PHASE TRANSITION OF A PB MONOLAYER ON GE(111)

We present an x-ray-diffraction structural analysis of the $\ensuremath{\beta}$-Ge(111)-$(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$-Pb $\ensuremath{\rightarrow}1\ifmmode\times\else\texttimes\fi{}1$ phase transition at $\ensuremath{\sim}180\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ 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 $\ensuremath{\beta}$ phase has a saturation coverage of $\frac{4}{3}$ 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.