Corrugation Function Research Articles

An effective procedure to determine corrugation functions from atomic beam-diffraction intensities

An effective procedure to determine corrugation functions from atomic beam-diffraction intensities

The diffraction of He atoms at the GaAs(110) surface

We present an experimental study of the diffraction of He beams at the GaAs(110) surface. Diffraction angular scans and specular intensity scans are obtained for a wide range of incident angles, azimuths, and at two energies ( E = 0.063 eV and E = 0.021 eV ). The data have been qualitatively analyzed from a classical scattering viewpoint and the hard wall eikonal scattered wave approximation. A hardwall corrugation function of the form ζ(x, y) = 1 2 d x cos( 2πx L x) + 1 2 d y cos( 2πy L y) yields a qualitative fit to the data with d x ~ 1.1 Å and d y ~ 0.3 Å, w deep corrugation corresponds to going across the surface troughs. This value of d x is approximately half the corrugation of the nuclear positions. Specular intensity scans are analyzed in terms of interference in the normal momentum transfer, Δk ⊥, which yields structural information about vertical displacements. We discuss what is required in order to appropriately describe scattering from strongly corrugated surfaces.

Scattering of atoms by solid surfaces: A CCGM theory of diffraction by a one-dimensional stationary periodic wall

The CCGM theory of elastic atom–surface scattering, proposed by Cabrera, Celli, Goodman, and Manson [Surf. Sci. 19, 67 (1970)], is applied to the now-popular corrugated wall model of the scattering. Instead of the original ’’hard’’ wall, a ’’softer’’ wall, with finite potential step height, is used. The CCGM soft-wall results are compared with corresponding exact hard-wall results, for corrugations of the sinusoidal type and of other types, for example those with nondifferentiable corrugation functions. It is concluded that the CCGM soft-wall results agree well with the exact hard-wall results provided that neither the dimensionless corrugation amplitude nor the dimensionless atom wave number is too large, although no explanation of the reason for this agreement is given. The results are important because a typical exact calculation may be far more time consuming than is a typical CCGM calculation, particularly for the ’’nastier’’ corrugation functions.

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.

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 He-diffraction measurements is considered. Possible conditions under which the ambiguity could be resolved are discussed.

Adatom Configurations of H(2×6) and H(2×1) on Ni(110) Analyzed Using He Diffraction

The first determination of two-dimensional adsorbate-induced corrugation functions from He-diffraction data is reported. Local maxima in the corrugations of both H(2\ifmmode\times\else\texttimes\fi{}6) and H(2\ifmmode\times\else\texttimes\fi{}1) on Ni(110) directly reflect adatom positions due to the localized charge distribution of the chemisorbed H atoms. Hence, genuine information on the adsorption sites is obtained leading to novel insight into coverage and adsorbate-adsorbate interactions. The transition to the reconstructed (1\ifmmode\times\else\texttimes\fi{}2) saturation phase is discussed.

Structural Investigation of an Adsorbate-Covered Surface with He Diffraction: Ni(110)+(1×2)H

This paper reports He diffraction from clean and hydrogen-saturated Ni(110) at 100 K. The clean surface can be described by a sinusoidal corrugation of amplitude 0.05 \AA{} in the [001] azimuth. The hydrogen-saturated surface requires an additional corrugation of amplitude 0.23 \AA{} on each second maximum of the basic corrugation. Possible adsorption structures consistent with this corrugation function are discussed.

The scattering of He atoms from a hard corrugated surface model using the GR method. I

Extensive computations on the scattering of atoms from a hard corrugated surface model (HCS) under the Rayleigh hypothesis by using the GR numerical method are presented. The computational applicability, the limits of convergence, as well as the sensitivity of the method are studied as a function of the scattering and corrugation parameters. We also calculate a set of curves, called topographic curves, of constant diffraction probabilities versus the incident angle and the corrugation parameters for a square unit cell. The effect of the strength and number of the Fourier coefficients of the corrugation function are analyzed obtaining rainbow disappearance when these coefficients increase in strength and number. A tentative analysis of the crystallography of the LiF(001) surface by using monoenergetic thermal helium beams is given in terms of the hard sphere and ’’contact’’ hard sphere model proposed here. The agreement with the experimental data on He/LiF(001) is excellent. We also discuss an empirical method for determining Debye–Waller factors by fitting the calculated peaks to the observed ones. We calculate the mean square displacement of the atoms vibrating at the surface for different directions on the He/LiF (001) system. These displacements and consequently the Debye–Waller factors are different than if the incident particles were electrons. Finally, several proposals for future experimental work are made.

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 kC 0 < 9 and C 0 < 0.35 A ̊ (where k is the incident wave vector and C 0 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.