Temperature and pressure dependences of the surface energy for a macro- and nanocrystal

Based on the RP-model of a nanocrystal, an analytical method is developed for calculating the specific surface energy $(\sigma)$, isochoric and isobaric derivatives of the $\sigma$ function with respect to temperature, and isothermal derivatives of the $\sigma$ function with respect to pressure and density. It is shown that the method is applicable for both macro-and nanocrystals with a given number of atoms and a certain surface shape. To implement this method, the parameters of the Mie–Lennard-Jones paired interatomic potential were determined in a self-consistent way based on the thermoelastic properties of the crystal. The method was tested on macrocrystals of 15 single-component substances: for 8-FCC crystals (Cu, Ag, Au, Al, Ni, Rh, Pd, Pt) and for 7-BCC crystals (Fe, V, Nb, Ta, Cr, Mo, W). The calculations were made at different temperatures and showed good agreement with the experimental data. Using the example of FCC-Rh, the change in surface properties with a decrease of the nanocrystal size along the isotherms of 10, 300, 2000 K is studied. It is shown that at high pressures and low temperatures, there is a region where the $\sigma$ function increases at an isomorphic-isothermal-isobaric decrease in the nanocrystal size. As the temperature increases, this area disappears.