Editing Entropy of ice phases
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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. | ||
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 | 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)] | |||
[[category: water]] | [[category: water]] |