Materials Transactions Online

Materials Transactions, Vol.59 No.06 (2018) pp.883-889
© 2018 The Japan Institute of Metals and Materials

Interaction Energies Among Rh Impurities in Pd and Solvus Temperatures of Pd-Rich PdRh Alloys

Chang Liu1, Mitsuhiro Asato2, Nobuhisa Fujima3, Toshiharu Hoshino4, Ying Chen5 and Tetsuo Mohri6

1National Institute for Materials Science, Tsukuba 305-0047, Japan
2National Institute of Technology, Niihama College, Niihama 792-8580, Japan
3Graduate School of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan
4Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan
5Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
6Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

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.


(Received 2017/12/22; Accepted 2018/03/22; Published 2018/05/25)

Keywords: KKR-Green’s function method, GGA, cluster variation method, Fermi-Dirac distribution, thermal vibration, Debye-Grüneisen model, local lattice distortion, real-space cluster expansion

PDF(member)PDF (member) PDF(organization)PDF (organization) Order DocumentOrder Document Table of ContentsTable of Contents


  1. Asato M., Mizuno T., Hoshino T. and Sawada H.: Mater. Trans. 42 (2001) 2216-2224.
  2. T.B. Massalski, H. Okamoto, P.R. Subramanian and L. Kacprazak: Binary Alloys Phase Diagrams, 2nd ed., (ASM International, New York, 1990).
  3. Hoshino T., Asato M., Zeller R. and Dederichs P.H.: Phys. Rev. B 70 (2004) 094118.
  4. Nakamura F., Hoshino T., Tanaka S., Hirose K., Hirosawa S. and Sato T.: Trans. Mater. Res. Soc. Jpn. 30 (2005) 873-876.
  5. Asato M., Takahashi H., Inagaki T., Fujima N., Tamura R. and Hoshino T.: Mater. Trans. 48 (2007) 1711-1716.
  6. Hoshino T., Asato M. and Fujima N.: J. Alloys Compd. 504 (2010) S534-S537.
  7. Asato M., Settles A., Hoshino T., Asada T., Blugel S., Zeller R. and Dederichs P.H.: Phys. Rev. B 60 (1999) 5202-5210.
  8. Wildberger K., Lang P., Zeller R. and Dederichs P.H.: Phys. Rev. B 52 (1995) 11502-11508.
  9. Liu C., Asato M., Fujima N., Hoshino T., Chen Y. and Mohri T.: Mater. Trans. 59 (2018) 338-347.
  10. Mohri T. and Chen Y.: J. Alloys Compd. 383 (2004) 23-31.
  11. Mohri T., Morita T., Kiyokane N. and Ishi H.: J. Phase Equilib. 30 (2009) 553-558.
  12. Hoshino T., Asato M., Mizuno T. and Fukushima H.: Mater. Trans. 42 (2001) 2206-2215.
  13. Zeller R.: Phys. Rev. B 55 (1997) 9400-9408.
  14. Zeller R., Asato M., Hoshino T., Zalbloudil J., Weinberger P. and Dederichs P.H.: Philos. Mag. B 78 (1998) 417-422.
  15. We are now studying the TFD dependence of the Fermi-Dirac distribution on the physical quantities such as total energies, lattice parameters, and magnetic moments of elemental and ordered alloys.
  16. Papanikolaou N., Zeller R., Dederichs P.H. and Stefano N.: Phys. Rev. B 55 (1997) 4157-4167.
  17. Hoshino T., Papanikolaou N., Zeller R., Dederichs P.H., Asato M. and Stefanou N.: Comput. Mater. Sci. 14 (1999) 56-61.
  18. Asato M., Liu C., Kawakami K., Fujima N. and Hoshino T.: Mater. Trans. 55 (2014) 1248-1256.
  19. C. Liu, M. Asato, N. Fujima and T. Hoshino: in PRICM, (John Wiley & Sons, Inc., Hoboken, NJ, USA, Sept. 2013) 78, pp. 2821-2825.
  20. Liu C., Asato M., Fujima N. and Hoshino T.: Phys. Procedia 75 (2015) 1088-1095.
  21. W. Schweika: Structural and Phase Stability of Alloys, ed. by J.L. Möran-Löpez et al., (Plenum Press, New York, 1992) pp. 53-64.
  22. W. Schweika: Disordered Alloys, Springer Tracts in Modern Physics 141, (Springer, 1998) pp. 51-54.
  23. D. de Fontaine: Solid State Physics, Vol. 47, ed. by H. Eherenreich and D. Turnbull, (Academic Press, London, 1994) pp. 33-176.


© 2018 The Japan Institute of Metals and Materials
Comments to us :