Photoelectron diffraction: from phenomenological demonstration to practical tool

The potential of photoelectron diffraction—exploiting the coherent interference of directly-emitted and elastically scattered components of the photoelectron wavefield emitted from a core level of a surface atom to obtain structural information—was first appreciated in the 1970s. The first demonstrations of the effect were published towards the end of that decade, but the method has now entered the mainstream armoury of surface structure determination. This short review has two objectives: First, to outline the way that the idea emerged and the way this evolved in my own collaboration with Neville Smith and his colleagues at Bell Labs in the early years: Second, to provide some insight into the current state-of-the art in application of (scanned-energy mode) photoelectron diffraction to address two key issue in quantitative surface structure determination, namely, complexity and precision. In this regard a particularly powerful aspect of photoelectron diffraction is its elemental and chemical-state specificity

Structure determination of PF3 adsorption on Cu(100) using X-ray standing waves

The local structure of the Cu(100)c(4x2)-PF3 adsorption phase has been investigated through the use of normal-incidence X-ray standing waves (NIXSW), monitored by P 1s and F 1s photoemission, together with P K-edge near-edge X-ray absorption fine structure (NEXAFS). NEXAFS shows the molecule to be oriented with its C3v symmetry axis essentially perpendicular to the surface, while the P NIXSW data show the molecule to be adsorbed in atop sites 2.37±0.04 Å above the surface, this distance corresponding to the Cu-P nearest-neighbour distance in the absence of any surface relaxation. F NIXSW indicates a surprisingly small height difference of the P and F atoms above the surface 0.44±0.06 Å, compared with the value expected for an undistorted gas-phase geometry of 0.77 Å, implying significant increases in the F-P-F bond angles. In addition, however, the F NIXSW data indicate that the molecules have a well-defined azimuthal orientation with a molecular mirror plane aligned in a substrate mirror plane, and with a small (5-10°) tilt of the molecule in this plane such that the two symmetrically-equivalent F atoms in each molecule are tilted down towards the surface

The local structure of SO2 and SO3 on Ni(1 1 1): a scanned-energy mode photoelectron diffraction study

O 1s and S 2p scanned-energy mode photoelectron diffraction (PhD) data, combined with multiple-scattering simulations, have been used to determine the local adsorption geometry of the SO2 and SO3 species on a Ni(1 1 1) surface. For SO2, the application of reasonable constraints on the molecular conformation used in the simulations leads to the conclusion that the molecule is centred over hollow sites on the surface, with the molecular plane essentially parallel to the surface, and with both S and O atoms offset from atop sites by almost the same distance of 0.65 Å. For SO3, the results are consistent with earlier work which concluded that surface bonding is through the O atoms, with the S atom higher above the surface and the molecular symmetry axis almost perpendicular to the surface. Based on the O 1s PhD data alone, three local adsorption geometries are comparably acceptable, but only one of these is consistent with the results of an earlier normal-incidence X-ray standing wave (NIXSW) study. This optimised structural model differs somewhat from that originally proposed in the NIXSW investigation

MEIS investigations of surface structure

The early work of the FOM-AMOLF group in Amsterdam clearly demonstrated the potential of medium energy ion scattering (MEIS), typically using 100 keV H+ incident ions, to investigate the structure of surfaces, but most current applications of the method are focussed on near-surface compositional studies of non-crystalline films. However, the key strengths of the MEIS technique, notably the use of blocking curves in double-alignment experiments and absolute yield measurements, are extremely effective in providing detailed near-surface structural information for a wide range of crystalline materials. This potential and the underlying methodology, is illustrated through examples of applications to the study of layer-dependent composition and structure in alloy surfaces, in studies of the surface crystallography of an oxide surface (rutile TiO2(1 1 0)) and in investigations of complex adsorbate-induced reconstruction of metal surfaces, including the pseudo-(1 0 0) reconstruction of Cu(1 1 1) induced by adsorption of atomic N and molecular methylthiolate (CH3S–). In addition to the use of calibrated blocking curves, the use of the detailed spectral shape of the surface peak in the scattered ion energy spectra, as a means of providing single-atomic layer resolution of the surface structure, is also discussed

Adsorbate-induced surface stress, surface strain and surface reconstruction : S on Cu(100) and Ni(100)

Density functional theory (DFT) calculations have been applied to investigate the known difference in behaviour of S adsorption on Cu(100) and Ni(100). Both surfaces form a 0.25 ML (2 × 2) adsorption phase, but while at higher coverage a 0.5 ML c(2 × 2) phase forms on Ni(100), on Cu(100) only a reconstructed 0.47 ML (√17 × √17)R14° structure occurs. Calculations of the energy, structure, and surface stress of (2 × 2) and c(2 × 2) phases on both substrates show there is an energy advantage on both surfaces to form the higher coverage phase, but that both surfaces show local surface strain around the S atoms in the (2 × 2) phase, a phenomenon previously investigated only on Cu(100). More than forty different structural models of the Cu(100)(√17 × √17)R14°-S phase have been investigated. The pseudo-(100)c(2 × 2) structure previously proposed, containing 16 Cu adatoms per unit mesh in the reconstructed layer, is found to be less energetically favourable than many other possible structures, even after taking account of local structural relaxations. Significantly more favourable is a structure with 12 Cu adatoms per (√17 × √17)R14° unit mesh, previously proposed on the basis of scanning tunnelling microscopy (STM), and found to yield simulated STM images in good agreement with experiment. This model has all S atoms in local 4-fold coordinated hollows relative to the Cu atoms below, half being located above Cu adatoms with the remainder lying above the underlying outermost substrate layer. However, an alternative model with only 4 Cu adatoms and with half the S atoms at 3-fold coordinated sites on the periphery of the Cu adatom cluster, has an even lower energy and gives simulated STM images in excellent agreement with experiment

Quantitative determination of the local structure of thymine on Cu(1 1 0) using scanned-energy mode photoelectron diffraction

The local adsorption structures of the surface species formed by interaction of thymine with a Cu(1 1 0) surface at room temperature, and after heating to not, vert, similar530 K, have been investigated. Initial characterisation by soft-X-ray photoelectron spectroscopy and O K-edge near-edge X-ray absorption fine structure (NEXAFS) indicates the effect of sequential dehydrogenation of the NH species and provides information on the molecular orientation. O 1s and N 1s scanned-energy mode photoelectron diffraction shows the species at both temperatures bond to the surface through both carbonyl O atoms and the deprotonated N atom between them, each bonding atom adopting near-atop sites on the outermost Cu surface layer. The associated bondlengths are 1.96 ± 0.03 Å for Cu–N and 1.91 ± 0.03 Å and 2.03 ± 0.03 Å for the two inequivalent Cu--O bonds. The molecular plane lies almost exactly in the close-packed View the MathML source azimuth, but with a tilt relative to the surface normal of approximately 20°. Heating to not, vert, similar530 K, or deposition at this temperature, appears to lead to dehydrogenation of the second N atom in the ring, but no significant change in the adsorption geometry

The local adsorption structure of methylthiolate and butylthiolate on Au(1 1 1): a photoemission core-level shift investigation

Measurements of the core-level shifts in Au 4f photoemission spectra from Au(1 1 1) at different coverages of methylthiolate and butylthiolate are reported. Adsorption leads to two components in addition to that from the bulk, one at lower photoelectron binding energy attributed to surface atoms not bonded to thiolate species, while the second component has a higher binding energy and is attributed to Au atoms bonded to the surface thiolate. The relative intensities of these surface components for the saturation coverage (mainly (√3 × √3)R30°) phases are discussed in terms of different local adsorption sites in a well-ordered surface, and favour adsorption of the thiolate species atop Au adatoms. Alternative interpretations that might be consistent with an Au-adatom-dithiolate model are discussed, particularly in the context of the possible influence of reduced coverage associated with a disordered surface. Marked differences from previously-reported results for longer-chain alkylthiolate layers are highlighted

The local adsorption geometry of benzenethiolate on Cu(1 0 0)

The local adsorption geometry of benzenethiolate in the ordered c(2 × 6) phase on Cu(1 0 0) has been investigated by a combination of S K-edge near-edge X-ray absorption fine structure (NEXAFS), normal incidence X-ray standing waves (NIXSW) and S 1s scanned-energy mode photoelectron diffraction (PhD). NEXAFS and PhD show that the molecular plane is tilted from the surface normal by 20 ± 15°, while NIXSW clearly identifies the S head-group as occupying the four-fold coordinated hollow sites. PhD shows the S atoms lies 1.34 ± 0.04 Å above the outermost Cu atomic layer, leading to a Cu–S bondlength of 2.25 ± 0.02 Å. The combination of the PhD and NIXSW results shows the Cu surface layer has an outward relaxation of 0.15 ± 0.06 Å. Possible origins for this large adsorbate-induced relaxation are discussed

On Streaming and Communication Complexity of the Set Cover Problem

We develop the first streaming algorithm and the first two-party communication protocol that uses a constant number of passes/rounds and sublinear space/communication for logarithmic approximation to the classic Set Cover problem. Specifically, for n elements and m sets, our algorithm/protocol achieves a space bound of O(m ·n [superscript δ] log[superscript 2] n logm) using O(4[superscript 1/δ]) passes/rounds while achieving an approximation factor of O(4[superscript 1/δ]logn) in polynomial time (for δ = Ω(1/logn)). If we allow the algorithm/protocol to spend exponential time per pass/round, we achieve an approximation factor of O(4[superscript 1/δ]). Our approach uses randomization, which we show is necessary: no deterministic constant approximation is possible (even given exponential time) using o(m n) space. These results are some of the first on streaming algorithms and efficient two-party communication protocols for approximation algorithms. Moreover, we show that our algorithm can be applied to multi-party communication model.National Science Foundation (U.S.) (Grant CCF-1161626)National Science Foundation (U.S.) (Grant CCF-1065125)United States. Defense Advanced Research Projects Agency (United States. Air Force Office of Scientific Research Grant FA9550-12-1-0423)David & Lucile Packard FoundationSimons FoundationDanish National Research Foundation. Center for Massiave Data Algorithmics (MADALGO

The local structure of OH species on the V2O3(0 0 0 1) surface: a scanned-energy mode photoelectron diffraction study

Scanned-energy mode photoelectron diffraction (PhD), using O 1s photoemission, together with multiple-scattering simulations, have been used to investigate the structure of the hydroxyl species, OH, adsorbed on a V2O3(0 0 0 1) surface. Surface OH species were obtained by two alternative methods; reaction with molecular water and exposure to atomic H resulted in closely similar PhD spectra. Both qualitative assessment and the results of multiple-scattering calculations are consistent with a model in which only the O atoms of outermost layer of the oxide surface are hydroxylated. These results specifically exclude significant coverage of OH species atop the outermost V atoms, i.e. in vanadyl O atom sites. Ab initio density-functional theory cluster calculations provide partial rationalisation of this result, which is discussed the context of the general understanding of this system