Abstract
We study the accuracy and convergence of the real space cluster expansion (RSCE) for the internal energies in the free energies of Pd-rich PdX (X = Rh, Ru) alloys, being used to study the phase stability and phase equilibria of Pd-rich PdX alloys in fcc structure. In the present RSCE from a dilute limit, the X atoms of minor element are treated as impurities in Pd. The n-body interaction energies (IEs) among X impurities in Pd are determined uniquely and successively from the low body to high body, by the ab-initio calculations based on the full-potential Korringa-Kohn-Rostoker Green’s function method (FPKKR) for the perfect and impurity systems (Pd-host and Xn in Pd, n = 1∼4), combined with the generalized gradient approximation in the density functional theory. We show that the total energies of the ordered Pd3X (X = Rh, Ru; X-concentration = 25%) alloys in L12 structure, obtained by the screened FPKKR band calculations, are reproduced very well (within the error of ∼1 mRy per atom) by the present RSCE including the 2-body IEs up to the 20th nearest neighboring pair (X2) and the 3-body IEs up to the clusters (X3) in the two cubic cells in fcc structure. We clarify the contribution from each term (of the 0∼4 body terms) in the RSCE to the total energies of Pd-rich PdX alloys, the distance dependence of the 2-body (X2) IEs, and the cluster-size dependence of 3-body (X3) and 4-body (X4) IEs. It is also shown that the contribution from the n-body (n = 2∼4) IEs becomes smaller and smaller with the increase in n and that the contribution from the 4-body IEs is very small (less than ∼0.2 mRy per atom).
