# Entropy of ice phases

## Ice rules[edit]

The **ice rules**, also known as the *Bernal-Fowler rules*
^{[1]},
describe how the hydrogen atoms are distributed in the ices. Each oxygen atom has two hydrogen atoms attached
to it, at a distance of approximately 1 ångström, one hydrogen atom resides on each O-O bond. There are
many ways to distribute the protons such that these rules are satisfied, and all are equally probable.
For this reason, the residual entropy of ice is correctly predicted. The observed residual entropy
was described for the first time using the statistical model for ice Ih introduced by Linus Pauling
^{[2]}.
Pauling suggested a random arrangement of protons. By means
of a simple calculation he showed that the resulting disordered phase requires the addition of
a combinatorial entropy of to the theoretical estimate. This finding demonstrated that a crystal
phase such as ice Ih could show full disorder at 0K, which is in contrast to the prediction from the third principle of thermodynamics.

## References[edit]

- ↑ J. D. Bernal and R. H. Fowler "A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions", Journal of Chemical Physics
**1**pp. 515- (1933) - ↑ Linus Pauling "The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement", Journal of the American Chemical Society
**57**pp. 2680–2684 (1935)

**Related reading**

- E. A. DiMarzio and F. H. Stillinger, Jr. "Residual Entropy of Ice", Journal of Chemical Physics
**40**1577 (1964) - J. F. Nagle "Lattice Statistics of Hydrogen Bonded Crystals. I. The Residual Entropy of Ice", Journal of Mathematical Physics
**7**1484 (1966) - Rachel Howe and R. W. Whitworth "The configurational entropy of partially ordered ice", Journal of Chemical Physics
**86**pp. 6443-6445 (1987) - Rachel Howe and R. W. Whitworth "Erratum: The configurational entropy of partially ordered ice [J. Chem. Phys. 86, 6443 (1987)]", Journal of Chemical Physics
**87**p. 6212 (1987) - Luis G. MacDowell, Eduardo Sanz, Carlos Vega, and José Luis F. Abascal "Combinatorial entropy and phase diagram of partially ordered ice phases", Journal of Chemical Physics
**121**pp. 10145-10158 (2004) - Bernd A. Berg and Wei Yang "Numerical calculation of the combinatorial entropy of partially ordered ice", Journal of Chemical Physics
**127**224502 (2007) - Jiří Kolafa "Residual entropy of ices and clathrates from Monte Carlo simulation", Journal of Chemical Physics
**140**204507 (2014) - Carlos P. Herrero and Rafael Ramírez "Configurational entropy of hydrogen-disordered ice polymorphs", Journal of Chemical Physics
**140**234502 (2014)