Surface x-ray-scattering measurements of the substrate-induced spatial modulation of an incommensurate adsorbed monolayer

We report in situ surface x-ray-scattering measurements of electrochemically deposited Tl monolayers on Ag(111). We find that the Tl adlayer forms an incommensurate, two-dimensional solid, and we determine the spatial modulation in the Tl monolayer that is induced by the periodic potential of the substrate. The modulation of the Tl monolayer changes the intensity of the x-ray scattering from the Ag substrate (the Ag crystal truncation rods), since the modulation wave vectors are commensurate with the substrate periodicity. By measuring the intensity changes along the Ag truncation rods, we determined the first Fourier component of the longitudinal part of the substrate-induced modulation to be 0.03 Å, and the spacing of the Tl monolayer above the Ag surface to be 3.05 Å. In addition, from the phase of the monolayer scattering amplitude (relative to the substrate scattering amplitude) required to fit the data, the lowest-energy sites on the surface are identified as the threefold-hollow sites. Using the Novaco-McTague model and estimates of the elastic susceptibility of the Tl monolayer, we also estimate the first Fourier component of the surface energy corrugation to be 2–3 meV (0.05–0.07 kcal/mol). To obtain the modulation amplitude, we have analyzed the ratio of the Ag truncation-rod intensities with and without the monolayer rather than the intensities. The use of this ‘‘ratio’’ method was very important because the ratio is considerably more accurate than the intensities. We also find that the bare Ag(111) surface in contact with electrolyte is very flat (a rms roughness of 0.7 Å) compared with similar metal surfaces prepared by sputtering and annealing in vacuum (rms roughness ∼3–5 Å).