ICE

Ice, the frozen form of liquid water, is abundant on the earth's surface, in the planetary system, and in interstellar space. If all the ice presently existing on earth melted, sea level would rise about 70 m. In some planets and in most moons, ice is the major constituent. Pluto is 80% ice; Jupiter's moons Ganymede and Callisto and Saturn's Titan contain 40% ice. Ice is also present in many other moons, in the planetary ring systems, and in comets. The mass of ice stored in the terrestrial polar ice sheets and in alpine glaciers is closely related to the climate.

All of the natural ice on earth is hexagonal ice, ice Ih, as manifested in six-cornered snow flakes (see Fig. 1). At lower temperatures and at pressures above 2 kbar many other ice phases with different crystalline structures exist. No other known substance exhibits such a variety of forms. The phase diagram of ice shows the conditions of stability for the ice phases ( Fig. 2 and Table I). The equilibrium line between water and ice Ih has negative slope. which is a consequence of the solid having a lower density than the liquid, unlike most other substances and the high-pressure ice phases. The equilibrium lines extend as metastable phase boundaries into the area of stability of other ice phases. Ice IV exists only as a metastable phase within the stability fields of ice III, V, and VI. After forming by nucleation from supercooled water, it quickly transforms into one of the other phases unless it is quenched to low temperatures.

The individual water molecule remains intact as the fundamental building unit in all the ice phases except ice X as noted later. Since there are equal numbers of protons and of lone electron pairs in the water molecule, each proton can match up with an electron pair of a neighboring molecule forming a hydrogen bond (H-bond). Each water molecule forms H-bonds to four nearest neighbors in a tetrahedral ar- rangement with one proton occupying each H-bond. The tetrahedral bond geometry explains the openness and relatively low density of the ice Ih structure. In ice Ih the O ... O ... O angles are nearly the same as the perfect tetrahedral angle (109.5),which matches fairly well the H-O-H angle of the water molecule, little changed from the angle in the free molecule (104.4). In the higher-pressure phases the tetrahedral bonding geometry is distorted; the bond angles are bent from perfect tetrahedral and the H-bonds are stretched. The distances to non-bonded near neighbors become shorter the higher the pressure. In ice Vil the non-bonded neighbors come as close as the nearest neighbors. Ice VII and ice VIII can be visualized as two ice Ic structures completely intertwined with one another. A general feature repeated in all of the ice structures is H-bonded rings. In ice I and II the smallest rings are of six molecules, but in higher-pressure phases rings of five and four molecules occur.

Since the H-bond lengths are in the range of 274 pm (ice Ih) to 296 pm (ice VIII) and the 0-H distances are only 98.5 pm (ice Ih), the position of the protons in the H-bonds is asymmetric. There are six different orientations possible for a water molecule in its tetrahedral bonding environment, each corresponding to a different arrangement of protons in its four H-bonds. If all the possible orientations of the water molecule at each lattice site are equally realized, the phase is proton-disordered: if one orientation is preferred the phase is proton-ordered. Most ice phases have a high- and low- temperature modification which are distinguished by their degree of proton order. Ice VIII is the proton-ordered version of ice VII and ice IX is the proton-ordered version of ice III. Partially proton-ordered modifications exist for ice V and ice VI. Ice II is a completely proton-ordered phase for which the proton-disordered version is unstable and is not observed. In most cases the existence of proton order or disorder affects the crystallographic symmetry of the ice phase. The cubic symmetry of fully disordered ice VII changes to tetragonal symmetry on transformation to ordered ice VIII.

If water vapor is condensed on a cold substrate between -80 C and 130 C, a cubic modification, ice Ic, is formed. Ice Ic is related to ice Ih in the same way as cubic diamond is related to hexagonal diamond, the cubic and hexagonal forms having almost the same density. Below -130 C a noncrystalline amorphous solid known as low-density amorphous ice, ice aI, appears. A high-density amorphous phase, ice aII, with a density of 1.31 Mg/m³ can be made at 77 K by compressing ice Ih to 10 kbar.

At a pressure of 44 GPa, the H-bonds in ice VII are so shortened by compression to 245 pm that the protons leave their asymmetric positions in the bonds and move to the centers, forming the structure of ice X, in which, because of the symmetric H-bonding, discrete H₂O molecules are no longer identifiable.

Many of the physical properties of ice are unique and relate to the special features of structure, especially the H-bonding ( Table II). Certain physical properties arise from defects in the ideal ice structure. Important among the point defects are the H₃O⁺ and OH^- ions and the D and L bond defect-sites where H-bonds are broken by violation of the rule that there be one and only one proton along each O ... O bond line. The violation is caused when a water molecule undergoes rotation from one of its six possible orientations to another without compensating adjustments by the adjacent molecules to which it is H-bonded. Such a rotation interchanges some of the molecule's protons and electron pairs. with the result that some of the H-bonds are converted to non-bonded O ... O contacts with no protons (L defect) or with two associated protons (D defect), The ions and orientational defects, together with substitutional or interstitial impurity atoms or ions, have important influence on the electrical and mechanical properties of ice and in some cases completely dominate them. Also important are crystal dislocations (line defects) and subgrain or grain boundaries (surface defects). the latter in polycrystalline ice.

The electrical conduction in ice is carried by the protons, whose motion is closely tied to the motion of ionic defects. An ionic defect can move from one lattice site to the next by a small jump of a proton from one off-center (asymmetric) position to the other in an H-bond that connects the two lattice sites. Since the small proton jumps occur collectively along a favorably oriented chain of H-bonds, the ionic defects and the effective charge carried by them have a very high mobility in the ice structure, 10 times greater than the mobility of ions in normal ionic conductors. Protonic conduction plays a major role in biological charge transfer processes across membranes. Proton conduction in ice and H-bonded materials is analogous to electron conduction in semiconductors. Ice Ih has an unusual high static dielectric constant (96.6 at 0 C compared to 88 for liquid water). The reorientation of the molecular dipoles in ice is facilitated by the mobility of orientational L and D defects, which are generated by thermal activation. The dielectric relaxation time is extremely slow compared to water (20 micros in ice and 10 ps in water at 0 C).

Ice is transparent to visible light. It has the lowest index of refraction for the sodium D line of any known crystalline material. It is doubly refracting, uniaxial, optically positive with very small birefringence. The proton-disordered phases have a broad infrared absorption band for the fundamental intramolecular bending and stretching vibrations (near 3220 cm^-1 and 1650 cm^-1 for ice Ih). The infrared band for hindered rotations of the water molecules in ice Ih is centered around 840 cm^-1. The translational lattice vibrations absorb in the range 350-50 cm^-1 (with peak for ice Ih at 229 cm^-1). The proton-ordered phases show distinct narrow peaks in their infrared and Raman spectra. From infrared and Raman spectroscopy on the ice phases, much has been learned about the intermolecular coupling mechanism, lattice dynamics, and the properties of H-bonds.

For electromagnetic waves with frequencies from 5 to 300 MHz the loss of energy by absorption in ice is sufficiently small that they can penetrate large ice masses great distances. Radio waves are reflected by inhomogeneities in the ice and at material boundaries, especially at the ice-water and ice-rock interfaces, and these waves can therefore be utilized to examine the internal structure of glaciers and to determine the depth and bottom topography of large polar ice sheets and ice shelves.

Ice is a viscoelastic material with a nonlinear flow law. When shear stress is applied to a single crystal of ice, it undergoes plastic shear strain easily parallel to the basal plane, which is perpendicular to the hexagonal c-axis. In other directions the stress needed to produce plastic shear deformation is much higher. When polycrystalline ice is subjected to stress, it immediately deforms elastically, followed by transient creep, and finally steady viscous flow called secondary creep is reached. For high stresses in excess of 400 kPa the creep curve accelerates which is called tertiary creep. Several physical processes are responsible for these deformations: movement of dislocations, sliding along grain boundaries, and recrystallization. The steady-state secondary creep rate sigma in secondary creep is related to the stress sigma by the flow law

d /dt = A ⁿ e^-Q/kT,

where A is a temperature-independent constant, Q is the activation energy for creep, n is the nonlinear exponent, k is the Boltzmann constant, and T is the absolute temperature. Values of A, Q, and n depend to some extent on the grain size, grain orientation distribution, and impurity content of the polycrystalline material. At temperatures between 0 and -10 C and for stresses between 100 and 250 kPa, A = 5 x 10^-15 s^-1 kPa^-3, Q = 139 kJ mol^-1, n = 3. At stresses lower than 100 kPa, n = 2.

The surface of ice Ih shows unique properties. Near the melting point, the surface contains many dangling broken bonds that promote the existence of a liquid-like layer. Consequences of the surface properties are sintering of snow to cohesive snowballs, recrystallization of snow to firn and its transformation to glacier ice, and the low friction of many materials on ice, which is useful for sled riding, skiing, and skating. Regelation is a unique ice property: melting of ice under pressure, coupled with adjacent refreezing of melt-water at lower pressure, is the mechanism by which a loop of wire can be pulled slowly through an ice block without cutting the block in two.

There is a whole class of solids, clathrates, where the ice forms a H-bonded host lattice that encages a great variety of small guest atoms or molecules like argon or methane. Ice VI, VII, and VIII can be viewed as self-clathrates, where two equal ice lattices interpenetrate each other but are not H-bonded to each other. Ice-like structures or structurally arranged water molecules are encountered in hydrates, and hydrated compounds including all macromolecules that would not be biologically active without their structured water or ice-like shells. Even water can be viewed as a partially broken down structure of ice.

H-bonds, so pervasive in the crystalline ice phases, play a major role in many substances from glues and mortar to the life-supporting structure of proteins. The properties of ice, and H-bonds are recognized in many aspects of physics, chemistry and biology, in several branches of geophysics, including glaciology (dynamics of large ice masses), meteorology (cloud physics). and in oceanography (sea ice), in planetary sciences and in astronomy.

BIBLIOGRAPHY

N. H. Fletcher. The Chemical Physics of Ice. Cambridge University Press. Cambridge, 1970. (An intermediate to advanced text that illustrates many aspects of solid-state physics using ice as an example.)

P. V. Hobbs, Ice, Physics. Clarendon Press. Oxford, 1974. (A com- prehensive treatment and documentation of ice at an intermediate and advanced level.)

B. Kamb. Crystallography of Ice, in Physics and Chemistry of Ice (E. Whalley, S. J. Jones, and L. W. Gold, eds.). Royal Society of Canada, Ottawa, 1973. (An advanced text)

E. Whalley, The Hydrogen Bond in Ice, in The Hydrogen Bond (P. Schuster, G. Zundel, and C. Sandorfy, eds.). North-Holland, Amsterdam, 1976. (An advanced text)

W. S. B. Paterson, The Physics of Glaciers, Pergamon Press, Oxford. 1981. (An intermediate text on applied ice physics.) Journal of Glaciology, published by the International Glaciological Society. Cambridge. (A professional journal)