Pendry's Reliability Research Articles

Quantitative Multilayer Cu(410) Structure and Relaxation Determined by QLEED

Industrially relevant catalytically active surfaces exhibit defects. These defects serve as active sites; expose incoming adsorbates to both high and low coordinated surface atoms; determine morphology, reactivity, energetics, and surface relaxation. These, in turn, affect crystal growth, oxidation, catalysis, and corrosion. Systematic experimental analyses of such surface defects pose challenges, esp., when they do not exhibit order. High Miller index surfaces can provide access to these features and information, albeit indirectly. Here, we show that with quantitative low-energy electron diffraction (QLEED) intensity analyses and density functional theory (DFT) calculations, we can visualize the local atomic configuration, the corresponding electron distribution, and local reactivity. The QLEED-determined Cu(410) structure (Pendry reliability factor RP ≃ 0.0797) exhibits alternating sequences of expansion (+) and contraction (−) (of the first 16 atomic interlayers) relative to the bulk-truncated interlayer spacing of ca. 0.437 Å. The corresponding electron distribution shows smoothening relative to the bulk-determined structure. These results should aid us to further gain an atomic-scale understanding of the nature of defects in materials.

Surface structure and electronic states of epitaxialβ−FeSi2(100)/Si(001) thin films: Combined quantitative LEED,ab initioDFT, and STM study

The surface structure of epitaxial $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{FeSi}}_{2}$(100) thin film grown on Si(001) was analyzed using the quantitative low-energy electron diffraction intensity-voltage (LEED I-V) method, ab initio density functional theory (DFT) calculations, and scanning tunneling microscopy (STM). LEED patterns measured on the $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{FeSi}}_{2}$(100) surface reveal two domains of a $p(2\ifmmode\times\else\texttimes\fi{}2)$ reconstruction with $p2gg$ diffraction symmetry. The iron-silicide film truncation and atomic surface structure were determined by LEED I-V method: The smallest Pendry's reliability factor ${R}_{P}=0.22\ifmmode\pm\else\textpm\fi{}0.02$ was achieved for the bare $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{FeSi}}_{2}$ film truncated by an Si layer, whereas Si and Fe ad-atom structures were excluded. Significant atomic relaxations within the topmost surface layers were revealed by the LEED I-V method and confirmed by DFT. The simulated STM patterns from the best-fit model agree well with the measured STM images on the $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{FeSi}}_{2}(100)/\mathrm{Si}(001)\text{\ensuremath{-}}p(2\ifmmode\times\else\texttimes\fi{}2)$ surface: Four Si atoms on a surface form one bright protrusion on STM patterns. Electronic band structure analysis of the bulk and epitaxial $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{FeSi}}_{2}$(100) was carried out. A bare truncated epitaxial film was found to be metallic. Surface electronic states were identified by a partial $k$-resolved atomic-orbital based local density-of-state analysis.

Structure determination of the [formula omitted] Bi–Ag(111) surface alloy using LEED I–V and DFT analyses

The deposition of 1/3 of a monolayer of Bi on Ag(111) leads to the formation of BiAg 2 surface alloy with a long range ordered 3 × 3 R 30 ∘ superstructure. A detailed analysis of this structure using LEED I–V measurements together with DFT calculations is presented. We find strong correlation between experimental and calculated LEED I–V data, with the fit between the two data sets having a Pendry's reliability factor of 0.16. The Bi atom is found to replace one top layer Ag atom in each unit cell, forming a substitutional BiAg 2 surface alloy, with the Bi atoms residing approximately 0.6 Å above the Ag atoms due to their size difference. DFT calculations are in good agreement with the LEED results.

A combined DFT/LEED-approach for complex oxide surface structure determination: Fe 3O 4(0 0 1)

A combination of density functional theory (DFT) calculations and low energy electron diffraction (LEED) analysis is used to determine the surface structure of Fe 3O 4 (1 0 0). We find that the surface is rich in oxygen and the observed ( 2 × 2 ) R 45 ∘ reconstruction is a result of a Jahn–Teller distortion as established by recent DFT-calculations [R. Pentcheva, F. Wendler, H.L. Meyerheim, W. Moritz, N. Jedrecy, M. Scheffler, Phys. Rev. Lett. 94 (2005) 126101]. The corresponding Pendry reliability factor is 0.34. Furthermore, we investigate the influence of the preparation conditions (temperature, oxygen pressure) on the LEED intensities of natural and synthetic samples. The electron scattering phase shifts used in the analysis of the LEED spectra are derived from two methods, one based on the DFT electron densities and another employing an overlap of atomic potentials with optimized muffin-tin radii. Both approaches lead to similar results.

Procedure for LEEDI−Vstructural analysis of metal oxide surfaces:Ca1.5Sr0.5RuO4(001)

Transition metal oxides (TMOs) are famous for the intimate coupling between the lattice, electrons, and spin, creating exotic functionality. Creating a surface, breaking the symmetry, should result in lattice distortions that due to the close coupling could create different ''surface phases.'' Historically it has been very difficult to use low energy electron diffraction I-V to quantitatively determine the surface structure of TMOs. A signature of this problem is the large values commonly reported in the literature of the Pendry reliability factor (R{sub P}), which is used to quantify the agreement between experimental data and calculated diffraction. In this paper we describe a consistent procedure for determining the phase shifts using an optimized muffin-tin potential approach combined with an energy-dependent real and imaginary inner potential. This procedure is used to determine the surface structure of the layered TMO Ca{sub 1.5}Sr{sub 0.5}RuO{sub 4}. An acceptable Pendry reliability factor is achieved (R{sub P}=0.28)

Determination of the structure of Cu{1 0 0}-p( [formula omitted]) R45°–Sn by dynamical LEED

The geometrical structure of 0.50 ML Sn adsorbed on Cu{1 0 0} surface has been studied using Symmetrized Automated Tensor LEED. At this coverage, a p( 3 2 × 2 ) R45° ordered surface structure is formed. The favoured structure is a substitutional surface alloy, that includes a missing row reconstruction. This structure might have originated a from c(2 × 2) superstructure. The p( 3 2 × 2 ) R45° phase is formed by bringing pairs of Sn atoms together in the Cu{1 0 0}-c(2 × 2)–Sn alloyed top layer and removing every third row of copper in the top layer. The two in-equivalent tin atoms in the first layer are buckled towards the solid-vacuum interface by 0.39/0.27 ± 0.07 Å with respect to the first layer copper atoms. The buckling between the Sn atoms is 0.12 ± 0.08 Å. The lateral displacement of Sn atoms is of magnitude 0.26 ± 0.10 Å. The first interlayer spacing is expanded by 4% with respect to the bulk value. Pendry reliability factor has been used to measure the level of agreement between theory and experiment giving a moderate value of 0.26 for the favoured structure.

Determination of the structure of Cu{ [formula omitted]}–c(4×4)-In by TLEED

Tensor low energy electron diffraction (LEED) has been used to study the structure of In adsorbed on Cu{1 0 0} surface at a coverage of 0.60±0.03 ML. At this coverage, a c(4×4) ordered surface structure is formed. The favoured structure is an overlayer in which the two top layers are pure indium. The indium layer closest to bulk has a c(2×2) periodicity, in which In atoms lie at fourfold hollow sites with respect to the substrate. This c(2×2)-In layer is overlayered by a c(4×4) layer in which indium atoms lie at fourfold hollow sites with respect to the c(2×2)-In layer. Indium atoms in the c(2×2)-In layer are laterally shifted off the hollow sites towards bridge sites by 0.28±0.09 Å. Pendry reliability factor has been used to measure the level of agreement between theory and experiment giving a value of 0.28 for the favoured structure.

Structural analysis of GaAs([formula omitted])-c(4×4) with LEED IV technique

By means of low energy electron diffraction intensity versus voltage (LEED IV) analysis with the help of scanning tunneling microscope (STM), the crystallography of GaAs(001)-c(4×4) surface has been determined. STM images indicate that the atomic structure of the surface at room temperature does not have rigorously a p2mm symmetry, which has been assumed in all the analyses conducted so far. Asymmetric three-dimer model, which consists of three As dimers in the unit cell on an As-terminated unreconstructed surface, has led to the best fit between the experimental and calculative IV curves with the Pendry's reliability factor of 0.27. The center dimer among the three is tightly dimerized with the bond length of 2.13 Å, while the outer two have achieved less complete dimerization with the bond length of 3.02 Å. Contrary to the case for the Si(001), it is not buckling perpendicular to the surface but in-plane twisting that dominantly makes the dimers asymmetric, which involves remarkably short bond length for some of the backbonds.

Atomic structure of monolayer graphite formed on Ni(111)

The atomic structure of monolayer graphite formed on a Ni(111) surface was investigated by means of LEED intensity analysis. We measured the I- V curves of the (1,0), (0,1) and (1,1) diffraction spots from a (1 × 1) atomic structure, and analyzed them using Van Hove's analytical program based on dynamical theory. Three different atomic structures meeting the experimental requirement of the 3m symmetry were evaluated with Pendry's reliability factor. The final best-fit structure characterized by the minimum Pendry's reliability factor of 0.22 is as follows: one carbon atom in a unit cell of the graphite overlayer is located at the on-top site of the topmost Ni atoms, while another carbon atom exists at the fcc hollow site. The spacing between the flat overlayer and the topmost Ni layer is 2.11 ± 0.07 A ̊ , which is much narrower than the interlayer spacing in bulk graphite (3.35 Å).

Atomic Structure of Monolayer Graphite Formed on Ni(111).

The atomic structure of monolayer graphite formed on a Ni (111) surface was investigated by means of LEED intensity analysis. We measured the I-V curves of the (1, 0), (0, 1) and (1, 1) diffraction spots from a 1×1 atomic structure, and analyzed them by using the Van Hove's analytical program based on dynamical theory. Three different atomic structures meeting the experimental requirement of the 3-m symmetry were evaluated with Pendry's reliability factor. The final best-fit structure characterized by the minimum Pendry's reliability factor of 0.22 is as follows; one carbon atom in a unit cell of the graphite overlayer is located at the on-top site of the topmost Ni atoms, while another carbon atom exists at the fcc-hollow site. The spacing between the flat overlayer and the topmost Ni layer is 2.11 ± 0.07 A, which is much narrower than the interlayer spacing in bulk graphite (3.35 A).

Crystallography of epitaxial face centered tetragonal Co/Cu(100) by low energy electron diffraction

A crystallographic LEED I/V characterization of thin Co/Cu(100) films is presented. Results from dynamical LEED calculations are compared with experiments via Pendry's reliability factor. The first Co layer grows with a small, but noticeable, amount of Co atoms in the second layer. For thicker films up to at least 10 ML, Co is found to grow on Cu layer by layer in a tetragonally distorted structure. The film adopts the lateral Cu spacing with an in-plane lattice expansion and a contraction of the vertical interplanar distances. By subsequent Cu on Co deposition, lateral and vertical Cu spacings are kept, reproducing the initial substrate structure.

LEED investigations of the Rh(111)-(2 × 2)-O surface structure: measurements with a video analyser in the presence of some electron beam disordering of the adsorbed layer

A multiple-scattering analysis of LEED intensities has been made for the Rh(111)-(2 × 2)-O surface structure. The measurements were made with a video LEED analyser under conditions where the O layer disorders in 2 min in the incident electron beam. The experimental and calculated intensities were compared with Pendry's reliability index, which was minimised with O atoms adsorbed 1.23 Å above the “expected” hollow sites of three-fold coordination.

Comparison of Zanazzi-Jona and Pendry reliability factors over an extended energy range

The theory-experiment fit necessary for surface structure determination is performed using the Zanazzi-Jona (1977) and Pendry (1980) r-factors-RZJ and RP respectively. Both methods lead to the same figures for surface relaxation, with however some increased accuracy and within much less computer time when the Pendry r-factor is used. The extended energy range 100-500 eV is split into the subranges 100-250 eV and 250-500 eV and the corresponding r-factors are calculated and compared. RZJ decreases rapidly when applied to higher energies, and the total-range r-factor is by no means an average over the subranges. However, RP is only slightly decreased at higher energies, corresponding to a slightly improved theory-experiment agreement. Moreover, RP for the total range is approximately the energy-weighted average for the subrange figures.

The Zanazzi-Jona and Pendry reliability indices compared in LEED crystallographic analyses for five surfaces

Topmost interlayer spacings and three measures of their associated uncertainties obtained with the reliability index proposed recently by Pendry (1980) are compared with results available from the authors' previous analyses with the reliability index proposed by Zanazzi and Jona for the surfaces Ni(311), Cu(311), Zr(0001), Rh(110)-c(2*2)-S and Rh(100)-(2*2)-S. Structural conclusions are essentially identical from both approaches. Advantages of the Pendry approach include its much shorter times for computation, and its tendency to give lower uncertainties for the interlayer spacing.