Ice Structure

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof Wisconsin - Green Bay


Ice? A mineral is a naturally occurring inorganic chemical compound. Whatpart of that definition doesn't apply to ice? Many mineralogy books list theproperties of ice, not because anyone needs help identifying it, but forcomparison with other materials.

At left is the phase diagram for water, ice, and vapor. Note, for those accustomed to seeing pressures in kilobars, that the pressure scale here is in millibars. The liquid-vapor curve predictably passes through 100 C and 1000 mb.

The liquid-ice curve actually has a slight negative slope, but it doesn't show at this scale. The melting point of ice actually decreases by about 1 degree per 100 bars pressure. At the deepest points in the ocean, pressures exceed one kilobar, where the freezing point of water would be about -10 C. Since the deep oceans are almost always at a temperature of 3-4 C, they are well above the freezing point.

A couple of additional points:

Ordinary Ice

Hydrogen Bonding and Proton Ordering.

The hydrogen atoms in a water molecule are about 108 degrees apart, which isjust about the right angle to build tetrahedral structures. The positivelycharged portion of one water molecule is attracted to the negatively chargedportion of a neighbor. This attraction, termed hydrogen bonding, giveswater many of its unique properties.

Here are two hypothetical networks of water molecules. Dark blue represents oxygen and red hydrogen. Magenta bonds are bonds within each water molecule, light blue bonds are hydrogen bonds between molecules. 

Some bonds extend up or down out of the plane of the diagram. Hydrogen-Oxygen bonds extending up are shown by a hydrogen atom superimposed on the oxygen. If a water molecule is show with only one bond, the other extends down. Hydrogen bonds in and out of the plane of the diagram are not shown.

In the left-hand diagram, the bonds are proton-ordered: hydrogen atomsare bonded to oxygen atoms in a regular pattern. In the right-hand diagram, thebonds are proton-disordered: hydrogen atoms are bonded to oxygen atoms ina random fashion, although there is a hydrogen atom between every pair ofadjacent oxygen atoms.

It doesn't take a lot of energy to break up proton ordering, so it tends toappear mostly at very low temperatures. Many of the polymorphs of ice haveproton-ordered forms at temperatures below -80 to -100 C.

It's generally not necessary to show hydrogen atoms in diagrams of the icestructure since we can assume a hydrogen atom is located between every pair ofoxygen atoms. In all ice structures known, hydrogen is in two-fold coordinationwith oxygen, and oxygen in fourfold (tetrahedral) coordination with hydrogen.This geometry is dictated by the bond structure of oxygen, not by considerationsof ionic radius. In size terms the hydrogen is a mere bump on the oxygen atom.In all known forms of ice, the water molecules retain their identities asdistinct molecules and bond to other molecules by hydrogen bonding.

Hexagonal Ice (Ice Ih)

Ordinary ice consists of two interpenetrating lattices with a hexagonal closepacked stacking arrangement. The stacking arrangement is that of hexagonal closepacking, but the molecules themselves are not close packed. To construct atetrahedron of equal spheres with a fifth sphere in the center, the vertices ofthe tetrahedron must be about 3.27 radii apart. 

The structure is shown below. The sets of layersare numbered 1 and 2 and colored for identification, with darker colors towardthe rear of the structure. Red lines show O-H-O links. Ordinary ice is called Ice Ih for reasons that will soon becomeobvious.

At left is a top view of the Ice Ih structure. Red dots on some atoms mark a B layer with O-H-O links pointing up to the next B layer. Other atoms are in an A layer and have O-H-O links pointing down to the next A layer.

Cubic Ice (Ice Ic)

It is natural to wonder if a structure like ordinary ice, but based on acubic close packing arrangement, is possible. It is. The structure is shownbelow.

If the structure above looks familiar, it should. The oxygen atoms have the same arrangement as the carbon atoms in diamond. This form of ice is called Ice Ic.

At left is a cubic unit cell of Ice Ic, with only the oxygens shown. O-H-O links are in orange.

The diagram below shows the relationship of the cubic unit cell to the close packing layers.

Ice Ic forms from the vapor below about -80 C and appears to be a metastableform of ice, although it has almost exactly the same density as Ice Ih. Ice Ihdoes not change to Ice Ic at very low temperatures but Ice Ic reverts readily toIce Ih when warmed above -80 C. Ice Ic may form in extremely high clouds andsome halo features not readily explainable in terms of hexagonal ice have beenattributed to Ice Ic.

High-Pressure Ice polymorphs

Ice exhibits a large number of polymorphs as shown at left. The ice in your tea is Ice I.

Ice I converts to Ice II or Ice III at about 2 kb. At the base of the Antarctic Ice Cap (5 km thick) the pressure is only about 0.5 kb. So ice on earth never gets thick enough to convert to a denser phase. We reach higher pressures in the crust, but at temperatures far beyond the melting points of any type of ice.

However, dense phases of ice almost certainly exist in the interiors of large satellites in the outer Solar System, and are probably easily produced by shock metamorphism during meteoroid impacts.

Where did Ice IV go? Ice IV is a little-studied metastable transitional form between IceV and Ice VI. What little data exists suggests it is a slight modification ofthe Ice VI structure. There is an Ice VIII which is a slight modification (protonordered) of Ice VII atlow temperatures. Fans of Kurt Vonnegut will be happy to know there is also anIce IX, a slight modification (proton ordered) of Ice III. However, since it melts well below 0 C(as opposed to the 60 C or so of Ice Nine in Vonnegut's novel Cat's Cradle)it poses no threat to the world.

Ice II

Ice II is rhombohedral. It has similarities, not surprisingly, to Ice I inthat it consists of undulating six-membered rings joined to another ring belowit. However, neighboring rings do not form a complete hexagonal network butinstead surround threefold screw axes. The diagram below shows the rings in Ice I(left) and Ice II (right). Altitudes of rings around the screw axes areindicated on the right diagram. Since the rings enclose vacancies, the Ice IIstructure actually has less void space and is denser. The density is 1.17 gm/cc.

The structure of Ice II is shown below. There are two sets of rings withslightly differing degrees of undulation, shown in green and light blue. In terms ofc-axis dimensions, one set is centered on altitudes 0, 1/3, 2/3 and one, theother on 1/6, 1/2 and 5/6. The two sets alternate vertically and are clusteredaround three-fold screw axes. If we denote the two sets of rings as P and Q,then the rings are linked around each three-fold axis in the mannerP-Q-P-Q-P-Q-. Links in the two types of rings are red and purple, cross-linksare dark blue.

Ice III

Ice II is tetragonal. The unit cell is cubic in dimensions (6.83 Angstromunits on a side) but tetragonal in symmetry. The density is 1.14 gm/cc. The tetrahedral O-H-O links aresomewhat distorted. In the diagram below, oxygen atoms are shown in blue withlarger atoms closer to the viewer. O-H-O links are in red, with thicker linescloser to the viewer. Links ending in an arrow are pointing down to a deeperlevel, those with pointed ends are pointing up to a higher level. Several levelsof the structure are shown. Atoms shown as the same size may actually be atslightly different elevations. For example, the L-shaped sets of three atoms ina right angle are actually slightly tilted relative to the plane of the diagram.The tilted squares of oxygens surround fourfold screw axes.

Ice V

Ice V is monoclinic. In the diagram below, oxygen atoms are shown in blue withlarger atoms closer to the viewer. O-H-O links are in red, with thicker linescloser to the viewer. Links ending in an arrow are pointing down to a deeperlevel, those with pointed ends are pointing up to a higher level. Several levelsof the structure are shown. Atoms shown as the same size may actually be atslightly different elevations. The unit cell is shown in gray (one set of edgesruns horizontally and is largely hidden by atoms and bonds, but it's there. Lookclosely).

Ice VI

Ice VI is tetragonal, with a = 6.27 Angstrom units and c = 5.79 - nearlycubic.  The density is 1.31 gm/cc. It can be described as a "self-clathrate." A clathrate is amolecule surrounded by a cage of water molecules. In Ice VI, there are clustersof five water molecules, a central molecule in a tetrahedral cage of fourothers. The centers of the clusters lie at the corners and centers of abody-centered tetragonal lattice, and the surrounding molecules are 3/8c aboveand below the central molecule.

Closely packed structures do not allow tetrahedral linkages very well. Ice VIand Ice VII achieve their density by having two interpenetrating butdisconnected lattices. In this diagram the O-H-O links in the two separatenetworks are shown in red and purple.

In the diagram above, oxygen atoms are shown in blue with larger atoms closerto the viewer. The two networks of O-H-O links are in red and purple, with thicker lines closer to the viewer.Links ending in an arrow are pointing down to a deeper level, those with pointedends are pointing up to a higher level. Several levels of the structure areshown.

Ice VII

In some ways Ice VII is easiest to understand, because it consists of twointerpenetrating Ice Ic lattices.

The two interpenetrating sets of lattices are shown in orange and red. The unit cell consists of eight body-centered cubes.

Ice VII has a density of 1.66 gm/cc.

The Ice VII unit cell consists of body-centered cubes, which are prettytightly packed. An ice structure based on close-packed water molecules wouldrequire highly distorted bonds, and theoretical calculations suggest that IceVII is the stable form up to at least 200 kilobars. At earth gravity, 200kilobars would correspond to a depth of about 1500 kilometers of ice, takingphase changes into account.

At extremely high pressures we might expect water molecules to break downentirely and a close packed structure with ionic bonding to form.


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Created 27 December 2001, Last Update 31 May 2020