Three dimensional structure from intensity correlations

We develop the analysis of x-ray intensity correlations from dilute ensembles of identical particles in a number of ways. First, we show that the 3D particle structure can be determined if the particles can be aligned with respect to a single axis having a known angle with respect to the incident beam. Second, we clarify the phase problem in this setting and introduce a data reduction scheme that assesses the integrity of the data even before the particle reconstruction is attempted. Finally, we describe an algorithm that reconstructs intensity and particle density simultaneously, thereby making maximal use of the available constraints.Comment: 17 pages, 9 figure

Extending holographic LEED to ordered small unit cell superstructures

Following on the success of the recent application of holographic LEED to the determination of the 3D atomic geometry of Si adatoms on a SiC(111) p(3x3) surface, which enabled that structure to be solved, we show in this paper that a similar technique allows the direct recovery of the local geometry of adsorbates forming superstructures as small as p(2x2), even in the presence of a local substrate reconstruction.Comment: 10 pages, 5 figures postscript included, revtex, Phys. Rev. B in pres

Patterson Function from Low-Energy Electron Diffraction Measured Intensities and Structural Discrimination

Surface Patterson Functions have been derived by direct inversion of experimental Low-Energy Electron Diffraction I-V spectra measured at multiple incident angles. The direct inversion is computationally simple and can be used to discriminate between different structural models. 1x1 YSi_2 epitaxial layers grown on Si(111) have been used to illustrate the analysis. We introduce a suitable R-factor for the Patterson Function to make the structural discrimination as objective as possible. From six competing models needed to complete the geometrical search, four could easily be discarded, achieving a very significant and useful reduction in the parameter space to be explored by standard dynamical LEED methods. The amount and quality of data needed for this analysis is discussed.Comment: 5 pages, 4 figure

Direct reconstruction of three-dimensional atomic adsorption sites by holographic LEED

We report on the application to measured data of an algorithm for holographic low-energy electron diffraction (LEED), which overcomes the two most important limitations of the technique to date: the ‘‘searchlight’’ effect, which tends to highlight only atoms forward scattered by the adsorbates, and the distorting effects on diffuse LEED intensities due to possible long-range order among the adsorbates. The only experimental input required is a set of the most reliably measured diffuse LEED patterns from normally incident electrons. The algorithm is applied to a set of 11 measured diffraction patterns from a K/Ni(001) surface. A fully three-dimensional image is reconstructed from these data by compensating for the anisotropy of the reference wave by an appropriate scattered-wave kernel. © 1996 The American Physical Society

Influence of the data base and algorithmic parameters on the image quality in holographic diffuse LEED

A detailed examination of the influence of different parameters used in diffuse low-energy-electron-diffraction holography is presented. Effects due to the finite and discrete character of the data that are input to the method's reconstruction algorithm are investigated, as well as the influence of additional parameters introduced both for the removal of experimental Bragg-spots and for the recently proposed correction for the anisotropy of the reference wave. As a test case, we applied the reconstruction algorithm to simulated data of the disordered adsorption system O/Ni(001). Guidelines for the width and resolution of the data base to be used, as well as for the proper selection of algorithmic parameters are deduced, which should hold also for other and unknown systems of disordered atomic adsorption. Using a parameter configuration optimized according to our results, a well-resolved and fully three-dimensional image of the local adsorption geometry is reconstructed from the data

LEED Holography applied to a complex superstructure: a direct view of the adatom cluster on SiC(111)-(3x3)

For the example of the SiC(111)-(3x3) reconstruction we show that a holographic interpretation of discrete Low Energy Electron Diffraction (LEED) spot intensities arising from ordered, large unit cell superstructures can give direct access to the local geometry of a cluster around an elevated atom, provided there is only one such prominent atom per surface unit cell. By comparing the holographic images obtained from experimental and calculated data we illuminate validity, current limits and possible shortcomings of the method. In particular, we show that periodic vacancies such as cornerholes may inhibit the correct detection of the atomic positions. By contrast, the extra diffraction intensity due to slight substrate reconstructions, as for example buckling, seems to have negligible influence on the images. Due to the spatial information depth of the method the stacking of the cluster can be imaged down to the fourth layer. Finally, it is demonstrated how this structural knowledge of the adcluster geometry can be used to guide the dynamical intensity analysis subsequent to the holographic reconstruction and necessary to retrieve the full unit cell structure.Comment: 11 pages RevTex, 6 figures, Phys. Rev. B in pres

Manifestation of quantum chaos on scattering techniques: application to low-energy and photo-electron diffraction intensities

Intensities of LEED and PED are analyzed from a statistical point of view. The probability distribution is compared with a Porter-Thomas law, characteristic of a chaotic quantum system. The agreement obtained is understood in terms of analogies between simple models and Berry's conjecture for a typical wavefunction of a chaotic system. The consequences of this behaviour on surface structural analysis are qualitatively discussed by looking at the behaviour of standard correlation factors.Comment: 5 pages, 4 postscript figures, Latex, APS, http://www.icmm.csic.es/Pandres/pedro.ht

Differential Photoelectron Holography: A New Approach for Three-Dimensional Atomic Imaging

We propose differential holography as a method to overcome the long-standing forward-scattering problem in photoelectron holography and related techniques for the three-dimensional imaging of atoms. Atomic images reconstructed from experimental and theoretical Cu 3p holograms from Cu(001) demonstrate that this method suppresses strong forward-scattering effects so as to yield more accurate three-dimensional images of side- and back-scattering atoms.Comment: revtex, 4 pages, 2 figure

Computation of photoelectron and Auger-electron diffraction II. Multiple scattering cluster calculation PAD2

Abstract In this paper, we describe the second (PAD2) of the suite of computer programs for the calculation of angle-resolved photo-or Auger-electron diffraction intensities, using a concentric-shell algorithm (CSA). The function of the present program is to evaluate the scattering matrix that relates the wavefunction of an electron immediately after its emission from an atomic core to the wavefield that may be detected outside a sample, using an angular-momentum expansion centered on the emitter atom. This program allows that matrix to be evaluated by any of the following schemes (in ascending order of accuracy, and computer requirements): single scattering (SS), outward multiple scattering (OS) and full multiple scattering (MS). c 1998 Elsevier Science B.V