Melting curve: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
(Added a recent publication)
(→‎Empirical "one-phase" rules: added Khrapak melting criteria)
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.
===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>  

Revision as of 14:51, 17 April 2018

Melting curve

Empirical "one-phase" rules

Lindemann melting law

[1]

Hansen-Verlet freezing rule

[2]

Raveché-Mountain-Street criteria

[3]

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.

Khrapak melting criteria

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

[6][7] [8]

Shock melting method

[9]

References

Related reading