Interaction energies among Rh impurities in Pd and solvus temperatures of Pd-Rich PdRh alloys

Chang Liu, Mitsuhiro Asato, Nobuhisa Fujima, Toshiharu Hoshino, Ying Chen, Tetsuo Mohri

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2 Citations (Scopus)


We present the ab-initio calculations for the solvus temperatures (Tsolvus = 820∼860 K) of Pd1-cRhc (0.09 ≤ c ≤ 0.12) in which the Rh atoms are treated as impurities in Pd. The interaction energies (IEs) among the Rh impurities in Pd, being used in the real-space cluster expansion for the internal energies in the free energies, are determined by the ab-initio calculations based on the full-potential Korringa-Kohn-Rostoker Green's function method, combined with the generalized gradient approximation in the density functional theory. The configurational entropy calculations are based on the cluster variation method within the tetrahedron approximation in which the 2∼4 body IEs are treated exactly within a tetrahedron of the 1st-nearest neighbor (nn) pairs. In order to take into account the 2-body IEs at the long-distance neighbors, we renormalize the 1st-nn 2-body IE by including the 2-body IEs up to the 10th-nn, because the 9th-nn 2-body IE is comparatively large. To realize the precise calculations for the Tsolvus of Pd1-cRhc, we also investigate the following three effects on the IEs among the Rh impurities: (1) the electron excitation due to the Fermi-Dirac distribution, (2) the thermal lattice vibration by the Debye-Grüneisen model, and (3) the local lattice distortion for the 1st-nn 2-body IE. The calculated results for the Tsolvus of Pd1-cRhc agree fairy well (within the error of ∼50 K) with the observed Tsolvus.

Original languageEnglish
Pages (from-to)883-889
Number of pages7
JournalMaterials Transactions
Issue number6
Publication statusPublished - 2018


  • Cluster variation method
  • Debye-Grüneisen model
  • Fermi-Dirac distribution
  • GGA
  • KKR-Green's function method
  • Local lattice distortion
  • Real-space cluster expansion
  • Thermal vibration


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