The structure of the Ni(111)()ϫ))R30°-Pb surface has been determined by quantitative low-energy electron diffraction ͑LEED͒, using multiple-scattering simulations of the measured diffracted beam intensities with a tensor-LEED program. The results confirm that the surface comprises a single-layer substitutional alloy of stoichiometry Ni 2 Pb ͑with all atoms in ''fcc'' sites relative to the underlying Ni͒ and clearly excludes a surface/subsurface stacking fault ͑with occupation of ''hcp'' sites͒ like that found for similar phases of Sb on Cu͑111͒ and Ag͑111͒. Within the surface alloy layer the Pb atoms are 0.73Ϯ0.05-Å higher above the surface than the surrounding Ni atoms in the alloy layer. This magnitude of rumpling is in excellent agreement with a recent medium-energy ion scattering investigation of this surface, but is significantly larger than that of an earlier low-energy ion scattering investigation. Compared to the rumpling amplitude of 1.67 Å expected from a simple hard-sphere model based on bulk metallic radii, however, it confirms a strong reduction of the effective atomic radii in this surface alloy.There are now many examples of the observation that the deposition on metal surfaces of atoms in the submonolayer coverage range can lead to these adsorbate atoms occupying substitutional sites in the outermost atomic layer to produce a single-layer surface alloy. 1 This can even occur for some adsorbate/substrate element combinations immiscible in the bulk, reflecting the different energetics of the surface. One question that has attracted some interest in these systems is what the role of effective atomic radii of the adsorbate atoms is in these surface alloys, which determines the degree of ''rumpling'' of the alloy layer. If the deposited atoms have larger atomic radii than that of the substrate atoms they replace, then because the periodicity of the surface alloy parallel to the surface is fixed at the value of the underlying substrate ͑i.e., the surface alloy layer is pseudomorphic͒, a simple hard-sphere picture would predict that the adsorbate atoms would have a larger layer spacing relative to the underlying second layer of the substrate than that of the undisplaced outer-layer substrate atoms. This simply reflects the inability of a larger atom to be fully accommodated in the vacant site produced by the removal of a smaller substrate atom from the surface layer. Recent quantitative structure determinations of quite a number of surface alloy phases, however, indicate that the rumpling observed is almost always less than that predicted by this simple hard-sphere model, and this has been suggested to be a consequence of the valence electron depletion in the surface layer due to spillover into the vacuum, allowing the surface-layer atoms to approach one another more closely than in a bulk solid. 2 One system for which this effect appears to be especially large is the Ni(111)()ϫ))R30°-Pb surface formed by 0.33 ML of Pb on Ni͑111͒. A structural investigation of this surface was made by low-energy ion scat...