Melting curve

Melting curve

Empirical "one-phase" rules

Ross melting rule

The Ross melting rule states (Eq. 4 ):

$A={\frac {1}{2}}NE(0)-Nk_{B}T\ln \upsilon -Nk_{B}T\ln \upsilon _{f}^{*}$

where $A$ is the Helmholtz energy function, $N$ is the number of cells, $E(0)$ is the potential at the centre of the cell, $k_{B}$ is the Boltzmann constant, $T$ 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.

Khrapak melting criteria

The Khrapak one-phase melting criteria for two dimensional crystals with soft long-ranged interactions is given by (Eq 3 in ):

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 $v_{T}$ is the thermal velocity.

References

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)