlated with the relatively low energy difference between the two structures.^[93] Hints of hydrogen-ordering in ice had been observed as early as 1964, when Dengel et al. attributed a peak in thermo-stimulated depolarization (TSD) current to the existence of a proton-ordered ferroelectric phase.^[94] However, they could not conclusively prove that a phase transition had taken place, and Onsager pointed out that the peak could also arise from the movement of defects and lattice imperfections. Onsager suggested that experimentalists look for a dramatic change in heat capacity by performing a careful calorimetric experiment. A phase transition to ice XI was first identified experimentally in 1972 by Shuji Kawada and others.^[95][96][97]

Water molecules in ice I_h are surrounded by four semi-randomly directed hydrogen bonds. Such arrangements should change to the more ordered arrangement of hydrogen bonds found in ice XI at low temperatures, so long as localized proton hopping is sufficiently enabled; a process that becomes easier with increasing pressure.^[98] Correspondingly, ice XI is believed to have a triple point with hexagonal ice and gaseous water at (~72 K, ~0 Pa). Ice I_h that has been transformed to ice XI and then back to ice I_h, on raising the temperature, retains some hydrogen-ordered domains and more easily transforms back to ice XI again.^[99] A neutron powder diffraction study found that small hydrogen-ordered domains can exist up to 111 K.^[100]

There are distinct differences in the Raman spectra between ices I_h and XI, with ice XI showing much stronger peaks in the translational (~230 cm⁻¹), librational (~630 cm⁻¹) and in-phase asymmetric stretch (~3200 cm⁻¹) regions.^[101][102]

Ferroelectric properties

Ice XI is

Although the parent phase ice VI was discovered in 1935, corresponding proton-ordered forms (ice XV) had not been observed until 2009. Theoretically, the proton ordering in ice VI was predicted several times; for example, density functional theory calculations predicted the phase transition temperature is 108 K and the most stable ordered structure is antiferroelectric in the space group Cc, while an antiferroelectric P2₁2₁2₁ structure were found 4 K per water molecule higher in energy.^[108]

On 14 June 2009, Christoph Salzmann and colleagues at the University of Oxford reported having experimentally reported an ordered phase of ice VI, named ice XV, and say that its properties differ significantly from those predicted. In particular, ice XV is antiferroelectric rather than ferroelectric as had been predicted.^[109][110]

Ice XVII

In 2016, the discovery of a new form of ice was announced.

In the absence of an applied electric field, H⁺ ions diffuse in the O²⁻ lattice.

When an electric field is applied, H⁺ ions migrate towards the anode.

A remarkable characteristic of superionic ice is its ability to act as a conductor.

In 1988, predictions of the so-called superionic water state were made.

As of 2013[update], it is theorized that superionic ice can possess two crystalline structures. At pressures in excess of 50 

In 2019, Alexander Rosu-Finsen and Christoph Salzman argued that there was no need to consider this to be a new phase of ice, and proposed a "deep-glassy" state scenario.[123] According to their DSC data, the size of the endothermic feature depends not only on quench-recovery pressure but also on the heating rate and annealing duration at 93 K. They also collected neutron diffraction profiles of quench-recovered deuterium chloride-doped, D₂O ice VI/XV prepared at different pressures of 1.0, 1.4 and 1.8 GPa, to show that there were no significant differences among them. They concluded that the low-temperature endotherm originated from kinetic features related to glass transitions of deep glassy states of disordered ice VI.

Distinguishing between the two scenarios (new hydrogen-ordered phase vs. deep-glassy disordered ice VI) became an open question and the debate between the two groups has continued. Thoeny et al. (Loerting's group) ^[124] collected another series of Raman spectra of ice beta-XV, and reported that (i) ice XV prepared by the protocol reported previously contains both ice XV and ice beta-XV domains; (ii) upon heating, Raman spectra of ice beta-XV showed loss of H-order. In contrast, Salzmann's group again argued for the plausibility of a 'deep-glassy state' scenario based on neutron diffraction and neutron inelastic scattering experiments.^[125] Based on their experimental results, ice VI and deep-glassy ice VI share very similar features based on both elastic (diffraction) scattering and inelastic scattering experiments, and are different from the properties of ice XV.

In 2021, further crystallographic evidence for a new phase (ice XIX) was individually reported by three groups: Yamane et al. (Hiroyuki Kagi and Kazuki Komatsu's group from Japan), Gasser et al. (Loerting's group), and Salzmann's group. Yamane et al. ^[79] collected neutron diffraction profiles in situ (i.e. under high pressure) and found new Bragg features completely different from both ice VI and ice XV. They performed Rietveld refinement of the profiles based on the ${\displaystyle {\sqrt {2}}\times {\sqrt {2}}\times 1}$ supercell of ice XV and proposed some leading candidates for the space group of ice XIX: P-4, Pca21, Pcc2, P21/a, and P21/c. They also measured dielectric spectra in situ and determined phase boundaries of ices VI/XV/XIX. They found that the sign of the slope of the boundary turns negative from positive at 1.6 GPa indicating the existence of two different phases by the Clausius–Clapeyron relation.

Gasser et al. ^[126] also collected powder neutron diffractograms of quench-recovered ices VI, XV, and XIX and found similar crystallographic features to those reported by Yamane et al., concluding that P-4 and Pcc2 are the plausible space group candidates. Both Yamane et al.'s and Gasser et al.'s results suggested a partially hydrogen-ordered structure. Gasser et al. also found an isotope effect using DSC; the low-temperature endotherm for DCl-doped D₂O ice XIX was significantly smaller than that of HCl-doped H₂O ice XIX, and that doping of 0.5% of H₂O into D₂O is sufficient for the ordering transition.

Several months later, Salzmann et al. published a paper based on in-situ powder neutron diffraction experiments of ice XIX.^[127] In a change from their previous reports, they accepted the idea of the new phase (ice XIX) as they observed similar features to the previous two reports. However, they refined their diffraction profiles based on a disordered structural model (Pbcn) and argued that new Bragg reflections can be explained by distortions of ice VI, so ice XIX may still be regarded as a deep-glassy state of ice VI. The crystal structure of ice XIX including hydrogen order/disorder is still under debate as of 2022.

Practical implications

Earth's natural environment

Virtually all ice in the

Besides ice I_h, a small amount of ice I_c may occasionally present in the upper atmosphere clouds.[130] It is believed to be responsible for the observation of Scheiner's halo, a rare ring that occurs near 28 degrees from the Sun or the Moon.^[131] However, many atmospheric samples which were previously described as cubic ice were later shown to be stacking disordered ice with trigonal symmetry,^{[132][133][134]} and it has been dubbed the ″most faceted ice phase in a literal and a more general sense.″^[135] Yhe first true samples of cubic ice were only reported in 2020.^{[136][137][138]}

Low-density ASW (LDA), also known as hyperquenched glassy water, may be responsible for

Ice XI is thought to be a more stable conformation than ice I_h, and so it may form on Earth. However, the transformation is very slow. According to one report, in Antarctic conditions it is estimated to take at least 100,000 years to form without the assistance of catalysts.^[citation needed] Ice XI was sought and found in Antarctic ice that was about 100 years old in 1998.^[145] A further study in 2004 was not able to reproduce this finding, however, after studying Antarctic ice which was around 3000 years old.^[146] The 1998 Antarctic study also claimed that the transformation temperature (ice XI => ice I_h) is −36 °C (237 K), which is far higher than the temperature of the expected triple point mentioned above (72 K, ~0 Pa). Ice XI was also found in experiments using pure water at very low temperature (~10 K) and low pressure – conditions thought to be present in the upper atmosphere.^[147] Recently, small domains of ice XI were found to form in pure water; its phase transition back to ice I_h occurred at 72 K while under hydrostatic pressure conditions of up to 70 MPa.^[148]

Human industry

Amorphous ice is used in some scientific experiments, especially in

Aside from storing hydrogen via compression or liquification, it can also be stored within a solid substance, either via a reversible chemical process (chemisorption) or by having the hydrogen molecules attach to the substance via the van der Waals force (physisorption).^[150] The storage method used by ice XVII falls in the latter category, physisorption.^[150] In physisorption, there is no chemical reaction, and the chemical bond between the two atoms within a hydrogen molecule remains intact. Because of this, the number of adsorption–desorption cycles ice XVII can withstand is "theoretically infinite".^[67][150]

One significant advantage of using ice XVII as a hydrogen storage medium is the low cost of the only two chemicals involved: hydrogen and water.

In outer space, hexagonal crystalline ice (the predominant form found on Earth) is extremely rare. Known examples are typically associated with volcanic action.[151] Water in the interstellar medium is instead dominated by amorphous ice, making it likely the most common form of water in the universe.^[152]

Amorphous ice can be separated from crystalline ice based on its

At longer IR wavelengths, amorphous and crystalline ice have characteristically different absorption bands at 44 and 62 μm in that the crystalline ice has significant absorption at 62 μm while amorphous ice does not.[156] In addition, these bands can be used as a temperature indicator at very low temperatures where other indicators (such as the 3.1 and 12 μm bands) fail.^[157] This is useful studying ice in the interstellar medium and circumstellar disks. However, observing these features is difficult because the atmosphere is opaque at these wavelengths, requiring the use of space-based infrared observatories.

Properties of the amorphous ice in the Solar System

In general, amorphous ice can form below ~130 K.

At temperatures less than 77 K, irradiation from ultraviolet photons as well as high-energy electrons and ions can damage the structure of crystalline ice, transforming it into amorphous ice.[162]^[156] Amorphous ice does not appear to be significantly affected by radiation at temperatures less than 110 K, though some experiments suggest that radiation might lower the temperature at which amorphous ice begins to crystallize.^[156]

Peter Jenniskens and David F. Blake demonstrated in 1994 that a form of high-density amorphous ice is also created during vapor deposition of water on low-temperature (< 30 K) surfaces such as interstellar grains. The water molecules do not fully align to create the open cage structure of low-density amorphous ice. Many water molecules end up at interstitial positions. When warmed above 30 K, the structure re-aligns and transforms into the low-density form.^[33][39]

Molecular clouds, circumstellar disks, and the primordial solar nebula

For the primordial solar nebula, there is much uncertainty as to the crystallinity of water ice during the circumstellar disk and planet formation phases. If the original amorphous ice survived the molecular cloud collapse, then it should have been preserved at heliocentric distances beyond Saturn's orbit (~12 AU).[161]

Comets

The possibility of the presence of amorphous water ice in comets and the release of energy during the phase transition to a crystalline state was first proposed as a mechanism for comet outbursts.^[165] Evidence of amorphous ice in comets is found in the high levels of activity observed in long-period, Centaur, and Jupiter Family comets at heliocentric distances beyond ~6 AU.^[166] These objects are too cold for the sublimation of water ice, which drives comet activity closer to the Sun, to have much of an effect. Thermodynamic models show that the surface temperatures of those comets are near the amorphous/crystalline ice transition temperature of ~130 K, supporting this as a likely source of the activity.^[167] The runaway crystallization of amorphous ice can produce the energy needed to power outbursts such as those observed for Centaur Comet 29P/Schwassmann–Wachmann 1.^[168][169]

Kuiper Belt objects

With radiation equilibrium temperatures of 40–50 K,^[170] the objects in the Kuiper Belt are expected to have amorphous water ice. While water ice has been observed on several objects,^[171][172] the extreme faintness of these objects makes it difficult to determine the structure of the ices. The signatures of crystalline water ice was observed on 50000 Quaoar, perhaps due to resurfacing events such as impacts or cryovolcanism.^[173]

Icy moons

The Near-Infrared Mapping Spectrometer (NIMS) on NASA's Galileo spacecraft spectroscopically mapped the surface ice of the Jovian satellites Europa, Ganymede, and Callisto. The temperatures of these moons range from 90 to 160 K,^[174] warm enough that amorphous ice is expected to crystallize on relatively short timescales. However, it was found that Europa has primarily amorphous ice, Ganymede has both amorphous and crystalline ice, and Callisto is primarily crystalline.^[175] This is thought to be the result of competing forces: the thermal crystallization of amorphous ice versus the conversion of crystalline to amorphous ice by the flux of charged particles from Jupiter. Closer to Jupiter than the other three moons, Europa receives the highest level of radiation and thus through irradiation has the most amorphous ice. Callisto is the farthest from Jupiter, receiving the lowest radiation flux and therefore maintaining its crystalline ice. Ganymede, which lies between the two, exhibits amorphous ice at high latitudes and crystalline ice at the lower latitudes. This is thought to be the result of the moon's intrinsic magnetic field, which would funnel the charged particles to higher latitudes and protect the lower latitudes from irradiation.^[175]

The surface ice of Saturn's moon Enceladus was mapped by the Visual and Infrared Mapping Spectrometer (VIMS) on the NASA/ESA/ASI Cassini space probe. The probe found both crystalline and amorphous ice, with a higher degree of crystallinity at the "tiger stripe" cracks on the surface and more amorphous ice between these regions.^[153] The crystalline ice near the tiger stripes could be explained by higher temperatures caused by geological activity that is the suspected cause of the cracks. The amorphous ice might be explained by flash freezing from cryovolcanism, rapid condensation of molecules from water geysers, or irradiation of high-energy particles from Saturn.^[153]

Medium-density amorphous ice may be present on Europa, as the experimental conditions of its formation are expected to occur there as well. It is possible that the MDA ice's unique property of releasing a large amount of heat energy after being released from compression could be responsible for 'ice quakes' within the thick ice layers.^[22]

Planets

Because ice XI can theoretically form at low pressures at temperatures between 50–70 K – temperatures present in astrophysical environments of the outer solar system and within permanently shaded polar craters on the Moon and Mercury. Ice XI forms most easily around 70 K – paradoxically, it takes longer to form at lower temperatures. Extrapolating from experimental measurements, it is estimated to take ~50 years to form at 70 K and ~300 million years at 50 K.^[176] It is theorized to be present in places like the upper atmospheres of Uranus and Neptune^[100] and on Pluto and Charon.^[176]

Ice VII may comprise the ocean floor of

Small domains of ice XI could exist in the atmospheres of Jupiter and Saturn as well.[100] The fact that small domains of ice XI can exist at temperatures up to 111 K has some scientists speculating that it may be fairly common in interstellar space, with small 'nucleation seeds' spreading through space and converting regular ice, much like the fabled ice-nine mentioned in Vonnegut's Cat's Cradle.^[100][179] The possible roles of ice XI in interstellar space^[176][180] and planet formation^[181] have been the subject of several research papers. Until observational confirmation of ice XI in outer space is made, the presence of ice XI in space remains controversial owing to the aforementioned criticism raised by Iitaka.^[182] The infrared absorption spectra of ice XI was studied in 2009 in preparation for searches for ice XI in space.^[183]

It is theorized that the

References