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'

Known ices

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

There are eighteen or so 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 the water molecules being hydrogen-bonded to four neighboring water molecules (see left, and [1300] for a recent review). In most cases, the two hydrogen atoms are equivalent with the 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, whereas 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 the tetrahedral angle (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, two 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		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		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		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		~3	liquid	Cubic	Fm3m	four C₃ three C₄		Superionic; fcc 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] and ice fifteen (XV) [1582 ] all possess (ice-nine and ice-fourteen incompletely) low entropy ordered hydrogen-bonding whereas in 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 pm around their crystallographic sites. Also, the disordered ices I, IV, V, VI, and XII, also 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, °	Ring penetration hole size
Ih, Hexagonal ice	1	6	None	All 109.47±0.16	None
Ic, Cubic ice	1	6	None	109.47	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	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	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	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	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	8 (2 bonds)
VII, Ice-seven	1	6	None	109.47	every 6
VIII, Ice-eight	1	6	None	109.47	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	None
X, Ice-ten	1	6	None	109.47	every 6
XI, Ice-eleven	1	6	None	109.47	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	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	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	8 (2 bonds)
XVI, Ice-sixteen	4 (6:6:4:1)	5(9), 6(1)	None	106, 108, 109, 120	None
Empty clathrate SIII ^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	None
XVIII, Ice-eighteen	2	n/a	n/a	90, 180	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 was found to increase 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].

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, but other ices have been found at confined surfaces. 'Metallic' water, 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.

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

There are many other possible crystalline structures of solid water (ice) that fit with the tetrahedrality of water's hydrogen-bonding, and that obey the ice rules. 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 has 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 ].

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].

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.

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 totally 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). Weaknesses (Bjerrum defects; 66 kJ ˣ mol^-1 [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 [3220]). 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 an ice hydrogen-bonded 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 perhaps, 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), and 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]