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We’ve all done the experiment. Take an aluminium tray divided into
sections, and fill with water. Place in freezer and wait a few hours. Remove
and tap firmly on a hard surface. Out fall perfectly formed ice cubes.

As you put your feet up and sip your Scotch on the rocks, do you ever
wonder how the tray of water becomes transformed into a solid block? Clearly,
it only takes place at subzero temperatures. And if you remove the tray
from the freezer too soon you’ll find, not a growing cube, but a skin of
ice with liquid water below it. During freezing, this boundary moves through
the liquid – it is at this boundary that the ice grows.

But any closer investigation of ice and its remarkable properties has
to start with water molecules – each with one oxygen atom joined to two
hydrogen atoms. Of the two types of atom, oxygen has more pull on the electrons
that they share to form the bonds between them, so the oxygen becomes slightly
negatively charged and the hydrogens slightly positive. Opposite charges
attract, so water molecules tend to stick to each other as a positive hydrogen
atom of one molecule attaches itself to the oxygen atom of its neighbour.

These bonds between molecules, which are called hydrogen bonds, dominate
the properties of water and ice. In water, the molecules jostle around,
continually breaking and making hydrogen bonds – although according to
a theoretical model developed last year by Sydney Benson and Eleanor Siebert
of the University of Southern California, Los Angeles, they like to form
short-lived networks of cubes and rings along the way. Lowering the temperature
towards 0 degreeC makes breaking hydrogen bonds increasingly difficult,
until eventually everything seizes up and water becomes ice.

Kepler’s crystals

But this is not the end of the story. In ice, the H₂O molecules
adopt fixed, repeating positions, just as molecules and ions do in diamond
and salt: in other words, ice is a crystal. This shows most strikingly in
the snow crystal, with its characteristic sixfold symmetry. The problem
of where this symmetry comes from intrigued the German astronomer Johannes
Kepler who, in 1611, wrote a brief essay, ‘On the six-cornered snowflake’.
He did not think of snow as crystalline, however, but as a collection of
globules of condensed moisture.

Kepler’s essay was the first attempt to link the observed symmetry of
a natural phenomenon with the close packing of spheres. Kepler understood
that the most efficient way to pack spheres is in a hexagonal array and
he conjectured, but could not prove, that the symmetry of the snow crystal
might arise from this arrangement.

The microscope brought further refinements in the study of snow crystals,
but did not shed much light on why they were symmetrical. In 1880, 15-year-old
Wilson Bentley of Vermont took a microscope he had been given for his birthday
and began photographing snow crystals, which he collected using a special
open-windowed hut facing into the northeasterly winds. Bentley survived
the cold New England winters, and half a century later, in 1931, published
a book of 2500 micrographs. Each crystal appeared unique, but sixfold symmetry
predominated.

Two years before Bentley’s book appeared, the arrangement of water molecules
in the ice crystal had finally been worked out, thanks to Max von Laue’s
X-ray diffraction technique. Kepler, it turned out, had not been far wrong.
Each water molecule is surrounded tetrahedrally by four others (each oxygen
atom has two bonds to hydrogens and two ’empty’ bonds), to which it is hydrogen
bonded, and the oxygen atoms are arranged hexagonally in layers.

But Kepler had no way of working out how snow crystals form. To do so
he would have needed to know that the shapes of growing crystals depend
on three things: first, the symmetry with which the atoms are arranged in
the crystal structure, or lattice; secondly, the need to minimise the energy
cost of maintaining crystal surfaces; and lastly, the relative speeds at
which various crystal faces grow.

The first of these is easy to understand. In ice, the sixfold symmetry
at the molecular level is reflected in the hexagonal shape of the crystal.
The second has to do with hydrogen bonds. The oxygen atoms in the large
top and bottom faces of an ice crystal have only one unsatisfied hydrogen
bond directed into the surrounding water, while oxygens in the side faces
have two such bonds. It takes less energy to break one bond than two. So
the larger the top or bottom surface, the less energy is needed to maintain
the boundary between solid ice and water. This leads to the third factor:
when a new layer of ice forms on the side faces, the crystal gets a better
deal in energy terms than when it forms on the top or bottom. So the side
faces advance more rapidly, and the crystal becomes a hexagonal plate.

As the snow crystal grows, it then has the problem of how to keep its
edges straight. Imagine being asked to cover a football pitch with lines
of people. Start with one line of people standing shoulder to shoulder on
the touchline. Then open the gates and try to fill the pitch by telling
the people as they come in to repeat the order in the line that has already
formed. If you let one person in at a time, and if the pitch is narrow,
this is easy. But with a real crowd spilling onto a full-size pitch it becomes
impossible to line them up tidily – impossible, that is, for the boundary
to stay straight.

The same principle applies to crystal surfaces. If the crystal is large
or if molecules try to join the surface too rapidly, it starts to become
uneven. This is particularly true for ice crystals growing from liquid,
as the physicist John Day realised in 1962 when he proposed a theory for
how snow crystals form. When ice forms from liquid water, there are lots
of water molecules around to join the crystal, and crystals produced under
these conditions tend to have curved surfaces. But when crystals grow from
vapour, there are fewer water molecules, especially when the humidity is
low. The rate at which molecules arrive at the surface is also low and crystals
grow slowly, so they can sustain flat edges and develop as plates or columns.

Growing points

As the humidity increases so does the rate of growth. Growth occurs
fastest at the six corners of the hexagon, which grow preferentially to
give the classic six-pointed star. Imagine concentric rings of equal concentration
of water molecules around the hexagon. A water molecule will not have as
far to travel to reach a point as it does to reach a face. So the points
grow out. Day realised that his theory would explain the uniqueness of each
crystal since each forms under slightly different atmospheric conditions
– the spacing of the ‘concentric rings’ would be different for each.

Earlier this year Etsuro Yokayama of Kyushu Institute of Technology
in Japan confirmed that this is indeed how snow crystals grow. Using a
computer model that describes both the movement of water molecules through
the vapour to the crystal and the rate of growth at its surfaces, he correctly
predicted the change from hexagon to star. His work also fits in well with
experiments done in the mid-1980s by D. Nenow and his colleagues at the
Bulgarian Academy of Sciences in Sofia. They made snow by bursting a paper
membrane, causing a shock wave that set off ice nucleation in a 50-litre
chamber containing water vapour held at -2 to -12 degreeC. They varied
the growth rates of the crystals by altering the temperature and vapour
pressure, and found hexagons at low growth rates, stars at high growth rates.

The shape of snow crystals could make all the difference to your skiing
holiday. Snow made of star-shaped crystals has a much larger surface area
than the same mass of hexagons. Star crystals would like to minimise their
surface energy, and they do this by reverting to hexagons. Star crystals
contain many edges which are highly curved, and when a snowflake is lying
on a mountain, the concentration of water molecules in the air in contact
with it depends on the curvature of the ice surface as well as on temperature
and humidity. The vapour in contact with curved regions contains more water
than that in contact with flat regions. This is because the greater the
curve the greater the difference in pressure between the inside and outside
of the crystal. This difference is evened out by the transfer of water molecules
from regions of high to low curvature. Water builds up and gradually transforms
stars into hexagons. On the piste, star snowflakes interlock to form a stable
network. Hexagons, which cannot interlock, easily slide over each other
and help create avalanche conditions. To be really sure your skiing holiday
this winter is safe, take a microscope.

While potentially deadly on the ground, hexagonal ice crystals can
produce some beautiful effects when they are suspended in the air. The
halo round a full Moon on a cold winter’s night is caused by ice crystals
in the atmosphere, and is a direct result of the hexagonal symmetry of
ice. If light passes symmetrically through alternate side faces of a hexagonal
ice crystal it is refracted through 22degree. Even if the ice crystals
are randomly oriented, the angle of refraction is insensitive to small deviations,
so light concentrates at or near this angle, forming a halo around the
Sun or Moon with an angular radius of 22degree.

In still air, the crystals tend to favour certain orientations, rather
than being at random angles. Plates tend to fall with their hexagonal cross-section
horizontal, while columns fall with their hexagonal cross-section vertical.
When the Sun is low in the sky the plates refract light to the observer
from the sides of the halo, giving spots either side of the real Sun, called
‘sun dogs’. Columns refract light from the top, so they should give one
spot above the Sun (and one below the horizon). In fact other atmospheric
effects turn the spot into a tangential arc.

A previously unknown type of halo with an angular radius of 28degree
was first reported by Christoph Scheiner in Rome on 20 March 1629 and has
been observed only six times since. It could be caused by a form of ice
with a different crystal structure altogether. In 1984, Edward Whalley
of Canada’s National Research Council in Ottawa showed that a halo appearing
at this angle can be explained by refraction through the faces of octagonal
crystals of ice in which the oxygen atoms are arranged in a diamond-like
lattice. This ‘cubic’ as opposed to hexagonal ice is only stable below about
-120 degreeC. But perhaps, in the upper atmosphere at, say, -45 degreeC,
such crystals could grow large enough to produce sharp refraction phenomena.

Despite previous research that suggested this was unlikely, Erwin Meyer
and Andreas Hallbrucker of Innsbruck University succeeded in producing cubic
ice of unexpectedly high stability from droplets of water by cooling them
extremely rapidly.

The hydrogen bonding that determines the shapes of ice crystals also
plays a major part in determining the properties of solid ice. Ice is brittle
– it shatters under sudden impact – but under a more modest shear stress
it undergoes plastic deformation. If the mass of ice is large enough, it
can even flow under its own weight, as in a glacier. This is possible because
hexagonal ice crystals are made up of parallel layers: the hydrogen bonding
is stronger within layers than between them, so they glide over one another
when a large enough stress is applied.

Extraordinary ice

This property of ice proved fatal to the extraordinary proposal, put
forward during the Second World War, to construct huge artificial icebergs
to serve as aircraft carriers. The idea was to allow aircraft to fly across
the North Atlantic at a time when nonstop flights of this distance were
impossible. In his book Is Science Necessary?, the biochemist Max Perutz
describes his involvement in the development of ‘pykrete’, a composite
of ice and 4 per cent wood pulp, the purpose of the pulp being to overcome
the problem of brittleness in pure ice. But while this material did not
flow as fast as pure ice, ‘creep’ would still have led to serious long-term
stability problems for such structures. Only if the temperature could be
kept below -15 degreeC would it have maintained its shape, and this would
have called for some impracticably large on-board freezing plants.

Trapped air bubbles often make ice look opaque, but the pure material
is transparent to visible light and virtually colourless in small amounts.
But it absorbs radiation weakly in a band that tails from the red to the
infrared end of the spectrum, and if there is enough of it, for instance
within ice caves in glaciers or in icebergs, the ice looks pale blue. Until
recently this absorption was thought to be caused by hydrogen bonding shifting
to higher energies the wavelength at which water molecules absorb. But this
year Charles Braun and Sergei Smirnov of Dartmouth College in New Hampshire
compared the vibration spectra of water vapour and liquid water. They concluded
that the hydrogen bonding moves these absorptions to lower energy, so it
would tend to lessen the colour.

Sinking feeling

The hydrogen bonding in ice holds the H₂O molecules further
away from each other than they are in liquid water. Consequently the density
of ice is only 0.92 that of water, and it floats. This is a very unusual
property – there are not many solids that float in the liquid formed when
they melt – and it only takes an increase of pressure to make ice conform
to the norm. Pressure distorts the hydrogen bonds and forces the molecules
closer together, giving an alternative form of ice that has a relative density
of 1.17.

If ice behaved like this at normal pressures, the world would be a different
sort of place. The good news is that with water no longer expanding when
it froze, burst pipes would be a thing of the past. Icebergs would lie below
the sea, so the Titanic might now be a floating hotel, moored in Boston
harbour. The bad news is that seas, lakes and rivers would freeze under
instead of over. There would be no polar bears, no skating on frozen ponds,
and the aquatic life that now happily spends the winter beneath a protective
sheet of ice would be entombed in frozen blocks. Fortunately, the possibility
of this happening in the foreseeable future is remote, as pressures of up
to 2000 atmospheres are needed to transform environmentally friendly ice
into its more sinister variety.

But if you like life as it is, you might like to try exploiting a property
of water discovered by Greg Fahy, a researcher at the American Red Cross.
He has found that a combination of pressure and special cryopreservants
will allow water to be cooled to -125 degreeC, at which point it forms not
a crystal but a glass. This limits damage to biological tissue, and may
be the way forward for those seeking an eternity on this watery planet.
So chuck in the ice and raise your glass to the wonders of solid H₂O.

Roger Davey is a research associate with Zeneca plc and holds the Zeneca
Chair of Molecular Engineering at the University of Manchester Institute
of Science and Technology. David Stanley is a senior research scientist
with ICI Chemicals and Polymers and an honorary research associate at the
University of Salford.