Ice rules

In chemistry, ice rules are basic principles that govern arrangement of atoms in water ice. They are also known as Bernal–Fowler rules, after British physicists John Desmond Bernal and Ralph H. Fowler who first described them in 1933.[1]

The rules state each oxygen is covalently bonded to two hydrogen atoms, and that the oxygen atom in each water molecule forms two hydrogen bonds with other water molecules, so that there is precisely one hydrogen between each pair of oxygen atoms.[2]

In other words, in ordinary Ih ice, every oxygen is bonded to the total of four hydrogens, two of these bonds are strong and two of them are much weaker. Every hydrogen is bonded to two oxygens, strongly to one and weakly to the other. The resulting configuration is geometrically a periodic lattice. The distribution of bonds on this lattice is represented by a directed-graph (arrows) and can be either ordered or disordered. In 1935, Linus Pauling used the ice rules to calculate the residual entropy (zero temperature entropy) of ice Ih.[3] For this (and other) reasons the rules are sometimes mis-attributed and referred to as "Pauling's ice rules" (not to be confused with Pauling's rules for ionic crystals).

A nice figure of the resulting structure can be found in Hamann.[4]

  1. ^ Bernal, J. D.; Fowler, R. H. (1 January 1933). "A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions". The Journal of Chemical Physics. 1 (8): 515. Bibcode:1933JChPh...1..515B. doi:10.1063/1.1749327. Retrieved 13 April 2012.
  2. ^ cf. Singer, S.; Kuo, J. L.; Hirsch, T.; Knight, C.; Ojamäe, L.; Klein, M. (2005). "Hydrogen-Bond Topology and the Ice VII/VIII and Ice Ih/XI Hydrogen-Ordering Phase Transitions" (PDF). Physical Review Letters. 94 (13). Bibcode:2005PhRvL..94m5701S. doi:10.1103/PhysRevLett.94.135701. hdl:1811/48120.
  3. ^ Pauling, Linus (1 December 1935). "The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement". Journal of the American Chemical Society. 57 (12): 2680–2684. doi:10.1021/ja01315a102.
  4. ^ Hamann, D. R. (1997). "H_{2}O hydrogen bonding in density-functional theory". Physical Review B. 55 (16): R10157. Bibcode:1997PhRvB..5510157H. doi:10.1103/PhysRevB.55.R10157. fig.1