Entropy of ice phases: Difference between revisions

Revision as of 11:11, 5 June 2009

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]

@@ Line 1: / Line 1: @@
-{{Stub-water}}
 ==Ice rules==
-Or the Bernal-Fowler rules<ref>[J. D. bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933)]</ref>,
+The '''ice rules''', also known as the  ''Bernal-Fowler rules''
-give us how the hydrogen atoms are distributed in the ices. Each oxygen atom has two hydrogen atoms attached
+<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>,
-to it at a distance about 1 amstrong, and one hydrogen atom resides on each O-O bond. There are
+describe  how the [[hydrogen]] atoms are distributed in the [[ice phases| ices]]. Each [[oxygen]] atom has two hydrogen atoms attached
-many ways to distribute the protons such that these rules are satisfied and all are equally probable.
+to it, at a distance of approximately   1 ångström, one hydrogen atom resides on each O-O bond. There are
-The ice with this random distribution must have null dipole moment.
+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
+The ice with this random distribution must have null [[dipole moment]].
-was descibed, for the first time, by the statistical model for ice Ih introduced by Pauling
+For this reason, the residual [[entropy]] of ice is correctly predicted. The observed residual entropy
-<ref>[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>. Who suggested a random arrangement of protons. By means
+was described for the first time using the statistical model for [[ice Ih]] introduced by Linus Pauling
-of a simple calculation, Pauling showed that the resulting disordered phase requires the addition of
+<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>.
-a combinatorial entropy -NKB ln 3/2 to the teorical estimate. This finding demostrated that a crystal
+Pauling suggested a random arrangement of protons. By means
-phase such as ice Ih could show full disorder at 0 K (against prediction from the third principe).
+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==
-#[J. D. bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933)]
+<references/>
-#[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)]
+'''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)]

Entropy of ice phases: Difference between revisions

Revision as of 11:11, 5 June 2009

Ice rules

References

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