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Glacier ice (1h)

 

Glacier ice

Ice phases

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

 

link Phase diagram
link Ice crystal data
V Known ices
V Computer ices (ice 0, ice χ)
V Vonnegut's ice-nine

V The 'ice-rules' and ice crystal imperfections

Known ices

 

The typical tetrahedral arrangement of hydrogen bonds

 

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

 

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, εS i 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 Fd bar3 m four C3    

Isd, 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 R bar3 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 R bar3 c 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 Pn bar3 m 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 Pn bar3 m 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 I bar4 2d 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 P bar1 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  p-4 3n 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 P bar4

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, °

Nets
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
Isd, 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 to top of page]

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 IE). 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 2H3Oδ++ O2δ + 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 (a)

obeying the 'ice rules'

 

An H2O  ice molecule 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

 

LDA-->Ic, HDA-->LDA, LDA-->HDA, III-->V, V-->VI, VI-->VII and VI-->VIII

 

[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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