Green function alloy surface

In this section, we extend the above formalism to that for an alloy surface within the CPA, which serves as the model for the pre-chemisorption substrate. The model discussed here is based on that of Ueba and Ichimura (1979a,b) and Parent et al (1980). For a comprehensive introduction to alloy surfaces see Turek et al (1996). A feature of surface-alloy models, which is different from bulk ones, is that the CP in layers near the surface is different from that in the bulk, due to the surface perturbation. Moreover, the alloy concentration in the surface layers may be quite different from that in the bulk, a feature known as surface segregation. (See Ducastelle et al 1990 and Modrak 1995 for recent reviews.) We assume that both of these surface effects are confined to the first surface layer only. 

The system under consideration consists of an isolated hydrogen-like atom and a DBA with a surface, as shown in Fig. 6.1. Following (6.28), the effective Hamiltonian for this system is 

The first term in (6.46) severs the bonds between the n = 0 and n = 1 sites, thereby creating a surface at the n = 1 site, while the second term perturbs the electronic environment on the surface atom, compared to that in the bulk. Substituting (6.46) into (6.45) and evaluating the matrix element (1 GS 1) = Gs(l, 1) leads to 

The surface CP as is found by putting gs in place of Ge in the CPA self-consistency equation (6.39), whence 

Substituting (6.49) into (6.50) and rearranging gives an explicit form for as  

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