Melting curve: Difference between revisions
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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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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 [[Maxwell speed distribution | 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> | ||
<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]] | ||
Latest revision as of 10:52, 18 April 2018
Melting curve
Empirical "one-phase" rules[edit]
Lindemann melting law[edit]
Hansen-Verlet freezing rule[edit]
Raveché-Mountain-Street criteria[edit]
Ross melting rule[edit]
The Ross melting rule states (Eq. 4 [4]):
where is the Helmholtz energy function, is the number of cells, is the potential at the centre of the cell, is the Boltzmann constant, is the temperature, is the volume of the cell, and is the dimensionless reduced volume in configuration space.
Khrapak melting criteria[edit]
The Khrapak one-phase melting criteria for two dimensional crystals with soft long-ranged interactions is given by (Eq 3 in [5]):
where is the transverse sound velocity, and is the thermal velocity.
Zero residual multiparticle entropy criterion[edit]
Shock melting method[edit]
References[edit]
- ↑ F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift 11 pp. 609-612 (1910)
- ↑ Jean-Pierre Hansen and Loup Verlet "Phase Transitions of the Lennard-Jones System", Physical Review 184 pp. 151-161 (1969)
- ↑ 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)
- ↑ Marvin Ross "Generalized Lindemann Melting Law", Physical Review 184 pp. 233-242 (1969)
- ↑ Sergey Khrapak "Note: Melting criterion for soft particle systems in two dimensions", Journal of Chemical Physics 148, 146101 (2018)
- ↑ 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)
- ↑ P. V. Giaquinta, G. Giunta and S. Prestipino Giarritta "Entropy and the freezing of simple liquids", Physical Review A 45 R6966–R6968 (1992)
- ↑ 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)
- ↑ 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)
- Related reading
- Hartmut Löwen "Melting, freezing and colloidal suspensions", Physics Reports 237 pp. 249-324 (1994)
- 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)
- 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)