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Numerical techniques for the calculation of binary phase diagrams

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Abstract

Numerical techniques are presented for the calculation of binary phase diagrams. Most compositions are obtained directly through a Taylor series expansion of the composition with respect to temperature. The series is limited to the second order term and analytic expressions of the slopes and curvatures of phase boundaries have been developed for its use. A Newton-Raphson iteration technique tests the convergence of the results. The method is efficient and accommodates various formalisms for the free energy functions. The series is not applicable to very dilute solutions of a component, near the critical point of a miscibility gap or in the vicinity of the congruent transformation point of a compound; in these cases, alternate equations have been derived.

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References

  1. R. Hullgren, L. R. Orr, P. D. Anderson, and K. K. Kellcy:Selected Values of Thermodynamic Properties of Metals and Alloys, John Wiley and Sons, Inc., New York, 1963.

    Google Scholar 

  2. M. Hansen and K. Anderko:Constitution of Binary Alloys, McGraw-Hill Book Co., New York, 1958.

    Google Scholar 

  3. L. Kaufman and M. Bernstein:Computer Calculations of Phase Diagrams, Academic Press, New York, 1970.

    Google Scholar 

  4. I. Ansara:Metallurgical Chemistry, Proceedings of a Symposium held at Brunel University and the National Physical Laboratory, July 1971, O. Kubaschewski, ed., pp. 403–30, 651, Her Majesty’s Stationery Office, London, 1972.

    Google Scholar 

  5. C. H. P. Lupis and J. F. Elliott:Acta Met., 1966, vol. 14, pp. 529–38.

    Article  CAS  Google Scholar 

  6. C. H. P. Lupis:Acta Met., 1968, vol. 16, pp. 1365–75.

    Article  CAS  Google Scholar 

  7. R. Hiskes and W. A. Tiller:Mater. Sci. Eng., 1967–68, vol. 2, pp. 320–30; 1969, vol. 4, pp. 163-84.

    Google Scholar 

  8. H. Gaye: Ph.D. thesis, Carnegie-Mellon University, 1971.

  9. D. R. Stull and H. Prophet,et al.:JANAF Thermo chemical Tables, 2nd ed., NSRDS-NBS 37, U.S. Govt. Print. Off., Washington, 1971.

    Google Scholar 

  10. P. S. Rudman:Advances in Materials Research, vol. IV, pp. 147–293, Interscience Publishers, New York, 1969.

    Google Scholar 

  11. C. H. P. Lupis and H. Gaye:Metallurgical Chemistry, Proceedings of a Symposium held at Brunel University and the National Physical Laboratory, July 1971, O. Kubaschewski, ed., pp. 469–82, Her Majesty’s Stationery Office, London 1972.

    Google Scholar 

  12. E-Hsin Foo and C. H. P. Lupis:Proceedings of the International Conference on the Science and Technology of Iron and Steel, Suppl. to Trans. Iron Steel Inst. Jap., 1971, vol. 11, pp. 404–08.

    Google Scholar 

  13. C. H. P. Lupis and J. F. Elliott:Acta Met., 1967, vol. 15, pp. 265–76.

    Article  CAS  Google Scholar 

  14. J. Warner and C. H. P. Lupis: Carnegie-Mellon Unversity, Pittsburgh, Pa., unpublished research, 1974.

  15. C. E. Wicks and F. E. Block:Thermodynamic Properties of 65 Elementstheir Oxides, Halides, Carbides and Nitrides, U. S. Govt. Print. Office, Washington, 1963.

    Google Scholar 

  16. R. L. Orr and J. Chipman:Trans. TMS-AIME, 1967, vol. 239, pp. 630–33.

    CAS  Google Scholar 

  17. J. C. Swartz:Trans. TMS-AIME, 1969, vol. 245, pp. 1083–92.

    CAS  Google Scholar 

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Authors and Affiliations

  1. IRSID, Maizieres-les-Metz, France

    Henri Gaye

  2. Carnegie-Mellon University, 15213, Pittsburgh, Pa.

    C. H. P. Lupis (Professor of Metallurgy and Materials Science)

Authors
  1. Henri Gaye
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  2. C. H. P. Lupis
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Formerly Graduate Student, Department of Metallurgy and Materials Science, Carnegie-Mellon University.

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Gaye, H., Lupis, C.H.P. Numerical techniques for the calculation of binary phase diagrams. Metall Trans A 6, 1049–1056 (1975). https://doi.org/10.1007/BF02661359

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