Work function changes produced by chemisorption due to site heterogeneity

A quantum theory of elastic scattering of atoms from crystal surfaces is presented, based on a hard corrugated surface model. It is shown in detail how the rainbow effect arises and determines the diffraction probabilities, such a rainbow effect being the quantum analogon of McClure's classical rainbow. Further topics considered are the influence of a potential well and the reasons why diffraction hardly occurs from metal surfaces. The basis for a possible extension to inelastic scattering is sketched.     

Vibrational dynamics and surface structure of Bi(111) from helium atom scattering measurements

The Bi(111) surface was studied by elastic scattering of helium atoms at temperatures between 118 and 423 K. The observed diffraction patterns with clear peaks up to third order were used to model the surface corrugation using the eikonal approximation as well as the GR method. Best fit results were obtained with a rather large corrugation height compared to other surfaces with metallic character. The corrugation shows a slight enhancement of the surface electron density in between the positions of the surface atoms. The vibrational dynamics of Bi(111) were investigated by measurements of the Debye-Waller attenuation of the elastic diffraction peaks and a surface Debye temperature of (84 ± 8) K was determined. A decrease of the surface Debye temperature at higher temperatures that was recently observed on Bi nanofilms could not be confirmed in the case of our single-crystal measurements.     

Diffraction and selective adsorption in the corrugated hard wall model

Numerical calculations are carried out for the elastic scattering of thermal energy atoms from a perfect crystalline surface with a square unit cell. The surface is treated as an infinitely-repulsive corrugated hard wall with an attractive square well in front of the hard wall. Closed, as well as open and bound, channels are included in the calculation, and multiple scattering effects are treated explicitly. It is concluded from these numerical studies that the single scattering approximation is inadequate, that closed channels must be included in any numerical calculations, and that selective adsorption can readily be understood within the framework of this simple model. Moreover, selective adsorption minima as well as maxima are found in this calculation without the necessity of invoking inelastic processes. The general quantitative agreement of the calculated results with the HeLiF diffraction experiments, the relative ease of handling more complicated corrugated surfaces, and the small amount of computer time required for these calculations suggest that the hard wall model is ideally suited in a parameterization scheme.     

Inversion of atom diffraction intensities for surface structural determination

Atom diffraction from surfaces has proved to be a very useful method for structural studies on surfaces, particularly for incommensurate layers and hydrogen adlayers which are not easily analyzed with LEED. We have developed a rapid method to obtain the surface corrugation function directly from the measured intensities within the hard wall model. This avoids a tedious search in parameter space to determine surface structures and is valid for surfaces whose corrugation amplitudes are below the Rayleigh limit. We will discuss the method and its sensitivity to experimental errors in determining the diffraction intensities as well as its applicability when only a fraction of the allowed diffraction beams are experimentally accessible.     

An exact iterative solution of the atom-surface scattering problem for realistic potentials

A general method, based on high order distorted wave perturbation theory, is developed to obtain exact reflection intensities for low energy atoms scattered by solid surfaces. Resonance shapes are calculated using projection techniques to obtain uniform convergence. Important differences with the hard corrugated wall model arise when the calculations for a corrugated Morse potential are compared with experiment for helium scattered by a Cu(110) surface.     

The scattering of atoms from a corrugated wall model with the GR method in the system He/LiF(001)

In this communication we present a new method, called GR, to calculate the diffraction probabilities of atomic beams from a hard corrugated surface model. The method is applied to the system He/LiF(001). We show that the method gives a convergent solution, within 10^?4 in unitarity, when β₀ ? 0.12, where β₀ is the dimensionless total corrugation amplitude. This limit suggests that the method converges for “any” crystallographic surface of interest. The agreement between the experimental data and the calculated curves is good. From this agreement we conclude that the surface corrugation for He/LiF(001) is cosine-like and the “best” corrugated surface is given.     

Diffraction by a Corrugated Interface. Complete Transformation of an Incident Wave to the Diffraction Lobe

Using the simplest (sinusoidal) corrugation profile in the approximation of absence of losses in the material as an example, we study the regimes of complete transformation of an incident wave to the diffraction lobe by a corrugated metal surface or a corrugated interface of two dielectric media. A numerical-intuitive pattern of appearance and evolution of such regimes with increasing corrugation amplitude is revealed. It is shown that the regimes of complete transformation of an incident wave to the diffraction lobe are possible in both the case of autocollimation and the case of a considerable deviation from it. The examination is based on a numerical method of solving the integral equation by means of a specially created interactive processing system in Visual Fortran.     

Diffraction of helium from a stepped surface: Cu(117) — An experimental study

The scattering of an helium nozzle beam (incident energy 21 and 63 meV) from a copper (117) stepped surface has been studied for crystal temperature ranging from 70 to 773 K. The diffraction pattern from the step array is readily seen. The influence of residual impurity on the surface is carefully discussed. Special attention has been paid to the influence of experimental factors upon peak shapes. True peak amplitudes are deduced. The peak intensities versus temperature and versus incidence angle has been measured. Extrapolation of the intensities to 0 K allows a direct comparison of the data with the prediction of a hard corrugated wall model. A corrugation profile is given which fits quite well the data. Clear evidence for resonances with bound states has been found. Three energy levels of the potential well are thus determined (5.9,4.0, 2.1 meV) which agrees with a Morse or a 3–9 potential.     

Diffraction by a corrugated interface of media: The influence of the corrugation shape and losses in the medium on total transformation regimes

We study regimes of total reflection of a plane wave to the diffraction lobe in the case where the wave is incident on a corrugated metal surface or a corrugated interface of two dielectric media. The purpose is to analyze the influence of both the corrugation shape and losses in the medium on the characteristics of the regimes of total reflection to the diffraction lobe. We consider a number of corrugation profiles differing from the sinusoid by the resonance-region width and the presence of additional elements, namely, (i) the profiles having pair resonance regions with scale of the order of the wavelength, for which qualitatively new diffraction regimes compared with those observed for the sinusoidal interface can be realized due to interaction of waves, and (ii) the profiles comprising small-scale deviations, which can be a model of actual gratings. To study the influence of losses in the problem of scattering from a corrugated interface of dielectrics, the dielectric permittivity is assumed complex. We compare the obtained results with data for a sinusoidal profile and loss-free media. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 5, pp. 391–405, May 2006.     

Hills or hollows? — An ambiguity in the determination of surface corrugation

The diffraction intensities from a corrugated hard wall are shown to be the same for a given corrugation function ζ(x, y) and ?ζ(?x, ?y), provided that coupling to evanescent waves is negligible. To illustrate the consequences of this ambiguity for both surface structure and surface bonding, the corrugation of the adsorbate system Ni(110) + H(1 × 2) determined from Hediffraction measurements is considered. Possible conditions under which the ambiguity could be resolved are discussed.     

On the diffraction of He by a Ni(110) surface

The diffraction of low-energy He atoms by a Ni(110) surface is studied using hard and soft wall models for the elastic scattering. The effects of thermal vibrations and inelastic processes on the He intensities are estimated. It is shown that the experimental spectra imply a corrugation height along the [001] direction that is maximally 0.12 au. A value of 0.30 au, calculated recently within a scheme that assumes the repulsive interaction to be proportional to the electron density of unperturbed Ni(110), leads to “double rainbow” diffraction patterns qualitatively different from those observed.     

Atom-solid scattering: He + graphite basal plane

Theoretical studies of scattering of atoms by solid surfaces and calculations of atomic band structure of adsorbed atoms are presented. Inelastic effects on the intensities of diffracted beams are considered within the framework of the optical model potential. The atom-solid potential used for carrying out the numerical calculation is the sum of Lennard-Jones 12-6 pair potentials for the He-graphite system. Resonances with bound states of adsorbed atoms are shown to enhance the diffraction into some of the open channels and inelastic scattering. The degree of enhancement for a certain process depends on the coupling between that process and the resonant bound state and the coupling between the bound state and the incident beam. For first order bound state resonances, minima in the specular intensity may result from a large increase in some of the diffracted intensities or enhancement of inelastic scattering.     

The determination of the He-Cu interaction potential by atomic beam scattering

Experimental results on the intensity of helium diffraction peaks for the scattering from Cu(110) and for the selective adsorption from Cu(113) and Cu(115) are reported. The usual hard corrugated wall potential is definitely unable to fit the data. While the corrugated Morse potential, recently proposed by Armand and Manson, gives a very much better agreement. The corrugation is found to be dependent upon incident energy, in good agreement with the prediction of Hamann's calculation     

Multiphonon atom-surface scattering from corrugated surfaces: derivation of the inelastic scattering spectrum for diffraction states

A strictly quantum mechanical derivation of the energy and parallel momentum resolved scattering spectrum formula that combines the effects of the diffraction of atoms from corrugated surfaces and multiple inelastic scattering by dispersive phonons is presented. The final result is expressed in the compact and numerically tractable form of a Fourier transform of a cumulant expansion in which each term embodies an interplay between the processes of projectile diffraction and multiphonon scattering to all orders in the respective interaction potentials. The Debye-Waller reduction of the intensities of diffraction peaks is explicitly formulated.     

On the relative strength of He and H2 diffraction from Ag(111)

Under equivalent incident conditions, H₂ diffraction beams on Ag(111) have recently been observed to be about one order of magnitude stronger than He beams. We show that this effect can be attributed to details of the interaction, in particular, the exponential increase of the corrugation amplitude towards the surface. By extending a previously developed theory for the interaction between He and a metal surface, we show that the H₂Ag(111) repulsion is roughly 1.5 times larger than for He. However, the Van der Waals attraction is about three times stronger for H₂, so that the classical turning points of low-energy H₂ particles lie closer to the surface. Because of the stronger corrugation at short distances, H₂ diffraction intensities can be up to an order of magnitude larger than for He.     

A classical path approximation for diffractive surface scattering

The well-known classical path approximation is applied to a calculation of diffraction intensities in the scattering of atoms from a rigid crystal with a soft interaction potential. A general expression is derived for the diffraction intensities which can be applied to potentials with several higher-order terms in the Fourier series. For an uncorrugated Morse potential with a first-order exponential corrugation term an analytic solution is obtained which is compared with the infinite order suddent (IOS) approximation calculations for Ne/W(110) and He/LiF(100). Both approximations are very accurate for the weakly corrugated Ne/W system. For He/LiF the present approximation is more accurate than the sudden (IOS) approximation and has the added advantage of providing an analytic solution. Several improvements are suggested.     

Anomalous mobility of strongly bound surface species: Cl on GaAs(001)-c(8 x 2)

Although strongly bound chemisorbates at low coverage readily diffuse on metal surfaces at 300 K, they generally do not diffuse on semiconductor surfaces because of a large corrugation in the adsorbate-surface interaction potential. Chlorine chemisorbed on the Ga-rich GaAs(001)-c(8x2) surface has anomalously fast diffusion even though the chemisorption state is tightly bound and highly specific. Simple Hartree-Fock total energy calculations suggest that this diffusion of strongly bound adsorbates can occur at 300 K because there are multiple nearly degenerate adsorbate sites.     

The structure of the Pt(100) surface

The atomic arrangement in the first two layers of the clean Pt(100) surface is described from a Fourier analysis of low energy electron diffraction (LEED) intensities. The Fourier transform and sensible platinum-platinum bond lengths require that the top layer is corrugated, the corrugation “step” being approximately 0.4 Å. The structure of the first layer is partly described by a hcp rearrangement from the bulk fcc structure. The rearrangement is related to geometrical and electronic properties of the metals. Some qualitative and quantitative comments are made on the general value of Fourier methods in surface crystallography.