Phase Transitions in Two Dimensions: The Case of Sn Adsorbed on Ge(111) Surfaces

Accurate atomic coordinates of the room-temperature ( √3×√3) R30^∘ and low-temperature ( 3×3) phases of $1/3$ monolayer 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 ( √3×√3) R30^∘ structure. In the low-temperature phase one of the three Sn atoms per ( 3×3) unit cell is displaced outwards by 0.26±0.04 relative to the other two. This displacement is accompanied by an increase in the first to second double-layer spacing in the Ge substrate.