Entropy of ice phases - Revision history

Carl McBride: /* References */ Added a recent publication

2014-06-23T11:45:30Z

References: Added a recent publication

← Older revision		Revision as of 13:45, 23 June 2014
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	*[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/10.1063/1.2800002 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/10.1063/1.4879061 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]]

Carl McBride: /* References */ Added a recent publication

2014-06-09T12:20:04Z

References: Added a recent publication

← Older revision		Revision as of 14:20, 9 June 2014
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	*[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/10.1063/1.1808693 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/10.1063/1.2800002 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)]


	[[category: water]]		[[category: water]]

147.96.5.67: correcting ice rules

2009-06-05T16:46:22Z

correcting ice rules

← Older revision		Revision as of 18:46, 5 June 2009
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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/>

Nice and Tidy: Changed numbering to bullet points.

2009-06-05T09:12:27Z

Changed numbering to bullet points.

← Older revision		Revision as of 11:12, 5 June 2009
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	<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/10.1063/1.1725363 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/10.1063/1.1705058 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/10.1063/1.452433 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/10.1063/1.453743 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/10.1063/1.1808693 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/10.1063/1.2800002 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]]

Nice and Tidy: Slight tidy.

2009-06-05T09:11:47Z

Slight tidy.

← Older revision		Revision as of 11:11, 5 June 2009
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	~~{{Stub-water}}~~
	==Ice rules==		==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==		==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/10.1063/1.1725363 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/10.1063/1.1705058 J. F. Nagle "Lattice Statistics of Hydrogen Bonded Crystals. I. The Residual Entropy of Ice", Journal of Mathematical Physics '''7''' 1484 (1966)]

Lufi: /* Ice rules references added*/

2009-06-04T17:12:50Z

Ice rules references added

← Older revision		Revision as of 19:12, 4 June 2009
Line 14:		Line 14:

	==References==		==References==
			#[J. D. bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933)]
	#[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)]
	#[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/10.1063/1.1725363 E. A. DiMarzio and F. H. Stillinger, Jr. "Residual Entropy of Ice", Journal of Chemical Physics '''40''' 1577 (1964)]

Lufi: /* Ice rules */

2009-06-04T17:10:54Z

Ice rules

← Older revision		Revision as of 19:10, 4 June 2009
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	{{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)]

Carl McBride: /* References */ Corrected page numbers.

2008-12-05T15:53:32Z

References: Corrected page numbers.

← Older revision		Revision as of 17:53, 5 December 2008
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	The so-called ''ice rules'' were proposed by Linus Pauling (Ref. 1).		The so-called ''ice rules'' were proposed by Linus Pauling (Ref. 1).
	==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. ~~2674 - 2680~~ (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)]
	#[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/10.1063/1.1725363 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/10.1063/1.1705058 J. F. Nagle "Lattice Statistics of Hydrogen Bonded Crystals. I. The Residual Entropy of Ice", Journal of Mathematical Physics '''7''' 1484 (1966)]

Carl McBride: Added a couple of references.

2008-11-03T14:04:39Z

Added a couple of references.

← Older revision		Revision as of 16:04, 3 November 2008
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	{{Stub-water}}		{{Stub-water}}
			==Ice rules==
			The so-called ''ice rules'' were proposed by Linus Pauling (Ref. 1).
	==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. 2674 - 2680 (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. 2674 - 2680 (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/10.1063/1.452433 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/10.1063/1.453743 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)]

Carl McBride: /* References */

2007-12-20T16:12:11Z

References

← Older revision		Revision as of 18:12, 20 December 2007
Line 5:		Line 5:
	#[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/10.1063/1.453743 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/10.1063/1.1808693 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]]