D. Wolf

Multilayer distortion in the reconstructed (110) surface of Au

A new LEED intensity analysis of the reconstructed Au(110)-(1×2) surface results in a modification of the missing row model with considerable distortions which are at least three layers deep. The top layer spacing is contracted by about 20%, the second layer exhibits a lateral pairing displacement of 0.07 A and the third layer is buckled by 0.24 A. Distortions in deeper layers seem to be probable but have not been considered in this analysis. The inter-atomic distances in the distorted surface region show both an expansion and a contraction compared to the bulk value and range from 5% contraction to about 4% expansion.

Structure determination of the reconstructed Au(110) surface

The LEED pattern of the Au(110) surface shows a (1 × 2) and also a (1× 3) superstructure. The (1 × 2) superstructure has been determined by comparison of LEED intensities with model calculations. The missing row model is the most probable model. A minimum of the averaged r-factor, r = 0.36, has been found for 15% contraction of the first layer spacing without atomic displacements in the second layer.

Diffuse LEED intensities of disordered crystal surfaces: III. LEED investigation of the disordered (110) surface of gold

The LEED pattern of clean (101) surfaces of Au show a characteristic (1 × 2) superstructure. The diffuseness of reflections in the reciprocal [010] direction is caused by one-dimensional disorder of chains, strictly ordered into spatial [101] direction. There is a transition from this disordered superstructure to the normal (1 × 1) structure at 420 + 15°C. The angular profiles of the (012) and (01) beam are measured at various temperatures and with constant energy and angles of incidence of the primary beam. The beam profiles are deconvoluted approximately with the instrument response function.

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.

The Ge(001) (2 × 1) reconstruction: asymmetric dimers and multilayer relaxation observed by grazing incidence X-ray diffraction

Abstract Grazing incidence X-ray diffraction has been used to analyze in detail the atomic structure of the (2 × 1) reconstruction of the Ge(001) surface involving far reaching subsurface relaxations. Two kinds of disorder models, a statistical and a dynamical were taken into account for the data analysis, both indicating substantial disorder along the surface normal. This can only be correlated to asymmetric dimers. Considering a statistical disorder model assuming randomly oriented dimers the analysis of 13 symmetrically independent in-plane fractional order reflections and of four fractional order reciprocal lattice rods up to the maximum attainable momentum transfer q z = 3c ∗ ( c ∗ = 1.77 × 10 −1 A −1 ) indicates the formation of asymmetric dimers characterized by R> D = 2.46(5) A as compared to the bulk bonding length of R = 2.45 A . The dimer height of Δ z = 0.74(15) A corresponds to a dimer buckling angle of 17(4)°. The data refinement using anisotropic thermal parameters leads to a bonding length of R D = 2.44(4) A and to a large anisotropy of the root mean-square vibration amplitudes of the dimer atoms ( 〈u 11 2 〉) 1 2 = 0.25 A , ( 〈u 22 2 〉) 1 2 = 0.14 A , ( 〈u 33 2 〉) 1 2 = 0.50 A ). We have evidence for lateral and vertical disp tenth layer below the surface.

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.

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 Beebys 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.

Surface X-ray structure analysis of the TiO2(100)-(1 × 3) reconstruction

Abstract Using grazing incidence surface X-ray diffraction, we have investigated the superstructure of TiO 2 (100)-(1 × 3) (rutile). The analysis of both fractional order superlattice rods and integer order crystal truncation rods (229 independent reflections in total), leads to a structure model which can basically be described as the formation of {110} micro-facets on the surface. In addition, strong lateral and vertical relaxations of the titanium and oxygen atoms exist down to about 9 A below the surface. The surface titanium atoms are found to reside in different environments, namely in three-, five- and six-fold oxygen coordination and in a bridge site. Furthermore, we determined a 40% occupancy of an interstitial site occupied by one titanium atom per (1 × 3) unit cell. The surface stoichiometry is given by the formula TiO 1.68 . Our structure model is significantly different from previous X-ray data [P. Zschack et al., Surf. Sci. 262 (1992) 395], but is in good agreement with spectroscopic experiments and scanning tunneling microscopy investigations.

X-ray structure analysis of the Cr2O3(0001)-(1 × 1) surface: evidence for Cr interstitial

The geometric structure of the unreconstructed Cr2O3(0001) surface has been investigated by surface X-ray diffraction. Our analysis provides evidence that at room temperature the surface is terminated by a disordered surface Cr3+ arrangement. It is characterized by a 2/3 occupation probability of the top layer site and a 1/3 occupation probability of the interstitial site between the first and second O2- layer. This site is unoccupied in the bulk. The total occupation of one Cr3+ ion per (1 × 1) unit cell is in agreement with the requirement for electrostatic stability. The surface Cr3+ ions relax vertically by -6\%. The coordination polyhedra around the top- and second-layer Cr3+ ions are almost identical with the bulk polyhedra. The interstitial site model provides an explanation for the order-disorder [(√3 × √3) → (1 × 1)] and order-order [(1 × 1) → (√3 × √3)] phase transitions at 150 K and 90 K respectively.

Adsorption induced reconstruction of the Cu(110) surface

The formation of the O/Cu(110)-(2 × 1) and H/Cu(110)-(1 × 2) superstructures has been investigated by a LEED beam profile analysis. The oxygen induced reconstruction proceeds at later stages by creation of holes on flat terraces. This could not be observed at the hydrogen induced missing row reconstruction. The formation of the missing row structure proceeds most probably via nucleation at steps and subsequent growth of (1 × 2) islands. The influence of different distributions of steps and islands on beam profiles is discussed.