Ab-initio calculations for solvus temperatures of Pd-rich PdRu alloys: real-space cluster expansion and cluster variation method

We present the ab-initio calculations for the solvus temperatures (Tsolvus) of Pd1−cRuc(0.03 ≤ c ≤ 0.12), in which the interaction energies (IEs) among the Ru impurities in Pd are determined by the full-potential Korringa-Kohn-Rostoker Greens function method, combined with the generalized gradient approximation in the density functional theory. The configurational entropy calculations are based on the cluster variation method (CVM) within the tetrahedron approximation. In order to take into account the long-range 2-body IEs, we renormalized the 1st-nearest neighbor (nn) IE by including the 210th-nn IEs. We also take into account the following three effects on the IEs among the Ru impurities; (1) the local lattice distortion for the 1st-nn IE, existing even at T = 0 K, (2) the lattice thermal vibration by the Debye-Grüneisen model, and (3) the T-dependence of the electron excitation due to the Fermi-Dirac distribution. The calculated results for the Tsolvusagree fairly well with the experimental results at low Ru-concentrations (up to 6%), while the discrepancy between the calculated and experimental results becomes significant for the high Ru-concentrations (812%). We discuss that the discrepancy may be corrected by the CVM calculations with the large basic cluster including up to the 4th-nn IE.