Editing Entropy of ice phases

==Ice rules==
The '''ice rules''', also known as the  ''Bernal-Fowler rules''
<ref>[http://dx.doi.org/10.1063/1.1749327 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)]</ref>,
describe  how the [[hydrogen]] atoms are distributed in the [[ice phases| 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
<ref>[http://dx.doi.org/10.1021/ja01315a102 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)]</ref>. 
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 <math>-Nk_B \ln (3/2)</math> 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 law of thermodynamics |third principle of thermodynamics]].

==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1063/1.1725363 E. A. DiMarzio and F. H. Stillinger, Jr. "Residual Entropy of Ice",  Journal of Chemical Physics '''40''' 1577 (1964)]
*[http://dx.doi.org/10.1063/1.1705058 J. F. Nagle "Lattice Statistics of Hydrogen Bonded Crystals. I. The Residual Entropy of Ice", Journal of Mathematical Physics '''7''' 1484 (1966)]
*[http://dx.doi.org/10.1063/1.452433     Rachel Howe and R. W. Whitworth "The configurational entropy of partially ordered ice", Journal of Chemical Physics '''86''' pp. 6443-6445 (1987)]
*[http://dx.doi.org/10.1063/1.453743     Rachel Howe and R. W. Whitworth "Erratum: The configurational entropy of partially ordered ice <nowiki>[J. Chem. Phys. 86, 6443 (1987)]</nowiki>", Journal of Chemical Physics '''87''' p. 6212 (1987)]
*[http://dx.doi.org/10.1063/1.1808693      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)]
*[http://dx.doi.org/10.1063/1.2800002 Bernd A. Berg and Wei Yang "Numerical calculation of the combinatorial entropy of partially ordered ice",  Journal of Chemical Physics '''127''' 224502 (2007)]
*[http://dx.doi.org/10.1063/1.4879061  Jiří Kolafa "Residual entropy of ices and clathrates from Monte Carlo simulation", Journal of Chemical Physics '''140''' 204507 (2014)]


[[category: water]]