Melting curve - Revision history

Carl McBride: /* Khrapak melting criteria */ Added an internal link

2018-04-18T09:52:01Z

Khrapak melting criteria: Added an internal link

← Older revision		Revision as of 11:52, 18 April 2018
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	:<math>\frac{C_T}{v_T}\approx 4.3</math>		:<math>\frac{C_T}{v_T}\approx 4.3</math>

	where <math>C_T</math> is the transverse [[Speed of sound \| sound velocity]], and <math>v_T</math> is the [[thermal velocity]].		where <math>C_T</math> is the transverse [[Speed of sound \| sound velocity]], and <math>v_T</math> is the [[Maxwell speed distribution \| thermal velocity]].

	==Zero residual multiparticle entropy criterion==		==Zero residual multiparticle entropy criterion==

Carl McBride: /* Empirical "one-phase" rules */ added Khrapak melting criteria

2018-04-17T13:51:37Z

Empirical "one-phase" rules: added Khrapak melting criteria

← Older revision		Revision as of 15:51, 17 April 2018
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	where <math>A</math> is the [[Helmholtz energy function]], <math>N</math> is the number of cells, <math>E(0)</math> is the potential at the centre of the cell,		where <math>A</math> is the [[Helmholtz energy function]], <math>N</math> is the number of cells, <math>E(0)</math> is the potential at the centre of the cell,
	<math>k_B</math> is the [[Boltzmann constant]], <math>T</math> is the [[temperature]], <math>\upsilon</math> is the volume of the cell, and <math>\upsilon_f^*</math> is the dimensionless reduced volume in configuration space.		<math>k_B</math> is the [[Boltzmann constant]], <math>T</math> is the [[temperature]], <math>\upsilon</math> is the volume of the cell, and <math>\upsilon_f^*</math> is the dimensionless reduced volume in configuration space.
			===Khrapak melting criteria===
			The Khrapak one-phase melting criteria for two dimensional crystals with soft long-ranged interactions is given by (Eq 3 in <ref>[https://doi.org/10.1063/1.5027201 Sergey Khrapak "Note: Melting criterion for soft particle systems in two dimensions", Journal of Chemical Physics 148, 146101 (2018)]</ref>):

			:<math>\frac{C_T}{v_T}\approx 4.3</math>

			where <math>C_T</math> is the transverse [[Speed of sound \| sound velocity]], and <math>v_T</math> is the [[thermal velocity]].

	==Zero residual multiparticle entropy criterion==		==Zero residual multiparticle entropy criterion==
	<ref>[http://dx.doi.org/10.1016/0378-4371(92)90415-M P.V. Giaquinta and G. Giunta "About entropy and correlations in a fluid of hard spheres", Physica A: Statistical Mechanics and its Applications '''187''' pp. 145-158 (1992)]</ref><ref>[http://dx.doi.org/10.1103/PhysRevA.45.R6966 P. V. Giaquinta, G. Giunta and S. Prestipino Giarritta "Entropy and the freezing of simple liquids", Physical Review A '''45''' R6966–R6968 (1992)]</ref>		<ref>[http://dx.doi.org/10.1016/0378-4371(92)90415-M P.V. Giaquinta and G. Giunta "About entropy and correlations in a fluid of hard spheres", Physica A: Statistical Mechanics and its Applications '''187''' pp. 145-158 (1992)]</ref><ref>[http://dx.doi.org/10.1103/PhysRevA.45.R6966 P. V. Giaquinta, G. Giunta and S. Prestipino Giarritta "Entropy and the freezing of simple liquids", Physical Review A '''45''' R6966–R6968 (1992)]</ref>

Carl McBride: Added a recent publication

2015-09-22T16:49:38Z

Added a recent publication

← Older revision		Revision as of 18:49, 22 September 2015
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	'''Melting curve'''		'''Melting curve'''
	=Empirical "one-phase" rules=		==Empirical "one-phase" rules==
	==Lindemann melting law==		===Lindemann melting law===
	<ref>F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift '''11''' pp. 609-612 (1910)</ref>		<ref>F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift '''11''' pp. 609-612 (1910)</ref>
	==Hansen-Verlet freezing rule==		===Hansen-Verlet freezing rule===
	<ref>[http://dx.doi.org/10.1103/PhysRev.184.151 Jean-Pierre Hansen and Loup Verlet "Phase Transitions of the Lennard-Jones System", Physical Review '''184''' pp. 151-161 (1969)]</ref>		<ref>[http://dx.doi.org/10.1103/PhysRev.184.151 Jean-Pierre Hansen and Loup Verlet "Phase Transitions of the Lennard-Jones System", Physical Review '''184''' pp. 151-161 (1969)]</ref>
	==Raveché-Mountain-Street criteria==		===Raveché-Mountain-Street criteria===
	<ref>[http://dx.doi.org/10.1063/1.1682198 Harold J. Raveché, Raymond D. Mountain, and William B. Streett "Freezing and melting properties of the Lennard‐Jones system", Journal of Chemical Physics '''61''' pp. 1970- (1974)]</ref>		<ref>[http://dx.doi.org/10.1063/1.1682198 Harold J. Raveché, Raymond D. Mountain, and William B. Streett "Freezing and melting properties of the Lennard‐Jones system", Journal of Chemical Physics '''61''' pp. 1970- (1974)]</ref>
	==Ross melting rule==		===Ross melting rule===
	The '''Ross melting rule''' states (Eq. 4 <ref>[http://dx.doi.org/10.1103/PhysRev.184.233 Marvin Ross "Generalized Lindemann Melting Law", Physical Review '''184''' pp. 233-242 (1969)]</ref>):		The '''Ross melting rule''' states (Eq. 4 <ref>[http://dx.doi.org/10.1103/PhysRev.184.233 Marvin Ross "Generalized Lindemann Melting Law", Physical Review '''184''' pp. 233-242 (1969)]</ref>):

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	<ref>[http://dx.doi.org/10.1016/0378-4371(92)90415-M P.V. Giaquinta and G. Giunta "About entropy and correlations in a fluid of hard spheres", Physica A: Statistical Mechanics and its Applications '''187''' pp. 145-158 (1992)]</ref><ref>[http://dx.doi.org/10.1103/PhysRevA.45.R6966 P. V. Giaquinta, G. Giunta and S. Prestipino Giarritta "Entropy and the freezing of simple liquids", Physical Review A '''45''' R6966–R6968 (1992)]</ref>		<ref>[http://dx.doi.org/10.1016/0378-4371(92)90415-M P.V. Giaquinta and G. Giunta "About entropy and correlations in a fluid of hard spheres", Physica A: Statistical Mechanics and its Applications '''187''' pp. 145-158 (1992)]</ref><ref>[http://dx.doi.org/10.1103/PhysRevA.45.R6966 P. V. Giaquinta, G. Giunta and S. Prestipino Giarritta "Entropy and the freezing of simple liquids", Physical Review A '''45''' R6966–R6968 (1992)]</ref>
	<ref>[http://dx.doi.org/10.1063/1.2916697 William P. Krekelberg, Vincent K. Shen, Jeffrey R. Errington, and Thomas M. Truskett "Residual multiparticle entropy does not generally change sign near freezing", Journal of Chemical Physics '''128''' 161101 (2008)]</ref>		<ref>[http://dx.doi.org/10.1063/1.2916697 William P. Krekelberg, Vincent K. Shen, Jeffrey R. Errington, and Thomas M. Truskett "Residual multiparticle entropy does not generally change sign near freezing", Journal of Chemical Physics '''128''' 161101 (2008)]</ref>
			==Shock melting method==
			<ref>[http://dx.doi.org/10.1063/1.4930974 Zhong-Li Liu, Xiu-Lu Zhang and Ling-Cang Cai "Shock melting method to determine melting curve by molecular dynamics: Cu, Pd, and Al", Journal of Chemical Physics '''143''' 114101 (2015)]</ref>
	==References==		==References==
	<references/>		<references/>
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	*[http://dx.doi.org/10.1063/1.2208357 Franz Saija, Santi Prestipino, and Paolo V. Giaquinta "Evaluation of phenomenological one-phase criteria for the melting and freezing of softly repulsive particles", Journal of Chemical Physics '''124''' 244504 (2006)]		*[http://dx.doi.org/10.1063/1.2208357 Franz Saija, Santi Prestipino, and Paolo V. Giaquinta "Evaluation of phenomenological one-phase criteria for the melting and freezing of softly repulsive particles", Journal of Chemical Physics '''124''' 244504 (2006)]
	*[http://dx.doi.org/10.1063/1.3605659 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Communication: Universality of the melting curves for a wide range of interaction potentials", Journal of Chemical Physics '''134''' 241101 (2011)]		*[http://dx.doi.org/10.1063/1.3605659 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Communication: Universality of the melting curves for a wide range of interaction potentials", Journal of Chemical Physics '''134''' 241101 (2011)]



	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride: Added mention of the Zero residual multiparticle entropy criterion

2011-06-24T13:40:02Z

Added mention of the Zero residual multiparticle entropy criterion

← Older revision		Revision as of 15:40, 24 June 2011
Line 14:		Line 14:
	where <math>A</math> is the [[Helmholtz energy function]], <math>N</math> is the number of cells, <math>E(0)</math> is the potential at the centre of the cell,		where <math>A</math> is the [[Helmholtz energy function]], <math>N</math> is the number of cells, <math>E(0)</math> is the potential at the centre of the cell,
	<math>k_B</math> is the [[Boltzmann constant]], <math>T</math> is the [[temperature]], <math>\upsilon</math> is the volume of the cell, and <math>\upsilon_f^*</math> is the dimensionless reduced volume in configuration space.		<math>k_B</math> is the [[Boltzmann constant]], <math>T</math> is the [[temperature]], <math>\upsilon</math> is the volume of the cell, and <math>\upsilon_f^*</math> is the dimensionless reduced volume in configuration space.
			==Zero residual multiparticle entropy criterion==
			<ref>[http://dx.doi.org/10.1016/0378-4371(92)90415-M P.V. Giaquinta and G. Giunta "About entropy and correlations in a fluid of hard spheres", Physica A: Statistical Mechanics and its Applications '''187''' pp. 145-158 (1992)]</ref><ref>[http://dx.doi.org/10.1103/PhysRevA.45.R6966 P. V. Giaquinta, G. Giunta and S. Prestipino Giarritta "Entropy and the freezing of simple liquids", Physical Review A '''45''' R6966–R6968 (1992)]</ref>
			<ref>[http://dx.doi.org/10.1063/1.2916697 William P. Krekelberg, Vincent K. Shen, Jeffrey R. Errington, and Thomas M. Truskett "Residual multiparticle entropy does not generally change sign near freezing", Journal of Chemical Physics '''128''' 161101 (2008)]</ref>
	==References==		==References==
	<references/>		<references/>

Carl McBride: Added some references

2011-06-24T13:13:33Z

Added some references

← Older revision		Revision as of 15:13, 24 June 2011
Line 1:		Line 1:
	'''Melting curve'''		'''Melting curve'''
			=Empirical "one-phase" rules=
	==Lindemann melting law==		==Lindemann melting law==
	<ref>F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift '''11''' pp. 609-612 (1910)</ref>		<ref>F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift '''11''' pp. 609-612 (1910)</ref>
	==Hansen-Verlet freezing rule==		==Hansen-Verlet freezing rule==
	<ref>[http://dx.doi.org/10.1103/PhysRev.184.151 Jean-Pierre Hansen and Loup Verlet "Phase Transitions of the Lennard-Jones System", Physical Review '''184''' pp. 151-161 (1969)]</ref>		<ref>[http://dx.doi.org/10.1103/PhysRev.184.151 Jean-Pierre Hansen and Loup Verlet "Phase Transitions of the Lennard-Jones System", Physical Review '''184''' pp. 151-161 (1969)]</ref>

	==Raveché-Mountain-Street criteria==		==Raveché-Mountain-Street criteria==
			<ref>[http://dx.doi.org/10.1063/1.1682198 Harold J. Raveché, Raymond D. Mountain, and William B. Streett "Freezing and melting properties of the Lennard‐Jones system", Journal of Chemical Physics '''61''' pp. 1970- (1974)]</ref>
	==Ross melting rule==		==Ross melting rule==
	The '''Ross melting rule''' states (Eq. 4 <ref>[http://dx.doi.org/10.1103/PhysRev.184.233 Marvin Ross "Generalized Lindemann Melting Law", Physical Review '''184''' pp. 233-242 (1969)]</ref>):		The '''Ross melting rule''' states (Eq. 4 <ref>[http://dx.doi.org/10.1103/PhysRev.184.233 Marvin Ross "Generalized Lindemann Melting Law", Physical Review '''184''' pp. 233-242 (1969)]</ref>):
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	;Related reading		;Related reading
	*[http://dx.doi.org/10.1016/0370-1573(94)90017-5 Hartmut Löwen "Melting, freezing and colloidal suspensions", Physics Reports '''237''' pp. 249-324 (1994)]		*[http://dx.doi.org/10.1016/0370-1573(94)90017-5 Hartmut Löwen "Melting, freezing and colloidal suspensions", Physics Reports '''237''' pp. 249-324 (1994)]
			*[http://dx.doi.org/10.1063/1.2208357 Franz Saija, Santi Prestipino, and Paolo V. Giaquinta "Evaluation of phenomenological one-phase criteria for the melting and freezing of softly repulsive particles", Journal of Chemical Physics '''124''' 244504 (2006)]
	*[http://dx.doi.org/10.1063/1.3605659 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Communication: Universality of the melting curves for a wide range of interaction potentials", Journal of Chemical Physics '''134''' 241101 (2011)]		*[http://dx.doi.org/10.1063/1.3605659 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Communication: Universality of the melting curves for a wide range of interaction potentials", Journal of Chemical Physics '''134''' 241101 (2011)]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride: /* Hansen-Verlet freezing rule */ Added reference

2011-06-24T13:03:37Z

Hansen-Verlet freezing rule: Added reference

← Older revision		Revision as of 15:03, 24 June 2011
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	<ref>F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift '''11''' pp. 609-612 (1910)</ref>		<ref>F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift '''11''' pp. 609-612 (1910)</ref>
	==Hansen-Verlet freezing rule==		==Hansen-Verlet freezing rule==
			<ref>[http://dx.doi.org/10.1103/PhysRev.184.151 Jean-Pierre Hansen and Loup Verlet "Phase Transitions of the Lennard-Jones System", Physical Review '''184''' pp. 151-161 (1969)]</ref>

	==Raveché-Mountain-Street criteria==		==Raveché-Mountain-Street criteria==
	==Ross melting rule==		==Ross melting rule==

Carl McBride: Created page with "'''Melting curve''' ==Lindemann melting law== F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift '''11''' pp. 609-612 (1910)
2011-06-24T12:49:40Z

Created page with "'''Melting curve''' ==Lindemann melting law== <ref>F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift '''11''' pp. 609-612 (1910)</ref..."

New page
'''Melting curve'''
==Lindemann melting law==
<ref>F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift '''11''' pp. 609-612 (1910)</ref>
==Hansen-Verlet freezing rule==
==Raveché-Mountain-Street criteria==
==Ross melting rule==
The '''Ross melting rule''' states (Eq. 4 <ref>[http://dx.doi.org/10.1103/PhysRev.184.233 Marvin Ross "Generalized Lindemann Melting Law", Physical Review '''184''' pp. 233-242 (1969)]</ref>):

:<math>A = \frac{1}{2} NE(0) - Nk_BT \ln \upsilon - Nk_BT \ln \upsilon_f^</math>

where <math>A</math> is the [[Helmholtz energy function]], <math>N</math> is the number of cells, <math>E(0)</math> is the potential at the centre of the cell,
<math>k_B</math> is the [[Boltzmann constant]], <math>T</math> is the [[temperature]], <math>\upsilon</math> is the volume of the cell, and <math>\upsilon_f^</math> is the dimensionless reduced volume in configuration space.
==References==
<references/>
;Related reading
[http://dx.doi.org/10.1016/0370-1573(94)90017-5 Hartmut Löwen "Melting, freezing and colloidal suspensions", Physics Reports '''237''' pp. 249-324 (1994)]
[http://dx.doi.org/10.1063/1.3605659 Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Communication: Universality of the melting curves for a wide range of interaction potentials", Journal of Chemical Physics '''134''' 241101 (2011)]
[[category: statistical mechanics]]