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Cubic Ice (Ice Ic and Ice XIc)

Cubic ice is a solid form of water that has been proposed to form in high clouds.

 

link Stacking-disordered ice

link Hexagonal ice


Ice Ic is a metastable b ice crystal that can be formed, by condensation of water vapor, at ambient pressure but low temperatures (less than -80 °C, see Phase Diagram), or below about -38 °C in small droplets (~6 μm diameter) [1013] or by reducing the pressure on high-pressure ices at 77 K. Often (perhaps usually [1236c]) found are transitional states between hexagonal and cubic ice depending on the formation and history of the cubic ice [1236]. Indeed, the structure of ice that crystallizes initially from supercooled water is reported to always be stacking-disordered [1236e]. Crystals of ice formed on homogeneous ice nucleation in deeply supercooled water nanodrops (r ≈ 10 nm) at ∼225 K were only 78 % cubic ice with 22% hexagonal ice; effectively 44% stacking-disordered ice [3032]. It seems very difficult to prepare cubic ice crystals with a greater proportion of cubic ice structure. However, the term 'cubic ice' has been historically used for these less-than pure ice crystals. With increasing time, metastable cubic ice converts to hexagonal ice through the increasingly disordered stacking-disordered ice.

 

Cubic ice structure

Cubic ice structure

Cubic ice melts slightly lower [2559] and has a slightly higher vapor pressure than ice Ih. It may naturally form in the upper atmosphere [751] and is often found in freezing confined (porous) aqueous systems. There is evidence that it may be the preferred phase for ice formed from water droplets smaller than 15 nm radius at 160-220 K [856, 996], due to its lower interfacial free energy than hexagonal ice. Larger cubic ice crystals convert, irreversibly but extremely slowly in the temperature range 170-220 K, to hexagonal ice crystals with up to 50 J mol-1 heat evolution [493].

 

It consists of a face-centered cubic lattice (Space group, Fd bar3 m, 227; Laue class symmetry m-3m; analogous to β-cristobalite silica) with half the tetrahedral holes filled. The starred molecules show the unit cell positions. The (H2O)10 cluster, shown in red, has been found in a super-molecular structure [32].

Cubic ice crystals

ice crystals giving miller indices

(x,y,z) of faces; from [2304]

 

ice crystals giving miller indices (x,y,z) of faces; from [2304]

Cubic ice has never been prepared or found as a pure crystal, but its crystal structure has been extracted from the available data. As with ice Ih, it possesses a fairly open low-density structure where the packing efficiency is low (~1/3) compared with simple cubic (~1/2) or true face-centered cubic (~3/4) structures. a

 

In contrast to ice Ih, however, water molecules have a staggered arrangement of hydrogen bonding with respect to all of their neighbors, rather than to 3/4 of them. The result is that the density is almost the same as ice Ih.

 

Comparison of the arrangements of second neighbors in cubic and hexagonal ice

 

Comparison of the arrangements of second neighbors in cubic and hexagonal ice

 

 

Ice Ih and ice Ic differ in the arrangement of second-neighbors (see left; the central water molecule is shown pale orange and first neighbor and hydrogen atoms are omitted for clarity). In ice Ic these form a cuboctahedron (far left) and in ice Ih these form an anticuboctahedron.

 

Cubic ice lattice

Cubic ice lattice

 

 

The cubic crystal has unit cell dimension 6.358 Å (a, b, c; 90º, 90º, 90º, 8 molecules) [383]. All molecules experience identical molecular environments. Interpenetrating ice Ic networks occur in the high-pressure ices ice-seven and ice-eight.

 

All atoms have four tetrahedrally arranged nearest neighbors and twelve second neighbors, as ice Ih. The crystals may be thought of as sheets of chair-form hexamers in any one of the tetrahedrally-arranged planes. Cubic ice contains solely chair-form hexamers in contrast to hexagonal ice that contains boat-form hexamers as well. Please note that in both these structural diagrams the hydrogen-bonding is drawn as ordered whereas in reality it is random  (obeying the 'ice rules': two hydrogen atoms near each oxygen, one hydrogen atom on each O····O bond) and protons can move between (ice) water molecules at temperatures above about 5 K [1504].

 

Distinct proton arrangements in cubic ice, from[2146]

 

Distinct proton arrangements in cubic ice, from [2146]

This disorder gives rise to a zero-point entropy close to 3.414 J mol-1 K-1 [2153]. c As the H-O-H angle does not vary much from that of the isolated molecule, the hydrogen bonds are not straight (although shown so in the figures). However, the ordered structure shown may exist in a proton-ordered form (ice XIc; comparable to the relationship of ice XI to Ice-Ih) [1753]. The configuration shown above is the energetically most stable form of hydrogen bonding and is ferroelectric (space group I41md, (a) left) with all H2O dipoles pointing in the same direction. A partial ordering into this configuration has been found using the methodology used for producing ice XI from hexagonal ice [2146]. Three other distinct proton arrangements are the weakly ferroelectric configurations (b) (space group Pna21) and (c) (space group P41) and the antiferroelectric (d) (space group P41212) where all H2O dipoles cancel out [2146].

There are differences in the numbers of water molecules in the hydration shells around water molecules in hexagonal and cubic ices. Notably, there is an extra water molecule in the second shell of hexagonal ice, which helps explain its greater stability. The cavities in cubic ice are formed from ten water molecules and are smaller than those in hexagonal ice; formed from twelve. These cavities in cubic ice form an identical network to the water molecules. Indeed if all the cavities contain a water molecule each, then the structure of ice-seven is formed.

 

Comparison of hexagonal and cubic ice
Hydration shell
1
2
3
4
5
6
Radius, nm (approx.)
0.28
0.45 (0.46)
0.53
0.65
0.70 (0.74)
0.78
Hexagonal ice, No.
4
12 (+1)
9
12
9 (+2)
18
Cubic ice, No.
4
12
12
6
12
24

 

Cubic ice shows an anomalous reduction in thermal conductivity with increasing pressure (as do hexagonal ice and low-density amorphous ice) but different from most crystals. This is due to changes in the hydrogen bonding decreasing the transverse sound velocity [617]. Cubic and hexagonal ices have been compared [996].

 

Interactive structures are available (Jmol).

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Footnotes

a    The exact packing efficiency for ice Ic is low

~pi/(48*(SIN((ACOS(1/3))/2)^3)) ~ 0.34,            ~1/3

compared with the simple cubic

                          pi/6 = 0.5236,                     ~1/2

or the true face-centered cubic

                         pi/(3xsqrt(2)) = 0.7408,                 ~3/4

structures [811]. [Back]

[Back]

 

b   The metastability of cubic ice relative to hexagonal ice is due to the greater symmetry of the cubic ice crystal. Although both crystal structures involve tetrahedrally placed oxygen atoms, cubic ice constricts the water H-O-H bond angle more strongly towards the tetrahedral angle (109.47°), relative to hexagonal ice, and further away from its gas phase value (104.47°). The difference in energy for the pure crystals has been estimated as greater than 135 J mol-1 [2390], but may be far lower at low temperatures (<200 K) [2559]. [Back]

 

c   Zero-point entropy is entropy (disorder) that would remain even if the material could be cooled to 0 K (absolute zero, 0 K = −273.15 °C). [Back]

 

 

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This page was established in 2002 and last updated by Martin Chaplin on 13 November, 2017


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