Entropy of ice phases: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
m (→‎References: Corrected page numbers.)
Line 1: Line 1:
{{Stub-water}}
{{Stub-water}}
==Ice rules==
==Ice rules==
The so-called ''ice rules'' were proposed by Linus Pauling (Ref. 1).
Or the Bernal-Fowler rules<ref>[J. D. bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933)]</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
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 descibed, for the first time, by the statistical model for ice Ih introduced by Pauling
<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
a combinatorial entropy -NKB ln 3/2 to the teorical estimate. This finding demostrated that a crystal
phase such as ice Ih could show full disorder at 0 K (against prediction from the third principe).
 
==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/10.1021/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)]

Revision as of 18:10, 4 June 2009

This article is a 'stub' about water and/or ice. It has no, or next to no, content. It is here at the moment to help form part of the structure of SklogWiki. If you add material to this article, remove the {{Stub-water}} template from this page.

Ice rules

Or the Bernal-Fowler rules[1], 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 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 descibed, for the first time, by the statistical model for ice Ih introduced by Pauling [2]. Who suggested a random arrangement of protons. By means of a simple calculation, Pauling showed that the resulting disordered phase requires the addition of a combinatorial entropy -NKB ln 3/2 to the teorical estimate. This finding demostrated that a crystal phase such as ice Ih could show full disorder at 0 K (against prediction from the third principe).

References

  1. 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)
  2. E. A. DiMarzio and F. H. Stillinger, Jr. "Residual Entropy of Ice", Journal of Chemical Physics 40 1577 (1964)
  3. J. F. Nagle "Lattice Statistics of Hydrogen Bonded Crystals. I. The Residual Entropy of Ice", Journal of Mathematical Physics 7 1484 (1966)
  4. Rachel Howe and R. W. Whitworth "The configurational entropy of partially ordered ice", Journal of Chemical Physics 86 pp. 6443-6445 (1987)
  5. 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)
  6. 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)
  7. Bernd A. Berg and Wei Yang "Numerical calculation of the combinatorial entropy of partially ordered ice", Journal of Chemical Physics 127 224502 (2007)
  1. [J. D. bernal and R. H. Fowler, J. Chem. Phys. 1, 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)]