Accuracy of Real Space Cluster Expansion for Total Energies of Pd-rich PdX (X=Rh, Ru) Alloys, based on Full-Potential KKR Calculations for Perfect and Impurity Systems

We study the accuracy and convergence of the real space cluster expansion (RSCE) for the total energies of the Pd-rich PdX (X=Ru, Rh) alloys, which are used to study the phase stability and phase equilibria of the Pd-rich PdX alloys. In the present RSCE, the X atoms of minor element are treated as impurities in Pd. The n-body interaction energies (IEs) among X impurities in Pd, being used in the expansion of the total energies of the Pd-rich PdX alloys, are determined uniquely and successively from the low body to high body, by the full-potential Korringa-Kohn-Rostoker (FPKKR) 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. In the previous paper, we showed that the RSCE, in which the perturbed potentials due to the insertion of Xn impurities in Pd were redetermined self-consistently up to the first-nearest neighboring (nn) host atoms around Xn impurities, reproduce fairly well (the error of ~ 0.2mRy per atom) the FPKKR-band-calculation result of the ordered Pd3Rh alloy in L12 structure, but a little wrongly (the error of ~ 0.7mRy per atom) for the ordered Pd3Ru alloy in L12 structure. In the present paper, we show that this small RSCE error for the Pd3Ru alloy is corrected very well (from ~ 0.7mRy to ~ 0.1mRy per atom) by enlarging the self-consistent region for the perturbed potentials up to the 2nd-nn host atoms around Run impurities in Pd. We also clarify the correction for each value of the n-body (n=1~ 4) IEs.