Real space cluster expansion for total energies of Pd-Rich PdX (X = Rh, Ru) alloys, based on full-potential KKR calculations: An approach from a dilute limit

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 = 134), 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 31 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 034 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 = 234) IEs becomes smaller and smaller with the increase in n and that the contribution from the 4-body IEs is very small (less than 30.2 mRy per atom).