Test of High-Angular-Resolution X-Ray Photoelectron Diffraction and Holographic Imaging for c(2x2)S on Ni(001)

We have obtained azimuthal X-ray photoelectron diffraction (XPD) data with a high angular resolution of ± 1.5° for S2p emission from the well-defined surface structure of c(2 × 2)S on Ni(001). The relatively high position of the adsorbate with respect to the substrate makes this a stringent test case of the structural sensitivity of forward-scattering-dominated XPD. With this higher resolution, the data are nonetheless found to be sensitive to atomic structure, including in particular both the vertical height of S above Ni (z) and the first-to-second layer Ni interplanar spacing (d₁₂). A single scattering cluster (SSC) theoretical analysis using R-factors to judge goodness of fit yields z = 1.39 ± 0.05 A ̊ and d₁₂ = 1.86 ± 0.05 A ̊, in excellent agreement with other recent experimental and theoretical studies. This analysis also indicates that clusters of up to at least 25 Å in radius (200-250 atoms) are needed to accurately describe all of the diffraction fine structure observed; thus, although XPD is primarily a short-range order probe, high-resolution data provides sensitivity to order that may go out as far as 10-15 neighbor shells. For takeoff angles with respect to the surface of less than about 10°, multiple scattering effects appear to become more important, as verified by fully converged multiple scattering cluster (MSC) calculations; however, for takeoff angles larger than 10°, these effects fall away rapidly, making a single-scattering analysis of such data still a useful approach. Finally, we have analyzed our experimental data and SSC simulations of it using recently suggested Fourier-transform holographic inversion methods. Although our data are too limited to permit fully accurate holographic imaging, features associated with the nearest neighbor S atoms in the adsorbate overlayer are seen in both experimental and theoretical images. In addition, the theoretical calculations indicate that the atomic images can be improved if: the solid angle of the hologram is limited so as to exclude the strong forward scattering features at low takeoff angles; effects due to non-constant scattering factor amplitudes and phases are corrected out using the scattered-wave-included Fourier-transform method of Saldin et al., and/or the hologram range is further limited so as to avoid the overlap of twin and real images. Several interesting directions for further study with such high-resolution data, SSC R-factor analyses, and holographic imaging, are thus suggested.