First Principles Calculations of Binary Alloy Phase Diagrams

  • C. Colinet
  • A. Pasturel
Part of the Data and Knowledge in a Changing World book series (DATAKNOWL)

Abstract

In the past decade attempts to obtain a theoretical knowledge of thermodynamic data and phase diagrams of alloys have been made by combining, at a high level of accuracy, both quantum-mechanical and statistical-thermodynamical contributions. These calculations have to take into account the local chemical environment in the alloy which is important in determining both the internal energy and the entropy of configuration. One of the most efficient methods for including short and long range order is the cluster variation method. This method needs, as input the effective cluster interactions which determine ordering or clustering reactions occurring in a given lattice. These interactions can be derived from experimental data such as critical temperatures or enthalpies of formation, but they can also be obtained within the tightbinding framework or by using purely “ab-initio” methods such as the linear muffin tin orbitals. These methods are presented and the results obtained in binary metallic alloys are reported.

Keywords

Entropy Enthalpy Calorimetry 

Résumé

Durant les dix dernières années des efforts pour obtenir une connaissance théorique des données de thermodynamique et des diagrammes de phase des alliages ont été menés en combinant, avec une grande précision, à la fois la mécanique quantique et la thermodynamique statistique. Ces calculs doivent prendre en compte l’environnement chimique local dans l’alliage qui est important pour déterminer conjointement l’énergie interne et l’entropie de la configuration. Une des méthodes les plus efficaces pour tenir compte de l’ordre à courte et longue distance est la méthode variationnelle des amas. Cette méthode nécessite en entrée les interactions d’amas apparaissant. Ces interactions peuvent être dérivées de données expérimentales telles que la température critique ou les enthalpies de formation, mais peuvent l’être également en utilisant des méthodes purement «ab-initio»

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References

  1. [1]
    F.D. Murnaghan, Proc. Natl. Acad. Sci., USA, 30, (1944), 244.CrossRefGoogle Scholar
  2. [2]
    R. Kikuchi, Phys. Rev., 81, (1951), 988.CrossRefGoogle Scholar
  3. [3]
    J.C. Slater and G.F. Koster, Phys. Rev, 94, (1954), 1498Google Scholar
  4. [4]
    O. Kubaschewski, Trans. Faraday Soc, 54, (1958), 814.CrossRefGoogle Scholar
  5. [5]
    F. Herman and S. Skillman, in Atomic Structure Calculations, Prentice Hall, Englewood Cliffs, NJ, (1965).Google Scholar
  6. [6]
    H. Shiba, Prog. Theor. Phys, 46, (1971), 77.CrossRefGoogle Scholar
  7. [7]
    R. Kikuchi and H. Sato, Acta Metall, 22, (1974), 1099.CrossRefGoogle Scholar
  8. [8]
    F. Gautier, F. Ducastelle, and J. Giner, Phil. Mag, 31, (1975), 1372.Google Scholar
  9. [9]
    A.R. Miedema, R. Boom, and F.R. de Boer, J. Less-Common Met, 41, (1975), 283.Google Scholar
  10. [10]
    F. Ducastelle and F. Gautier, J. Phys. F, 6, (1976), 2039Google Scholar
  11. [11]
    R. Kikuchi and D. de Fontaine, Applications of Phase Diagrams in Metallurgy and Ceramics, ed. G.C. Carter, NBS Publications, SP 496, (1977), 967.Google Scholar
  12. [12]
    V.L. Moruzzi, J.F. Janak, and A.R. Williams, Calculated Electronic Properties of Metals, Pergamon, New York, 2 (1978).Google Scholar
  13. [13]
    R.C. Kittler and L.M. Falicov, Phys. Rev. B, 18, (1978), 2506.Google Scholar
  14. [14]
    D.G. Pettifor, Phys. Rev. Lett, 42, (1979), 846.CrossRefGoogle Scholar
  15. [15]
    W.A. Harrison, Electronic Structure and the Properties of Solids, Freeman, San Francisco (1980).Google Scholar
  16. [16]
    R.E. Watson and L.H. Bennett, Calphad, 5, (1981), 25.CrossRefGoogle Scholar
  17. [17]
    M.O. Robbins and L.M. Falicov, Phys. Rev. B, 25, (1982), 2343.Google Scholar
  18. [18]
    J.W.D. Connolly and A.R. Williams, Phys. Rev. B, 27, (1983), 5169.CrossRefGoogle Scholar
  19. [19]
    O.K. Andersen, NATO ASI on Electronic Structure of Complex Systems, P. Phariseau and W. M. Temmerman eds., Plenum, New York, p. 11 (1984).Google Scholar
  20. [20]
    M.O. Robbins and L.M. Falicov, Phys. Rev. B, 29, (1984), 1333.Google Scholar
  21. [21]
    R.E. Watson and L.H. Bennett, Calphad, 8, (1984), 307.CrossRefGoogle Scholar
  22. [22]
    C. Colinet, A. Pasturel and P. Hicter, Calphad, 9, (1985), 71.CrossRefGoogle Scholar
  23. [23]
    R.J. Hawkins, M. O. Robbins, and J.M. Sanchez, Solid State Commun., 55, (1985), 253.CrossRefGoogle Scholar
  24. [24]
    A. Pasturel, J Hafner and P. Hicter, Phys. Rev. B, 32, (1985), 5009.CrossRefGoogle Scholar
  25. [25]
    A. Bieber and F. Gautier, Acta Metall., 34, (1986), 2291.CrossRefGoogle Scholar
  26. [26]
    K. Binder, Monte Carlo Methods in Statistical Physics, K. Binder, edt., Springer Series on Topics in Current Physics, Springer, Berlin (1986).Google Scholar
  27. [27]
    R.J. Hawkins, M.O. Robbins, and J.M. Sanchez, Phys. Rev. B, 33, (1986), 4782.CrossRefGoogle Scholar
  28. [28]
    D. Mayou, D. Nguyen Manh, A. Pasturel, and F. Cyrot-Lackmann, Phys, Rev. B, 33, (1986), 3384.CrossRefGoogle Scholar
  29. [29]
    A. Pasturel and J. Hafher, Phys. Rev. B, 34, (1986), 8357.CrossRefGoogle Scholar
  30. [30]
    C. Sigli, M. Kosugi, and J.M. Sanchez, Phys. Rev. Lett., 57, (1986), 253.CrossRefGoogle Scholar
  31. [31]
    A. Bieber and F. Gautier, Acta Metall., 35, (1987), 1839.CrossRefGoogle Scholar
  32. [32]
    A.E. Carlsson, Phys. Rev. B, 35, (1987), 4858.CrossRefGoogle Scholar
  33. [33]
    C. Colinet and A. Pasturel, Calphad, 11, (1987), 335.CrossRefGoogle Scholar
  34. [34]
    P. Turchi, M. Sluiter, and D. de Fontaine, Phys. Rev. B, 36, (1987), 3161.Google Scholar
  35. [35]
    F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, and A.K. Niessen, “Cohesion in Metals. Transition Metal Alloys”, Vol. 1, F.R. de Boer, D.G. Pettifor, edts, North-Holland (1988).Google Scholar
  36. [36]
    C. Colinet, A. Bessoud, and A.Pasturel, J. Phys. F: Met. Phys., 18, (1988), 903.Google Scholar
  37. [37]
    L. G. Ferreira, A. A. Mbaye, and A. Zunger, Phys. Rev. B, 37, (1988), 10547.CrossRefGoogle Scholar
  38. [38]
    R.J. Hawkins and J.M. Sanchez, J. Phys. F, 18, (1988), 767.CrossRefGoogle Scholar
  39. [39]
    C. Sigli and J.M. Sanchez, Acta Metall., 36, (1988), 367.CrossRefGoogle Scholar
  40. [40]
    M. Sluiter, P. Turchi, F. Zezhong, and D. de Fontaine, Phys. Rev. Lett., 60, (1988), 716.Google Scholar
  41. [41]
    C. Colinet, A. Bessoud, and A. Pasturel, J. Phys.: Condens. Matter, 1, (1989), 5837.CrossRefGoogle Scholar
  42. [42]
    M. Sluiter and P.E.A. Turchi, Phys. Rev. B, 40, (1989), 11215.CrossRefGoogle Scholar
  43. [43]
    A.T. Dinsdale, Calphad, 15, (1991), 317.CrossRefGoogle Scholar
  44. [44]
    G. Inden and W. Pitsch, Atomic Ordering in Materials Science and Technology, R.W. Cahn, P. Haasen, E.J. Kramer, edts, vol.5, VCH, Weinheim, p. 97 (1991).Google Scholar
  45. [45]
    D.H. Le, C. Colinet, P. Hicter, and A. Pasturel, J. Phys.: Condens. Matter, 3, (1991), 7895.CrossRefGoogle Scholar
  46. [46]
    D.H. Le, C. Colinet, P. Hicter, and A. Pasturel, J. Phys.: Condens. Matter, 3, (1991), 9965.CrossRefGoogle Scholar
  47. [47]
    M. Van Schilfgaarde, A.T. Paxton, A. Pasturel, and M. Methfessel, MRS, Symp. Vol. 186, Ed. G.M. Stocks, D.P. Pope and A.F. Giamei, MRS, Pittsburgh, PA:, p. 107 (1991).Google Scholar
  48. [48]
    C. Colinet, P. Hicter, and A. Pasturel, Phys. Rev. B, 45, (1992), 1571.Google Scholar
  49. [49]
    A. Pasturel, C. Colinet, A.T. Paxton, and M. Van Schilfgaarde, J. Phys.: Condens. Matter, 4, (1992), 945.CrossRefGoogle Scholar
  50. [50]
    A. Pasturel, unpublished work (1992).Google Scholar
  51. [51]
    M. van Schilfgaarde, A.T. Paxton, and M. Methfessel, unpublished work (1992).Google Scholar
  52. [52]
    P.E.A. Turchi, Electronic Theories of Alloy Phase Stability, in: Intermetallic Compounds: Principles and Practice, J.H. Westbrook and R.L. Fleischer, eds, John Wiley & Sons, Ltd, Chichester, U.K., p21 (1993).Google Scholar
  53. [53]
    C. Colinet and A. Pasturel, Physica, B192, (1993), 238.CrossRefGoogle Scholar
  54. [54]
    C. Colinet, J. Eymery, A. Pasturel, A. T. Paxton, and M. van Schilfgaarde, J. Phys: Condens. Matter, 6, (1994), L47.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • C. Colinet
    • 1
  • A. Pasturel
    • 1
  1. 1.Laboratoire de Thermodynamique et Physico-Chimie MétallurgiquesI.N.P.G., ENSEEGSaint Martin d’Hères CedexFrance

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