Melting curve

Melting curve

Empirical "one-phase" rules

Ross melting rule

The Ross melting rule states (Eq. 4 ):

$A=\frac{1}{2}NE(0)-N{k}_{B}T\ln \upsilon -N{k}_{B}T\ln \underset{f}{\overset{*}{\upsilon }}$

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, $\upsilon$ is the volume of the cell, and $\underset{f}{\overset{*}{\upsilon }}$ 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 ):

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

where $C_T$ 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)