## No full-text available

To read the full-text of this research,

you can request a copy directly from the authors.

Total cross sections for He scattering from isolated imperfections on surfaces are calculated using the Sudden approximation, and in some cases also by a numerically exact, time‐dependent quantum‐mechanical wave packet method. Systems studied include: CO adsorbates on Pt(111); mono‐, di‐, and trivacancies on Pt(111). The main results are: (1) the incidence angle and energy dependence of the cross section for He/[Pt(111)+CO] are very sensitive to the CO distance from the Pt plane. Interactions with the adsorbate image have little effect on the cross section. (2) The cross sections for clusters of vacancies are given within 10% or better, by the geometric sum of the monovacancy cross sections, the latter being treated as circles centered at each monovacancy. (3) The dependence of the cross section on the energy is sufficiently sensitive to distinguish between the ‘‘electron density hole’’ and ‘‘electron density hump’’ models for vacancies and vacancy clusters. (4) The Sudden approximation compares well with the exact quantum‐mechanical results at typical experimental energies, when the incidence angle is not too far from the normal. These results indicate that experimental measurements of He scattering cross sections as a function of energy and incidence angle, combined with Sudden or wave packet scattering calculations, can provide detailed information on surface defects and their interactions with gas‐phase atoms.

To read the full-text of this research,

you can request a copy directly from the authors.

... Theoretical studies by Gerber and co-workers [16][17][18][19] utilizing both time independent (Sudden approximation) and time-dependent methods (quantum wave-packets), have analyzed the calculated angular distribution and specular peak attenuation. These authors have been able to identify connections between the features of the distribution and the attenuation, and microscopic characteristics related to the surface defects. ...

... Due to the inversion symmetry of the Heptamer about the y-z plane, the inflexion points appear as symmetric pairs along the x-axis. Each such pair gives rise to corresponding symmetrically located Rainbow peaks, as is clear from eq. (19). The similarity between η(x) and the Heptamer's isopotential ( fig. ...

... However, using the quantitative predictions of eqs. (18,19), we identify the peaks at ∆Kx = ±0.33 bohr −1 and the hidden peaks at ∆Kx = ±0.13 bohr −1 as R1 and R2 ...

The angular intensity distribution of He beams scattered from compact clusters and from diffusion limited aggregates, epitaxially grown on metal surfaces, is investigated theoretically. The purpose is twofold: to distinguish compact cluster structures from diffusion limited aggregates, and to find observable {\em signatures} that can characterize the compact clusters at the atomic level of detail. To simplify the collision dynamics, the study is carried out in the framework of the sudden approximation, which assumes that momentum changes perpendicular to the surface are large compared with momentum transfer due to surface corrugation. The diffusion limited aggregates on which the scattering calculations were done, were generated by kinetic Monte Carlo simulations. It is demonstrated, by focusing on the example of compact Pt Heptamers, that signatures of structure of compact clusters may indeed be extracted from the scattering distribution. These signatures enable both an experimental distinction between diffusion limited aggregates and compact clusters, and a determination of the cluster structure. The characteristics comprising the signatures are, to varying degrees, the Rainbow, Fraunhofer, specular and constructive interference peaks, all seen in the intensity distribution. It is also shown, how the distribution of adsorbate heights above the metal surface can be obtained by an analysis of the specular peak attenuation. The results contribute to establishing He scattering as a powerful tool in the investigation of surface disorder and epitaxial growth on surfaces, alongside with STM. Comment: 41 pages, 16 postscript figures. For more details see http://www.fh.huji.ac.il/~dani

... Some efforts have also been directed to the dependence on the scattering parameters, such as incidence energy and angle. These cross section studies have attracted significant theoretical interest, [7][8][9][10][11][12][13][14] concentrating almost exclusively on the dependence on the scattering parameters. Relatively little attention has been paid to the inverse question of the information content of the cross section. ...

... First we shall examine the relative role of the long range dispersion forces vs the short range repulsive part of the potential in determining the interaction of a He atom with an adsorbed defect. It is a well-recognized fact in surface scattering theory, [24,7,11,6] that the magnitude of the total cross section of a defect is dominated by small angle deflections caused by the long range forces. We will show that they are mostly effective in setting the magnitude of the cross section, whereas at least for the high-energy regime the short-range forces tend to determine its qualitative shape. ...

... However, due to the assumption (6), the Sudden approximation is particularly useful for the evaluation of specular intensities at incidence angles close to the specular direction, as confirmed by comparison with numerically exact wave packet calculations. [11] In the context of the present work, only the specular intensities are required (which are obtained by setting q ′ = q in eq. (7)), which constitutes the most favorable condition for the Sudden. ...

The information content and properties of the cross section for atom scattering from a defect on a flat surface are investigated. Using the Sudden approximation, a simple expression is obtained that relates the cross section to the underlying atom/defect interaction potential. An approximate inversion formula is given, that determines the shape function of the defect from the scattering data. Another inversion formula approximately determines the potential due to a weak corrugation in the case of substitutional disorder. An Optical Theorem, derived in the framework of the Sudden approximation, plays a central role in deriving the equations that conveniently relate the interaction potential to the cross section. Also essential for the result is the equivalence of the operational definition for the cross section for scattering by a defect, given by Poelsema and Comsa, and the formal definition from quantum scattering theory. This equivalence is established here. The inversion result is applied to determine the shape function of an Ag atom on Pt(111) from scattering data. Comment: 29 pages, 9 Postscript figures, more info available at http://www.fh.huji.ac.il/~dani

... We derive Eq. (15). This requires first the evaluation of Eq. (14). The task at hand is the calculation of the probabilities Pr(z j ; R 1 , R 2 ), to observe a given height difference between points located at R 1 and R 2 on the surface. ...

... Collecting Eqs. (11), (14), (17), we obtain: ...

A theoretical study is made on He scattering from three fundamental classes of disordered ad-layers: (a) Translationally random adsorbates, (b) disordered compact islands and (c) fractal submonolayers. The implications of the results to experimental studies of He scattering from disordered surfaces are discussed, and a combined experimental-theoretical study is made for Ag submonolayers on Pt(111). Some of the main theoretical findings are: (1) Structural aspects of the calculated intensities from translationally random clusters were found to be strongly correlated with those of individual clusters. (2) Low intensity Bragg interference peaks appear even for scattering from very small ad-islands, and contain information on the ad-island local electron structure. (3) For fractal islands, just as for islands with a different structure, the off-specular intensity depends on the parameters of the He/Ag interaction, and does not follow a universal power law as previously proposed in the literature. In the experimental-theoretical study of Ag on Pt(111), we use first experimental He scattering data from low-coverage (single adsorbate) systems to determine an empirical He/Ag-Pt potential of good quality. Then, we carry out He scattering calculations for high coverage and compare with experiments. The conclusions are that the actual experimental phase corresponds to small compact Ag clusters of narrow size distribution, translationally disordered on the surface. Comment: 36 double-spaced pages, 10 figures; accepted by J. Chem. Phys., scheduled to appear March 8. More info available at http://www.fh.huji.ac.il/~dani/

... Comsa and coworkers have developed an interesting approach for the characterization of adsorption on terraces versus defect sites based on measurements of the cross section for He scattering, and applied it to the case of CO adsorption on platinum surfaces with planes of orientations slightly off the (111) plane [191,192]. The large scattering cross section seen with small amounts of carbon monoxide adsorbed on those surfaces, $ 250 Å 2 (much larger than expected from the Van der Waals radii of He and CO), was taken as an indication of preferential CO occupation at defect sites [193]. ...

In this review we survey the contributions that molecular beam experiments have provided to our understanding of the dynamics and kinetics of chemical interactions of gas molecules with solid surfaces. First, we describe the experimental details of the different instrumental setups and approaches available for the study of these systems under the ultrahigh vacuum conditions and with the model planar surfaces often used in modern surface-science experiments. Next, a discussion is provided of the most important fundamental aspects of the dynamics of chemical adsorption that have been elucidated with the help of molecular beam experiments, which include the development of potential energy surfaces, the determination of the different channels for energy exchange between the incoming molecules and the surface, the identification of adsorption precursor states, the understanding of dissociative chemisorption, the determination of the contributions of corrugation, steps, and other structural details of the surface to the adsorption process, the effect to molecular steering, the identification of avenues for assisting adsorption, and the molecular details associated with the kinetics of the uptake of adsorbates as a function of coverage. We follow with a summary of the work directed at the determination of kinetic parameters and mechanistic details of surface reactions associated with catalysis, mostly those promoted by late transition metals. This discussion we initiate with an overview of what has been learned about simple bimolecular reactions such as the oxidation of CO and H2 with O2 and the reaction of CO with NO, and continue with the review of the studies of more complex systems such as the oxidation of alcohols, the conversion of organic acids, the hydrogenation and isomerization of olefins, and the oxidative activation of alkanes under conditions of short contact times. Sections 6 and 7 of this review deal with the advances made in the use of molecular beams with more realistic models for catalysis, using surfaces comprised of metal nanoparticles dispersed on the oxide surfaces used as catalyst support and high-flux beams to approach the pressures used in catalysis. The next section deals with the study of systems associated with fields other than catalysis, mainly with the etching and oxidation of semiconductor surfaces and with the chemistry used to grow thin solid films by chemical means (chemical vapor deposition, CVD, or atomic layer deposition, ALD). We end with a personal assessment of the past accomplishments, present state, and future promise of the use of molecular beams for the study of the kinetics of surface reactions relevant to practical applications.

... This has been criticized for adatom pairs [13]. For other systems [8,14,15] it is strongly corroborated by test cases. We accepted it here, by assumption, as a method valid for all systems, for sufficiently low coverages. ...

We propose a novel method to measure the fractal dimension of a submonolayer metal adatom system grown under conditions of limited diffusivity on a surface. The method is based on measuring the specular peak attenuation of He atoms scattered from the surface, as a function of incidence energy. The (Minkowski) fractal dimension thus obtained is that of contours of constant electron density of the adatom system. Simulation results are presented, based on experimental data. A coverage dependent fractal dimension is found from a two-decade wide scaling regime.

... While the original formulation of the SA applied to periodic surfaces, it was extended by Gersten et al. to deal with scattering from disordered surfaces [10]. The SA was subsequently used to study a large variety of disordered systems, such as isolated adsorbates on crystalline surfaces [11][12][13][14], mixed overlayers of Xe+Ar [15,12] and Xe+Kr on Pt(111) [16], randomly corrugated hard walls [17], vacancies and CO adsorbates on Pt(111) [18,19], percolation lattices of substitutionally disordered Xe+Kr monolayers [20], amorphous mixed monolayers and liquids [21], compact islands and diffusion limited aggregates [22][23][24], and fractals [25,26]. Common to many of these studies was the achievement of detailed insight into the collision dynamics, the prediction and understanding of interesting features in the angular intensity distribution of the scattered atoms. ...

The Sudden Approximation (SA) for scattering of atoms from surfaces is
generalized to allow for double collision events and scattering from
time-dependent quantum liquid surfaces. The resulting new schemes retain the
simplicity of the original SA, while requiring little extra computational
effort. The results suggest that inert atom (and in particular He) scattering
can be used profitably to study hitherto unexplored forms of complex surface
disorder.

This is the story of a career in theoretical chemistry during a time of dramatic changes in the field due to phenomenal growth in the availability of computational power. It is likewise the story of the highly gifted graduate students and postdoctoral fellows that I was fortunate to mentor throughout my career. It includes reminiscences of the great mentors that I had and of the exciting collaborations with both experimentalists and theorists on which I built much of my research.
This is an account of the developments of exciting scientific disciplines in which I was involved: vibrational spectroscopy, molecular reaction mechanisms and dynamics, e.g., in atmospheric chemistry, and the prediction of new, exotic molecules, in particular noble gas molecules.
From my very first project to my current work, my career in science has brought me the excitement and fascination of research. What a wonderful pursuit!
Expected final online publication date for the Annual Review of Physical Chemistry, Volume 72 is April 20, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

This document is part of Part 4 'Adsorbate Species on Surfaces and Adsorbate-Induced Surface Core Level Shifts' of Subvolume A 'Adsorbate Layers on Surfaces' of Volume 42 'Physics of Covered Solid Surfaces' of Landolt-Börnstein - Group III Condensed Matter. It contains: CO adsorption on fcc, bcc, hcp and simple cubic metal surfaces; CO adsorbed on relevant binary systems modelled by ultra-thin metal overlayers.

In the present work the most recent studies in the area of quantum mechanical applications to surface chemistry are reviewed, with emphasis on those methods and calculations not treated in preceding Chapters of this book. Results of ab initio, density functional, semiempirical, and other methods are critically discussed particularly with respect to the correlation between theory and experiment.

We propose a novel method to measure the fractal dimension of a submonolayer metal adatom system grown under conditions of limited diffusivity on a surface. The method is based on measuring the specular peak attenuation of He atoms scattered from the surface, as a function of incidence energy. The (Minkowski) fractal dimension thus obtained is that of contours of constant electron density of the adatom system. Simulation results are presented, based on experimental data. A coverage dependent fractal dimension is found from a two-decade wide scaling regime.

This document is part of Subvolume A2 `Adsorbed Layers on Surfaces. Part
2: Measuring Techniques and Surface Properties Changed by Adsorption' of
Volume 42 `Physics of Covered Solid Surfaces' of Landolt-Börnstein
- Group III Condensed Matter.

This document is part of Subvolume A2 `Adsorbed Layers on Surfaces. Part
2: Measuring Techniques and Surface Properties Changed by Adsorption' of
Volume 42 `Physics of Covered Solid Surfaces' of Landolt-Börnstein
- Group III Condensed Matter.

Atomic beam techniques are presently being used in many branches of surface physics such as studies of the particle-surface physisorption potential, surface structure, surface phonons, nucleation and growth on metal and insulator surfaces, surface diffusion and accommodation and sticking of molecules. This review concentrates on diffractive phenomena from surfaces, which up to now were investigated mainly with helium. The theoretical background for diffraction calculations is outlined and representative examples of different applications are given. The main subjects covered are: structural determinations of chemisorbed and physisorbed systems, investigations of disordered surfaces, selective adsorption resonances, diffusion and nucleation studies and investigations of growth and phase transitions on surfaces. Diffraction results obtained with Ne, Ar, and are also summarized.

We present a general discrete Bessel transform based on the Bessel functions of the first kind for any integer or half-integer order ν. This discrete Bessel transform shares a number of similitudes with the discrete Fourier transform in that we have discretized both the coordinate and momentum continuums, and since the discrete transform of order 1/2 exactly specializes to the discrete sine Fourier transform. We demonstrate that our discrete Bessel transform is comparable to the discrete Fourier transform in terms of both the accuracy and the efficiency. Indeed, our discretization procedure provides an optimal sampling grid for Bessel functions of the first kind, and the accuracy of the transform converges exponentially as the number of grid points is increased. We successfully apply the optimally discretized Bessel methodology to the harmonic oscillator in both cylindrical and spherical coordinates.

This paper shows that the He diffraction specular intensity does not depend in a simple, predictable way on single statistical parameters describing the surface defect lateral distribution. In particular it shows the lack of correlation between specular intensity and the geometrical overlap of single defect cross sections, a parameter widely used in the literature for a qualitative interpretation of He atom diffraction data. An approach to the problem of surface structure determination is attempted on the basis of a cluster expansion of the scattering matrix at reflection angle.

Calculations are reported on He scattering from clusters of different numbers of CO molecules adsorbed in an ordered way on flat Pt(111) surfaces. The sudden approximation is used to obtain both the integral cross sections for scattering by adsorbates and the angular intensity distribution of the scattered atoms. The cross section values have been discussed on the basis of the Comsa and Poelsema overlap approach that, already successfully tested for clusters of vacancies, has been found to hold good even in the case of molecular adsorbates as surface defects. The angular intensity distribution curves show Fraunhofer interferences and rainbow maxima, as in the case of isolated adsorbates, and periodic diffraction peaks caused by the ordered structure of CO molecules on the Pt surface. Basically it has been demonstrated that from these peaks it is possible to obtain information on the geometric structure of the adlayer if the adsorbates form a two-dimensional crystal on the surface.

On the basis of the sudden approximation, a theoretical analysis has been performed on He scattering from two CO molecules adsorbed on Pt(111) at different mutual distances dCO (10 au≲dco≲ 50 au) and for the incident collision wavenumber kz from 1.0 to 4.0 bohr−1. The values obtained for the cross section Σ show that Comsa and Poelsema's hypothesis of cross-section geometric overlap (GO) breaks down. In fact, in a dCO range of nearly 22 au, and at all collision energies, the Σ values are higher than twice the cross section of the isolated adsorbed CO. Obviously this finding is not consistent with the GO hypothesis: the corresponding overlap between the two CO should be negative and therefore meaningless.

We employ the multiple-scattering expansion of the transition operator to evaluate the role of multiple collisions in elastic scattering of atoms from adsorbates on solid surfaces at superthermal energies (E ≳ 0.1 eV). The adsorbatesurface system is treated as a rigid-body model in the present work. Mixed-species periodic overlayers are considered as well as two-layer systems simultaneously involving periodic and non-periodic configurations. The calculated scattering patterns show rich structure due to the interference between waves scattered from different adsorbates. The enhanced sensitivity provided by wavevectors k ≳ 10 Å−1 could be exploited for surface characterization by scattering experiments. We find that the single-collision approximation qualitatively reproduces the trends of the intensity with respect to final angles. Double-collision terms are evaluated with the pole approximation and found to play an important role in large transfers of parallel momentum.

Close-coupled calculations of atom-adsorbate total cross sections have been carried out for HeXe/Ag and HeCO/Pt, within the hard-wall approximation. It was found that previous calculations within the renormalized distorted wave Born approximation give reasonable results at higher collision energies. At low energies and small angles of incidence, substrate-mediated van der Waals forces contribute up to 10% to the cross section and are thus experimentally measurable.

Since the specular intensity and scattering matrix are related by a quadratical relation, a term is present in the intensity which scales as the square of the defect surface coverage. One can directly account for the term in every calculation which provides the scattering matrix. The explicit formulas under the sudden approximation are reported and their implications discussed. Any relation between cross-section and specular intensity which does not take it into account is demonstrated to be inadequate even at very low coverage values. Consequently cross-sections calculated on phenomenological grounds cannot give correct information on surface structure.

The theoretical interpretation of experimental results on He scattering from metal adatoms epitaxially grown on metal substrates makes use, in general, of an interaction potential that, as far as the He-adatom interaction is concerned, is a pairwise sum of Lennard-Jones (VLJ) terms. This approach results in more corrugated metal surfaces than expected on the basis of both experimental data and qualitative considerations on the contribution of the electron densities of the metal adatoms to the repulsive part of the interaction potential. The present work suggests a very simple way to significantly reduce or eliminate the surface corrugation by averaging the He-adsorbate potential over a unit cell of the substrate lattice. The so obtained potential (VAV) was compared with VLJ for the HeAg/Pt(111) colliding system on the basis of turning point surfaces, specular and diffractive intensities vs. surface coverage and angular intensity distribution of scattered atoms, calculated under the sudden approximation. These data show that VAV, although too simple to correctly reproduce all the features of the He-adatom interaction, could represent a useful tool in the study of the growth of metal adlayers.

We present a three‐dimensional, fully quantum study of the diffractive scattering of He from isolated CO adsorbates on Pt(111). The nonspecular scattered He distributions are dominated by quantum interference effects such as Fraunhofer diffraction and rainbows. The determination of the final scattering distributions hence requires an exact treatment of the translational motion of the helium atom. Our wave packet simulations are free of dynamical approximations in the gas phase and provide the whole diffractive scattering distributions. One important motivation of this work was to assess the adequacy of a reduced dimensionality treatment to derive the geometrical parameters of the adsorption. It is found that, even if the interaction is characterized by azimuthal symmetry, a two‐dimensional Fourier treatment is not sufficient to give reasonable estimates of both the size of the adsorbate and its position above the surface. We further investigate the scattering distributions as a function of the collision energy and discuss the appropriateness of a pure Fraunhofer model to interpret the results and derive geometrical parameters.

A projected continuum formulation for time‐independent quantum scattering from a continuum of channels is presented and applied to atomic scattering from disordered surfaces. Projecting out the channel continua gives rise to explicitly constructed optical potentials for the coherently diffracted scattering amplitudes, while the continuum diffuse scattering contribution is obtained in terms of these wave functions. Numerical application is made to atomic scattering from weakly corrugated disordered surfaces, for which a truncated set of coupled equations can be used within which the theory is shown to be unitary. The occurrence of a new phenomenon of disorder‐induced sticking on rigid surfaces is demonstrated and comparison with phonon‐induced sticking is made. These new disorder‐induced sticking processes are shown to have very different energy dependence than phonon‐induced sticking, with strong resonant sticking and oscillatory behavior seen at low incident energies.

The properties of different definitions of the cross section for helium scattering of perfectly diffuse adsorbates on highly corrugated surfaces have been investigated experimentally. For the adsorption of CO on Rh(311) we found that the normalized cross section associated with each diffraction beam scatters strongly with the angle of incidence, the incident energy, and the intensity of the diffraction beam. In particular, our results demonstrate that, contrary to the suggestion of a recent work, no simple relation exist between the intensity of a given diffraction beam and the associated cross section. On the other hand, a total cross section defined by including all diffraction beams was found to vary smoothly as a function of incident parameters, in a way similar to that observed on low corrugated surfaces and in gas phase scattering. © 2000 American Institute of Physics.

Molecular beam scattering experiments have emerged in recent years as an important tool for investigating structural disorder on surfaces. This paper gives a brief overview of the developing theory of scattering from disordered surfaces, which is essential for the interpretation of such experiments, and presents new results on this topic. A brief discussion is given of the methods developed for calculating atom scattering disordered systems (e.g. time-dependent quantum wavepackets; distorted-wave approximation; sudden approximation) and of simulations of disordered surface structures (by Monte Carlo or molecular dynamics). The paper focuses, however, on features of the scattering intensities and their relation to disordered surface structures. The main topics include: (1) The concept of cross section for He scattering by an isolated defect on a surface, and its application to the study of interactions between defects. Comsa and his coworkers developed this into a most powerful tool for studying surface defects and defect interactions. We examine the assumptions involved, and the information contained in the measured cross section on defect shape and geometry, and on He/defect potentials. (2) Angular intensity distribution for He scattering from isolated defects; defect rainbow and Fraunhofer effects. (3) He scattering from periodic, substitutionally disordered surfaces. New results are presented on He scattering from mixed Xe + Kr monolayers on Pt(111), comparing theory with the experiments of Comsa et al. The results indicate that these monolayers are indeed periodic and (almost) perfectly substitutionally disordered for all Xe: Kr ratios. Rainbow intensity features due to the substitutional disorder are calculated and analyzed. (4) He scattering from amorphous mixed monolayers, with application to Xe + Ar mixtures on Pt(111). (5) Atom scattering from liquid surfaces, e.g. structure and dynamics of liquid Hg probed by Ar scattering.The paper concludes by emphasizing some of the outstanding open problems in the field.

The scattering of He atoms from O2 molecules adsorbed on a flat surface is studied, and comparison is made of models in which the O2 is respectively perpendicular and parallel to the surface. The sudden approximation is used to calculate both the angular intensity distribution of the scattered atoms at fixed incidence energy, and the integral cross section for scattering by the adsorbate as a function of collision energy. Significant differences are found in both the cross sections and the angular intensities between scattering by the parallel and by the perpendicular adsorbate. The possible use of He scattering to study adsorbate orientation is discussed in the light of the results.

The sudden approximation can be the foundation of a code for performing inexpensive calculations on light particle scattering from huge surface systems. The paper describes the mathematical framework and a sample code which can be used to perform sudden calculations either in the semiclassical approximation or in an exact numerical approach. Also a straightforward extension to the treatment of inelastic collisions in a discrete set of excited states is derived and implemented. 2001 Elsevier Science B.V. All rights reserved.

A theoretical analysis of the hypothesis of geometric overlap (GO) among cross sections has been performed by studying He scattering from two vacancies arranged on Pt(111) at mutual distances dvac ranging from 5.24 to 52.4 au and for collision wave-numbers kz = 1.0, 2.0, 3.0, and 4.0 bohr−1. Comparison between quantum cross sections and the corresponding quantities obtained by the GO assumption shows that this hypothesis breaks down because in a wide dvac range the difference between the two kinds of cross sections is greater than experimental error and the overlap between cross sections is negative and therefore physically meaningless.

Helium atom scattering has been used to probe the surface damage created on GaAs(110) by Ar+ ion bombardment. The scattering cross section, Σ, of a single monovacancy is found to be ~150 Å2. The average number of defects comprising isolated impact craters, estimated from the scattering cross section per crater, is found to decrease with increasing crystal temperature during bombardment. This decrease occurs during or shortly following the bombardment event, and is different from simple thermal annealing. We propose that thermal accommodation of target adatom energy, which requires the number of adatom hops before freezing to increase with increasing crystal temperature, increases the adatom-vacancy recombination probability. Increasing the ion energy from 600 to 2400 eV does not change the cross section per single crater, but apparently impedes the probability of recombin

The study of interactions among surface defects by He scattering technique is mainly based on the hypothesis of geometric overlap (GO) of defect cross sections. Recently, quantum calculations have shown that this hypothesis is not valid. This result has been obtained by considering He scattering from targets consisting of a Pt(111) surface containing two defects, i.e. two CO admolecules or two vacancies arranged at different mutual distances, ddef. Quantum cross sections Σ2, calculated by sudden approximation for both kinds of defects and in a wide ddef range, were in large disagreement — up to 34%, namely more than the 3xperimental and sudden errors on cross section — with the corresponding quantities Σ2Δ obtained on a pure geometric ground by the GO hypothesis. Therefore, the main purpose of the present paper is to detect the reason for the GO hypothesis failure. To this end, because a more fruitful comparison can be made between homogeneous quantities, and Σ2and Σ2Δ are not, suitable target models have been built, containing two CO admolecules or two vacancies on Pt(111) arranged as in the case of the above-mentioned targets. The new targets are such that calculations on He scattering from them give the cross sections σ2and σ2Δ — both obtained by taking into account He-target interaction, and therefore homogeneous — whose trends versus ddef are completely analogous to those of Σ2and Σ2Δ, respectively. In this way the comparison between σ2and σ2Δ, is useful to demonstrate that the GO hypothesis fails because it implies — translated in terms of atom-target interaction — that, in the region between the two defects, i.e. where their cross sections overlap, He scattering process could be described by taking into account the interaction of impinging atom with just one of the two defects and neglecting the contemporaneous effect of the other one.

The role of surface defects in elastic gas-solid collisions is investigated by means of a recently developed numerical procedure based on the Møller operator and wavepackets. Since the procedure explicitly evaluates the scattering wavefunction, it yields the probabilities for scattering from the given initial state into all possible final states as well as the sensitivity of the probabilities with respect to variations in the gas-surface potential. Probabilities and their functional sensitivities are calculated for a simulated Pt surface exhibiting various configurations of vacancies: isolated sites, “interacting” di-vacancies and closely-packed tri-vacancies. The functional sensitivities indicate which regions of the gas-defect-solid potential are most relevant to the scattering dynamics. The resultant physical insight should be ultimately helpful for inverting experimental data to obtain the interaction potential.

We review the projected continuum approach to quantum scattering from disordered surfaces, placing it in the context of previous time-independent and time-dependent approaches. The method provides a one K-vector expansion of the scattering with a coherent field potential average, which leads to a unitary set of equations describing specular and non-specular scattering. Of particular significance is the capability to describe sticking due to surface disorder, which increases at low collision energies. Application to a model partial monolayer of molecular adsorbate is made, illustrating the efficiency and usefulness of the approach for study of finite coverage, disordered adsorbate systems.

The first conclusive molecular beam scattering experiment on surfaces has been performed in 1915 by Knudsen. This and a few other classical experiments which led to the modern period will be outlined, and the conclusions drawn from these experiments as well as their influence on the further development will be discussed in the first part. In the second part, the three main modes in which He-beams are currently used as a probe for surface investigations are commented on, with emphasis on the study of disordered surfaces.

The interaction of hydrogen with an (almost) defect-free Pt(111) surface (step density ∼ 0.1%) is revisited in a combined thermal energy atom scattering/thermal desorption spectroscopy (TEAS/TDS) study. We propose a novel kinetic precursor-mediated adsorption/desorption model for hydrogen/Pt(111) to reconcile seemingly conflicting results, such as extremely different dissociative adsorption kinetics at 25 and 155 K. Up to a perpendicular energy of (at least) 60 meV, highly relevant for hydrogenation reactions, the initial sticking probability scales with perpendicular energy to the power 1.9. This atypical behaviour is attributed to probing larger corrugation amplitudes at higher normal energy, leading to scattering of hydrogen into a dynamic precursor prior to dissociation and thus to increased trapping. Scrutiny of the data demonstrates that only a small minority of the surface sites (most probably steps) is active in dissociation. The observed decay of the heat of adsorption with coverage indicates strong repulsion between hydrogen atoms. The TDS-spectra of hydrogen from the defect-'free' Pt(111) consist definitively of a single (β(2)-)peak in contrast to the frequently measured double (β(1), β(2)-)peak structure and at variance with the yet widely accepted conjecture that repulsive interactions lead to double (β(1), β(2)-)peak structures in TDS-spectra. TDS-spectra simulated by applying the micro-reversibility principle and using TEAS-data are in agreement with the experimental ones. The TEAS-data, probing hydrogen whilst on the surface, are thus consistent with TDS-data, probing hydrogen after leaving the surface.

The dissociation of hydrogen at atomic surface defects is the strongly dominant, if not the decisive, step in the chain of events eventually leading to chemisorbed H-atoms on Pt(111). This holds for perpendicular kinetic energies of the gas phase molecules from 8 to 60 meV, i.e., covering the range relevant to hydrogenation reactions. This insight has been gained in the present study in which we reversibly varied the defect density on one and the same crystal in a controlled way. Information has been derived from measuring the adsorption kinetics as a function of coverage. Two distinct adsorption channels are distinguished. The first, indirect one, prevails at lower H-coverage and involves capture into a non-accommodated molecular precursor state followed by dissociation at step sites as described in our recent paper. The second one, dominant at higher coverage and non-negligible defect densities, obeys second order Langmuir kinetics. Here the dissociative adsorption takes place directly at step sites with a cross section of 0.24 unit cells (initial sticking probability 24% of the step density). These results are consistent with thermally programmed desorption data: the direct channel is responsible for the emergence of the low temperature peak in thermal desorption spectroscopy, usually denoted with β(1), while the indirect channel is represented by the β(2) state. The dependence on the perpendicular component of the hydrogen kinetic energy is distinctly different for the two channels: the indirect one shows power law behavior with an exponent 1.9 ± 0.1, while the direct one shows no perpendicular energy dependence at all.

He scattering from Cu(001) and adsorbed layers of Kr, Xe, and CO has been studied. It is shown here how the various components of scattering, namely the one-phonon inelastic, the coherent elastic, and the off-specular incoherent elastic yield information on surface modes of vibration and the mechanism of condensation and nucleation. Changes induced in the surface, such as defects due to ion bombardment and adsorption of a containment layer are shown to influence the various components of scattering.

A comment is made on the shape and the relaxation shift of the 2π∗ derived resonance observed in inverse photoemission from the CO/Cu(110) system. The magnitude of the relaxation shift, asymmetry and width of the peaks detected experimentally by Rogozik et al. are interpreted and evaluated using the formerly developed formalism of the transient surface electronic response. The results obtained indicate a relatively small contribution of the 2π∗ derived level to the chemisorptive bonding of the CO on the Cu(110) surface.

Using the Feynman diagrammatic technique, the Van der Waals interaction between an atom and an anisotropic adsorbate is shown to derive from three contributions: the direct interaction, the image force and an interference term. The last two contributions are three-body interactions due to the presence of the surface, and are responsible for the anisotropy of the resulting potential, even when the adsorbate is spherically symmetrical. Employing the flat hard wall approximation, the atom-adsorbate total cross section is expressed in terms of S- or T-matrix elements for collision in the absence of the surface. The distorted wave Born approximation is then applied to the cross section, yielding an expression consisting of an isotropic term and a correction term, which could account for the dependence of the cross section on the angle of incidence.

A theory is developed for linewidths and line shifts in molecular spectra of gases. A semiclassical method is used, which does not make the approximations of perturbation theory and a straight‐line trajectory upon which previous work has been based. General formulas are given for linewidths and line shifts in microwave, infrared and Raman spectra of linear molecules. Numerical application of the results is made to the widths of a number of spectra, and the results are in good agreement with both the magnitude and J dependence of the experimental values.

Large-angle-diffraction oscillations in the intensity of helium atoms
elastically scattered from randomly stepped Pt(111) are reported. A
formalism based on the concept of reflection-symmetry interference
explains the observed features and the data analysis yields a value of
4.4-4.6 Å for the hard-core repulsive cross section of a single
step. The observed oscillations are sensitive to the presence of
adsorbates at step sites.

He and H 2 beams striking a Pt(997) surfce in step-down incidence give rise to a “terrace rainbow” diffraction pattern indicative of specular reflection from flat terraces. The rainbow angle, however, does not coincide with the “terrace specular” direction but shows a shift that increases with angle of incidence, much like a “refraction shift” caused by the attractive potential. A quantative analysis in these terms using the hard corrugated wall plus attractive tail (HCWT) model revealed a difference between He and H 2 beams. For He, the model was able to reproduce the experimental intensities adequately over a wide range of incident energies and angles. For H 2 , however, the same was not true and we conclude that the HCWT model does not adequately represent the H 2 -metal interaction. Some reasons for this difference are discussed.

Large-angle-diffraction oscillations in the intensity of helium atoms elastically scattered from randomly stepped Pt(111) are reported. A formalism based on the concept of reflection-symmetry interference explains the observed features and the data analysis yields a value of 4.4-4.6 Å for the hard-core repulsive cross section of a single step. The observed oscillations are sensitive to the presence of adsorbates at step sites.

Exact quantum-mechanical calculations are present for He scattering from one-dimensional models of disordered, mixed Xe + Ar overlayers. A time-dependent wavepacket approach is used with a recent technique for solving the Schrödinger equation. Results are given for several overlayers of different Xe : Ar concentration ratios. The dependence of scattering intensities on the disordered structures is discussed. The results provide a reference for testing approximations for scattering from disordered surfaces.

Coherent and incoherent elastic scattering of He was observed from Cu(001) and adsorbed layers of CO and Xe. It is shown that specular and off-specular elastic scattering can yield insight into adsorption mechanisms at low coverages. The variation of incoherent elastic scattering with coverage shows different behavior for CO (random) and Xe (island) adsorption. A maximum appears in the incoherent elastic for CO as predicted theoretically for site adsorption.

The measured velocity dependence of the total scattering cross section for the scattering of He, HD, and D2 by the molecules CH4, N2, O2, NO, CO, HD, and D2 can be described relatively well by a Lennard-Jones-(12.6)-potential. Only for the systems with a CO2 target are large deviations from the L. J.(12,6) predictions found: the measured glory amplitudes are considerably smaller. The deformation of the spherically symmetric potential which must be made in order to fit the CO2 glory pattern is given. Furthermore, the CO2 systems were calculated using an angle-dependent L.J.(12.6)-potential, taking into account only elastic processes. The agreement with the measurements is good.

A brief commentary is presented on the strengths and limitations of various probes of surface structure presently in use. The sensitivity of He diffraction to structure is examined in more detail. The requirements for an open lattice, compared with the scattering cross-section of He, is displayed graphically based on analytical expressions for the He surface potential. The sensitivity argument is highlighted with experimental data as examples. Recent He diffraction studies of open semiconductor surfaces are then specifically discussed to demonstrate the nature of the topographical information which can be extracted.

The van der Waals interaction between an atom and an adsorbate consists of the usual two-body direct interaction as well as three-body interactions from the image force and an interference effect. The three-body interactions are caused by the presence of the surface and render the resulting potential anisotropic even when the adsorbate is spherically symmetrical. Expressions for the leading coefficients of the van der Waals forces and the corresponding reference-plane positions are given in terms of the polarizabilities of the atom, the adsorbate and the substrate. A theory of atomic scattering from a single adsorbate is given and numerical results for the total cross-sections of the He–Xe/Ag system are presented.

The recent application of the scattering of thermal He beams to the study of disordered adsorbates is featured by both an extreme sensitivity (coverages down to θ≈ 0.001 are accessible) and non-destructiveness. The sensitivity is a consequence of the very large cross-section (ca. 100 Å) for diffuse scattering exhibited by adsorbates. The cross-section overlap is substantial even at low coverages and the degree of overlap depends on the nature of the adsorbate distribution along the surface, i.e. on the mutual interaction of the adsorbates. Thus information on the latter can be obtained from the former; this is the overlap approach. A recent development has shown that this is also true if ‘monovacancy’ is substituted for ‘adsorbate’.

A multiple scattering theory is developed for the scattering of light atoms from a disordered adsorbate on a smooth surface. Using gas phase potentials for adatom potentials, excellent agreement is found with data for He scattering from adsorbed Xe and surprisingly good agreement with the extensive data for He scattering from adsorbed CO. The attractive adatom potential must be included in the calculation if quantitative comparison with experimental data is to be made. An important contribution to the total cross section of an adatom are quantum mechanical oscillations similar to glory oscillations in gas phase scattering. The dependence of the total cross section on the incident angle is strongly influenced by the varying number of adatoms seen by the probe.

We report on thermal He scattering from CO/Pt(111) at low coverages (θCO<0.01), which was shown to be dominated by long-range attractive forces centered at the adsorbed CO molecules. The scattering cross section of adsorbed CO is measured as a function of both the velocity of the incident He atoms and the angle of incidence. In first approximation the angular dependencies can be understood in terms of simple geometric “shadowing like” effects. The velocity dependencies, measured at different angles of incidence, coincide on a universal curve after correction for refractive and geometric effects.

The scattering cross section of an adsorbed CO molecule is about 1 order of magnitude larger than expected from the van der Waals radius. The dependences on the He and H2 incident velocities reveal glory structures similar to those in corresponding gas-phase experiments. Accordingly the long-standing puzzle of the extreme sensitivity of molecular beams to adsorbates is explained by inhomogeneities of the attractive potential.

The polarized Raman spectra of an oriented single crystal of NaBF4 were measured at 298 and 77°K in the region above 50 cm−1. The polarized infrared transmission and reflection spectra of single crystal NaBF4 were also measured at room temperature in the region above 300 cm−1. From the polarized vibrational spectra, the intramolecular modes were assigned, and estimates were made of the magnitude of the static field effects in crystalline NaBF4.

We present a theory for the scattering of low-energy atoms from molecules adsorbed at low coverage on a metal surface. The theory is used to obtain the He-CO potential from the measured cross sections when CO is adsorbed on the platinum(111) surface. While the spherical potential can reproduce the energy dependence of the total cross section for a fixed incidence angle, the analysis of the total cross section as a function of incidence angle indicates a strong anisotropy of the long-range van der Waals attraction, arising from the orientation of the dynamical dipole of the adsorbed molecule.

Thermal He scattering is proposed as a method to investigate two-dimensional gas-solid phase transitions down to very low coverages (~0.1%). The two-dimensional Xe gas-solid phase transition on a clean and defect-free Pt(111) surface is studied. The heat of vaporization of the two-dimensional solid phase into the two-dimensional ideal gas phase is 1.1+/-0.1 kcal/mole.

CO adsorption on Pt(111) is investigated by means of thermal He scattering. The relation between the relative height of the He specular peak and the coverage is approximated well by an exponential at low coverages for 63 meV He atoms incident at 40°. This relationship is used to monitor the CO coverage throughout this paper. The activation energy for CO desorption has been found to decrease linearly with increasing coverage up to θ ≈ 0.13, i.e. Ed = Ed0 − ϵθ, where Edo = 133 kJ/mol and ϵ = 68.5 kj/mol. The preexponential factor for desorption is about 1.4 × 1014 s−1 at Ts = 400 K. This set of three parameters allows a fully consistent description of the CO adsorption, desorption and equilibrium measurements.

The capability of a He-scattering experiment to detect the migration of adsorbed molecules on monocrystal surfaces is demonstrated for the first time. CO migration and island formation can be investigated at very low coverages because of the very large cross section for He scattering of CO adsorbed on Pt(111). The activation energy for CO migration on Pt(111) is found to be 7 kcal/mole. No island formation at low CO coverages on a defect-free Pt(111) surface was detected in the temperature range 120-400 K.

A theory for light-atom scattering by low-coverage adsorbates on metal surfaces is presented. A model including attractive adatom potentials successfully explains data for CO and Xe adsorption. The radius of the repulsive potential for CO is found to increase by 10-20% upon adsorption. It is shown theoretically that random adsorption and island formation can be distinguished, all data for CO being consistent with the former. Xe data show both mechanisms, depending on coverage.

A new quantum mechanical time dependent integrator was used in the study of wave packet dynamics on potentials which include a deep well. The purpose of the study was to find the conditions, if any, for complex formation. The integrator, which is stable, conserves energy and norm and was used on the H++H2 system whose classical trajectory had been previously worked out. Almost no complex formation is found for the H++H2 system and its isotopic analogs. For high translational energies there was a good correspondence with the classical trajectory results, while for low translational energies where the classical trajectories become complex, the quantum calculations still show nonstatistical behavior. For even lower energies, a quantum effect took place leading to zero reactivity.

It was recently proposed that the sudden approximation should be a powerful tool for the calculation of the angular intensity distribution in high‐energy atom scattering from disordered surfaces. In the present study the sudden approximation is applied to scattering from one‐ and two‐dimensional models of: (1) Isolated adsorbed impurities on crystalline surfaces (Ar on Cu); (2) Mixed overlayers on an underlying surface (Xe+Ar mixtures on a smooth surface). The results are tested against numerically exact quantum‐mechanical wave packet calculations. Except for very low collision energies, the sudden approximation gives results of excellent quantitative accuracy for both types of noncrystalline surfaces. At low energies, several features of the intensity distribution are not produced correctly by the sudden: These are found to be due mainly to double collision effects. The accuracy and validity range of the method are discussed in the light of the results obtained in the test calculations.

Rotational and reorientational transitions in molecular collisions with solid surfaces are investigated by a model based on a sudden approximation with respect to both the rotational and the diffraction states that play a role in the scattering. The approximation developed leads to computationally simple expressions and provides detailed insight into the physical properties of the processes involved. A detailed quantitative study is made of the rotational state distribution produced by the collision, the variation of rotational excitation probabilities with the scattering angle, and related questions. A number of factorizations, sum‐rule, and scaling properties are predicted for ‖ Sjmj,00;j′m′j′,mn @qL ‖2, the transition probability between the initial (jmj) and the final (j′m′j′) rotational states for scattering into the (mn) diffraction channel. The strongest sum rules and scaling laws are obtained using additional approximations beyond the sudden decoupling. Among the latter results: (1) The j,j′ dependence of ‖ Sj0,00;j’m’0,mn ‖2 is determined entirely by the difference variable Δj=j′−j. (2) The diffractive intensity distribution summed over all final rotational states is the same as that obtained for a mass‐equivalent atom (with an interaction that is the orientation‐averaged molecule–surface potential). (3) The rotational state distribution, summed over all diffraction states, equals that calculated from a corresponding flat surface. (4) All rotational transition probabilities for the (m,n) diffraction spot can be obtained from the diffraction–rotational transition probabilities in the (m,0) and (n,0) diffraction spots. The above and other properties are tested numerically in the framework of the full sudden approximation for a model of H2/LiF(001) in the energy range 0.5–0.9 eV. They are found to hold to excellent accuracy. Systematics of the results with regard to variation of the surface corrugation parameter are noted.

The angular intensity distribution of atomic beams scattered from partially disordered solid surfaces is investigated. Quantitative relations are established between correlation functions that describe the structural disorder, and several features of the scattered intensity distribution. To simplify the collision dynamics, the study is carried out in the framework of the sudden approximation, which assumes that momentum changes perpendicular to the surface are large compared with momentum transfer due to surface corrugation. Simple relations are obtained between the structural correlation functions and the scattering at near‐specular angles, at extreme off‐specular angles, and for directions close to that at which the surface scattering rainbow appears for the corresponding ordered lattice system. Detailed expressions for the case of step disorder are presented. The results suggest that molecular beam scattering should be a powerful probe of structural properties of disordered surfaces.

We used a randomly corrugated hard wall model and the sudden approximation to analyze two experiments on atom scattering from disordered surfaces. In one, the structural surface disorder was caused by ion bombardment. In the other, the disorder was due to an incomplete overlayer of adsorbed atoms. We also present a study of the scattering of a rigid rotor by a randomly corrugated hard wall using the sudden approximation.

The adsorption and desorption of hydrogen, oxygen, carbon monoxide, and ethylene on Ni(110) and of hydrogen on Ni(100) were monitored with He‐atomic beam scattering. The attenuation of the specular beam during gas adsorption initially shows a linear dependence on the adsorbate partial pressure and dose, which, when extrapolated, corresponds to a decrease of 100% for about one‐half a Langmuir (1 L=1.33×10−4 Pa s). This can be related to total collision cross sections of the adsorbed particles in the range of 30 to 100 Å2, indicating dominance of the attractive interaction of the He atoms with adsorbates in dilute concentrations. Statistical occupation or depletion of sites in the adlayer structures suffice to explain the changes in coherent specular intensity upon adsorption and desorption processes. Near the Curie temperature of Ni (Tc=631 K), diffracted intensities of H2 and He show non‐Debye–Waller behavior in their temperature dependence. Connections to changes in carbon surface concentration and to a (structural) phase transition (‘‘surface roughening’’) near Tc are discussed.

A recent method for time-dependent wavepacket scattering calculations is applied to He scattering from a Cu surface with isolated Ar impurities. Several effects are found: (i) broad tails superimposed on each diffraction spike; (ii) shallow impurity rainbow maxima; (iii) impurity—surface interference peaks. A sudden approximation is applied to the interpretation of the newly found features.

Two versions of the sudden approximation are introduced to decouple and solve the equations that describe atom- surface scattering with many open diffraction channels. Both approximations require a high incident beam wave number compared with the magnitude of the reciprocal space vector of the lattice. In this framework, simple explicit expressions are obtained for the observable diffraction intensifies, making calculations feasible even for systems with hundreds of open diffraction channels. Further considerable simplifications ensue when the approximations are specialized to the case of a Lennard-Jones-Devonshire potential, or to that of a weakly corrugated surface. The approximations were applied to the systems He/LiF(001); Ne/LiF(001) and Ne/W(110) and the results are compared with other calculations or with experiment. The sudden approximation is found to be of good accuracy in these cases.

Differential cross sections have been measured for the scattering of helium atoms from isolated CO molecules on a Pt(111) surface. The cross sections reveal an oscillatory structure as a function of scattering angle extending to large momentum transfer on both sides of the specular peak. Using a hard hemisphere model to approximate the interaction potential, the data can be well reproduced by a hard core of radius about 2.5 Å. This result is compared to the charge density profile of the adsorbed molecule and also to the gas phase interaction potential, and in both cases good agreement with the experimentally predicted classical turning points is found.

A time dependent wavepacket approach is applied to diffractive scattering from surfaces with imperfections. This semiclassical method is based on Gaussian wavefunctions whose average positions and momenta are those of classical trajectories. The approach can be applied to arbitrary potentials. Positions, shapes and magnitudes of the diffraction peaks are obtained in a single calculation. In a first example the wavepacket method is applied to a stepped surface. The diffraction pattern is calculated for different incident scattering angles and for various regular and random distributions of steps with two different sizes. Second, the approach is used to study the scattering for an interaction potential modeling a corrugated surface with adsorbed atoms. The diffraction intensities are examined for several final scattering directions and again for regular and random arrangements of the adsorbed atoms.

A new method is presented for the solution of the time dependent Schrödinger equation in its application to physical and chemical molecular phenomena. The method is based on discretizing space and time on a grid, and using the Fourier method to produce both spatial derivatives, and second order differencing for time derivatives. The method conserves norm and energy, and preserves quantum mechanical commutation relations. One- and two-dimensional examples, where a comparison to analytic results is possible, are investigated.

A new propagation scheme for the time dependent Schrödinger equation is based on a Chebychev polynomial expansion of the evolution operator Û=exp(−i Ĥt). Combined with the Fourier method for calculating the Hamiltonian operation the scheme is not only extremely accurate but is up to six times more efficient than the presently used second order differencing propagation scheme.

The question addressed in the title was investigated experimentally for low coverage CO and H on Pt(111). The consistent result of two kinds of experiments is that the scattering cross section is in general not influenced by the surface temperature, except for H on Pt(111) in the limit of small changes of the normal component of the He wave vector, Δ kz. The result simplifies substantially the use of He scattering as an analytical technique for surface dynamics investigations. Semi-classical arguments indicate that the lack of influence of the surface temperature at low coverages is related to two circumstances: (1) the small contribution to the specular He beam of the scattering from adsorbate induced disturbances of the repulsive potential and (2) the absence of long range modifications of the vibrational properties of Pt induced by adsorbed CO or H.