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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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 : 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

A LEED determination of the structures of Ru(001) and of CO/Ru(001)−(√3 × √3)R30°

The structures of Ru(001) and of the √3 × √3 R30° overlayer of CO on Ru(001) have been determined by LEED I–V measurements and comparison to calculations. Special attention was paid to accurate angular alignment, selection of a well-ordered portion of the surface, and avoidance of beam-induced changes of the CO layer. Five orders of reflexes over a range of 300 eV each were used for the clean surface and 7 orders over 200 eV each for the CO superstructure. For the clean surface, a slight contraction of the first layer spacing (by 2%) was found which gave r-factors of 0.04 (Zanazzi-Jona) and 0.16 (Pendry) for 5 non-degenerate beams. For the CO structure the most probable geometry is the on-top site with spacings d(Ru---C) = 2.0 ± 0.1 Åandd(C---O) = 1.10 ± 0.1 Å (rZJ = 0.21; rP = 0.51). The two threefold hollow and the bridge sites can be clearly excluded

Züchtung von orientierten lithiumflourid-einkristallen aus der dampfphase

A high vacuum oven was constructed to grow LiF single crystals from the vapor phase by the vertical pulling method. Using a special crucible top it is possible to grow oriented single crystals of 23 mm diameter and 70 mm length. At a temperature of about 150 °C above the melting point the maximum pulling rate was found to be 8 mm/h. The purification effect of the sublimation was investigated for Na+-, K+-, Ca++-ions and it was found that the concentration of these impurities is of the order of 10-6, except for sodium for which the purification is much less effective