On the Disappearance of the Crystal-Liquid Phase Transition as the Number of Atoms in the System Decreases

An expression for the Helmholtz free energy of a nanocrystal that contains vacancies in lattice and the delocalized (diffusional) atoms is obtained on the basis of the previously proposed three-phase model of a simple matter and the RP(vac)-model of a nanocrystal. A model of the Gibbs surface, on which a portion of cells are vacant and a part of atoms are in the delocalized state, is proposed. The fact that a proportion of delocalized atoms are delocalized in a "bulk" way and a proportion of them are delocalized in a "surface way" is taken into account. The equation of state is calculated for argon, whose atoms interact via the Mie-Lennard-Jones pairwise potential. Calculations for the macrosystem were show that, at average temperatures, the equation of state has two S loops on isotherms corresponding to the crystal-liquid (C-L) and liquid-gas (L-G) phase transitions (PTs). At high temperatures, the S loop of the L-G PT contracts to the critical point. At low temperatures, two S loops of the C-L and L-G PTs merge into one large S loop corresponding to the C-G PT. As the number of atoms (N) in the nanosystem decreases, the S loops of both phase transitions in the isotherm decrease, and the C-L S loop disappears at a certain value of the number of atoms (N-0). It is shown that N-0 increases as the temperature of the isotherm increases and the nanosystem shape deviates from the most energetically optimal one (it is cubic for the RP(vac)-model). The C-L PT disappears in a cluster consisting of N < N-0 atoms. Such a cluster gradually transforms into the liquid phase in the case of an isothermal increase in the specific volume.