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.     

Threshold and Lennard-Jones resonances and elastic lifetimes in the scattering of atoms from crystalline surfaces

In this paper we apply the GR method for solving the scattering equations of atoms from a hard corrugated surface, on accelerated particles above a hard corrugated surface and a hard corrugated surface with an attractive well. The solutions are given for the Rayleigh hypothesis that under the range of corrugation presented in this paper leads to the exact ones. Threshold resonances are studied observing that the appearance and disappearance of beams must be for a general theory with vertical tangent. The structure of the Lennard-Jones resonances given for the model mentioned above. For the first time it is stressed that Lennard-Jones resonances are not observed in metal surfaces in general, and, accordingly, they are unobserved in compact metallic surfaces. This is correlated with the fact that diffraction has not been observed. Both facts are due to the very weak corrugation of the gas-metal interaction potential. According to our results, the Lennard-Jones resonances in metals present greater difficulties to be observed experimentally. We also note that the absence of diffraction in compact metal surfaces is because they are almost plane and not because of the Debye-Waller effect. Finally, we have calculated the lifetimes of the atoms at the crystal surfaces. These are larger, the smaller the incident energy and the larger the corrugation. But the lifetimes are particularly large at resonance condition (10^?11 s).     

Reflection and transmission of SH-waves at a corrugated interface between two semi-infinite anisotropic magnetoelastic half-spaces

An analysis has been carried out for reflection and transmission of a plane SH-wave incident at a corrugated interface between two anisotropic magnetoelastic half-spaces. Rayleigh’s method of approximation is applied to derive the reflection and transmission coefficients for first order approximation of corrugation. The expressions for reflection and transmission coefficients for first order approximation of corrugation are obtained in closed form for a special type of interface. It is found that these coefficients are proportional to the amplitude of corrugation and are functions of magnetoelastic properties of materials of the half-spaces as well as the angle of incidence. Special cases are deduced for anisotropic and isotropic materials for particular case of corrugation. Numerical computations are performed for a specific model of two different anisotropic magnetoelastic media. The effects of anisotropic magnetoelastic coupling parameter, the angle at which wave crosses the magnetic field, frequency factor, wave length of corrugation, and the amplitude of corrugation are shown through figures.     

Low energy He atom scattering from Ag(110) and Ag(111): Is there an effective two-body potential?

A rather wide range of scattering potentials is consistent with the extensive data for He scattering from Ag(110). This illustrates the nonuniqueness of potentials obtained by fitting scattering data for weakly corrugated surfaces. However, the corrugation of the equipotential surface for these potentials only differs by ∼ 20% and is therefore quite well determined by the data. An effective pair potential between the He atom and a Ag atom can be found which is consistent with scattering data for both the (110) and the (111) face of Ag, but it is unrealistic in some other respects.     

Relating temperature dependence of atom scattering spectra to surface corrugation

It is suggested that a measurement of the temperature dependence of the most probable intensity of energy-resolved atom-surface scattering spectra can reveal the strength of the surface corrugation. To support this conjecture, a classical mechanical theory of atom scattering from a corrugated surface, valid in the weak corrugation limit, is developed. The general result for the scattering probability is expressed in terms of spatial integrals over the impact parameter within a surface unit cell. For the case of a one-dimensional corrugation, approximate expressions for the scattering probability are obtained in terms of analytic closed form expressions. As an indicator of its relation to experimental measurements, calculations using a one-dimensional corrugation model are compared with data for Ar scattering from a molten Ga surface and an approximate value of the corrugation height parameter is extracted.     

Atom-surface elastic scattering with additive potential

An additive corrugated potential with linear repulsion and long range attractive well is proposed for atom-surface scattering. The computational procedure yielding the scattering probabilities (essentially linear algebra) proves to be much simpler than with other potentials. For a given shape of the corrugation function and for high values of the steepness parameter one obtains results close to those of the hard corrugated wall model, while an important enhancement of the specular intensity appears, in particular at large angles of incidence, when the steepness parameter is small.     

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 role of ionic quadrupolar deformation in atom-surface potential

We show that the quadrupolar deformation of surface ions gives appreciable contribution to the potential energy between the atom and an ionic surface. Calculations are presented for a number of alkali halides. The validity of Fumi and Tosi crystal radii in the surface region is discussed in connection with the depth and the corrugation parameter.     

Quantum theory of molecule-surface scattering: Rotational transitions

The quantum theory of atomic scattering from hard surfaces, previously developed, is extended to cover molecular scattering, taking into account rotational transitions. Two methods (a perturbative and a nonperturbative approach) are considered: the former is applied to H₂ scattering, the latter to HD scattering from LiF. A comparison with recent experimental data gives satisfactory results when a potential well of 440 K and a corrugation amplitude of 0.17 Å are assumed for the H₂ — LiF interaction.     

Supernumerary rainbows in the angular distribution of scattered projectiles for grazing collisions of fast atoms with a LiF(001) surface

Fast atoms with keV energies are scattered under a grazing angle of incidence from a clean and flat LiF(001) surface. For scattering along low index azimuthal directions within the surface plane ("axial surface channeling") we observe pronounced peak structures in the angular distributions for scattered projectiles that are attributed to "supernumerary rainbows." This phenomenon can be understood in the framework of quantum scattering only and is observed here up to projectile energies of 20 keV. We demonstrate that the interaction potential and, in particular, its corrugation for fast atomic projectiles at surfaces can be derived with a high accuracy.     

Mechanism of contrast formation in atomic force microscopy in water

We use computer modeling to investigate the mechanism of atomic-scale corrugation in frequency-modulation atomic force microscopy imaging of inorganic surfaces in solution. Molecular dynamics simulations demonstrate that the forces acting on a microscope tip result from the direct interaction between a tip and a surface, and forces entirely due to the water structure around both tip and surface. The observed force depends on a tip structure and is a balance between largely repulsive potential energy changes as the tip approaches and the entropic gain when water is sterically prevented from occupying sites near the tip and surface.     

Enhanced atomic-scale contrast on Fe3O4 (100) observed with an Fe STM tip

Clean (100) surfaces of a synthetic single crystal of magnetite (Fe₃O₄) have been prepared in situ using current pulses in a scanning tunneling microscope without subsequent annealing. We have observed atomically resolved terraces with rows of Fe²⁺ and Fe³⁺ ions of the B-sublattice (octahedrally coordinated lattice sites). Along these rows a long-distance corrugation (∼12 ?) has been observed at 300 K using in situ prepared Fe tunneling tips. This corrugation is interpreted as a Wigner localization associated with a Verwey transition above 300 K in the top surface layer. Received: 26 September 2000 / Accepted: 27 October 2000 / Published online: 3 May 2001     

Thermal activation in atomic friction: revisiting the theoretical analysis

The effect of thermal activation on atomic-scale friction is often described in the framework of the Prandtl-Tomlinson model. Accurate use of this model relies on parameters that describe the shape of the corrugation potential β and the transition attempt frequency f(0). We show that the commonly used form of β for a sinusoidal corrugation potential can lead to underestimation of friction, and that the attempt frequency is not, as is usually assumed, a constant value, but rather varies as the energy landscape evolves. We partially resolve these issues by demonstrating that numerical results can be captured by a model with a fitted β and using harmonic transition state theory to develop a variable form of the attempt frequency. We incorporate these developments into a more accurate and generally applicable expression relating friction to temperature and velocity. Finally, by using a master equation approach, we verify the improved analytical model is accurate in its expected regime of validity.     

Atomistic origin of radial corrugation in a few-walled carbon nanotubes: A molecular dynamics study

We perform molecular dynamics simulations of a few-walled (with 3–4 walls) carbon nanotubes using empirical interatomic potential. We demonstrate that the radial corrugation occurs in such thin nanotubes under hydrostatic pressure, which is apparently similar to the corrugation in thicker (e.g., several tens-walled) nanotubes that had been predicted using continuum mechanics approximation. The mechanism underlying the corrugation of a few-walled nanotubes, however, is found to be much distinct from thick nanotubes; i.e., the sp³ bonds between adjacent concentric walls and registry of atom arrangement take important roles in the formation and stabilization of corrugation modes in a few-walled nanotubes.     

On argon beams as tools to probe surfaces

We present experimental data and a theoretical analysis for the scattering of an argon beam from the (001) surface of LiF. The scattering pattern of the Ar beam was investigated for incident energies between 0.089 and 0.350 eV and for a variety of polar and azimuthal incidence angles. We find a bilobular scattering pattern for small incidence angles and along the direction of maximum corrugation on the surface, and a broad peak centered around the specular direction for higher incidence angles. An interaction potential based on the effective medium theory has been evaluated. The corrugation of this potential across the surface is in fair agreement with the data interpreted using the classical rainbow angles. Such corrugation is smaller than the one determined by He scattering, in agreement with previous Ar/metal surface investigations.     

AFM and SNOM characterization of carboxylic acid terminated silicon and silicon nitride surfaces

Silicon and silicon nitride surfaces have been successfully terminated with carboxylic acid monolayers and investigated by atomic force microscopy (AFM) and scanning near-field optical microscopy (SNOM). On clean Si surface, AFM showed topographical variations of 0.3-0.4 nm while for the clean Si₃N₄ surface the corrugation was around 3-4 nm. After material deposition, the corrugation increased in both samples with a value in topography of 1-2 nm for Si and 5-6 nm for Si₃N₄. The space distribution of specific chemical species was obtained by taking SNOM reflectivity at several infrared wavelengths corresponding to stretch absorption bands of the material. The SNOM images showed a constant contribution in the local reflectance, suggesting that the two surfaces were uniformly covered.     

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.     

Simulation of spin-resolved scanning tunneling microscopy: influence of the magnetization of surface and tip

We develop a first principles method to compute the magnetic axis of a crystal surface from corrugation amplitudes of spin-polarized scanning tunneling microscopy measurements. In this paper, we present the detailed electronic structure information of antiferromagnetic and ferromagnetic Mn overlayers on W(1 1 0), our model system for spin-polarized tunneling on the atomic scale. We also perform image simulations on all surfaces. It is shown that the images of Mn overlayers are very sensitive to magnetic ordering of the surface, and while a high magnetic contrast can in principle be obtained, surface corrugation itself is generally at the lower limit of image resolution.     

Analysis of the methods proposed for computing the scattering of atoms from a hard corrugated surface model of He/LiF (001)

It appears that the scattering of atoms on crystal surfaces is accounted for by a corrugated infinite wall model of the surface. To determine the “corrugation function” which represents best the experimental scattering intensities, it is necessary to choose among many possible versions, the simplest and most effective computational method of the theoretical scattering amplitudes. It is the purpose of this paper to analyze the relative merits of three particular versions which we call HDM, NHM and GR, and which are described in section 3. This comparison is carried out on the He/LiF(001) system for variable incident wave vector (k) and orientation (θ_i) as well as a number of Fourier components (ζ_G) used to describe the “corrugation function”. We conclude that the GR method presents advantages over the other two: (i) it reduces the computer time necessary for the HDM and NHM methods, (ii) converges and computes to within 10^?4 in unitarity the scattering amplitudes in a larger range of energies as well as angular and corrugation parameters, and (iii) it presents a great simplicity and the corrugation is very handy. The size of that range depends on the computer facilities used. In our case, the GR method works for any calculation in which kC₀ < 9 and $\text{C}{}_0\text{< 0.35}\text{A}\text{?}$ (where k is the incident wave vector and C₀ twice the amplitude of the corrugation). These characteristics prove to make the GR method a good tool for the study of surface crystallography by parametrization of the surface corrugation.