Metastable extension of the melting line and the critical endpoint

Molecular-dynamics methods have been employed to calculate the (p, ρ, T)-properties and the internal energy of the Lennard-Jones crystal and liquid phases in both stable and metastable states to the boundaries of limiting supersaturations. Thermal and caloric equations of state have been formulated for determining the parameters of phase equilibrium and approximating the boundaries of essential instability (the spinodal curves). The results of calculations of phase equilibrium parameters from the condition of chemical potentials equality show that the melting line in the region of its metastable extension approaches the spinodal of a stretched liquid. The point of contact (the critical endpoint) is characterized by the following parameter values: Tm⁎ = 0.5286, pm⁎ = − 1.7128, ρm,l⁎ = 0.7374, ρm,c⁎ = 0.9423. The melting line and its metastable extension were also calculated by simulations of two-phase liquid–crystal systems. A comparison of these two approaches has been performed.