| Lack of phase information in typical x-ray diffraction measurements makes it very difficult to recover the atomic-scale structure of a crystal by direct inversion of the measured amplitudes. We have developed a direct method for surface x-ray diffraction (SXRD) to recover the part of the surface structure that is different from the truncated bulk. The iterative algorithm we have developed employs prior knowledge of the bulk structure and alternately satisfies constraints in real and reciprocal space.; Our method has recently been applied on experimental SXRD data of the known clean Au (110) (1x2) reconstruction as well as the unknown Sb/Au (110) c(2x2) and Sb/Au (110) ( 3 x 3 ) R54.7° reconstructions.; We were able to recover all the features of the clean Au (110) (1x2) reconstruction previously established by researchers using different experimental techniques, including missing row, first-layer contraction, second-layer expansion, third-layer buckling and second- and fourth- layer pairing. None of the previous studies was able to show all these features.; Our results for Sb/Au (110) c(2 x 2) reconstruction suggested a model in which Sb adatoms occupied every other surface substitutional site, the rest occupied by Au adatoms, forming a checkerboard pattern.; For the Sb/Au (110) ( 3 x 3 ) R54.7° system, our direct-method algorithm was adapted to deal with the presence of four symmetry-related domains. Our results suggested a model in which two Sb adatom diagonal rows alternated with a row of Au adatoms, all adatoms in surface substitutional sites.; In both of these unknown structures, quantitative conventional refinement of these suggested starting models yielded good agreement with the scattering data, supporting the veracity of the starting models. |
