Atomic structure of GaP (110) and (111) faces

LOW-ENERGY electron diffraction (LEED) has become the most successful technique in surface crystallography1, but because of the complexity of the surface-electron scattering interactions, analyses of LEED data are still conducted on a trial-and-error basis: a direct-inversion method for treating LEED intensity data remains an attractive goal2. Building on recent theoretical and experimental developments in electron holography from surface structures3–16, we show here that three-dimensional images with atomic resolution can be obtained by a direct transform of conventional LEED intensity spectra.

The surface reconstructions of the (100) crystal faces of iridium, platinum and gold: I. Experimental observations and possible structural models

We report on the temperature dependent low energy electron diffraction (LEED) studies of 12 nm epitaxial Sr3Ir2O7(001) thin films. The Debye temperature has been extracted from the temperature-dependence of LEED intensity at elevated temperatures and different electron kinetic energies. For the most surface sensitive LEED, obtained at the lowest electron kinetic energies, the extracted surface Debye temperature is 270 ± 22 K, which is much lower than the 488 ± 40 K Debye temperature obtained using higher electron kinetic energies. Surprisingly, the LEED diffraction intensity, at the lowest electron kinetic energies, increases rather than decreases, with increasing sample temperatures up to about 440 K. This anomalous behavior has been attributed to the reduction of the lattice vibrational amplitudes along the surface normal. This damping of the normal mode vibrations with increasing temperature results from the enhanced electronic screening via thermally activated carriers. This scenario is corroborated by the transport measurement, showing that Sr3Ir2O7is a narrow band Mott insulator with a band gap of about 32 meV. We have identified criteria for finding anomalous scattering behavior in other transition metal oxide systems.

The structure of Rh(111)(2 × 2)-3CO from LEED intensities: Simultaneous bridge and near-top adsorption in a distorted compact hexagonal CO overlayer

The surface structure of Bi(111) was investigated by low-energy electron diffraction (LEED) intensity analysis for temperatures between 140 and $313\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and by first-principles calculations. The diffraction pattern reveals a $(1\ifmmode\times\else\texttimes\fi{}1)$ surface structure and LEED intensity versus energy simulations confirm that the crystal is terminated with a Bi bilayer. Excellent agreement is obtained between the calculated and measured diffraction intensities in the whole temperature range. The first interlayer spacing shows no significant relaxation at any temperature while the second interlayer spacing expands slightly. The Debye temperatures deduced from the optimized atomic vibrational amplitudes for the two topmost layers are found to be significantly lower than in the bulk. The experimental results for the relaxations agree well with those of our first-principles calculation.

Band structure treatment of low energy electron diffraction intensities

Multiple scattering effects in the fourier transform deconvolution procedure for leed analysis

Four aspects of low-energy electron diffraction (LEED) have been investigated: interpretation of spot patterns to determine the surface unit cell and possible ambiguities, development of a photographic method for measuring angles of incidence and determining alignment of the LEED instrument, study of reliability factors used for intensity analysis, and justification for equivalent beam averaging. The interpretation of LEED spot patterns to determine the geometry of the surface unit cell can be involved when there are several symmetrically equivalent structural domains contributing to the pattern. Complex patterns can be deciphered by the algorithm described in Chapter II. The algorithm determines a surface unit cell that is often unique but not always, as where a p(2 x 2) pattern from a fcc(111) surface can be produced by a true (2 x 2) overlayer or by three domains of a (2 x 1) structure. This ambiguity arises on surfaces with 6m symmetry, such as fcc(111) and hcp(0001), for spot patterns with threefold rotational symmetry. In Chapter III, a broadly applicable photographic method for measuring angles of incidence and determining the alignment of the LEED instruments is described. Two published methods for determining the angle of incidence are special cases of this general procedure. The procedure extends the photographic methods and facilitates the verification of the alignment of the components of the LEED instrument. Reliability factors are used to evaluate correspondence between computed and observed LEED intensity spectra. Zanazzi and Jona, Pendry, and Sobrero and Weinberg have proposed reliability factors that are examined in Chapter IV. Chapter V provides a theoretical analysis and shows that averaging over momentum space gives the best resolution of the surface structure while energy averaging smears out information in the intensity spectra. Chapter VI provides a theoretical basis for the procedure of equivalent beam averaging, which provides a first-order correction to LEED intensities for systematic error due to angular misalignment of the incident beam and corrects for misorientation (where the actual surface plane is at a slight angle to the desired crystal plane). The potential of higher-order corrections is discussed.

Irrationally related lattices and LEED intensities

Analysis of dynamical low-energy electron diffraction mechanisms

Growth and crystalline structure of Co layers on Cu(0 0 1)

Growth and surface structure of vanadium oxide on anatase (0 0 1)

We report on the formation of ultrathin Co oxide films by oxidation of correspondingly thin Co films epitaxially grown on the unreconstructed---i.e., metastable---$(1\ifmmode\times\else\texttimes\fi{}1)$ phase of Ir(100), on both the clean surface and the surface precovered with half a monolayer of oxygen. As investigated by low-energy electron diffraction patterns and intensities and by atomically resolved images from scanning tunneling microscopy (STM) the oxide forms mainly in its fcc-type rocksalt structure CoO. This is with exception of the submonolayer range and the surface precovered with oxygen for which the ${\mathrm{Co}}_{3}{\mathrm{O}}_{4}$ spinel-structured phase develops. Rather unusual, the CoO films appear in the polar (111) orientation and so, though the hexagons are slightly distorted, should become increasingly instable with growing thickness. However, STM images recorded under special conditions indicate that there are oxygen vacancies which lead to charge compensation and so may contribute to stabilize the (111) orientation. Also, STM retrieves a considerable buckling of cobalt layers which is inevitable when fcc(111) layers are accommodated on an fcc(100) substrate.

An error-analysis procedure that gives statistically significant error estimates for surface-structure parameters extracted from analyses of measured low-energy electron and positron diffraction (LEED and LEPD) intensities is proposed. This procedure is applied to a surface-structure analysis of Cu(100) in which experimental data are simulated by adding Gaussian-distributed random errors to the calculated intensities for relaxed surface structures. Quantitative expressions for the variances in the surface-structural parameters are given and shown to obey the expected scaling laws for Gaussian errors in the experimental data. The procedure is shown to describe rigorously parameter errors in the limit that the errors in the measured intensities are described by uncorrelated Gaussian statistics. The analysis is valid for structure determinations that are of sufficient quality to admit errors that have magnitudes within the region of convergence of a linear theory that relates perturbations of diffracted intensities to perturbations in structural parameters. It is compared with previously proposed error-estimation techniques used in LEED, LEPD, and x-ray intensity analyses.

Origin of 3×3 diffraction on the Sn 1− xSi x/Si(1 1 1) [formula omitted] surface