Temperature Dependent Interaction Energies among X (=Ru, Rh) Impurities in Pd-Rich PdX Alloys
We study the temperature dependence of the interaction energies (IEs) of X (=Ru, Rh) impurities in Pd, due to the Fermi-Dirac (FD) distribution and the thermal vibration effect by the Debye-Grüneisen model. The n-body (n=2~4) IEs among X impurities in Pd, being used to calculate the internal energies in the free energies of the Pd-rich PdX alloys, are determined uniquely and successively from the lower-order to higher-order, by the full-potential Korringa-Kohn-Rostoker Green’s function method (FPKKR), combined with the generalized gradient approximation in the density functional theory. We found that the temperature dependence of IEs due to the FD distribution, being usually neglected, is very important to reproduce the X-concentration dependence of the observed solvus temperatures of the Pd-rich PdX (X=Ru, Rh) alloys.
 T. B. Massalski, H. Okamoto, P. R. Subramanian, and L. Kacprazak: Binary Alloys Phase Diagrams, 2nd. ed., (ASM International, New York 1990.
 M. Asato, T. Mizuno, T. Hoshino, and H.Sawada, Mater. Trans. 42 (2001), 2216-2224.
 C. Liu, M. Asato, N. Fujima, T. Hoshino, Y. Chen, and T. Mohri, to be published to Mater. Trans. 59 (2018).
 T. Hoshino, R. Zeller, and P. H. Dederichs, Phys. Rev. B70 (2004), 094118(1-7).
 F. Nakamura, T. Hoshino, S. Tanaka, K. Hirose, S. Hirosawa, and T. Sato, Trans. Mat. Res. Soc. Japan 30 (2005), 873-876.
 T. Hoshino, M. Asato, N. Fujima, Intermetallic 14 (2006), 908-912.
 M. Asato, H. Takahashi, T. Inagaki, N. Fujima, R. Tamura, and T. Hoshino, Mater. Tran. 48 (2007), 1711-1716.
 T. Hoshino, M. Asato, and N. Fujima, J. Alloys. Compd. 504 (2010), S534-S537.
 T. Mohri and Y. Chen, J. Alloys. Compd.383 (2004), 23-31.
 K. Wildberger, P. Lang, R. Zeller, and P. H. Dederichs, Phys. Rev. B 52 (1995), 11502-11508.
 M. Asato, A.Settles, T. Hoshino, T. Asada, S. Blugel, R. Zeller, and P. H. Dederichs, Phys. Rev. B 60 (1999), 5202-5210.
 T. Hoshino, M. Asato, T. Mizuno, and H. Fukushima, Mater. Trans. 42 (2001), 2206-2215.
 R. Zeller, Phys. Rev. B55 (1997), 9400-9408.
 R. Zeller, M. Asato, T. Hoshino, J. Zalbloudil, P. Weinberger, and P. H. Dederichs: Philos. Mag. B78 (1998), 417-422.
 N. Papanikolaou, R. Zeller, P. H. Dederichs, and N. Stefano, Phys. Rev. B 55 (1997), 4157-4167.
 T. Hoshino, N. Papanikolaou, R. Zeller, P.H. Dederichs, M. Asato, and N. Stefanou, Comput. Mater. Sci. 14 (1999), 56-61.
 M. Asato, C. Liu, K. Kawakami, N. Fujima, and T. Hoshino, Mater. Tran. 55 (2014), 1248-1256.
 C. Liu, M. Asato, N. Fujima, and T. Hoshino, Physics Procedia 75 (2015), 1088-1095.
 C. Liu, M. Asato, N. Fujima, T. Hoshino, Y. Chen, and T. Mohri, submitted to Mater. Trans.
 W. Schweika, Disordered Alloys, (SpringerTracts in Modern Physics 141, Springer 1998), pp.51-54.