Entropy of ice phases: Difference between revisions
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to it, at a distance of approximately 1 ångström, one hydrogen atom resides on each O-O bond. There are | 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. | 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 | 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 | was described for the first time using the statistical model for [[ice Ih]] introduced by Linus Pauling | ||
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a combinatorial entropy of <math>-Nk_B \ln (3/2)</math> to the theoretical estimate. This finding demonstrated that a crystal | 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]]. | 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== | ||
<references/> | <references/> | ||
'''Related reading''' | '''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)] | |||
*[http://dx.doi.org/10.1063/1.4882650 Carlos P. Herrero and Rafael Ramírez "Configurational entropy of hydrogen-disordered ice polymorphs", Journal of Chemical Physics '''140''' 234502 (2014)] | |||
[[category: water]] | [[category: water]] | ||
Latest revision as of 13:45, 23 June 2014
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)