Entropy of ice phases

Ice rules

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. The ice with this random distribution must have null dipole moment. 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 $-Nk_{B}\ln(3/2)$ 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

Related reading

[1] 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)

[2] 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)

[1]

[2]

Entropy of ice phases

Ice rules

References

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