Order-to-disorder phase-transition study of Pb on Ge(111)

X-ray standing-wave (111) and (11[bar 1]) measurements have been performed on the room-temperature and high-temperature phases of a Pb layer on Ge(111). At room temperature, our results support a four-atom--unit-cell surface structure. On passing into the high-temperature phase, we find that there is an increase in the Fourier coefficient along the surface [11[bar 2]] direction for the Pb density distribution. Our model, which requires a 0.6-A in-plane thermal vibration amplitude, is similar to one previously proposed by Hwang and Golovchenko and disagrees with a strictly two-dimensional-liquid interpretation.