Phase and amplitude recovery and diffraction image generation method: structure of Sb/Au(110)–√3 × √3R54.7° from surface X-ray diffraction

The discovery that the phase problem of diffraction from non-periodic objects may be solved by oversampling the diffraction intensities in reciprocal space with respect to a Nyquist criterion has opened up new vistas for structure determination by diffraction methods. A similar principle may be applied to the problem of surface X-ray diffraction (SXRD), where, owing to the breaking of a crystal periodicity normal to its surface, diffraction data consist of a set of superstructure rods (SRs) due to scattering from the parts of the surface whose structure is different from that of the truncated bulk and of crystal truncation rods (CTRs), formed by interfering contributions from the surface and the bulk. A phase and amplitude recovery and diffraction image generation method (PARADIGM) is described that provides a prescription for finding the unmeasured amplitudes and phases of the surface contributions to the CTRs in addition to the phases of the SRs, directly from the diffraction data. The resulting `diffraction image' is the basis of a determination of the previously unknown multidomain structure of Sb/Au(110)–√3 × √3R54.7°.