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.
===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>  

Latest revision as of 11:52, 18 April 2018

Melting curve

Empirical "one-phase" rules[edit]

Lindemann melting law[edit]

[1]

Hansen-Verlet freezing rule[edit]

[2]

Raveché-Mountain-Street criteria[edit]

[3]

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, 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.

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]):

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 \frac{C_T}{v_T}\approx 4.3}

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 C_T} is the transverse sound velocity, and is the thermal velocity.

Zero residual multiparticle entropy criterion[edit]

[6][7] [8]

Shock melting method[edit]

[9]

References[edit]

  1. ↑ F. A. Lindemann "The calculation of molecular natural frequencies", Physikalische Zeitschrift 11 pp. 609-612 (1910)
  2. ↑ Jean-Pierre Hansen and Loup Verlet "Phase Transitions of the Lennard-Jones System", Physical Review 184 pp. 151-161 (1969)
  3. ↑ 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)
  4. ↑ Marvin Ross "Generalized Lindemann Melting Law", Physical Review 184 pp. 233-242 (1969)
  5. ↑ Sergey Khrapak "Note: Melting criterion for soft particle systems in two dimensions", Journal of Chemical Physics 148, 146101 (2018)
  6. ↑ 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)
  7. ↑ P. V. Giaquinta, G. Giunta and S. Prestipino Giarritta "Entropy and the freezing of simple liquids", Physical Review A 45 R6966–R6968 (1992)
  8. ↑ 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)
  9. ↑ 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)
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