Atom positions on the vicinal face of a fcc crystal

Abstract

An approximate expression for the free energy of a single crystal is derived to determine equilibrium positions of atoms on vicinal faces of a fcc crystal at various temperatures thermodynamically. The obtained free energy has a peculiarity ͑critical temperature͒ in all the considered cases: infinite crystal, low-index face, adatom on a low-index face, and vicinal face. The physical meaning of the critical temperature is special for each case. The calculated temperature dependence of the lattice constant agrees well with experiment, and the critical temperature for an infinite crystal corresponds to the melting temperature of the crystal. The variance of the thermal vibrations near this critical point of the free energy agrees with the empirical Lindemann criterion. For an adatom on a low-index face, the critical temperature corresponds to its becoming delocalized ͑spread over the surface͒. Similarly, there is a temperature at which an atom at a step edge breaks away and becomes a delocalized adatom.