High-Temperature X-Ray Standing-Wave Study: Application to Melting of Monolayers of Pb on Ge(111) Surfaces

The effect of a substrate temperature of about twice the Debye temperature on the X-ray standing-wave fields has been explored. An atomic scattering amplitude modified by the Debye-Waller factor appears to be adequate for the description of the standing-wave fields. The high-temperature standing-wave method has been applied to study the temperature dependence of Pb monolayers on Ge(111) surfaces. We obtain evidence that the high-temperature (1 × 1) phase of the reversible phase transition √3 × √3 R 30° ⇄ 1 × 1 is not consistent with a model of a two-dimensional isotropic liquid Pb layer. Rather it appears to be composed of small islands of the original √3 × √3 R 30° crystalline overlayer.