Ice nucleation and growth
Is ice slippery?
Hexagonal ice (ice Ih) is the form of all natural snow and ice on Earth (see Phase Diagram), as evidenced in the six-fold symmetry in ice crystals grown from water vapor (that is, snow flakes).
Hexagonal ice (Space group P63/mmc, 194; symmetry D6h, Laue class symmetry 6/mmm; analogous to β-tridymite silica) possesses a fairly open low-density structure, where the packing efficiency is low (~1/3) compared with simple cubic (~1/2) or face centered cubic (~3/4) structuresa (and in contrast to face centered cubic close packed solid hydrogen sulfide).
The crystals may be thought of as consisting of sheets lying on top of each other. The basic structure consists of a hexameric box where planes consist of chair-form hexamers (the two horizontal planes, opposite) or boat-form hexamers (the three vertical planes, opposite). In this diagram the hydrogen bonding is shown ordered whereas in reality it is random,b as protons can move between (ice) water molecules at temperatures above about 130 K [1504].
The water molecules have a staggered arrangement of hydrogen bonding with respect to three of their neighbors, in the plane of the chair-form hexamers. The fourth neighbor (shown as vertical links opposite) has an eclipsed arrangement of hydrogen bonding.
There is a small deviation from ideal hexagonal symmetry as the unit cellc is 0.3 % shorter in the c-direction (in the direction of the eclipsed hydrogen bonding, shown as vertical links in the figures). All molecules experience identical molecular environments.
There is space enough inside each box to hold an interstitial water molecule. Although this is generally not thought to occur, interstitial water molecules have been recently found by neutron diffraction of effectively-powdered ice [154].
Hexagonal ice has triple points with liquid and gaseous water (0.01°C, 612 Pa), liquid water and ice-three (-21.985°C, 209.9 MPa) and ice-two and ice-three (-34.7°C, 212.9 MPa). The dielectric constant of hexagonal ice is 97.5 [94].
The melting curve for hexagonal ice is given by 
MPa [1320]. The IAPWS release on the equation of state for hexagonal ice is available.
Hexagonal ice crystals form hexagonal plates and columns where the top and bottom faces are basal planes {0 0 0 1}, and the six equivalent side faces are called the prism faces {1 0 -1 0}di . Secondary prism faces {1 1 -2 0} dii may be formed down the planes formed by the sides of the chair structures.
Hexagonal ice shows anomalous reduction in thermal conductivity with increasing pressure (as do cubic 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].
The hydrogen bonding in the surface of hexagonal ice is predicted to be more ordered than that within the bulk structure [1529].
Interactive structures of hexagonal ice (Chime,
22 KB) are available. [Back to Top 
]
Ice nucleation occurs greatly enhanced, by a factor of 1010, at the air-water surface rather than within bulk water [914]. Hexagonal ice crystals may form by (slowly) growing in the direction of the c-axis (S1 ice) as inside vertical freezing pipes or where ice crystals grow down vertically from crystal platelets nucleated on still water with their c-axes vertical, and where sideways growth is prevented but axial growth allowed. Alternatively they may grow more rapidly from the prism faces (S2 ice), as at the disturbed randomly-directed surface of rapidly freezing or agitated lakes. Growth from the {1 1 -2 0} faces is at least as fast as that from the prism faces but such growth turns these faces into prism faces [827]. Ice crystal growth data has been critically examined elsewhere. The relative speeds of this crystal growth, on the different faces depend on the ability of these faces to form greater extents of cooperative hydration. The temperature of the (supercooled) surrounding water determines the degree of branching in the ice crystal. Crystal growth is limited by the rate of diffusion at a low degree of supercooling (i.e < 2°C; giving rise to more branching) but limited by the kinetics of growth at higher degrees of supercooling (i.e. > 4°C; giving rise to needle-like growth) [883]. The hexagonal crystal structure, the different growth characteristics of the crystal faces and the temperature of the surrounding (supercooled) water are behind the flat six-pointed shapes of snowflakes.
Solutes cannot be incorporated into the ice Ih structure at ambient pressuref but are expelled to the surface or the amorphous ice layer between the microcrystalline ice crystals. This may be made use of when purifying water (for example, degassing) using successive freeze-thaw cycles. Some solutes (for example, chaotropic ions such as NH4+ and Cl-) are incorporated more easily into freezing ice than others (for example, kosmotropic ions such as Na+ and SO42-), so removing them from the remaining thin films of liquid between the crystals. This may result in the electrical charging of the surface due to surface water ionization balancing the remaining charges (which also may give rise to electromagnetic emission) and changes in the pH of the residual liquid films (for example, (NH4)2SO4 becomes more acidic [1010] and NaCl becomes more alkaline [1089]).
Views perpendicular to the faces of the ice (1h) crystal
showing the next layer attached (with O-atoms black).
(a) Slow growing basal face (viewing down the c-axis); where only isolated water
molecules attach. (b) faster growing prism face (viewing down the a-axis), where
pairs of newly-attached water molecules may hydrogen bond
to each other; one hydrogen bond/two water molecules.
(c) Fastest growing {1 1 -2 0} face, where chains of newly-attached
water molecules may cooperatively hydrogen bond to each
other; one hydrogen bond/water molecule. These form ridges
which divide and encourage conversion into two prism faces. [Back to Top ]
Although ice is often perceived as 'slippery'
(for example, ice skating), it is also very 'sticky' (for example, the difficulty in removing ice from from car windscreens,
the compaction of snow to form 'snowballs' and the ease with
which two ice cubes stick together). Capillary condensation of liquid water between a tungsten tip and a hydrophobic graphite surface using a friction force microscope has been proposed to form a sticky 'ice' at room temperature [1033].e These different perceptions
depend on the speed of the relative movement between the surfaces
and the presence and properties of the ultra-thin
layer of quasiliquid water/amorphous ice on the crystalline
surfaces [937] that may be 10 nm thick or greater [1303]. This surface layer is easily melted further by frictional
heating (so leaving trails behind the skates) with the low thermal conductivity of ice reducing
the loss of heat. There is good evidence that the surface
layer is indistinguishable from normal liquid water with a
thickness that depend upon the temperature (that is, the further below the freezing point, the thinner the layer; it being many nm thick at -1°C but has disappeared at about -38°C). Hexagonal ice is a very soft material (1.5 on
Moh's scale) being scratched by most crystalline solids except
soapstone, Mg3Si4O10(OH)2. [Back to Top ]
a The exact packing efficiency
for ice Ih
is low (~
~ 0.34, ~1/3) compared with simple cubic (
= 0.5236, ~1/2) or true face centered cubic (
= 0.7408, ~3/4) structure [811].
[Back]
b In all these structural diagrams the hydrogen bonding is ordered whereas in reality it is random and constantly changing (obeying the 'ice' rules: each water molecule 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). This disorder gives rise to a zero-point entropy of 3.41 J mol-1 K-1. This is close to R.Ln(3/2) = 3.371 J mol-1 K-1, which makes no allowance for correlations introduced by closed hydrogen-bonded loops; see [717] for a discussion of this point. A recent estimate of the zero-point entropy is R.Ln(1.507606) = 3.4133 J mol-1 K-1 [1090]. As the H-O-H angles are about 106.6º [717], the hydrogen bonds are not straight (although shown so in the figures).
Although the proton order in bulk ice is disordered, the surface of the ice probably has a preference for proton order in terms of stripes of dangling H-atoms and O-lone pairs [1551]. [Back]
c The unit cell may be considered as a group of four molecules (three shown starred in the top figure, with the fourth linked as indicated). The crystallographic c-axis is in the vertical direction. The hexagonal crystal has unit cell dimensions 4.5181 Å (a) and 7.3560 Å (c) (90º, 90º, 120º, 4 molecules, at 250 K) [382]. In a perfect crystal the 'c' cell parameter would be 2√(2/3) times the 'a' cell parameter (that is, 7.3780 Å). The cell dimensions for D2O are 4.5216 Å (a) and 7.3627 Å (c) [382], with its c-axis very slightly less affected. [Back]
d (i) There are six prism face planes around the hexagonal crystal; going anticlockwise {0 1 -1 0} {-1 1 0 0} {-1 0 1 0} {0 -1 1 0} {1 -1 0 0} {1 0 -1 0}. (ii) There are six such secondary prism face planes across similar diagonals in the hexagonal crystal; going anticlockwise {1 1 -2 0} {-1 2 -1 0} {-2 1 1 0} {-1 -1 2 0} {1 -2 1 0} {2 -1 -1 0}.[Back]
e Such confined meniscus water has been shown to possess 106-107 times greater viscosity than bulk water [1304]. [Back]
f Hoiwever, the close match of the crystal lattice constants between hexagonal ice and hexagonal β-AgI makes the AgI an effective ice nucleating agent. [Back]
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This page was last updated by Martin Chaplin on 2 February, 2009
