Site occupancy pair correlation functions and structure factors of partially ordered overlayers: I. Formalism

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Abstract In a previous paper, it has been shown that the elastic diffuse intensity of electrons scattered by a short-range ordered adlayer depends on structure factors and on renormalized t-matrices for each kind of occupied bonding sites. In many cases, the computation of these structure factors is a crucial point for the application of this theory. This paper is part I of a work devoted to this problem. In this part rather addressed to theoreticians, two methods of calculation of the site occupancy pair correlation functions and of their Fourier transform, that is to say the structure factors, are developed. The first method is based upon a molecular field approximation and yields a finite set of linear equations from which coverage and pair correlation functions can be computed in a self-consistent way. Provided that the surface coverage is small, this theory can be applied in the cases of a weak attractive or a strong repulsive coupling between adsorbates. The second one is a cumulant expansion method in which a decoupling approximation is applied: cumulants of order greater than 2 are neglected. This method leads to a finite set of nonlinear equations. The linearization of these equations leads to a set of equations which have the same form as those obtained from the molecular field approximation but their coefficients are different. In the next paper, it will be shown that both methods lead to qualitatively equivalent results. However, for short-range ordered adlayers, the results obtained from the second one are closer to the results obtained from a Monte Carlo simulation than those obtained from the molecular field approximation. In the present work, both methods are developed in the particular case where identical adsorbates, which interact by a nearest-neighbour potential, are distributed with a short-range order at one kind of sites belonging to a square lattice. However, the methods presented here can be generalized to the cases of several adsorbates located at different kinds of chemisorption site.