On the Equation of State of the Simple Matter, which Describes the Three-Phase Equilibrium

The statistical model of simple matter is developed where N-Nd particles are localized in cells of the virtual lattice (L-particles) while Nd particles are delocalized (D-particles), i.e., can migrate along the entire volume of the system. The virtual lattice is a regular lattice consisting of Nv vacant and N occupied cells with equal volumes. Based on the pairwise interatomic Mie-Lennard-Jones potential and with the use of approximation of "only nearest neighbors" interactions, the expression is derived for a specific (per particle) free energy (f) of the model, which transfers in the limiting cases to expressions for gas or crystal. The calculations of the equation of state P = - (df/dv) T for argon have shown that the function P (v) at intermediate temperatures has two S-loops on isotherms, which correspond to the crystal-liquid and liquid-gas phase transitions.

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