Cluster expansion surface applications

The site occupation variables, c, take on a value of 1 or —1, following the Ising convention, and in this application of the cluster expansion to a two-dimensional (2D) surface-adsorbate system, 1 represents an occupied site and —1 represents a vacant site. Eqn 2.11 is valid for a system with any number of non-equivalent lattice sites, as long as each site is occupied by the same pair of species (in this case the adsorbate and vacancy). Generalizations can be made to multi-component systems with three or more species per site or multisublattice systems where different sites may contain different pairs of species, but we do not discuss these elaborations in this chapter. 

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