Melting curve: Difference between revisions
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'''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]] | ||
Revision as of 14:13, 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]):
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A = \frac{1}{2} NE(0) - Nk_BT \ln \upsilon - Nk_BT \ln \upsilon_f^*}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} is the Helmholtz energy function, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} is the number of cells, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E(0)} is the potential at the centre of the cell, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_B} is the Boltzmann constant, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} is the temperature, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \upsilon} is the volume of the cell, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \upsilon_f^*} is the dimensionless reduced volume in configuration space.
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)
- 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)