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We have performed a detailed x-ray diffraction study of the structure of the 7×7 and 5×5 reconstructions that are observed after deposition of submonolayers of Sn on the Ge(111) surface and subsequent annealing. The structure factors for both reconstructions show considerable similarity with those of Si(111)7×7. Our analysis shows that the dimer-adatom-stacking-fault model is applicable to the Sn-induced Ge(111)7×7 and Ge(111)5×5 structures. The adatoms are identified to be Sn. The structural refinement shows that the atoms in the upper five atomic layers are displaced from their ideal positions. The displacements around the adatoms are similar to the displacements of the Ge(111)√3 × √3 -Sn surface. Furthermore, the observed relaxations are in good agreement with the predictions of total-energy calculations. In order to perform a detailed comparison between the experimentally and theoretically determined atomic positions, a series of elastic strain calculations using a Keating model have been carried out. It is demonstrated that this model gives a good description of the atomic relaxations of the surfaces

X-ray diffraction study of the Ge(111)5×5-Sn and Ge(111)7×7-Sn surfaces