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Modeling of solidification microstructures in concentrated solutions and intermetallic systems

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Abstract

Most of the theoretical models for the predictions of solidification microstructure and solute segregation are based on the assumption mat the solute distribution coefficient,k, is independent of temperature. For concentrated alloys and for alloys near intermetallic compounds,k may vary significantly with temperature. A theoretical analysis which shows the necessary modifications in the theoretical models which must be made ifk varies with temperature is developed. It is shown that for phase diagrams with linear liquidus and solidus segments, many of the results derived with constantk can be used if the solute distribution coefficientk is replaced by a modified parameterk* which includesk as well as the derivative ofk with composition. The application of the model to concentrated alloys and to compositions near intermetallic phases is discussed. It is shown that the variation ink with temperature can significantly alter the composition dependence of dendritic microstructural scales and change the solute segregation profiles in solidified alloys.

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References

  1. W.W. Mullins and R.F. Sekerka:J. Appl. Phys., 1964, vol. 35, pp. 444–51.

    Article  Google Scholar 

  2. R. Trivedi:J. Cryst. Growth, 1980, vol. 49, pp. 219–32.

    Article  CAS  Google Scholar 

  3. W. Kurz and D.J. Fisher:Acta Metall., 1981, vol. 11, pp. 11–20.

    Google Scholar 

  4. J.D. Hunt: inSolidification and Casting of Metals, The Metals Society, Book 192, London, 1979, pp. 3–9.

    Google Scholar 

  5. H.D. Brody and M.C. Flemings:Trans. TMS-AIME, 1966, vol. 236, pp. 615–24.

    CAS  Google Scholar 

  6. M.C. Flemings:Solidification Processing, McGraw-Hill, New York, NY, 1974.

    Google Scholar 

  7. J. Bower, H.D. Brody, and M.C. Flemings:Trans. TMS-AIME, 1966, vol. 236, pp. 624–34.

    CAS  Google Scholar 

  8. K.A. Jackson and J.D. Hunt:Trans. TMS-AIME, 1966, vol. 236, pp. 1129–42.

    CAS  Google Scholar 

  9. A. J. McAlister: inBinary Alloy Phase Diagrams, T.B. Massalski, ed., ASM INTERNATIONAL, Metals Park, OH, 1987, p. 5.

    Google Scholar 

  10. W. Kurz, B. Giovanola, and R. Trivedi:Acta Metall., 1986, vol. 34, pp. 823–30.

    Article  CAS  Google Scholar 

  11. Y. Wu, T. Piccone, Y. Shiohara, and M.C. Flemings:Metall. Trans. A, 1987, vol. 18A, pp. 915–24.

    CAS  Google Scholar 

  12. S.R. Coriell and R.F. Sekerka:J. Cryst. Growth, 1983, vol. 61, pp. 499–508.

    Article  CAS  Google Scholar 

  13. S.R. Coriell, G.B. McFadden, P.W. Voorhees, and R.F. Sekerka:J. Cryst. Growth, 1987, vol. 82, pp. 295–302.

    Article  CAS  Google Scholar 

  14. R. Trivedi and W. Kurz:Acta Metall., 1986, vol. 34, pp. 1663–70.

    Article  CAS  Google Scholar 

  15. J.S. Langer and H. Müller-Krumbhaar:Acta Metall., 1978, vol. 26, pp. 1681–90.

    Article  CAS  Google Scholar 

  16. D. Meiron:Phys. Rev., 1986, vol. 33A, pp. 2704–15.

    Google Scholar 

  17. A. Barbieri, D.C. Hong, and J.S. Langer:Phys. Rev., 1987, vol. A35, pp. 1802–08.

    Google Scholar 

  18. P. Pelcè and Y. Pomeau:Stud. Appl. Math., 1986, vol. 74, pp. 245–58.

    Google Scholar 

  19. D. Kessler and H. Levine:Phys. Rev. Lett., 1986, vol. 57, pp. 3069–72.

    Article  Google Scholar 

  20. J. Lipton, M.E. Glicksman, and W. Kurz:Mater. Sci. Eng., 1984, vol. 65, pp. 57–63.

    Article  CAS  Google Scholar 

  21. R. Trivedi:Metall. Trans. A, 1984, vol. 15A, pp. 977–82.

    CAS  Google Scholar 

  22. R. Trivedi and K. Somboonsuk:J. Mater. Sci. Eng., 1984, vol. 65, pp. 65–74.

    Article  CAS  Google Scholar 

  23. H. Esaka and W. Kurz:J. Cryst. Growth, 1985, vol. 72, pp. 578–84.

    Article  CAS  Google Scholar 

  24. R. Trivedi and J.T. Mason:Metall. Trans. A, in press.

  25. K. Somboonsuk, J.T. Mason, and R. Trivedi:Metall. Trans. A, 1984, vol. 15A, pp. 967–75.

    CAS  Google Scholar 

  26. J.A.E. Bell and W.C. Winegard:J. Inst. Met., 1963–64, vol. 92, pp. 357–59.

    Google Scholar 

  27. P.C. Dann, J.A. Eady, and L.M. Hogan:J. Aust. Inst. Met., 1984, vol. 19, pp. 140–47.

    Google Scholar 

  28. C.M. Klaren, J.D. Verhoeven, and R. Trivedi:Metall. Trans. A, 1980, vol. 11A, pp. 1853–61.

    CAS  Google Scholar 

  29. B.C. Fuh: Ph.D. Thesis, Iowa State University, Ames, IA, 1984.

    Google Scholar 

  30. J.A. Juarez Islas, H. Jones, and W. Kurz:Mater. Sci. Eng., 1988, vol. 98, pp. 201–08.

    Article  CAS  Google Scholar 

  31. J.A. Murray: ALCOA Laboratories, Pittsburgh, PA, unpublished work, 1989.

  32. T.W. Clyne and W. Kurz:Metall. Trans. A, 1981, vol. 12A, pp. 965–71.

    Google Scholar 

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Trivedi, R., Kurz, W. Modeling of solidification microstructures in concentrated solutions and intermetallic systems. Metall Trans A 21, 1311–1318 (1990). https://doi.org/10.1007/BF02656547

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