Ice phases

Water has many solid phases (ices), given with their properties below.

Phase diagram
Ice crystal data
Known ices
Computer ices (ice 0, ice χ)
Vonnegut's ice-nine
The 'ice-rules' and ice crystal imperfections

Known ices

Typical tetrahedral arrangement of hydrogen bonds, as found (on average) in liquid water — The typical tetrahedral arrangement of hydrogen bonds

There are twenty or so three-dimensional crystalline phases [3500 ] (where the oxygen atoms are in fixed positions relative to each other, but the hydrogen atoms may or may not be disordered, and three amorphous (non-crystalline) phases (see [2145 , 2349 ] for recent reviews of ice research). This large number is due to the open tetrahedrally arranged water molecular structure of hexagonal ice under normal atmospheric pressure and the large number of possible crystal structures that this ice can form as it is progressively crushed under high pressure.

All the crystalline phases of ice involve hydrogen-bonding water molecules with four neighboring water molecules (see left, and [1300] for a recent review). In most cases, the two hydrogen atoms are equivalent with hydrogen bonds of similar strength. The water molecules retain their symmetry obey the 'ice rules' ^j. For the most part, the ordering of the protons (in fixed positions with lower entropy) occurs at lower temperatures. In contrast, the pressure reduces the distances between second shell neighbors (lower volume and greater van der Waals effects). The H-O-H angle in the ice phases is expected to be a little less than tetrahedral (109.47°), at about 107°. The Clausius Clapeyron equation ⁿ for many ice phase changes has to be adapted due to water's negative expansion coefficient and anomalous change in entropy with volume [1147c].

**Structural data on the ice polymorphs**
Ice polymorph	Density, g ˣ cm⁻³^a		Protons ^f	Crystal ^h		Symmetry	Dielectric constant, ε_Sⁱ	Notes
Ih, Hexagonal ice	0.92	0.926	disordered	Hexagonal	P6₃/mmc	one C₆	97.5
Ic, Cubic ice	0.93 ^q	0.933	disordered	Cubic		four C₃
I_sd, Stacking dis-ordered ice	0.93	0.933	disordered	Trigonal	P3m₁	one C₃
LDA, Ia^b	0.925^q		disordered	Non-crystalline				As prepared, may be mixtures of several types
HDA ^c	1.17		disordered	Non-crystalline				As prepared, may be mixtures of several types
VHDA ^d	1.25		disordered	Non-crystalline
II, Ice-two	1.17	1.195	ordered	Rhombohedral		one C₃	3.66
III, Ice-three	1.14	1.160	disordered	Tetragonal	P4₁2₁2	one C₄	117	protons may be partially ordered
IV, Ice-four	1.27	1.275	disordered	Rhombohedral		one C₃		metastable in ice V phase space, an interpenetrating ice frameworks
V, Ice-five	1.23	1.233	disordered	Monoclinic	C2/c	one C₂	144	protons may be partially ordered
VI, Ice-six	1.31	1.314	disordered	Tetragonal ^e	P4₂/nmc	one C₄	193	two interpenetrating frameworks
VII, Ice-seven	1.50	1.591	disordered	Cubic ^e		four C₃	150	two interpenetrating ice Ic frameworks
VIII, Ice-eight	1.46	1.885	ordered	Tetragonal ^e	I4₁/amd	one C₄	4	low-temperature form of ice VII
IX, Ice-nine	1.16	1.160	ordered	Tetragonal	P4₁2₁2	one C₄	3.74	low-temperature form of ice III, metastable in ice II space
X, Ice-ten	2.51	2.785	symmetric	Cubic ^e		four C₃		symmetric proton form of ice VII
XI, Ice-eleven	0.92	0.930	ordered	Orthorhombic	Cmc2₁	three C₂	~4	ordered form of ice Ih phase (needs OH⁻)
XI, Ice-eleven ^k	>2.51		symmetric	Orthorhombic ^e	PBcm	distorted		Superionic
Metallic [1818 ] ^k		≈ 12^o	symmetric, O-H-O bent	Monoclinic ^e	C2∕m			Superionic
XII, Ice-twelve	1.29	1.301	disordered	Tetragonal		one C₄		metastable in ice V phase space
XIII, Ice-thirteen	1.23	1.247	ordered	Monoclinic	P2₁/a	one C₂	~4	ordered form of ice V phase (needs H⁺)
XIV, Ice-fourteen	1.29	1.294	mostly ordered	Orthorhombic	P2₁2₁2₁	one C₄		ordered form of ice XII phase (needs H⁺)
XV, Ice-fifteen	1.30	1.328	ordered	Pseudo-orthorhombic		one C₄	~4	ordered form of ice VI phase (needs H⁺)
XVI, Ice-sixteen	0.81		disordered	Cubic	Fd3m			empty SII clathrate
Empty clathrate SIII ^r	0.59		disordered	Cubic		three C₄		empty SIII clathrate
XVII, Ice-seventeen		0.85	disordered	Hexagonal	P6₁22	one C₆		empty, was H₂-filled ice
XVIII, Ice-eighteen	1.25 [4362]		fluid	Cubic	Fm3m	four C₃ three C₄		Superionic; fcc oxygens
XIX, Ice-nineteen [3987]	~1.32	~1.33	ordered	Tetragonal		one C₄	~4	ordered form of ice VI phase (needs H⁺)
XX Ice-twenty [4362] (also called Ice-nineteen [4057 ])	1.25		fluid	Cubic		six C₂ four C₃ three C₄		Superionic; bcc oxygens

Ice Ih may be metastable with respect to empty clathrate structures (Ice-sixteen, [2252 and Ice-seventeen [2796]]) of lower density under negative pressure conditions (that is, stretched) at very low temperatures [520 ]. Different research groups have described two different forms of ice-eleven; (a) the high-pressure form (also known as ice-thirteen) involves hydrogen atoms equally-spaced between the oxygen atoms [84] (like ice-ten) in a distorted hexagonal close-packed structure whereas (b) the lower pressure, low temperature, form uses the incorporation of hydroxide defect doping (and interstitial K⁺ ions) to order the hydrogen-bonding of ice Ih [207], that otherwise occurs too slowly. Another ice-ten has been described, being the proton-ordered form of ice-six (VI); this is now known as ice fifteen. Only hexagonal ice-one (Ih), ice-three (III), ice-five (V), ice-six (VI), ice-seven (VII), and, perhaps, ice-ten (X) can be in equilibrium with liquid water (ice-ten with supercritical water), whereas all the others ices, including ice-two (II, [273]), are not stable in its presence under any conditions of temperature and pressure. The low-temperature ices, ice-two, ice-eight (VIII), ice-nine (IX), ice-eleven (low-pressure form), ice-thirteen (XIII) [1002], ice-fourteen (XIV) [1002], ice fifteen (XV) [1582 ], and one of the proposed ice nineteens (XIX) [3987] all possess (ice-nine and ice-fourteen incompletely) low entropy ordered hydrogen-bonding. In contrast, the other ices (except ice-ten [80] and ice-eleven where the hydrogen atoms are symmetrically placed and molecules of H₂O do not have individual existence) the hydrogen-bonding is disordered even down to 0 K, where reachable; these include all the ices that share a phase boundary with liquid water. Their zero-point energies have been described [3780 ]. Disordered hydrogen bonding causes positional disorder in the oxygen atoms of several picometers around their crystallographic sites. Also, the disordered ices I, IV, V, VI, and XII, show glass transitions at low temperatures [2601 ], associated with the unfreezing of the reorientation dynamics. Ice-four (IV) and ice-twelve (XII) [82] are both metastable within the ice-five phase space. Cubic ice (Ic) is metastable with respect to hexagonal ice (Ih). Ice-seven (VII) undergoes X-ray-induced (≈ 9.7 keV) dissociation to an O₂ - H₂ alloy ^g at high pressure (>2.5 GPa) but reverts to ice-seven near its melting point at 700 K and 15 GPa [1383 ]. A new ice phase has been reported to lie on what had been thought to be the liquid (supercritical) side of ice-seven at high pressures, with approximate triple points of about 700 K, 20 GPa with liquid (supercritical) water and ice-seven and about 1500 K, 40 GPa with liquid (supercritical) and ice-ten [1521 ]. This may be a plastic phase where only molecular rotations are allowed [2078 ].

**More structural data on the ice polymorphs**
Ice polymorph	Molecular environments	Small ring size(s)^p	Helix	Approximate O-O-O angles, °	Net ^s	Ring penetration hole size
Ih, Hexagonal ice	1	6	None	All 109.47±0.16	lon	None
Ic, Cubic ice	1	6	None	109.47	dia	None
I_sd, Stacking dis-ordered ice	1	6	None	109.47		None
LDA, Ia^b	3+	5(9), 6(55)	None	mainly 108, 109 and 111		None
HDA ^c	6+	5(9), 6(55)	None	broad range		None
VHDA ^d	6+	5(9), 6(55)	None	broad range		None [747 ]
II, Ice-two	2 (1:1)	6(7), 8(9),10(15)	None	80,100,107,118,124,128; 86,87,114,116,128,130	ict	None
III, Ice-three	2 (1:2)	5(1), 7(1), 8(1)	4—fold	(1) 91,95,112,112,125,125 (2) 98,98,102,106,114,135	kea	None
IV, Ice-four	2 (1:3)	6(7), 8(18),10(42)	None	(1) 92,92,92,124,124,124 (3) 88,90,113,119,123,128	icf single	some 6
V, Ice-five	4 (1:2:2:2)	4(2), 5(3), 6(2), 8(3),9(2),10(12),12(1)	None	(1) 82,82,102,131,131,131 (2) 88,91,109,114,118,128 (3) 85,91,101,103,130,135 (4) 84,93,95,123,125,126	icv	8 (1 bond)
VI, Ice-six	2 (1:4)	4(5), 8(9)	None	(1) 77,77,128,128,128,128 (2) 78,89,89,128,128,128	edi 2-fold	8 (2 bonds)
VII, Ice-seven	1	6	None	109.47	dia 2-fold	every 6
VIII, Ice-eight	1	6	None	109.47	dia 2-fold	every 6
IX, Ice-nine	2 (1:2)	5(1), 7(1), 8(1)	4—fold	(1) 91,95,112,112,125,125 (2) 98,98,102,106,114,135	kea	None
X, Ice-ten	1	6	None	109.47	dia 2-fold	every 6
XI, Ice-eleven	1	6	None	109.47	lon single	None
XI, Ice-eleven ^k	undetermined	6/4	None	undetermined		every 6
XII, Ice-twelve	2 (1:2)	7(2), 8(3)	5—fold	(1) 107,107,107,107,115,115 (2) 67,83,93,106,117,132		None
XIII, Ice-thirteen	7 (all equal)	4(2), 5(3), 6(2), 8(3),9(2),10(12),12(1)	None	(1) 82,82,102,131,131,131 (2) 88,91,109,114,118,128 (3) 85,91,101,103,130,135 (4) 84,93,95,123,125,126	icv	8 (1 bond)
XIV, Ice-fourteen	2 (1:2)	7(2), 8(3)	5—fold	(1) 107,107,107,107,115,115 (2) 67,83,93,106,117,132	itv	None
XV, Ice-fifteen	2 (1:4)	4(5), 8(9)	None	(1) 77,77,122,122,134,134 (2) 87,90,94,124,129,135	edi 2-fold	8 (2 bonds)
XVI, Ice-sixteen	4 (6:6:4:1)	5(9), 6(1)	None	106, 108, 109, 120	mtn	None
Empty SIII clathrate ^r	2 (1:3)	4(12), 6(8), 8(6)	None	90, 120, 135		None
XVII, Ice-seventeen	1	5	6-fold	103, 106, 111, 125	unj	None
XVIII, Ice-eighteen	2	n/a	n/a	90, 180		n/a
XIX, Ice-nineteen		4(5), 8(9)	None			8 (2 bonds)
XX, Ice-twenty	1	n/a	n/a	45, 90		n/a

n/a = not applicable

The thermal conductivities properties of crystalline and amorphous ices have been reviewed [1202]. The OD/OH Raman stretch bands for D₂O/H₂O ices have been analyzed and compared [3508 ]. The vibrational amplitudes and the degree of the phonon localization in nineteen ice forms, both crystalline and amorphous, have been determined by a quasi-harmonic approximation with a classical intermolecular interaction model for water [3783b]. The amplitude in the low-pressure ices increased with compression, while the opposite trend was observed in the medium and high-pressure ices. The mean square displacements of the ices' oxygen and hydrogen atoms were determined against temperature for ice Ih (O 0.107 ˣ Å⁻²; H 0.129 ˣ Å⁻² at 200 K), LDA (O 0.105 ˣ Å⁻²; H 0.129 ˣ Å⁻² at 200 K), and HDA at 100 MPa (H 0.131 ˣ Å⁻² at 200 K), ice III at 300 MPa (O 0.095 ˣ Å⁻²; H 0.130 ˣ Å⁻² at 200 K), VI at 1 GPa (O 0.054 ˣ Å⁻²; H 0.083 ˣ Å⁻² at 200 K), and ice VII at 7 GPa (O 0.032 ˣ Å⁻²; H 0.058 ˣ Å⁻² at 200 K) by a quasi-harmonic approximation method [3783b].

The near-infrared spectra of high-density crystalline H₂O ices, ice-two, ice-four, ice-five, ice-six, ice-nine, and ice-twelve, have been compared with hexagonal ice [4189 ]. The first overtone of the OH-stretching mode, at about 6700 cm⁻¹, was identified as the marker band most suitable to distinguish between these ices. There was a clear blue shift of this band that increased with increasing topological density and a significant narrowing of the band.

Other stable or metastable phases of ice have been proposed (for example, Ice XIII and ice XIV were proposed earlier than their discovery [958 ]), but their structures were not established. Several new phases (for example, ice i, 'Hexagonal Bilayer Water' and 'Pleated Sheet Water', [1985 ]) have only been found (so far) in modeling studies. However, other ices have been found at confined surfaces. 'Metallic' water,^m where electrons are freed to move extensively throughout the material and the atoms of water exist as ions, probably exists as an antifluorite type structure ^m above 1.76 TPa [1138 ]. It is not thought that any other phases are stable at higher pressures than this. A highly conductive warm dense state of water (similar to liquid metal), observed with ultrafast pump-probe free-electron-lasers, has measured the brief reflection and transmission of ultrathin water sheet samples that approach a highly conducting state at electron temperatures exceeding 20,000 K [4332 ].

The proposed topology of the transformations between ice XI ice II ice IX, and ice VIII ice X has been described [1237]. The mechanism of ice crystal formation has been investigated by molecular dynamics by overcoming its timescale limitation. It was suggested that the formation of each ice crystal occurred via high-density water with a similar structure to the formed ice crystal [3908 ]. [Back to Top ]

Computer ices

Many other possible crystalline structures of solid water (ice) fit with the tetrahedrality of water's hydrogen bonding, and obey the ice rules [4046 ]. Nearly 75,000 putative ice structures have been generated using known silica structures, including all known ice structures except ice IV [4037 ]. These 'metastable' states may be generated using molecular models but whether they are important in the real world needs to be determined by experiment. One such ice is ice 0 (see below), a tetragonal structure (unit cell 12 molecules; 90º, 90º, 90º, 5.93 Å, 5.93 Å, 10.74 Å; 0.95 g ˣ cm⁻³) containing 5-, 6-, and 7-membered rings that have been proposed as a structure formed during the crystallization of ice Ic and ice Ih from supercooled water [2149 ]. Interestingly this ice 0 structure contains partial dodecahedral clusters consisting of three linked pentamers (H₂O)₁₁ as thought to exist in supercooled water and ES.

Ice 0 [2149]; 3 x 3 x3 unit cells viewed down the x- and z-axes. The view down the y-axis is similar to that down the x-axis

Ice 0 [2149]; 3 x 3 x3 unitcells viewed down the x- and z-axes. The view down the y-axis is similar to that down the x-axis

In these diagrams of ice 0, the hydrogen bonding is shown ordered whereas, in reality, it is random, obeying the ice rules. Interactive structures of ice 0 (Jmol) are available. Another computer ice has been proposed as a metastable link in the crystallization of ice VII at 10 GPa, 425 K [2163 ]. A quantum-mechanical exploration of the phase diagram of water has been made, showing the completeness of the 2020 experimental water phase diagram [4199].

The empty clathrate S-III ice has been proposed to be the most stable ice phase at very high negative (i.e., very stretched conditions) pressures [2507 ].

Ice χ (ice-chi, [3589 ]). Using free-energy computations a further high density (1.272 g ˣ cm⁻³) ice is found under high external electric field (2.3 V ˣ nm⁻¹) as the most stable structure in the high-pressure/low-temperature region, located between ice II and ice VI, and the low-temperature neighbor of ice V exhibiting two triple points at 606 MPa, 131.23 K (ice II ice V, ice χ) and 945 MPa, 144.24 K (ice V, ice χ, ice VI). The computed ferroelectric crystal structure is orthorhombic with space group Fdd2 with the lattice parameters of the 56-water molecule unit cell being a = 24.34 Å, b = 12.53 Å, and c = 4.32 Å. All water molecules are oriented in the direction of the external electric field. [3589].

Other two-dimensional ices have been found on surfaces. These include a helical monolayer ice consisting of helical hexamers normal to the basal plane and an ice monolayer with every two neighboring water hexamers connected by a water square yet folded into two distinct planes [4081 ].

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Cats Cradle. This edition published by Henry Holt and Company, 1999

Vonnegut's ice-nine

Kurt Vonnegut's highly entertaining story concerning an (imaginary) ice-nine, which was capable of crystallizing all the water in the world [83], fortunately, has no scientific basis (see also I_E). Ice-nine, in reality, is a proton-ordered form of ice-three, and only exists at very low temperatures and high pressures and cannot exist alongside liquid water under any conditions.

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Footnotes

^a Left column: experimental density at atmospheric pressure but at the temperature of stability (this will contain crystal boundaries and faults); right column: crystallographic density [1717]. [Back]

^b Low-density amorphous ice (LDA). The structural data in the Table is given, assuming LDA has the structure of ES. [Back]

^c High-density amorphous ice (HDA). The structural data in the Table is given, assuming HDA has the structure of crushed CS. [Back]

^d Very high-density amorphous ice (VHDA). The structural data in the Table assumes no hydrogen bond rearrangements from LDA or HDA. As VHDA is likely to be a relaxed form of HDA, this assumption seems unlikely [935 ]. [Back]

^e Structure consists of two interpenetrating frameworks. [Back]

^f Although primarily ordered or disordered, ordered arrangements of hydrogen-bonding may not be perfect and disordered arrangements of hydrogen-bonding are not completely random as there are correlated and non-bonded preferential effects. [Back]

^g This ice is reported to be more likely a trigonal structure made up of 2H₃O^δ++ O_2^δ⁻ + H₂ rather than a 2H₂ + O₂ alloy [1419 ]. [Back]

^h Crystal cell parameters have been collated. The right-hand column gives the space group. [Back]

ⁱ Relative permittivities (dielectric constants) fall into two categories depending on whether the hydrogen bonds are ordered (low values) or disordered (high values). [Back]

An H2O ice molecule obeying the 'ice rules' — An H₂O ice molecule (a)

obeying the 'ice rules'

^j The 'ice rules': [3844 ] (also called the Bernal–Fowler rules [766 ]) Each water molecule (right labeled 'a') has four hydrogen-bonded neighbors, two hydrogen atoms near each oxygen (≈ 1 Å), one hydrogen atom on each O····O bond; thus H-O-H···OH₂ and H₂O···H-O-H are allowed, but H-O-H···H-O-H and H₂O···OH₂ are not; see H₂O molecule a right). As the H-O-H angles are about 106.6º [717], the hydrogen bonds are not straight (although shown so in the figures). All ices are subject to crystal imperfections [4085 ]. Weaknesses (Bjerrum defects; 66 kJ ˣ mol⁻¹ in hexagonal ice, [3220 ]) in the ice crystal are apparent where the ice rules are disobeyed. Both O····O contacts, without an intervening proton (L defect, 'leer' defect) and O-H····H-O contacts (D defect, 'doppelt' defect, with two protons between the pair of oxygen atoms) may occur due to molecular rotations where neighboring water molecules fail to adjust their hydrogen-bonding. Another type of defect is the ionic defect caused by the presence of H₃O⁺ and OH⁻ ions (135 kJ ˣ mol⁻¹ in hexagonal ice, [3220]). The presence of these ion defects (particularly H⁺), and their movement by the Grotthuss mechanism, are responsible for the conduction of electricity by the ices. The addition of ammonium fluoride as a hydrogen-disordering agent in ordered hydrogen bond ices (e.g., ice II and ice VIII) can destroy the hydrogen bond ordering as F⁻ can accept up to 4 H-bonds and NH₄⁺ can donate up to 4 H-bonds and both ions can fit in a hydrogen-bonded ice lattice [3608 ]). [Back]

^k Ice XI was first described as a fully-ionic antifluorite structure formed at around 100 GPa [2539 ]. Ice XI is also known as ice XIII. These structures have not been experimentally verified and, therefore, are best not referred to with the numerical designations first used. [Back]

^m The antifluorite structure consists of a face-centered cubic (FCC) unit cell with oxygen anions occupying the FCC lattice points (corners and faces). Hydrogen cations occupy the eight tetrahedral sites within the FCC lattice. [Back]

ⁿ The Clausius Clapeyron equation can be stated as dT/dP=TΔV/ΔH=ΔV/ΔS where P, T, H, V, and S are the pressure, temperature, enthalpy, volume, and entropy. This may be extended to be

dT/dP=T(sign α₂V₂ - sign α₁V₁)ΔV/ΔH

where α represents the thermal expansion coefficients, for use with phases with negative expansion coefficients, including the ice phase changes

LDAIc, HDALDA, LDAHDA, IIIV, VVI, VIVII and VIVIII

[1147b]. [Back]

^o At 5 TPa. [Back]

^p The figures in brackets are the relative number of such rings. For the crystalline ices, they are from [2021 ].

^q Data corrected to 0 °C, for direct comparison to ice Ih. The densities were determined at ≈ 80 K (ice Ih 0.932 g ˣ cm⁻³, ice Ic 0.943 g ˣ cm⁻³, LDA 0.937 g ˣ cm⁻³) [2032]. [Back]

^r This ice has not been experimentally confirmed [Back]

^s The networks (see also [4084 ]) are as described in http://rcsr.net/nets, as I was told by Prof. Davide M. Proserpio [Back]

^t A version of metallic ice has been created by addiing tiny amounts of water vapor at 10⁻⁷ bar to a sodium-potassium alloy under vacuum. A transient gold-coloured layer of a metallic water solution covering the metal alloy drops forms [4324 ]. [Back]

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