The approximation to free energy of the atoms of a monocrystal surface

Abstract

Thermodynamic perturbation theory was applied to find the second-order term to the free energy approximation of the semi-infinite rectilinear atomic chain and the fcc crystal with surface, whose interatomic potential was described by the Morse function. The system of harmonic oscillators was chosen as the system of origin. The second order term was shown to be of the same order of magnitude as the first, and there is a temperature at which the chain, the square lattice and the fcc lattice lose their mechanical stability. There is a simple way to find the Helmholtz free energy of the system in this approximation. The expressions obtained were used to calculate the lattice constant, the mean-square displacement of an atom (MSD) and other parameters of the surface and the bulk of a monocrystal, and also the temperature dependencies of these parameters. As temperature increases, surface relaxation (the displacement of the top layer) increases, while the anisotropy of the MSD of surface atoms changes slightly. The data on anisotropy of the MSD of surface atoms are in good agreement with available experimental results.