Ice phases

Phase diagram

Water has many solid phases (ices), There are sixteen or so crystalline phases and three amorphous (non-crystalline) phases All the crystalline phases of ice involve the water molecules being hydrogen bonded to four neighboring water molecules (see [1300] for a recent review). In most cases the two hydrogen atoms are equivalent, with the water molecules retaining their symmetry, and they all obey the 'ice' rules: two hydrogen atoms near each oxygen, one hydrogen atom on each O····O bond.^j 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 Clapeyron equation^o 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 cm^-3^a	Protons^f	Crystal^h	Symmetry	Dielectric constant, ε_Sⁱ	Notes
Hexagonal ice, Ih	0.92	disordered	Hexagonal	one C₆	97.5
Cubic ice, Ic	0.92	disordered	Cubic	four C₃
LDA, Ia^b	0.94	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	ordered	Rhombohedral	one C₃	3.66
III, Ice-three	1.14	disordered	Tetragonal	one C₄	117	protons may be partially ordered
IV, Ice-four	1.27	disordered	Rhombohedral	one C₃		metastable in ice V phase space
V, Ice-five	1.23	disordered	Monoclinic	one C₂	144	protons may be partially ordered
VI, Ice-six	1.31	disordered	Tetragonal^e	one C₄	193	protons can be partly ordered
VII, Ice-seven	1.50	disordered	Cubic^e	four C₃	150	two interpenetrating ice Ic frameworks
VIII, Ice-eight	1.46	ordered	Tetragonal^e	one C₄	4	low temperature form of ice VII
IX, Ice-nine	1.16	ordered	Tetragonal	one C₄	3.74	low temperature form of ice III, metastable in ice II space
X, Ice-ten	2.51	symmetric	Cubic^e	four C₃		symmetric proton form of ice VII
XI, Ice-eleven	0.92	ordered	Orthorhombic	three C₂		low temperature form of ice Ih
XI, Ice-eleven ^k	>2.51	symmetric	Hexagonal close packed ^e	distorted		Found in simulations only
XII, Ice-twelve	1.29	disordered	Tetragonal	one C₄		metastable in ice V phase space
XIII, Ice-thirteen	1.23	ordered	Monoclinic	one C₂		ordered form of ice V phase
XIV, Ice-fourteen	1.29	mostly ordered	Orthorhombic	one C₄		ordered form of ice XII phase
XV, Ice-fifteen ⁿ	1.31 (?)	ordered	?	?		ordered form of ice VI phase

Two different forms of ice-eleven have been described by different research groups: the high-pressure form (also known as ice-thirteen) involves hydrogen atoms equally-spaced between the oxygen atoms [84] (like ice-ten) whereas 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) occurring below about 110 K. 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] and ice-fourteen (XIV) [1002] 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) the hydrogen-bonding is disordered even down to 0 K, where reachable. 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). It is worth emphasizing that liquid water is stable throughout its phase space above. However, 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 (supercritica)l side of ice-seven at high pressures, with approximate triple points of about 700 K, 20 MPa with liquid and ice-seven and about 1500 K, 40 MPa with liquid and ice-ten [1521 ].

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) as ice-nine, in reality, is a proton ordered form of ice-three, only exists at very low temperatures and high pressures and cannot exist alongside liquid water under any conditions. Ice Ih may be metastable with respect to empty clathrate structures of lower density under negative pressure conditions (that is, stretched) at very low temperatures [520 ].

**More structural data on the ice polymorphs**
Ice polymorph	Molecular environments	Small ring size(s)	Helix	Approximate O-O-O angles, °	Ring penetration hole size
Hexagonal ice, Ih	1	6	None	All 109.47±0.16	None
Cubic ice, Ic	1	6	None	109.47	None
LDA, Ia^b	3+	5, 6	None	mainly 108, 109 and 111	None
HDA ^c	6+	5, 6	None	broad range	None
VHDA ^d	6+	5, 6	None	broad range	None [747 ]
II, Ice-two	2 (1:1)	6	None	80,100,107,118,124,128; 86,87,114,116,128,130	None
III, Ice-three	2 (1:2)	5, 7	4—fold	(1) 91,95,112,112,125,125 (2) 98,98,102,106,114,135	None
IV, Ice-four	2 (1:3)	6	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, 5, 6, 8	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, 8	None	(1) 77,77,128,128,128,128 (2) 78,89,89,128,128,128	8 (2 bond)
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, 7	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	None	undetermined	every 6
XII, Ice-twelve	2 (1:2)	7, 8	5—fold	(1) 107,107,107,107,115,115 (2) 67,83,93,106,117,132	None
XIII, Ice-thirteen	7 (all equal)	4, 5, 6, 8	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, 8	5—fold	(1) 107,107,107,107,115,115 (2) 67,83,93,106,117,132	None
XIV, Ice-fifteen ⁿ	2 (1:4)	4, 8	None	(1) 77,77,128,128,128,128 (2) 78,89,89,128,128,128	8 (2 bond)

The thermal conductivities properties of crystalline and amorphous ices have been reviewed [1202]. Other stable or metastable phases of ice have been proposed (for example, Ice XIII and ice XIV [958 ]) and may exist but their structures have not been established. Such new phases are thought particularly likely to be found within the phase space of ice II and ice V. Several new phases (for example ice i) 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]. [Back to Top ]

Footnotes

^a density at atmospheric pressure. [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 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 [711]. [Back]

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

^j Weaknesses (Bjerrum defects) in the ice crystal are apparent where the ice rules are disobeyed. Both O····O contacts, without an intervening proton (L defect) and O-H····H-O contacts (D defect) may occur due to molecular rotations where neighboring water molecules fail to adjust their hydrogen bonding. Other defects may be caused by the presence of H₃O⁺ and OH^- ions. [Back]

^k Also known as ice XIII. [Back]

^m The antifluorite structure consists of an 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 This ice has not yet been prepared. [Back]

^o The Clapeyron equation is normally 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]