Low-energy electron diffraction from disordered surfaces

Model calculations are presented of L E E D intensities diffracted by a onedimensionally disordered overlayer adsorbed on a well ordered substrate. Multiple scattering amplitudes are calculated by an extension of Beeby's multiple scattering method. The surface layers are divided into overlapping configurations of atoms, the diffraction of each of which is described by individual scattering amplitudes. In this way the surrounding of each adsorbed atom is divided into two parts: the immediate vicinity, in which multiple scattering is treated self-consistently, and the outer region which is represented by an averaged Τ matrix. The results of the model calculations indicate that the intensities are not correctly described if only averaged Τ matrices are used, and that in a first approximation the half-widths of the diffuse streaks observed in the experiment can be analysed using the kinematic theory

Determination of domain distribution by analysis of LEED beam profiles

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The domain matrix method: a new calculation scheme for diffraction profiles

A new calculation scheme for diffraction profiles is presented that combines the matrix method with domain approaches. Based on a generalized Markov chain, the method allows the exact solution of the diffraction problem from any one-dimensionally disordered domain structure. The main advantage of this model is that a domain statistic is used instead of a cell statistic and that the domain-length distribution can be chosen independently from the domain-type stacking. A recursive relation is derived for the correlations between the domains and a double recursive algorithm, not reducible to a simpler one, is obtained as solution. The algorithm developed here is referred to as the domain matrix method. Results and applications of the new approach are discussed

Diffuse LEED intensities of disordered crystal surfaces : II. Multiple scattering on disordered overlayers

The diffraction of low energy electrons from disordered overlayers adsorbed on ordered substrates is treated theoretically by an extension of Beeby's multiple scattering method. A lattice gas model is assumed for the disordered adsorbate layer. Multiple scattering within a certain area around each atom — each atom of the overlayer and within the ordered substrate — is treated self-consistently, the remaining contributions to the total scattering amplitude being averaged. The theory can be used in the limiting cases of random distribution and of long range order within the adsorbate layer

Diffuse LEED intensities of disordered crystal surfaces : IV. Application of the disorder theory

The principles of the statistical disorder theory are discussed briefly. The theory is applied to a model of the disordered (101)Au surface with the characteristic (1 × 2) supersstructure. A fit procedure is described, by which the experimental angular intensity profiles are used directly to determine the disorder parameters and the interaction energies between the chains of surface atoms

Diffuse LEED intensities of disordered crystal surfaces : I. Correlations between statistics and multiple diffraction

It is shown that the diffraction of slow electrons from disordered crystal surfaces is correlated with the problem of thermodynamical statistics. The correlation functions are completely determined by the self-energies and interaction energies of neighboring complexes. These quantities solve the problem of a-priori probabilities and the cooperative phenomenon of correlation functions of these complexes. If the calculation of a certain set of multiple scattering amplitudes is possible, the remaining problem of determining the diffuse LEED pattern becomes solvable. The calculation of angular beam profiles follows the same lines as already described for the kinematic theory of X-ray diffraction

Resolution correction for surface X-ray diffraction at high beam exit angles

Owing to the two-dimensional periodicity of a superstructure on the crystal surface, the intensity in reciprocal space is continuously distributed along rods normal to the sample surface. The analysis of rod scans in surface X-ray diffraction provides information about the structure parameters normal to the sample surface. For high resolution to be achieved, the measurements must extend to momentum transfers q that are as large as possible. At large exit angles, the conventional Lorentz factor must be modified to take account of the finite aperture of the detector and the continuous intensity along the lattice rod. For two types of Z-axis diffractometer used in surface X-ray crystallography, an analytical expression for the resolution correction of rod-scan intensity data has been developed. It takes into account an anisotropic detector resolution T(, ), the finite width of the diffracted beam and the primary-beam divergence parallel to the sample surface, . The calculation of the convolution functions is simplified by a projection onto the q = 0 plane. The effects of different detector settings and the influences of the primary-beam divergence and the sample quality on the measured intensity are demonstrated for several examples