First-Principles Study of Phase Equilibria in the Ni-Cr System

  • J. M. Sanchez
  • P. J. Craievich


The relative importance of various free energy contributions to phase stability in the Ni-Cr system is investigated using total energy calculations in the local density approximation combined with the cluster expansion and the cluster variation method. In particular, we develop a formalism to calculate the vibrational free energy in disordered alloys exhibiting short-range order. The methodology is well adapted to be used in conjunction with first-principles total energy calculations. It is found that the coupling between configurational and displacive degrees of freedom is crucial for the accurate description of the equilibrium phase diagram of the Ni-Cr system, with electronic excitations playing a less important role and the effects of short-range order being essentially negligible.


Bulk Modulus Electronic Excitation Equilibrium Phase Diagram Total Energy Calculation Force Constant Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. M. Sanchez, F. Ducastelle, and D. Gratias, Physica A 128, 334 (1984).CrossRefGoogle Scholar
  2. 2.
    J. M. Sanchez, Phys. Rev. B 46, 14013 (1993).Google Scholar
  3. 3.
    J.M. Sanchez, in Theory and Applications of the Cluster Variation and Path Probability Methods, edited by J. L. Moran-López and J. M. Sanchez, ( Plenum, New York, 1996 ).Google Scholar
  4. 4.
    W. Kohn and L. J. Sham, Phys. Rev. A 140, 1133 (1965).CrossRefGoogle Scholar
  5. 5.
    C. Wolverton and A. Zunger, Phys. Rev. B 52, 8813 (1995).CrossRefGoogle Scholar
  6. 6.
    E. G. Moroni, G. Grimvall, and T. Jarborg, Phys. Rev. Lett. 76, 2758 (1996).CrossRefGoogle Scholar
  7. 7.
    P. J. Craievich, J. M. Sanchez, M. Weinert, and R. E. Watson, Phys. Rev. B 55, 787 (1997).CrossRefGoogle Scholar
  8. 8.
    S. de Gironcoli, P. Giannozzi, and S. Baroni, Phys. Rev. Lett. 66 2116 (1991)CrossRefGoogle Scholar
  9. 9.
    Z. W. Lu et al., Phys. Rev. B 44, 512 (1991).Google Scholar
  10. 10.
    V. L. Moruzzi, J. F. Janak, and K. Schwartz, Phys. Rev. B 37, 790 (1988).CrossRefGoogle Scholar
  11. 11.
    J. M. Sanchez, J. P. Stark, and V. L. Moruzzi, Phys. Rev. B 44, 5411 (1991).CrossRefGoogle Scholar
  12. 12.
    M. Asta, R. McCormack, and D. de Fontaine, Phys. Rev. B 48, 748 (1993).CrossRefGoogle Scholar
  13. 13.
    J. D. Becker and J. M. Sanchez, Mater. Sci. Eng. A 170, 161 (1993).CrossRefGoogle Scholar
  14. 14.
    T. Mohri, S. Takizawa, and K. Terakura, J. Phys. Condens. Matter 35, 1473 (1993)CrossRefGoogle Scholar
  15. 15.
    C. Amador, W. R. L. Lambrecht, and B. Segall, Mat. Res. Symp. Proc. 253, 297 (1992).CrossRefGoogle Scholar
  16. 16.
    J. M. Sanchez, in Structural and Phase Stability of Alloys, edited by J. L. Moran-López, F. Mejía-Lira, and J. M. Sanchez, ( Plenum Press, New York, 1992 ).Google Scholar
  17. 17.
    C. Colinet et al., J. Phys. Condens. Matter 6, L47 (1994).Google Scholar
  18. 18.
    G. D. Garbulsky and G. Ceder, Phys. Rev. B 53, 8993 (1996).CrossRefGoogle Scholar
  19. 19.
    A. Chiolero and D. Baeriswyl, J. Stat. Phys. 76, 347 (1994)CrossRefGoogle Scholar
  20. 20.
    P. J. Craievich, Ph.D. Thesis, The University of Texas at Austin, 1997.Google Scholar
  21. 21.
    P. J. Craievich, M. Weinert, J. M. Sanchez, and R. E. Watson, Phys. Rev. Lett. 72, 3076 (1994).CrossRefGoogle Scholar
  22. 22.
    H. L. Skriver, The LMTO Method ( Springer-Verlag, Berlin, 1984 ).CrossRefGoogle Scholar
  23. 23.
    R. Hultgren et al., Selected Values of the Thermodynamic Properties of Binary Alloys (Am. Soc. Metals, Metals Park, OH, 1973).Google Scholar
  24. 24.
    N. C. Tso, M. Kosugi, and J. M. Sanchez, Acta Metall. 37, 121 (1989).CrossRefGoogle Scholar
  25. 25.
    R. Kikuchi, Phys. Rev. 81, 988 (1951).CrossRefGoogle Scholar
  26. 26.
    J. M. Sanchez and D. de Fontaine, Phys. Rev. B 17, 2926 (1978).CrossRefGoogle Scholar
  27. 27.
    J. M. Sanchez, M. C. Cadeville, V. Pierron-Bohnes, and G. Irden, Phys. Rev. B 54, 8958 (1996).CrossRefGoogle Scholar
  28. 28.
    T. B. Massalski, J. L. Murray, L. H. Bennett, and Hugh Baker, Binary Alloy Phase Diagrams; Selected Values of the Thermodynamic Properties of Binary Alloys (Am. Soc. Metals, Metals Park, OH, 1973 ).Google Scholar
  29. 29.
    R. P. Feynman, Statistical Mechanics, A set of Lectures (W. A. Benjamin Inc., Reading, Massachusetts, 1972 ).Google Scholar
  30. 30.
    B. T. M. Willis and A. W. Pryor, Thermal Vibrations in Crystallography ( Cambridge University Press, Cambridge, 1975 ).Google Scholar
  31. 31.
    R. J. Birgeneau, J. Cordes, G. Dolling, and A. D. B. Woods, Phys. Rev. 136, 1359 (1964).CrossRefGoogle Scholar
  32. 32.
    W. M. Shaw and L. D. Muhlestein, Phys. Rev. B 4, 969 (1971).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • J. M. Sanchez
    • 1
  • P. J. Craievich
    • 1
  1. 1.Center for Materials Science and EngineeringThe University of Texas at AustinAustinUSA

Personalised recommendations