The Frenkel-Kontorova model was applied to the case of surfaces where the natural bond-length within the surface layer was different to the substrate bond-length. A reconstruction could occur in which the surface density of atoms was either less than or greater than the bulk density. The stability of the unreconstructed surface was controlled by the ratio of two parameters which have simple physical interpretations. They discuss the stability of real metallic surfaces in terms of the values of these parameters, with particular reference to the (111) surfaces of gold, platinum, iridium and aluminium.

Application of the Frenkel-Kontorova Model to Surface Reconstructions. M.Mansfield, R.J.Needs: Journal of Physics - Condensed Matter, 1990, 2[10], 2361-74