Effective site energy and cluster expansion approaches for the study of phase diagrams

We apply the cluster expansion (CE) method to determine the effective cluster interactions (ECIs) from a simple energetic model that depends on both local and global composition. This model is defined by the site energies of random solid solutions of a one-dimensional alloy Co-Pt. We explore how these local and global dependencies are reflected on the cluster interactions. The energies of the structures are not well reproduced with concentration-independent interactions. Moreover, the interactions have a larger range than the energetic model which is limited to the nearest neighbors. This problem does not seem to have been addressed until now. By fitting the ECIs on the site energies we suggest a mean-field type weighting of the excess variables present in large clusters size. We show that the site energy formalism controls the clusters size required for CE convergence and their concentration dependence. Finally, we take advantage of the site energy formalism to describe the elastic and chemical effects that control the thermodynamics of the alloy as a function of the ECIs.