Melting curve
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)