Editing Entropy of ice phases
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==Ice rules== | ==Ice rules== | ||
Or the Bernal-Fowler rules<ref>[J. D. bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933)]</ref>, | |||
<ref>[ | give us how the hydrogen atoms are distributed in the ices. Each oxygen atom has two hydrogen atoms attached | ||
to it at a distance about 1 amstrong, and one hydrogen atom resides on each O-O bond. There are | |||
to it | 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 | The ice with this random distribution must have null dipole moment. | ||
For this reason, the residual | For this reason, the residual entropy of ice is correctly predicted. The observed residual entropy | ||
was | was descibed, for the first time, by the statistical model for ice Ih introduced by Pauling | ||
<ref>[ | <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 | ||
of a simple calculation, Pauling showed that the resulting disordered phase requires the addition of | |||
of a simple calculation | a combinatorial entropy -NKB ln 3/2 to the teorical estimate. This finding demostrated that a crystal | ||
a combinatorial entropy | phase such as ice Ih could show full disorder at 0 K (against prediction from the third principe). | ||
phase such as ice Ih could show full disorder at | |||
==References== | ==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)] | |||
''' | #[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]] |