Editing Melting curve

'''Melting curve'''
==Empirical "one-phase" rules==
===Lindemann melting law===
<ref>F. A. Lindemann "The calculation of molecular natural frequencies",  Physikalische Zeitschrift '''11''' pp. 609-612 (1910)</ref>
===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>
===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===
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>):

:<math>A = \frac{1}{2} NE(0) - Nk_BT \ln \upsilon  - Nk_BT \ln \upsilon_f^*</math>

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.
==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>
==Shock melting method==
<ref>[http://dx.doi.org/10.1063/1.4930974  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)]</ref>
==References==
<references/>
;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/10.1063/1.2208357 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)]



[[category: statistical mechanics]]
@@ 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,
 <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==
 <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>