Temperature and Pressure Dependences of the Surface Energy for a Macro- and Nanocrystal
М. Н. Магомедов
Abstract
An analytic method of calculations of the specific surface energy σ, the isochoric and isobaric derivatives of function σ in temperature, and isothermic derivatives of function σ with respect to pressure and density has been developed based on the RP model of a nanocrystal. The method is shown can be applied for both a macro- and a nanocrystal with given number of atoms and with a certain surface shape. To realize this method, the parameters of the pair interatomic Mie–Lennard-Jones potential were determined by the self-consistent method on the base of the thermoelastic properties of a crystal. The method was tested on macrocrystals of 15 single-component substances for eight fcc crystals (Cu, Ag, Au, Al, Ni, Rh, Pd, and Pt) and for seven bcc crystals (Fe, V, Nb, Ta, Cr, Mo, and W). The calculations have been carried out at various temperatures and showed good agreement with the experimental data. Using fcc-Rh as an example, the change in the surface properties with a decrease in the nanocrystal size are studied along isotherms 10 K, 300 K, and 2000 K. It is shown that, at high pressures and low temperatures, there is a region, where function σ increases in the case of isomorphous–isothermic–isobaric decrease in the nanocrystal size. This region disappears as temperature increases