Physical Properties of Ice Crystalline Structure of Ice. Ice can assume a large number of different crystalline structures, more than any other known material. At ordinary pressures the stable phase of ice is called ice I, and the various high-pressure phases of ice number up to ice XIV so far. (Ice IX received some degree of notoriety from Kurt Vonnegut's novel Cat's Cradle.)

There are two closely related variants of ice I: hexagonal ice Ih, which has hexagonal symmetry, and cubic ice Ic, which has a crystal structure similar to diamond. Ice Ih is the normal form of ice; ice Ic is formed by depositing vapor at very low temperatures (below 140°K). Amorphous ice can be made by depositing water vapor onto a substrate at still lower temperatures.

Each oxygen atom inside the ice Ih lattice is surrounded by four other oxygen atoms in a tetrahedral arrangement. The distance between oxygens is approximately 2.75 Angstroms. The hydrogen atoms in ice are arranged following the Bernal-Fowler rules: 1) two protons are close (about 0.98A) to each oxygen atom, much like in a free water molecule; 2) each H 2 0 molecule is oriented so that the two protons point toward two adjacent oxygen atoms; 3) there is only one proton between two adjacent oxygen atoms; 4) under ordinary conditions any of the large number of possible configurations is equally probable. Phase Diagram of Water and Ice. The plot at right shows the phase diagram of water (click on the image for an expanded version). The triple point of water -- when ice, water, and water vapor can coexist -- is at a temperature of 0.01C (0C = 273.16K), and a pressure of 6.1 mbar. Water is the only substance which we commonly experience near its triple point in everyday life. Equilibrium Vapor Pressure of Ice and Water. The plot at right shows the equilibrium water vapor pressure of ice and water as a function of temperature, over the range of interest for snow crystal growth [1]. The pressure units are in mbar, and one can convert to other units using a conversion calculator (1 mbar = 100 Pascal (Newtons/square meter) = 0.75 mm Hg = 0.001 atmospheres.)

The vapor pressure is well described by the Clausius-Clapeyron relation, and a fit to the data yields the approximations: P water (T) = [2.8262e9 - 1.0897e6*T - 94934*T2 + 582.2*T3]exp(-5450/T K ) P ice (T) = [3.6646e10 - 1.3086e6*T - 33793*T2]exp(-6150/T K ) where pressures P are in mbar, the temperature T is in degrees Celsius, and T K is in degrees Kelvin (Note 0C = 273.16K). These approximate expressions are accurate to better than 0.1 percent from -50C to 50C.

The plot at the right shows the water vapor supersaturation value, equal to (P water -P ice )/P ice . This is the supersaturation level that is typically found in dense clouds, which after all are made of water droplets. Supersaturation levels higher than this are probably quite unusual in the atmosphere. Various constants related to Ice and the Formation of Snow Crystals.

Mass of a water molecule:

Ice density (near 0°C):

Latent heats of sublimation, evaporation, and melting:

Heat capacity of ice, water (near 0°C):

Electric dipole moment of a water molecule:

Intrinsic dielectric polarizability of a water molecule:

Total dielectric polarizability of a water molecule (near 0°C):

Ice surface energy:

Diffusion constant for water molecules in air at STP:

Critical radius for nucleation:

Coefficient of thermal expansion of ice:

Thermal conductivity of ice (near -20°C):



[1] From B. J. Mason, The Physics of Clouds (Clarendon Press, 1971)..