Low-energy Electron Diffraction Calculations Research Articles

On the determination of surface antiferromagnetism by low-energy electron diffraction

We explore the potential of Low-Energy Electron Diffraction (LEED) for studying antiferromagnetic transition metal overlayers on nonmagnetic substrates, which were recently predicted by total energy calculations. Dynamical LEED calculations for a monolayer of Cr on Pd(0 0 1) show that the “extra spot” intensity vs energy profiles generated by the c(2 × 2) antiferromagnetic ordering are, for a range of incidence angles, sizeable enough to be measureable by present-day apparatus.

The missing-row model for the reconstructed Pt(110)−(1 × 2) surface: A leed intensity analysis showing multilayer distortions

The (1 × 2) missing-row reconstruction of clean Pt(110) is studied with a new low-energy electron diffraction (LEED) intensity analysis. In order to obtain theoretical intensity-voltage curves in good agreement with experiment, it is necessary to consider distortions from the basic missing-row model in the theoretical treatment. In our calculations, alternating row-pairing and vertical buckling distortions down to the fourth layer are allowed for the first time. Large contractions are seen in the first three layer spacings, and significant distortions are found even in the fourth layer. The distortions are similar to those seen in Ir and Au LEED results as well as those predicted by the embedded atom method (EAM) for Pt. In the optimum geometry, the top-layer spacing contracts by 18%. The atoms in the second layer pair towards the missing rows, in agreement with Ir and Au LEED but in the direction opposite to that predicted by EAM. The R-factors are especially sensitive to the third-layer buckling. The fourth-layer pairing is also towards the missing rows, in agreement with the EAM prediction. It is shown that full dynamical LEED calculations of this kind can be realistically run on a personal computer with suitable coprocessor board.

Current image diffraction patterns of molybdenum disulphide

Current image diffraction (CID) patterns are reported for very low energy electron incidence on the basal (001) MoS 2 surface. Comparisons are made between such patterns and the results of low energy electron diffraction calculations performed using the multislice scattering matrix method. From the good agreement between experiment and calculation it is concluded that the contrast changes in the CID patterns are determined by elastic diffraction effects and that the CID technique can provide information on surfaces of such layered transition metal dichalcogenide compounds.

Atomic structure of the Si(001)c(4 x 2) surface.

We have studied the atomic structure of the Si(001)c(4\ifmmode\times\else\texttimes\fi{}2) surface with kinematic low-energy electron diffraction calculations compared with the constant-momentum-transfer-averaged low-energy electron diffraction intensity curves collected by Webb et al. The results show that the reconstruction mechanism of the surface is unbuckled dimerization, that the c(4\ifmmode\times\else\texttimes\fi{}2) reconstruction extends to about the sixth atomic layer, and that there is an oscillatory multilayer relaxation in the surface. We present a model for the atomic structure of the surface which gives a reasonably good agreement with the experimental curves.

Calculated low energy electron total current spectra for the A1(111) surface

AbstractResults of low energy electron diffraction calculations using the scattering matrix method are presented for the incident energy range 0.5 to 40 eV for the (111) A1 face and a comparison is made with reported measured total current spectroscopy results. It is concluded that the structure of the experimental spectra is determined by elastic diffraction effects and that the TCS technique provides information on the mean inner and absorption potentials in the very low incident energy region.

A comparison for the Al (001) and (111) surfaces between scattering matrix calculations and current image diffraction patterns

Results of low energy electron diffraction calculations using the scattering matrix method are presented for the incident energy range 22 to 29 eV and 7.5 to 11 eV for, respectively, the (001) and (111) Al faces. Comparisons are made with reported measured current image diffraction patterns. In particular it is shown that even at the low range of energies considered in this paper, the structure of the measured patterns is dominated by the elastically backscattered electrons. The role of geometrical analysis in these type of results is discussed.

The surface geometry of GaAs(110)

Results of a fully dynamical low-energy electron diffraction calculation show that the GaAs(110) surface reconstructs with a top-layer tilt-angle of 27° ≤ ω ≤ 31°. The smaller tilt angle 7° ≤ ω ≤ 10° reported earlier is outside the error limits of the analysis and can be clearly ruled out. The results are independent of which R-factor or which set of existing experimental data is used. Lateral shifts larger than 0.1 Å for the surface atoms are necessary to obtain acceptable agreement with the measured intensity spectra.

Surface-sandwich segregation on nondilute bimetallic alloys: Pt50Ni50 and Pt78Ni22 probed by low-energy electron diffraction.

A short-wave large-amplitude compositional oscillation versus depth at the (111) surface of ${\mathrm{Pt}}_{50}$${\mathrm{Ni}}_{50}$ and ${\mathrm{Pt}}_{78}$${\mathrm{Ni}}_{22}$ alloys is observed by means of low-energy electron diffraction (LEED). In the LEED calculation, the substitutional disorder of the alloys is successfully mimicked by the averaged t-matrix approximation. The occurrence of a well-developed Pt-Ni surface sandwich on top of the Pt-Ni alloys is interesting in view of the chemisorptive and catalytic properties of these alloys.

Corrugation studies forp(2×2) and c(2×2)phases of oxygen on Ni(001) and Cu(001)

Chemisorption of oxygen on Ni(001) shows $p(2\ifmmode\times\else\texttimes\fi{}2)$ low-energy electron diffraction (LEED) patterns at low exposures changing to $c(2\ifmmode\times\else\texttimes\fi{}2)$ at higher exposures. A recent quantum-mechanical cluster calculation and a lattice-dynamical calculation have suggested different vertical heights for the two phases of oxygen. Another ab initio cluster calculation and extended x-ray-absorption fine-structure data indicate a single vertical height, in agreement with earlier LEED studies. More recent LEED calculations, however, do not rule out a closer distance for the $c(2\ifmmode\times\else\texttimes\fi{}2)$ phase. A He-diffraction study has just been completed for the $c(2\ifmmode\times\else\texttimes\fi{}2) \mathrm{and} p(2\ifmmode\times\else\texttimes\fi{}2)$ phases. We compare our calculated corrugation with these data and conclude that in both phases oxygen is at a vertical distance of about 0.9 \AA{}. We predict similar results for oxygen on Cu(001).

Stability of low-energy electron diffraction fractional-order beam intensities and intralayer multiple scattering

Low-energy electron diffraction (LEED) intensity measurements on adsorbed oxygen on Cu{001} at varying coverage and LEED calculations of spectra of adsorbed Al on Si{111} at several coverages show the fractional-order spectra to be remarkably independent of surface coverage. Such stability of the fractional-order spectra implies both negligible scattering between adsorbed atoms and the same substrate environment around each adsorbed atom. When such stability is found in LEED intensity measurements during adsorption experiments, the adsorbate environment can sometimes be determined by LEED intensity analysis for complicated structures and even for structures with no long-range order.

Theoretical scattering amplitudes for the atomic scattering of low-energy electrons for use in surface crystallography by low-energy electron diffraction

As the use of low-energy electron diffraction (LEED) for surface structural analysis has increased, the need for accurate values of scattering amplitudes and cross sections in the angle and energy range of interest to those doing LEED work has also increased. Presently available tables of atomic scattering factors, which could serve as a standard starting point for more sophisticated LEED calculations, are unfortunately limited in angle and energy and do not include a number of elements of interest to the surface-science community. In order to calculate these scattering amplitudes as well as total elastic cross sections for atomic scattering of low-energy electrons, the Dirac equation was solved numerically. Various analytic and numerical forms for the atomic potential, including relativistic, self-consistent Hartree–Fock–Slater scattering potentials were used. The exchange of the incoming electron with the atomic electrons was neglected because this effect is negligible for atomic scattering in the ranges where this work is applicable. Care is taken to demonstrate the validity of this work for LEED calculations and the limits of its application. The complete set of data for relativisitic partial-wave phase shifts is available for H, He, Li, C, N, O, Ne, Na, Si, S, Ar, K, Ca, Sc, Cr, Fe, Co, Ni, Zn, Ge, Se, Kr, Rb, Y, Mo, Rh, Cd, Sn, Te, Xe, Cs, La, W, Ir, Hg, Pb, Po and Rn. The data covers the energy range from 15 to 305 eV in 10 eV increments. To ensure convergence of the series when calculating the atomic scattering factors and subsequently the total elastic cross section, the actual calculations were performed with 50 to 80 partial waves depending on the energy of the incident electron. Owing to space limitations the phase shifts as well as the complex atomic scattering factors and elastic cross sections are not presented in the paper. They are available from the authors on request.

Approach to structure determination of compound semiconductor surfaces by kinematical LEED calculations: GaAs(110) and ZnSe(110)

Because of the expense of dynamical low-energy electron diffraction (LEED) computational analyses, a more economical approach to the comparison between measured and computed LEED intensity profiles of nonpolar compound semiconductor surfaces consists of determining an initial estimate of surface atomic position coordinates via comparison of experimental data with kinematical calculations. Once an acceptable region of position parameter space has been identified, further refinements can be obtained by dynamical LEED analyses. This paper presents the results of the kinematical portion of such an analysis applied to GaAs(110) and ZnSe(110) surfaces. It is found that both materials exhibit similar surface atomic rearrangements characterized by bond length distortions and vertical displacements of the two sublattices in the uppermost atomic layer. These rearrangements differ from the ’’rotated’’ rearrangement reported earlier for GaAs(110) principally in that the structures identified herein involve small changes in bond lengths.

Surface structure refinements of 2HMoS 2, 2HNbSe 2 and W(100)p(2 × 1)O via new reliability factors for surface crystallography

We define five formulae which evaluate the reliability of a given surface structure analysis by calculating numerical values based on the degree of agreement between calculated and measured low-energy electron diffraction (LEED) intensity-voltage ( I– V) curves. These so-called reliability factors (R-factors) are tested on three surface systems previously investigated by visual judgment. It is found that in each case, the R-factors are able to pick out unambiguously a single optimal surface structure. The five R-factors, used collectively, are sensitive to all features in an I– V curve deemed important in a theory-experiment comparison. Furthermore, the R-factors can determine best choices of dynamical inputs used in LEED calculations, e.g. the inelastic damping, inner potential, etc. These R-factors are easy to calculate and program. The program can be conveniently attached to any plotting routine of I– V curves, thus allowing simultaneous generation of I– V spectra and R-factor plots.

A study of ion-core potentials used in low-energy electron diffraction calculations

Various models for the construction of ion-core potentials presently used in LEED intensity spectra calculations are tested for nickel. We find that self-consistent iterations of these ion-core potentials do not produce significant improvement over the simple linear superposition scheme in building LEED potentials. For the exchange part of the potential, the non-local Hartree-Fock scheme works poorly compared to the Slater approximation. The better results of the Slater exchange are attributed to its compensating for the omission of correlation effects from the Hartree-Fock formula.

Abstract: SCF‐Xα‐SW ionization energies for chemisorbed chalcogens on Ni(001)

The ionization energies for a series of chalcogen–nickel clusters were calculated by the self‐consistent‐field Xα scattered‐wave (SCF‐Xα‐SW) method.1 In accord with the most recent theoretical interpretations2,3 of low‐energy electron diffraction (LEED) data, the chalcogen atoms were assumed to be located in a pyramidal position above a cluster of five nickel atoms whose geometry simulated the (001) surface of nickel. It was assumed that each surface Ni atom contributed to bonding with exactly one chalcogen atom. To consider the resulting four‐fold‐site symmetry found in p (2×2) coverages, C4v symmetry functions were employed; to consider the resulting two‐fold‐site symmetry found in c (2×2) coverages, C2v symmetry functions were employed. Thus, by using the same cluster, two different physical coverages were considered by merely changing the symmetry of the basic functions employed.The lone‐pair electrons which occur on the chalcogen atoms in these very localized bonding descriptions were not properly treated due to the muffin‐tin (MT) averaging used in the calculations. In analogy with SCF‐Xα‐SW calculations on H2O,4,5 overlapping of the MT spheres5,6 was employed to improve the consideration of these lone pairs. Significant improvement resulted due to the greater effective directionality obtained.Since the chalocogens are more electronegative than the nickel atoms, charge is removed from the five nickel atoms and is transferred to the chalcogen. In an actual metal the same transfer occurs, except that in the metal the source of the electrons is not confined to just the metal atoms surrounding the chemisorbed species.7 That is, the metal atoms throughout the solid contribute a small electronic charge to the chemisorbed species. To compensate for this, calculations were also performed in which electronic charge was added to the cluster until the core levels were approximately equal to those of an isolated Ni5 cluster.Further variations in the spacings of the atoms allowed within the error limits of the LEED calculations were considered.8 Specifically, vertical displacements of the chalcogens and horizontal displacements of the atoms involved in bonding for two‐fold‐site symmetry were studied.The ionization energies obtained for the various calculations are compared to the INS (ion neutralization spectroscopy) spectra of Hagstrum and Becker for chalcogens on Ni(001).9 Their surface molecule interpretation of their spectra for chemisorbed chalcogens is discussed in view of our calculations. The importance of relating to a physical picture in order to interpret the results of SCF‐Xα‐SW calculations is stressed and illustrated by example.

Symmetrization of low-energy electron diffraction patterns

Using the layer-by-layer approach to low-energy electron diffraction (LEED) the authors explain how to symmetrize the beam scattering matrix for layers. The coincidence structure formed by the layers may be dense or open and may possess any of the 17 two-dimensional space group symmetries. The beams of the electron field become diffracted by the layers in a manner determined by von Laue's diffraction conditions. These conditions turn out to arrange the beams in mutually independent bundles. After establishing the transformation properties of bundles of beams under the point group part of the two-dimensional space group the authors derive a scheme for finding symmetrized combinations of interacting beams. The formalism is applied to the layer-KKR method for LEED calculation. In particular the symmetrization of the beam patterns created by three overlayer structures on surfaces of face-centred cubic crystals are described: the primitive 2*2 structure and the ( square root 2* square root 2)45 degrees structure on the (100) surface together with the ( square root 3* square root 3)30 degrees structure on the (111) surface.

Small Ni-S bond lengths in a c(2 × 2) overlayer of sulfur on Ni (001)

We conclude from the close agreement between low-energy electron diffraction calculations and experiment that sulfur adsorbed in a c (2 × 2) structure on Ni (001) is located 1.30 ± 0.1 Å above the surface in a four- fold coordinated bonding site. This location corresponds to a Ni-S bond length which is smaller than occurs in several bulk compounds or than suggested in a previous calculation by Duke et al.