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Diffusion-controlled growth in ternary systems

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Abstract

Diffusion-controlled growth of particles, dendrites, and plates in infinite media is examined for ternary systems. The growth kinetics associated with planar, cylindrical, and spherical particles are shown to be limiting cases of a more complete analysis (also presented) for shape-preserving growth. The theory is applied to the growth of allotriomorphic ferrite from austenite in ternary Fe-C-X steels, where X represents a substitutional alloying element. Numerical results are given, the analysis relying on the ability to predict multicomponent phase equilibria. The work represents an attempt at coupling together thermodynamic and kinetic models for the diffusion-controlled3 phase transformations that occur in steels.

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References

  1. CALPHAD Journal, Pergamon Press, Oxford.

  2. B. Sundman: Report D53, The Royal Institute of Technology Stockholm, 1984.

    Google Scholar 

  3. NPL Metallurgical and Thermochemical Databank (MTDATA) National Physical Laboratory, Teddington, Middlesex, United Kingdom.

  4. J.W. Christian:The Theory of Transformations in Metals and Alloys. 2nd ed., Pergamon Press, Oxford, 1975. Part 1.

    Google Scholar 

  5. J.S. Kirkaldy and D.J. Young:Diffusion in the Condensed State. The Institute of Metals, London, 1987.

    Google Scholar 

  6. J.R. Bradley, J.M. Rigsbee, and H.I. Aaronson:Metall. Trans. A, 1977, vol. 8A, pp. 323–33.

    CAS  Google Scholar 

  7. H.K.D.H. Bhadeshia:Prog. Mater. Sci., 1985, vol. 29, pp. 321–86.

    Article  CAS  Google Scholar 

  8. C. Atkinson, H.B. Aaron, K.R. Kinsman, and H.I. Aaronson:Metall. Trans., 1973, vol. 4, pp. 783–92.

    Article  CAS  Google Scholar 

  9. C. Zener,J. Appl. Phys., 1949, vol. 20, pp. 950–53.

    Article  CAS  Google Scholar 

  10. F.C. Frank:Proc. R. Soc, 1950, vol. A201, pp. 586–99.

    Google Scholar 

  11. F.S. Ham:J. Phys. Chem. Solids, 1958, vol. 6, pp. 335–51.

    Article  CAS  Google Scholar 

  12. F.S. Ham:Q. Appl. Math., 1959, vol. 17, pp. 137–45.

    Google Scholar 

  13. G. Horvay and J.W. Cahn:Acta Metall., 1961, vol. 9, pp. 695–705.

    Article  CAS  Google Scholar 

  14. G.P. Ivantsov:Dokl. Akad. Nauk SSSR, 1947, vol. 58, pp. 567–70.

    Google Scholar 

  15. R. Trivedi and G.M. Pound:J. Appl. Phys., 1967, vol. 38, pp. 3569–76.

    Article  CAS  Google Scholar 

  16. C. Atkinson:J. Appl. Phys., 1969, vol. 40, pp. 4859–65.

    Article  CAS  Google Scholar 

  17. C. Atkinson :Q.J. Mech. Appl. Math., 1974, pp. 299-316.

  18. M. Enomoto and C. Atkinson:Acta Metall. Mater., 1993, vol. 41, pp. 3237–3244.

    Article  CAS  Google Scholar 

  19. I.I. Kolodner:Comm. Pure Appl. Math., 1956, vol. 6, pp. 1–31.

    Article  Google Scholar 

  20. J.S. Kirkaldy:Can. J. Phys., 1958, vol. 36, pp. 899–925.

    CAS  Google Scholar 

  21. J.S. Kirkaldy:Can. J. Phys., 1959, vol. 37, pp. 30–34.

    CAS  Google Scholar 

  22. J.S. Kirkaldy, D. Weichen, and Zia Ul-Haq:Can. J. Phys., 1963, vol. 41, pp. 2166–73.

    CAS  Google Scholar 

  23. J.S. Kirkaldy:Adv. Mater. Res., 1970, vol. 4, pp. 55–100.

    CAS  Google Scholar 

  24. D.E. Coates:Metall. Trans., 1973, vol. 4, pp. 1077–86.

    CAS  Google Scholar 

  25. D.E. Coates:Metall. Trans., 1973, vol. 4, pp. 2313–25.

    CAS  Google Scholar 

  26. D.E. Coates:Metall. Trans., 1973, vol. 4, pp. 395–96.

    CAS  Google Scholar 

  27. Computer Simulation of Microstrudural Evolution, D.J. Srolovitz, ed., TMS-AIME. Warrendale, PA, 1986.

    Google Scholar 

  28. Phase Transformations, G.W. Lorimer, ed., The Institute of Metals, London, 1987.

    Google Scholar 

  29. J. Ågren:Didra Program, The Royal Institute of Technology, Stockholm, 1993.

    Google Scholar 

  30. B. Sundman and J. Ågren:J. Phys. Chem. Solids, 1981, vol. 42, pp. 297–301.

    Article  CAS  Google Scholar 

  31. M. Hillert and L.-I. Staffansson:Acta Chem. Scand., 1970, vol. 24, pp. 3618–26.

    Article  CAS  Google Scholar 

  32. P. Gustafson:Scand. J. Metall., 1985, vol. 14, pp. 259–67.

    CAS  Google Scholar 

  33. J.-O. Andersson:CALPHAD, 1988, vol. 12, pp. 9–23.

    Article  CAS  Google Scholar 

  34. J. Lacaze and B. Sundman:Metall. Trans. A, 1991, vol. 22A, pp. 2211–23.

    CAS  Google Scholar 

  35. W. Huang:Metall. Trans. A, 1991, vol. 22A, pp. 1911–20.

    CAS  Google Scholar 

  36. M. Hillert and C. Qiu:Metall. Trans. A, 1991, vol. 22A, pp. 2187–98.

    CAS  Google Scholar 

  37. The NAG Fortran Library Manual, NAG Ltd., Wilkinson House, Oxford, 1991.

  38. J. Fridberg, L. Toradahl, and M. Hillert:Jernkontorets Ann., 1969, vol. 153, pp. 263–76.

    CAS  Google Scholar 

  39. M. Abramowitz and I.A. Stegun:Handbook of Mathematical Functions, Dover, London, 1955.

    Google Scholar 

  40. G. Horvay and J.W. Cahn: G.E. Research Report No. 60-RL-2561M, General Electric Research and Development Center, Schenectady, NY, 1960. $

    Google Scholar 

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Bourne, J.P., Atkinson, C. & Reed, R.C. Diffusion-controlled growth in ternary systems. Metall Mater Trans A 25, 2683–2694 (1994). https://doi.org/10.1007/BF02649221

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