Statistical aspects of the diffuse LEED problem

Abstract

Diffuse low-energy electron diffraction (LEED) intensities can be observed in all situations where the surface cannot be represented by a perfect biperiodic array of atoms or molecules. For instance, this occurs when binding sites are either occupied or not by adatoms, when several atoms or molecules are co-adsorbed, when one absorbed species can be located at several possible binding sites, etc. So far, the statistical aspects of this problem have been disregarded. In fact, under certain circumstances, it is possible to extract from diffuse intensities a quantity that only depends on the local atomic arrangement near a binding site. A method based upon this possibility has been systematically used in all diffuse LEED studies and consequently these studies have been totally devoted to the determination of this local atomic arrangement. The authors show in this paper that this method only works if one binding site is occupied or not (binary chemisorption). In the other cases, investigation of diffuse LEED intensities requires knowledge of the statistical distribution of occupied sites and thus the statistical aspects of this problem can no longer be bypassed. For this reason and also because this problem is intrinsically interesting, the authors particularly focus on it here. Diffuse LEED intensity can be approximated by a sesquilinear form of the form factors for each adsorbed species. The coefficients of this form are the Fourier transforms on the two-dimensional surface lattice of the site-occupancy pair correlation functions. A self-consistent molecular-field approximation of these correlation functions is given in this paper. Particularly, the validity of this approximation is discussed in detail for the binary chemisorption case. Diffuse LEED intensities are provided in some other cases: (i) two kinds of atom are distributed at the surface of a binary metallic alloy; (ii) two adsorbed species coexist at a single crystal surface. The authors arrive at the conclusion that investigation of diffuse LEED intensities generally requires the direct comparison of measured and calculated intensities.