Phase transitions in two dimensions - the case of Sn adsorbed on Ge(111) surfaces

Accurate atomic coordinates of the room-temperature (root3xroot3)R30degree and low-temperature (3x3) phases of 1/3 ML Sn on Ge(111) have been established by grazing-incidence x-ray diffraction with synchrotron radiation. The Sn atoms are located solely at T4-sites in the (root3xroot3)R30degree structure. In the low temperature phase one of the three Sn atoms per (3x3) unit cell is displaced outwards by 0.26 +/- 0.04 A relative to the other two. This displacement is accompanied by an increase in the first to second double-layer spacing in the Ge substrate.