Liquid-Solid Transitions in Systems of Soft Repulsive Forces: Softness of Potentials and a Maximum in Melting Curves

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Abstract
Liquid-Solid transitions are investigated from both the liquid and the solid sides and it is shown that a maximum in melting curves occurs owing to a certain kind of softness of repulsive forces. This confirms the mechanism of this phenomenon proposed previously by the use of lattice models. For the liquid free energy, the Mansoori and Canfield variational method is used, which yields an effective volume- and temperature-dependent hard-sphere packing fraction. The solid free energy is calculated by means of the Lennard-Jones and Devonshire cell model, the Lindemann fraction also being evaluated. The freezing criterion which states that the packing fraction is constant along the freezing curve and the melting criterion which states that the Lindemann fraction is constant along the melting curve are both shown to be approximately valid near the maximum melting point, including the region of descending melting curves.

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