Gibbs-Duhem integration, solid-fluid

The n= 12 soft sphere model is the high-temperature limit of the 12-6 Lennard-Jones (LJ) potential. Agrawal and Kofke [182] used this limit as the starting point for another Gibbs-Duhem integration, which proceeded to lower temperatures until reaching the solid-liquid-vapor triple point. The complete solid-fluid coexistence line, from infinite temperature to the triple point, can be conveniently represented by the empirical formula [182]... 

The Gibbs-Duhem integration method excels in calculations of solid-fluid coexistence [48,49], for which other methods described in this chapter are not applicable. An extension of the method that assumes that the initial free energy difference between the two phases is known in advance, rather than requiring it to be zero, has been proposed by Meijer and El Azhar [51]. The procedure has been used in [51] to determine the coexistence lines of a hard-core Yukawa model for charge-stabilized colloids. 

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