Interaction of surface misfit and steps on unreconstructed {110} surfaces of anisotropic f.c.c. crystals II: The surface stresses, and the energy of formation of a step

Abstract

Abstract We have calculated the energy of formation per unit length of step on the {110} surface of an anisotropic f.c.c. crystal and its dependence on orientation of the ledge, in the presence of surface misfit. The surface stresses could be modelled using phenomenological techniques described previously, the main simplyfying limitations being that the misfit be small and extend to monatomic depth only. With the surface stresses known and the crystal modelled as an anisotropic elastic continuum, using Voigt's averaged elastic constants, the stress-strain fields and the elastic energy E stored in the crystal could be calculated using standard boundary value techniques. The energy EF of formation of a step is made up of (i) a positive contribution E, (ii) an energy gain ϵ due to the relaxation of the strained monolayers and (iii) a positive electronic contribution estimated as the surface free energy γ of the exposed face of the ledge. The results have been applied to crystals of rhodium, nickel and copper for which most of the necessary data are available. The calculations show, not surprisingly, that E is more than cancelled by ϵ. EF, which is accordingly dominated by γ, has cusped minima at orientations for which the ledge is parallel to either the [001] or the [1 1 0] direction. The levels of the cusps depend on surface energy anisotropy.