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Govt. of India Trust : E/11049/Rajkot
Income tax of India 80G : AADTK8161HF20221
Income tax of India 12A : AADTK8161HE20217

Volume 3 – Issue 1 – 2022

Original Research Article

Dependencies Of Surface Energy On Temperature, Pressure, And Crystal Size

Mahach N. Magomedov

Institute for Geothermal Problems and Renewable Energy – branch of Joint Institute for
High Temperatures of Russian Academy Sciences, 39-a Shamil str.,
Makhachkala, Republic of Dagestan, 367030, (RUSSIA)

PAGE NO: 45-61


An analytical method has been developed for calculating the specific surface energy (), the isochoric and isobaric derivatives of the  function with respect to temperature, and the isothermal derivatives of the  function with respect to pressure and density. It is shown that the method is applicable for both macrocrystal and nanocrystal with a given number of atoms and a definite 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 carried out at different temperatures and showed good agreement with the experimental data. Using the example of fcc-Rh, the changes in surface properties with a decrease of the nanocrystal size along the isotherms of 10, 300, 2000 K are studied. It is shown that at high pressures and low temperatures, there is a region where the  function increases at an isomorphic-isothermal-isobaric decrease of the nanocrystal size. As the temperature increases, this area disappears.