Phase transition of a Pb monolayer on Ge(111)

We present an x-ray-diffraction structural analysis of the beta-Ge(111)-(root 3 x root 3)R30 degrees-Pb --> 1 x 1 phase transition at similar to 180 degrees C for a Pb coverage of 1.25 ML. We have studied the atomic structure below and above the phase transition by measuring the distribution of diffracted intensities along integer-order rods of Bragg scattering. Below the phase transition, the beta phase has a saturation coverage of 4/3 ML. We find that above the phase transition the single layer of Pb gives rise to a ring of diffuse scattering indicative of a two-dimensional liquid. However, of all the Pb geometries considered, an ordered layer with high in-plane thermal vibration amplitude is found to provide the best agreement between calculated and measured structure factors. The Pb layer thus has both liquid and solid properties. [S0163-1829(99)08019-4].