Melting curve: Difference between revisions
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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. | ||
==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/> | ||
Revision as of 14:40, 24 June 2011
Melting curve
Empirical "one-phase" rules
Lindemann melting law
Hansen-Verlet freezing rule
Raveché-Mountain-Street criteria
Ross melting rule
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.
Zero residual multiparticle entropy criterion
References
- ↑ 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)
- ↑ 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)
- 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)