Anisotropic roughening theory of the (110) faces of Cu, Ni, Pd, and Ag

The thermal behavior of the unreconstructed (110) surface of some noble and near-noble metals (Ni, Cu, Pd, Ag) is described in terms of anisotropic defects similar to the missing-rows which explain the reconstruction of their heavier counterparts Ir, Pt and Au. Such defects include microscopic but extended (111) facets which terminate at dislocations. A mapping is performed onto an anisotropic, antiferroelectric version of the exactly solved 6-vertex model, the vertex energies being obtained from the surface energies of the (110), (111) and (100) faces. The order-disorder transition of the model is shown to correspond, in the surface case, to a roughening transition dominated by missing-row defects. From the well-known solution of the 6-vertex model the relevant properties of the metal surfaces near the transition are derived, including the roughening transition temperatures, the surface free energy, the specific heat, the stepping probability, the step free energy and the facet shape. The scattering intensities from the surfaces are calculated for both 4He atoms and X-rays, and a comparison is made with recent experimental data obtained with both probes on Cu and Ag (110).