snotitle.jpg (19016 bytes)

grow.gif (10037 bytes)
Snowcrystals.com Home
Natural Snowflakes
  --Photo Gallery I
  --Photo Gallery II
  --Photo Gallery III
  --Guide to Snowflakes
  --Snowflake Books
  --Historic Snowflakes
  --Ice Crystal Halos
  --Snowflake Store
Designer Snowflakes
  --I: First Attempts
  --II: Better Snowflakes
  --III: Precision Snow
  --Snowflake Movies
  --Free-falling Snow
  --Designer's Page
Frost Crystals
  --Guide to Frost
  --Frost Photos
Snowflake Physics
  --Snowflake Primer
  --Snow Crystal FAQs
  --No Two Alike?
  --Crystal Faceting
  --Snowflake Branching
  --Electric Growth
  --Ice Properties
  --Myths and Nonsense
Snow Activities
  --Snowflake Watching
  --Photographing Snow
  --Make Your Own
  --Snowflake Fossils
  --Ice Spikes
  --Activities for Kids
Snowflake Touring
  --Snowflake Hot Spots
  --Northern Ontario
  --Hokkaido, Japan (2) (3)
  --Michigan U. P.
  --Vermont
  --California Mountains
Copyright Issues
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 140K).  Amorphous ice can be made by depositing water vapor onto a substrate at still lower temperatures.iceIhx.gif (3796 bytes)
   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 H20 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.

h2ophasex.gif (4965 bytes)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.

Vapor.gif (4173 bytes)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:

Pwater(T) = [2.8262e9 - 1.0897e6*T - 94934*T2 + 582.2*T3]exp(-5450/TK)

Pice(T) = [3.6646e10 - 1.3086e6*T - 33793*T2]exp(-6150/TK)

where pressures P are in mbar, the temperature T is in degrees Celsius, and TK is in degrees Kelvin (Note 0C = 273.16K).  These approximate expressions are accurate to better than 0.1 percent from -50C to 50C.
   Sigmax.gif (3346 bytes)The plot at the right shows the water vapor supersaturation value, equal to (Pwater-Pice)/Pice.   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:
molmass.gif (1230 bytes)
Ice density (near 0C):
density.gif (672 bytes)
Latent heats of sublimation, evaporation, and melting:
      latent.gif (2896 bytes)
Heat capacity of ice, water (near 0C):
     
heatcap.gif (657 bytes)
Electric dipole moment of a water molecule:
polar.gif (656 bytes)
Intrinsic dielectric polarizability of a water molecule:
polar2.gif (752 bytes)
Total dielectric polarizability of a water molecule (near 0C):
polar3.gif (1376 bytes)
Ice surface energy:
surface.gif (2856 bytes)
Diffusion constant for water molecules in air at STP:
diffusion.gif (642 bytes)
Critical radius for nucleation:
critical.gif (1339 bytes)
Coefficient of thermal expansion of ice:
expansion.gif (648 bytes)
Thermal conductivity of ice (near -20C):
thermco.gif (694 bytes)


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

Return to SnowCrystals.com
SnowCrystals.com was created by Kenneth G. Libbrecht, Caltech
Comments?  Send an e-mail....
page views since February 1, 1999