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Ordering tendencies in Pd-Pt, Rh-Pt, and Ag-Au alloys

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Journal of Phase Equilibria

Abstract

First-principles quantum-mechanical calculations indicate that the mixing enthalpies for Pd-Pt and Rh-Pt solid solutions are negative, in agreement with experiment. Calculations of the diffuse-scattering intensity due to short-range order also exhibits ordering tendencies. Further, the directly calculated enthalpies of formation of ordered intermetallic compounds are negative. These ordering tendencies are in direct conflict with a 1959 prediction of Raub that Pd-Pt and Rh-Pt will phase-separate below ~760 °C (hence their mixing energy will be positive), a position that has been adopted by all binary alloy phase diagram compilations. The present authors predict that Pd1-xPtx will order in the L12, L10, and L12 structures ([001] superstructures) at compositionsx = 1/4, 1/2, and 3/4, respectively, while the ordered structures of Rh1-xPtx are predicted to be superlattices stacked along the [012] directions. While the calculated ordering temperatures for these intermetallic compounds are too low to enable direct growth into the ordered phase, diffuse-scattering experiments at higher temperatures should reveal ordering rather than phase-separation characteristics (i.e., off-F peaks). The situation is very similar to the case of Ag-Au, where an ordering tendency is manifested both by a diffuse scattering intensity and by a negative enthalpy of mixing. An experimental reexamination of PdPt and Rh-Pt is needed.

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Cited References

  1. E. Raub,J. Less-Common Met., 7,3–18 (1959).

    Article  Google Scholar 

  2. E. Raub and G. Falkenburg,Z Metallkd., 55,392–397 (1964).

    Google Scholar 

  3. V.E. Antonov, T.E. Antonova, I.T. Belash, E.G. Ponyatovshii, and V.l. Rashupkin,Phys. Status Solidi(a), 78,137–146 (1983).

    Article  ADS  Google Scholar 

  4. S.R. Bharadwaj, A.S. Kerkar, S.N. Tripathi, and S.R. Dharwadkar,J. Less-Common Met., 169,167–172 (1991).

    Article  Google Scholar 

  5. H. Noh, T.B. Flanagan, and Y. Sakamoto,Scr. Metall. Mater., 29, 445–450(1993).

    Article  Google Scholar 

  6. J. Van Der Rest, F.Gautier, and F. Breuers,J. Phys..F,5,2283 (1975); M. Cyrot and F. Cyrot-Lackmann,J. Phys. F 6, 2257 (1976); G. Tregliaand F. Ducastelle,J. Phys. F 17,1935 (1987); M. Sluiter, P. Turchi, and D. de Fontaine,J. Phys. F, 17, 2163 (1987).

    Article  ADS  Google Scholar 

  7. Z.W. Lu, S.-H. Wei, and A. Zunger,Phys. Rev. Lett., 66(13), 1753- 1756(1991).

    Article  ADS  Google Scholar 

  8. Cohesion in Metals: Transition Metal Alloys, F.R. de Boer et al., Ed., North Holland, Amsterdam (1988).

    Google Scholar 

  9. D.G. Pettifor,New Sci., 110(1510), 48–53 (1986).

    Google Scholar 

  10. R.P Elliott,Constitution of Binary Alloys, First Supplement, Genium Publishing Corporation, Schenectady, NY, 748 (1965).

    Google Scholar 

  11. F. A. Shunk,Constitution of Binary Alloys, Second Supplement, Genium Publishing Corporation, Schenectady, NY, 607, 622 (1969).

    Google Scholar 

  12. W.G. Moffatt,Handbook of Binary Phase Diagrams, Genium Pub- lishing Corporation, Schenectady, NY (1978).

    Google Scholar 

  13. T.B. Massalski, PR. Subramanian, H. Okamoto, and L. Kacprzak,Binary Alloy Phase Diagrams, Vol 3, ASM International, Materials Park, OH, 3020,3022,3033–3034 (1990).

    Google Scholar 

  14. H. Okamoto,J.Phase Equilibria, 72(5), 617–618 (1991).

    Article  Google Scholar 

  15. H. Okamoto,J. Phase Equilibria, 13(2), 223–224 (1992).

    Article  Google Scholar 

  16. A. Zunger, inStat and Dynamics of Alloy Phase Transitions, P.E. A. Turchi and A. Gonis, Ed., NATO ASI Series, Kluwer Academic Publishers, Dordrecht, The Netherlands (1994).

    Google Scholar 

  17. A. Kidron,Phys. Lett. A, 25,112–113 (1967).

    Article  ADS  Google Scholar 

  18. F.H. Hayes and O. Kubaschewski,Met. Sci. J., 5,37 (1971).

    Article  Google Scholar 

  19. J.B. Darby and K.M. Myles,Metall. Trans., 3,653–657 (1972).

    Article  Google Scholar 

  20. Phase Diagrams of Binary Gold Alloys, H. Okamoto and T.B. Mas- salski, Ed., ASM International, Metals Park, OH, 76 (1987).

    Google Scholar 

  21. N. Norman and B.E. Warren,J. Appl. Phys., 22,483 (1951).

    Article  ADS  Google Scholar 

  22. J.L. White, R.L. Orr, and R. Hultgren,Acta Metall, 5, 747–760 (1957).

    Article  Google Scholar 

  23. K. Ziesemer, Ph.D. thesis, Universität Frankfurt, 1976.

  24. B. Schönfeld, J. Traube, and G. Kostorz,Phys. Rev. B, 45(2), 613- 621 (1992).

    Article  ADS  Google Scholar 

  25. S.-H. Wei, A.A. Mbaye, L.G. Ferreira, and A. Zunger,Phys. Rev. B, 56,4163(1987).

    Article  ADS  Google Scholar 

  26. K. Terakura, T. Oguchi, T Mohri, and K. Watanabe,Phys. Rev. B, 35(5), 2169–2173 (1987); T. Mohri, K. Terakura, T. Oguchi, and K. Watanabe,Acta Metall. Mater., 36(3), 547–553 (1988);T. Mohri, K. Terakura, S. Takizawa, and J.M. Sanchez,Acta Metall. Mater., 39(4), 493–501 (1991); T Mohri, S. Takizawa, and K. Terakura,J. Phys. Condens. Matter, 5,1473–1480 (1993).

    Article  ADS  Google Scholar 

  27. R.A. Johnson,Phys. Rev. B, 39(17), 12554–12559 (1989);47(14), 9717-9720(1990).

    Article  ADS  Google Scholar 

  28. G.J. Ackland and V. Vitek,Phys. Rev. B, 41(15), 10324–10333 (1990).

    Article  ADS  Google Scholar 

  29. B.M. Klein and C.Y. Fong, inMetallic Alloys: Experimental and Theoretical Perspectives, J.S. Faulkner and R.G. Jordan, Ed., 291, Kluwer Academic Publishers, Dordrecht, The Netherlands (1994).

    Chapter  Google Scholar 

  30. Z.W. Lu, B.M. Klein, and A. Zunger, manuscript in preparation.

  31. E. Raub, H. Beeskow, and D. Menzel,Z Metallkd., 50,428 (1959).

    Google Scholar 

  32. J.E. Shield and R.K. Williams,Scr. Metall., 21,1475 (1987).

    Article  Google Scholar 

  33. D.D. Johnson, P.E.A. Turchi, M. Sluiter, D.M. Nicholson, F.J. Pin- ski, and G.M. Stocks, inAlloy Phase Stability and Design, G.M.Stocks, D. Pope, and A. Giamei, Ed., MRS Symposia Proceedings No 186, Materials Research Society, Pittsburgh, 21 (1991); B.L. Gyorffy, D.D. Johnson, F.J Pinski, D.M. Nicholson, and G.M. Stocks, inAlloy Phase Stability, G.M. Stocks and A. Gonis, Ed., NATO ASI Series 163, Kluwer Academic Publishers, Dordrecht, The Netherlands, 421 (1989).

    Google Scholar 

  34. C. Wolverton, D. de Fontaine, and H. Dreyssé,Phys. Rev. B, 48, 5766(1993).

    Article  ADS  Google Scholar 

  35. Y. Wang, J.S. Faulkner, and G.M. Stocks,Phys. Rev. Lett., 70,3287 (1993).

    Article  ADS  Google Scholar 

  36. V.L. Moruzzi, J.F. Janak, and A.R. Williams,Calculated Electronic Properties of Metals, Pergamon Press, Inc., New York (1978);Elec- tronic Structure, Dynamics, and Quantum Structural Properties of Condensed Matter, J.T. Devreese and D. Van Camp, Ed., Plenum Publishing Corp., New York (1985).

    Google Scholar 

  37. P. Hohenberg and W. Kohn,Phys. Rev., 136, B864 (1964).

    Article  ADS  Google Scholar 

  38. W. Kohn and L.J. Sham,Phys. Rev., 140, A1133 (1965).

    Article  ADS  Google Scholar 

  39. O.K. Andersen,Phys. Rev. B, 12, 3060 (1975); E. Wimmer, H. Krakauer, M. Weinert, and A.J. Freeman,Phys. Rev. B, 24, 864 (1981); D.R. Hamann,Phys. Rev. Lett., 42, 662 (1979); S.-H. Wei and H. Krakauer,Phys. Rev. Lett., 55, 1200 (1985); S.-H. Wei, H. Krakauer, and M. Weinert,Phys. Rev. B, 32,7792 (1985).

    Article  ADS  Google Scholar 

  40. D.J. Singh,Planewaves, Psuedopotentials, and the LAPWMethod, Kluwer Academic Publishers, Boston (1994).

    Book  Google Scholar 

  41. J.M. Sanchez, F. Ducastelle, and D. Gratias,Physica A, 128, 334 (1984); J.M. Sanchez,Phys. Rev. B, 48,14013 (1993).

    Article  MathSciNet  ADS  Google Scholar 

  42. R. Kikuchi,Phys. Rev., 81,988 (1951).

    Article  MathSciNet  ADS  Google Scholar 

  43. K. Binder and D.W. Heermann,Monte Carlo Simulations in Statis- tical Physics, Springer-Verlag, Berlin (1988).

    Book  Google Scholar 

  44. N. Metropolis et al.,J Chem. Phys., 21,1087(1953).

    Article  ADS  Google Scholar 

  45. Z.W. Lu, D.B. Laks, S.-H. Wei, and A. Zunger,Phys. Rev. B, 50, 6642(1994).

    Article  ADS  Google Scholar 

  46. J.M. Cowley,J Appl. Phys., 27,24 (1950).

    Article  ADS  Google Scholar 

  47. Z.W. Lu and A. Zunger,Phys. Rev. B, 50,6626 (1994).

    Article  ADS  Google Scholar 

  48. Z.W. Lu, S.-H. Wei, A. Zunger, S. Frota-Pessoa, and L.G. Ferreira,Phys. Rev. B, 44(2), 512–544 (1991).

    Article  ADS  Google Scholar 

  49. E. Wigner,Phys. Rev., 46,1002 (1934).

    Article  ADS  Google Scholar 

  50. D.M. Ceperley and B.J. Alder,Phys. Rev. Lett., 45,566 (1980).

    Article  ADS  Google Scholar 

  51. J. P.Perdewand A. Zunger,Phys. Rev., B, 23,5048 (1981).

    Article  ADS  Google Scholar 

  52. H.J. Monkhorstand J.D. Pack,Phys. Rev. B, 13,5188 (1976).

    Article  MathSciNet  ADS  Google Scholar 

  53. Z.W. Lu, S.-H. Wei, and A. Zunger,Europhys. Lett., 21, 221–226 (1993).

    Article  ADS  Google Scholar 

  54. R. Magri, S.-H. Wei, and A. Zunger,Phys. Rev. B, 42(17), 11388- 11391(1990).

    Article  ADS  Google Scholar 

  55. C. Wolverton and A. Zunger, unpublished.

  56. K.M. Myles,Metall. Trans. AIME, 242,1523 (1968).

    Google Scholar 

  57. L.G. Ferreira, A.A. Mbaye, and A. Zunger,Phys. Rev. B, 35, 6475 (1987);Phys. Rev. B, 37,10547 (1988).

    Article  ADS  Google Scholar 

  58. J.W.D. Connolly and A.R. Williams,Phys. Rev. B, 27,5169 (1983).

    Article  ADS  Google Scholar 

  59. G.M Kuznetsov, E.I. Rytvin, and I.V. Nikomova,Izv. Akad. Nauk SSSR, Met., 4,194–197 (1985)in Russian;TR-.Russ. Metall., 4,189- 192(1984).

    Google Scholar 

  60. A.K. Niessen, FR. de Boer, R. Boom, FF. de Chatel, W.C.M. Mat- tens, and A.R. Miedetna,Calphad, 7(1), 51–70 (1983).

    Article  Google Scholar 

  61. V. Gerold and J. Kern,Acta Metall., 35,393 (1987).

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of California, 95616, Davis, CA

    Z. W. Lu & B. M. Klein

  2. National Renewable Energy Laboratory, 80401, Golden, CO

    A. Zunger

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Lu, Z.W., Klein, B.M. & Zunger, A. Ordering tendencies in Pd-Pt, Rh-Pt, and Ag-Au alloys. JPE 16, 36–45 (1995). https://doi.org/10.1007/BF02646247

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