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Currently, 19 solid phases of water (both crystalline and amorphous) have been observed at various densities, along with hypothetical proposed phases of ice that have not been observed.^[2]

Theory

Most liquids under increased pressure freeze at higher temperatures because the pressure helps to hold the molecules together. However, the strong hydrogen bonds in water make it different: for some pressures higher than 1 atm (0.10 MPa), water freezes at a temperature below 0 °C, as shown in the phase diagram below. The melting of ice under high pressures is thought to contribute to the movement of glaciers.^[3]

Ice, water, and water vapour can coexist at the triple point, which is exactly 273.16 K (0.01 °C) at a pressure of 611.657 Pa.^[4]^[5] The kelvin was defined as 1/273.16 of the difference between this triple point and absolute zero,^[6] though this definition changed in May 2019.^[7] Unlike most other solids, ice is difficult to superheat. In an experiment, ice at −3 °C was superheated to about 17 °C for about 250 picoseconds.^[8]

Subjected to higher pressures and varying temperatures, ice can form in nineteen separate known crystalline phases. With care, at least fifteen of these phases (one of the known exceptions being ice X) can be recovered at ambient pressure and low temperature in metastable form.^[9]^[10] The types are differentiated by their crystalline structure, proton ordering,^[11] and density. There are also two metastable phases of ice under pressure, both fully hydrogen-disordered; these are IV and XII. Ice XII was discovered in 1996. In 2006, XIII and XIV were discovered.^[12] Ices XI, XIII, and XIV are hydrogen-ordered forms of ices I_h, V, and XII respectively. In 2009, ice XV was found at extremely high pressures and −143 °C.^[13] At even higher pressures, ice is predicted to become a metal; this has been variously estimated to occur at 1.55 TPa^[14] or 5.62 TPa.^[15]

Non-crystalline ice

As well as crystalline forms, solid water can exist in amorphous states as amorphous solid water (ASW) of varying densities. Water in the interstellar medium is dominated by amorphous ice, making it likely the most common form of water in the universe. Low-density ASW (LDA), also known as hyperquenched glassy water, may be responsible for noctilucent clouds on Earth and is usually formed by deposition of water vapor in cold or vacuum conditions. High-density ASW (HDA) is formed by compression of ordinary ice I_h or LDA at GPa pressures. Very-high-density ASW (VHDA) is HDA slightly warmed to 160 K under 1–2 GPa pressures.

In outer space, hexagonal crystalline ice (the predominant form found on Earth) is extremely rare. Amorphous ice is more common; however, hexagonal crystalline ice can be formed by volcanic action.^[16]

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 body-centered cubic structure. However, at pressures in excess of 1,000,000 bars (15,000,000 psi) the structure may shift to a more stable face-centered cubic lattice. It is speculated that superionic ice could compose the interior of ice giants such as Uranus and Neptune.^[17]

Known phases

Phase	Characteristics
Amorphous ice	Amorphous ice is ice lacking crystal structure. Amorphous ice exists in four forms: low-density (LDA) formed at atmospheric pressure, or below, medium-density (MDA), high-density (HDA) and very-high-density amorphous ice (VHDA), forming at higher pressures. LDA forms by extremely quick cooling of liquid water ("hyperquenched glassy water", HGW), by depositing water vapour on very cold substrates ("amorphous solid water", ASW) or by heating high density forms of ice at ambient pressure ("LDA"). Recently, a medium-density amorphous form ("MDA") has been shown to exist, created by ball-milling ice I_h at low temperatures.^[18]
Ice I_h	Normal hexagonal crystalline ice. Virtually all ice in the biosphere is ice I_h, with the exception only of a small amount of ice I_c.
Ice I_c	A metastable cubic crystalline variant of ice. The oxygen atoms are arranged in a diamond structure. It is produced at temperatures between 130 and 220 K, and can exist up to 240 K,^[19]^[20] when it transforms into ice I_h. It may occasionally be present in the upper atmosphere.^[21] More recently, it has been shown that many samples which were described as cubic ice were actually stacking disordered ice with trigonal symmetry.^[22] The first samples of ice I with cubic symmetry (i.e. cubic ice) were only reported in 2020.^[23]
Ice II	A rhombohedral crystalline form with highly ordered structure. Formed from ice I_h by compressing it at temperature of 190–210 K. When heated, it undergoes transformation to ice III.
Ice III	A tetragonal crystalline ice, formed by cooling water down to 250 K at 300 MPa. Least dense of the high-pressure phases. Denser than water.
Ice IV	A metastable rhombohedral phase. It can be formed by heating high-density amorphous ice slowly at a pressure of 810 MPa. It does not form easily without a nucleating agent.^[24]
Ice V	A monoclinic crystalline phase. Formed by cooling water to 253 K at 500 MPa. Most complicated structure of all the phases.^[25]
Ice VI	A tetragonal crystalline phase. Formed by cooling water to 270 K at 1.1 GPa. Exhibits Debye relaxation.^[26]
Ice VII	A cubic phase. The hydrogen atoms' positions are disordered. Exhibits Debye relaxation. The hydrogen bonds form two interpenetrating lattices.
Ice VII_t	Forms at around 5 GPa, when Ice VII becomes tetragonal.^[27]
Ice VIII	A more ordered version of ice VII, where the hydrogen atoms assume fixed positions. It is formed from ice VII, by cooling it below 5 °C (278 K) at 2.1 GPa.
Ice IX	A tetragonal phase. Formed gradually from ice III by cooling it from 208 K to 165 K, stable below 140 K and pressures between 200 MPa and 400 MPa. It has density of 1.16 g/cm³, slightly higher than ordinary ice.
Ice X	Proton-ordered symmetric ice. Forms at pressures around 70 GPa,^[28] or perhaps as low as 30 GPa.^[27]
Ice XI	An orthorhombic, low-temperature equilibrium form of hexagonal ice. It is ferroelectric. Ice XI is considered the most stable configuration of ice I_h.^[29]
Ice XII	A tetragonal, metastable, dense crystalline phase. It is observed in the phase space of ice V and ice VI. It can be prepared by heating high-density amorphous ice from 77 K to about 183 K at 810 MPa. It has a density of 1.3 g·cm⁻³ at 127 K (i.e., approximately 1.3 times denser than water).
Ice XIII	A monoclinic crystalline phase. Formed by cooling water to below 130 K at 500 MPa. The proton-ordered form of ice V.^[30]
Ice XIV	An orthorhombic crystalline phase. Formed below 118 K at 1.2 GPa. The proton-ordered form of ice XII.^[30]
Ice XV	A proton-ordered form of ice VI formed by cooling water to around 80–108 K at 1.1 GPa.
Ice XVI	The least dense crystalline form of water, topologically equivalent to the empty structure of sII clathrate hydrates.
Square ice	Square ice crystals form at room temperature when squeezed between two layers of graphene. The material was a new crystalline phase of ice when it was first reported in 2014.^[31]^[32] The research derived from the earlier discovery that water vapor and liquid water could pass through laminated sheets of graphene oxide, unlike smaller molecules such as helium. The effect is thought to be driven by the van der Waals force, which may involve more than 10,000 atmospheres of pressure.^[31]
Ice XVII	A porous hexagonal crystalline phase with helical channels, with density near that of ice XVI.^[33]^[34]^[35] Formed by placing hydrogen-filled ice in a vacuum and increasing the temperature until the hydrogen molecules escape.^[33]
Ice XVIII	A form of water also known as superionic water or superionic ice in which oxygen ions develop a crystalline structure while hydrogen ions move freely.
Ice XIX	Another phase related to ice VI formed by cooling water to around 100 K at approximately 2 GPa.^[2]

Ice Ih

Ice I_h (hexagonal ice crystal) (pronounced: ice one h, also known as ice-phase-one) is the hexagonal crystal form of ordinary ice, or frozen water.^[36] Virtually all ice in the biosphere is ice I_h, with the exception only of a small amount of ice I_c that is occasionally present in the upper atmosphere. Ice I_h exhibits many peculiar properties that are relevant to the existence of life and regulation of global climate. For a description of these properties, see Ice, which deals primarily with ice I_h.

The crystal structure is characterized by the oxygen atoms forming hexagonal symmetry with near tetrahedral bonding angles. Ice I_h is stable down to −268 °C (5 K; −450 °F), as evidenced by x-ray diffraction^[37] and extremely high resolution thermal expansion measurements.^[38] Ice I_h is also stable under applied pressures of up to about 210 megapascals (2,100 atm) where it transitions into ice III or ice II.^[39]

Physical properties

The density of ice I_h is 0.917 g/cm³ which is less than that of liquid water. This is attributed to the presence of hydrogen bonds which causes atoms to become closer in the liquid phase.^[40] Because of this, ice I_h floats on water, which is highly unusual when compared to other materials. The solid phase of materials is usually more closely and neatly packed and has a higher density than the liquid phase. When lakes freeze, they do so only at the surface while the bottom of the lake remains near 4 °C (277 K; 39 °F) because water is densest at this temperature. No matter how cold the surface becomes, there is always a layer at the bottom of the lake that is 4 °C (277 K; 39 °F). This anomalous behavior of water and ice is what allows fish to survive harsh winters. The density of ice I_h increases when cooled, down to about −211 °C (62 K; −348 °F); below that temperature, the ice expands again (negative thermal expansion).^[37]^[38]

The latent heat of melting is 5987 J/mol, and its latent heat of sublimation is 50911 J/mol. The high latent heat of sublimation is principally indicative of the strength of the hydrogen bonds in the crystal lattice. The latent heat of melting is much smaller, partly because liquid water near 0 °C also contains a significant number of hydrogen bonds. The refractive index of ice I_h is 1.31.

Crystal structure

The accepted crystal structure of ordinary ice was first proposed by Linus Pauling in 1935. The structure of ice I_h is the wurtzite lattice, roughly one of crinkled planes composed of tessellating hexagonal rings, with an oxygen atom on each vertex, and the edges of the rings formed by hydrogen bonds. The planes alternate in an ABAB pattern, with B planes being reflections of the A planes along the same axes as the planes themselves.^[41] The distance between oxygen atoms along each bond is about 275 pm and is the same between any two bonded oxygen atoms in the lattice. The angle between bonds in the crystal lattice is very close to the tetrahedral angle of 109.5°, which is also quite close to the angle between hydrogen atoms in the water molecule (in the gas phase), which is 105°. 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.

Hydrogen disorder

The Wurtzite structure. In Ice I_h, the oxygen atoms are arranged on the lattice points, and the hydrogen atoms are on the bonds between lattice points. Each oxygen atom has 4 neighboring ones. Note that the lattice bipartites into two subsets, here colored black and white.

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. 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.^[42] This residual entropy $S 0$ is equal to 3.4±0.1 J mol⁻¹ K⁻¹ $=R\ln(1.50\pm 0.02)$ .^[43]

By contrast, the structure of ice II is hydrogen-ordered, which helps to explain the entropy change of 3.22 J/mol when the crystal structure changes to that of ice I. Also, ice XI, an orthorhombic, hydrogen-ordered form of ice I_h, is considered the most stable form at low temperatures.

Theoretical calculation

There are various ways of approximating this number from first principles. The following is the one used by Linus Pauling.^[44]^[45]

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

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

Using Boltzmann's entropy formula, we conclude that

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

where

k

is the Boltzmann constant and R is the molar gas constant. So, the molar residual entropy is

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 $6^{N}\times (1/2)^{2N}=(3/2)^{N}$ , 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 $R\ln(1.50685\pm 0.00015)$ .^[46]

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 $6^{6}\times (1/2)^{6}=729$ 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 $R\ln(1.5\times (730/729)^{2})=R\ln(1.504)$ .^[47]

Ice Ic

Ice I_c (pronounced "ice one c" or "ice I c") is a metastable cubic crystalline variant of ice. Hans König was the first to identify and deduce the structure of ice I_c.^[48] The oxygen atoms in ice I_c are arranged in a diamond structure and is extremely similar to ice I_h having nearly identical densities and the same lattice constant along the hexagonal puckered-planes.^[49] It forms at temperatures between 130 and 220 kelvins (−143 and −53 degrees Celsius) upon cooling, and can exist up to 240 K (−33 °C) upon warming,^[50]^[51] when it transforms into ice I_h.

Apart from forming from supercooled water,^[52] ice I_c has also been reported to form from amorphous ice^[49] as well as from the high-pressure ices II, III and V.^[53] It can form in and is occasionally present in the upper atmosphere^[54] and 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.^[55]

Ordinary water ice is known as ice I_h (in the Bridgman nomenclature). Different types of ice, from ice II to ice XIX,^[56] have been created in the laboratory at different temperatures and pressures.

Some authors have expressed doubts whether ice I_c really has a cubic crystal system, claiming that it is merely stacking-disordered ice I (“ice I_sd”),^[57]^[58]^[59] and it has been dubbed the ″most faceted ice phase in a literal and a more general sense.″^[60]

However, in 2020, two research groups individually prepared ice I_c without stacking disorder. Komatsu et al. prepared C₂ hydrate at high pressure and decompressed it at 100 K to make hydrogen molecules extracted from the structure, resulting in ice I_c without stacking disorder.^[61] Del Rosso et al. prepared ice XVII from C₀ hydrate and heated it at 0 GPa to obtain pure ice I_c without stacking disorder.^[62] Pure ice I_c prepared in the latter method transforms into ice I_h at 226 K with an enthalpy change of -37.7 J/mol.^[63]

Ice II

Ice II is a rhombohedral crystalline form of ice with a highly ordered structure. It is formed from ice I_h by compressing it at a temperature of 198 K at 300 MPa or by decompressing ice V. When heated it undergoes transformation to ice III.^[64] Ordinary water ice is known as ice I_h, (in the Bridgman nomenclature). Different types of ice, from ice II to ice XIX, have been created in the laboratory at different temperatures and pressures. It is thought that the cores of icy moons like Jupiter's Ganymede may be made of ice II.^{[citation needed]}

History

The properties of ice II were first described and recorded by Gustav Heinrich Johann Apollon Tammann in 1900 during his experiments with ice under high pressure and low temperatures. Having produced ice III, Tammann then tried condensing the ice at a temperature between −70 and −80 °C (203 and 193 K; −94 and −112 °F) under 200 MPa (2,000 atm) of pressure. Tammann noted that in this state ice II was denser than he had observed ice III to be. He also found that both types of ice can be kept at normal atmospheric pressure in a stable condition so long as the temperature is kept at that of liquid air, which slows the change in conformation back to ice I_h.^[65]

In later experiments by Bridgman in 1912, it was shown that the difference in volume between ice II and ice III was in the range of 0.0001 m³/kg (2.8 cu in/lb). This difference hadn't been discovered by Tammann due to the small change and was why he had been unable to determine an equilibrium curve between the two. The curve showed that the structural change from ice III to ice II was more likely to happen if the medium had previously been in the structural conformation of ice II. However, if a sample of ice III that had never been in the ice II state was obtained, it could be supercooled even below −70 °C without it changing into ice II. Conversely, however, any superheating of ice II was not possible in regards to retaining the same form. Bridgman found that the equilibrium curve between ice II and ice IV was much the same as with ice III, having the same stability properties and small volume change. The curve between ice II and ice V was extremely different, however, with the curve's bubble being essentially a straight line and the volume difference being almost always 0.0000545 m³/kg (1.51 cu in/lb).^[65]

Quest for a hydrogen-disordered counterpart of ice II

As ice II is completely hydrogen ordered, the presence of its disordered counterpart is a great matter of interest. Shephard et al.^[66] 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.,^[67] the phase boundary between ice II and its disordered counterpart is estimated to be in the stability region of liquid water.

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@@ Line 152: / Line 152: @@
 However, in 2020, two research groups individually prepared ice I<sub>c</sub> without stacking disorder. Komatsu et al. prepared C<sub>2</sub> hydrate at high pressure and decompressed it at 100&nbsp;K to make hydrogen molecules extracted from the structure, resulting in ice I<sub>c</sub> without stacking disorder.<ref name="pmid32015342">{{cite journal |author=Komatsu K, Machida S, Noritake F, Hattori T, Sano-Furukawa A, Yamane R |display-authors=etal |title=Ice Ic without stacking disorder by evacuating hydrogen from hydrogen hydrate. |journal=Nat Commun |year=2020 |volume=11 |issue=1 |pages=464 |pmid=32015342 |doi=10.1038/s41467-020-14346-5 |pmc=6997176|arxiv=1909.03400 |bibcode=2020NatCo..11..464K }}</ref> Del Rosso et al. prepared [[ice&nbsp;XVII]] from C<sub>0</sub> hydrate and heated it at 0 GPa to obtain pure ice I<sub>c</sub> without stacking disorder.<ref name="pmid32015533">{{cite journal |author=Del Rosso L, Celli M, Grazzi F, Catti M, Hansen TC, Fortes AD |display-authors=etal |title=Cubic ice Ic without stacking defects obtained from ice XVII. |journal=Nat Mater |year=2020 |volume=19 |issue=6 |pages=663–668 |pmid=32015533 |doi=10.1038/s41563-020-0606-y |pmc= |arxiv=1907.02915 |bibcode=2020NatMa..19..663D |s2cid=195820566 |url=https://pubmed.ncbi.nlm.nih.gov/32015533 }}</ref> Pure ice I<sub>c</sub> prepared in the latter method transforms into ice I<sub>h</sub> at 226&nbsp;K with an enthalpy change of -37.7 J/mol.<ref name="pmid37227149">{{cite journal| author=Tonauer CM, Yamashita K, Rosso LD, Celli M, Loerting T| title=Enthalpy Change from Pure Cubic Ice Ic to Hexagonal Ice Ih. | journal=J Phys Chem Lett | year= 2023 | volume= 14 | issue= 21 | pages= 5055–5060 | pmid=37227149 | doi=10.1021/acs.jpclett.3c00408 | pmc=10240532 }}</ref>
+== Ice II ==
+Ice II is a [[rhombohedral]] crystalline form of [[ice]] with a highly ordered structure. It is formed from [[ice Ih|ice I<sub>h</sub>]] by compressing it at a temperature of 198 [[Kelvin|K]] at 300 [[MPa]] or by decompressing [[ice V]]. When heated it undergoes transformation to [[ice III]].<ref>{{cite web |url=http://www.lsbu.ac.uk/water/ice_ii.html |title=Ice-two structure |author=Chaplin, Martin |date=October 18, 2014 |work=Water Structure and Science |publisher=[[London South Bank University]] |access-date=December 6, 2014}}</ref> Ordinary [[water]] ice is known as [[Ice Ih|ice I<sub>h</sub>]],  (in the [[Percy Williams Bridgman|Bridgman]] nomenclature).  Different types of ice, from ice II to [[ice XIX]], have been created in the laboratory at different temperatures and pressures. It is thought that the cores of [[icy moon]]s like [[Jupiter|Jupiter's]] [[Ganymede (moon)|Ganymede]] may be made of ice II.{{citation needed|date=January 2020}}
+===History===
+The properties of ice II were first described and recorded by [[Gustav Heinrich Johann Apollon Tammann]] in 1900 during his experiments with ice under high pressure and low temperatures. Having produced ice III, Tammann then tried condensing the ice at a temperature between {{convert|-70|and|-80|C|K F}} under {{convert|200|MPa|atm|abbr=on|comma=}} of pressure. Tammann noted that in this state ice II was denser than he had observed ice III to be. He also found that both types of ice can be kept at normal [[atmospheric pressure]] in a stable condition so long as the temperature is kept at that of [[liquid air]], which slows the change in conformation back to ice I<sub>h</sub>.<ref name="Hobbs">{{cite book |last=Hobbs |first=Peter V. |date=May 6, 2010 |title=Ice Physics |url=https://books.google.com/books?id=7Is6AwAAQBAJ&pg=PA61 |publisher=[[Oxford University Press]] |pages=61–70 |isbn=9780199587711 |access-date=December 6, 2014}}</ref>
+In later experiments by Bridgman in 1912, it was shown that the difference in volume between ice II and ice III was in the range of {{convert|0.0001|m3/kg|cuin/lb|abbr=on|comma=gaps}}. This difference hadn't been discovered by Tammann due to the small change and was why he had been unable to determine an [[Vapor–liquid equilibrium|equilibrium curve]] between the two. The curve showed that the structural change from ice III to ice II was more likely to happen if the medium had previously been in the structural conformation of ice II. However, if a sample of ice III that had never been in the ice II state was obtained, it could be supercooled even below −70&nbsp;°C without it changing into ice II. Conversely, however, any superheating of ice II was not possible in regards to retaining the same form. Bridgman found that the equilibrium curve between ice II and [[ice IV]] was much the same as with ice III, having the same stability properties and small volume change. The curve between ice II and [[ice V]] was extremely different, however, with the curve's bubble being essentially a straight line and the volume difference being almost always {{convert|0.0000545|m3/kg|cuin/lb|abbr=on|comma=gaps}}.<ref name="Hobbs"/>
+=== Quest for a hydrogen-disordered counterpart of ice II ===
+As ice II is completely hydrogen ordered, the presence of its disordered counterpart is a great matter of interest. Shephard et al.<ref>{{Citation | vauthors=((Shephard, J. J.)), ((Slater, B.)), ((Harvey, P.)), ((Hart, M.)), ((Bull, C. L.)), ((Bramwell, S. T.)), ((Salzmann, C. G.)) | year=2018 | title=Doping-induced disappearance of ice II from water's phase diagram | journal=Nature Physics | volume=14 | issue=6 | pages=569–572 | publisher=Springer Science and Business Media LLC | doi=10.1038/s41567-018-0094-z | bibcode=2018NatPh..14..569S | s2cid=54544973 | url=http://dx.doi.org/10.1038/s41567-018-0094-z}}</ref> investigated the phase boundaries of NH<sub>4</sub>F-doped ices because NH<sub>4</sub>F has been reported to be a hydrogen disordering reagent. However, adding 2.5 mol% of NH<sub>4</sub>F 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.,<ref>{{Citation | vauthors=((Nakamura, T.)), ((Matsumoto, M.)), ((Yagasaki, T.)), ((Tanaka, H.)) | year=2015 | title=Thermodynamic Stability of Ice II and Its Hydrogen-Disordered Counterpart: Role of Zero-Point Energy | journal=The Journal of Physical Chemistry B | volume=120 | issue=8 | pages=1843–1848 | publisher=American Chemical Society (ACS) | doi=10.1021/acs.jpcb.5b09544 | pmid=26595233 | url=http://dx.doi.org/10.1021/acs.jpcb.5b09544}}</ref> the phase boundary between ice II and its disordered counterpart is estimated to be in the stability region of liquid water.
 {{ice}}