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

Abstract

A computational method is described, which, starting from given difraction intensities, approaches effectively the best-fit corrugation function ζ( R) . Because of the approximations involved, the procedure works well for smooth corrugations with amplitudes not exceeding ∼10% of the lattice constant. The method rests on two crucial observations: (i) With the full knowledge of the scattering amplitudes A G = ¦A G¦ exp( iϑ G) (absolute values plus phases), the corrugation function can be calculated to a high degree of accuracy from ζ( R) = (2 ik i) −1 In ¦−ΣA G exp( i G·R)¦ which is derived easily from the hard corrugated wall scattering (HCWS) equation by approximating k G by − k i ( k i and k G being the wavevectors of the incoming and diffracted beams, respectively), (ii) With only the ¦A G¦'s (or intensities) known, approximate solutions of the HCWS equation can be obtained with a rough estimate of the relative phases of only a few intense diffraction beams; the estimate is readily performed by investigating systematically a coarse mesh of phases. In this way, approximate corrugations are found with which a full set of phases can be generated, which allows the calculation of an improved ζ( R ); this step is repeated in a loop, until optimum agreement between calculated and given intensities is obtained. The effectiveness of the procedure is demonstrated for three one-dimensional model corrugations described by several Fourier coefficients. The method is finally applied to the case of H 2 diffraction from the quasi-one-dimensional adsorbate corrugation Ni(110) + H(1 × 2).