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

Atom positions on the vicinal face of a fcc crystal

“…͑2͒ ͑in what follows we will call this, for convenience, the total system͒ in the same way as for the Morse system. 8 As an origin system we used a system of harmonic oscillators whose free energy is known. The potential energy of a harmonic oscillator is taken as U 0 (r ␣ )ϭ 1 2 …”

“…2 More real ͑but simple enough͒ structures, such as a geometrically ideal threedimensional monocrystal with interaction of some neighbors, are usually described by various approximations of the free energy, [3][4][5][6][7][8][9] which are found either theoretically from the perturbation theory, [6][7][8][9] or by extension over a parameter, 5 or by adding a semiempirical term to the known free energy. 3,4 We will derive an approximate expression for the crystal free energy in the framework of the thermodynamical perturbation theory which was used earlier to study some systems interacting via the Morse potential, and to find the first-order correction to the free energy of a system of harmonic oscillators for a rectilinear chain with an edge, 6 a threedimensional ideal crystal, [7][8][9] and the second-order correction for these cases. 8 The main aim of this work is to determine some properties of crystal bulk and surface in thermodynamical equilibrium.…”

“…3,4 We will derive an approximate expression for the crystal free energy in the framework of the thermodynamical perturbation theory which was used earlier to study some systems interacting via the Morse potential, and to find the first-order correction to the free energy of a system of harmonic oscillators for a rectilinear chain with an edge, 6 a threedimensional ideal crystal, [7][8][9] and the second-order correction for these cases. 8 The main aim of this work is to determine some properties of crystal bulk and surface in thermodynamical equilibrium.…”