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Cellular precipitation

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Abstract

A theory of cellular precipitation is developed that assumes the interlamellar spacing to be controlled by the nucleation of new precipitate lamellae in recesses that develop in the advancing grain boundary at a sufficiently large interlamellar spacing. The theory also assumes a grain-boundary diffusion mechanism of mass transport, the maximum possible departure from local equilibrium across the grain boundary, and a grain-boundary model developed by Hillert. Application of the theory to all existing data that are sufficiently complet gives values for grain-boundary diffusivities that are both reasonable and in accord with existing diffusitivity data. It also suggests strongly that the velocity of grain-boundary migration is much more strongly dependent on driving force than the linear dependence given in most current theories. The interlamellar-spacing criterion proposed here is in reasonably good agreement with existing experimental data and with the experimental observation of Tu and Turnbull.

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References

  1. J. M. Shapiro and J. S. Kirkaldy:Acta Met., 1968, vol. 16, p. 1239.

    Article  CAS  Google Scholar 

  2. Y. C. Liu and H. I. Aaronson:Acta Met., 1968, vol. 16, p. 1343.

    Article  CAS  Google Scholar 

  3. B. Predel and H. Ruge:Z. Metallk., 1968, vol. 59, p. 777.

    CAS  Google Scholar 

  4. R. G. Rose:Acta Met., 1957, vol. 5, p. 404.

    Article  CAS  Google Scholar 

  5. G. R. Speich:Trans. TMS-AIME, 1963, vol. 227, p. 754.

    CAS  Google Scholar 

  6. H. Böhm:Z. Metallk., 1959, vol. 50, p. 87.

    Google Scholar 

  7. G. R. Speich:Trans. TMS-AIME, 1968, vol. 242, p. 1359.

    CAS  Google Scholar 

  8. H. I. Aaronson and Y. C. Liu:Scr. Met., 1968, vol. 2, p. 1.

    Article  CAS  Google Scholar 

  9. D. Turnbull and H. N. Treaftis:Trans. TMS-AIME, 1958, vol. 212, p. 33.

    CAS  Google Scholar 

  10. R. Watanabe and S. Kuda:Trans. Nat. Res. Inst. Metals, 1965, vol. 7, p. 87.

    CAS  Google Scholar 

  11. Ram Kossowsky:Met. Trans., 1970, vol. 1, p. 1623.

    Article  CAS  Google Scholar 

  12. H. I. Aaronson and J. B. Clark:Acta Met., 1968, vol. 16, p. 845.

    Article  CAS  Google Scholar 

  13. H. I. Aaronson and Y. C. Liu:Met. Trans., 1970, vol. 1, p. 3465.

    CAS  Google Scholar 

  14. K. N. Tu and D. Turnbull:Acta Met., 1967, vol. 15, p. 1317.

    Article  CAS  Google Scholar 

  15. K. N. Tu and D. Turnbull:Acta Met., 1967, vol. 15, p. 369.

    Article  CAS  Google Scholar 

  16. J. W. Cahn:Acta Met., 1959, vol. 7, p. 18.

    Article  CAS  Google Scholar 

  17. D. Turnbull:Acta Met., 1955, vol. 3, p. 55.

    Article  CAS  Google Scholar 

  18. M. Hillert: The Mechanism of Phase Transformations in Crystalline Solids, p. 231, Monograph and Report Series No. 33, Inst. of Metals, 1969.

  19. C. Zener:Trans. AIME, 1946, vol. 167, p. 550.

    Google Scholar 

  20. M. Hillert:Jernkontorets Ann., 1957, vol. 141, p. 757.

    CAS  Google Scholar 

  21. J. C. Fisher:Thermodynamics in Physical Metallurgy p. 201, ASM, Cleveland. 1950.

    Google Scholar 

  22. B. E. Sundquist:Acta Met., 1968, vol. 16, p. 1413.

    Article  CAS  Google Scholar 

  23. K. N. Tu and D. Turnbull:Acta Met., 1969, vol. 17, p. 1263.

    Article  CAS  Google Scholar 

  24. K. N. Tu and D. Turnbull:Scr. Met., 1967, vol. 1, p. 173.

    Article  CAS  Google Scholar 

  25. M. S. Sulonen:Acta Met., 1964, vol. 12, p. 749.

    Article  Google Scholar 

  26. E. Hornbogen:Trans. TMS-AIME, 1963, vol. 227, p. 1411.

    CAS  Google Scholar 

  27. Yu. A. Skakov, K. V. Varli, and G. S. Milovzorov:Acad. Sciences USSR Bull. Phys. Ser., 1970, vol. 34, p. 1393.

    Google Scholar 

  28. G. F. Bolling and W. C. Winegard:Acta Met., 1958, vol. 6, p. 283.

    Article  CAS  Google Scholar 

  29. J. W. Cahn:Acta Met., 1962, vol. 10, p. 789.

    Article  CAS  Google Scholar 

  30. D. McLean:Grain Boundaries in Metals, p. 116, Oxford Press, 1957.

  31. T. Crank:The Mathematics of Diffusion, p. 44, Oxford Press, 1956.

  32. H. A. Wriedt, C. W. Haworth, and J. A. Gula: E. C. Bain Laboratory, U.S. Steel Corp., Monroeville, Pa., unpublished work, 1965.

  33. G. R. Speich, L. Zwell, and H. A. Wriedt:Trans. TMS-AIME, 1964, vol. 230, p. 939.

    CAS  Google Scholar 

  34. J. J. Kramer, G. M. Pound, and R. E. Mehl:Acta Met., 1958, vol. 6, p. 763.

    Article  CAS  Google Scholar 

  35. K. N. Tu and B. Chalmers:Proc. Roy. Soc. A, 1951, vol. 204, p. 359.

    Google Scholar 

  36. K. N. Tu and D. Turnbull:Met. Trans., 1971, vol. 2, p. 2509.

    Article  CAS  Google Scholar 

  37. G. Kirchner, H. Harvig, K. R. Moquist, and M. Hillert:Arch Eisenhüttenw., 1973, vol. 44, p. 227.

    CAS  Google Scholar 

  38. H. A. Wriedt:Trans. TMS-AIME, 1967, vol. 239, p. 1120.

    CAS  Google Scholar 

  39. R. R. Hultgren,et al.:Selected Values of Thermodynamic Properties of Metals and Alloys, Suppl. Vol. II, Wiley, New York, 1963.

    Google Scholar 

  40. B. Predel and W. Schwermann:Acta Met., 1971, vol. 19, p. 85.

    Article  CAS  Google Scholar 

  41. J. P. Stark and W. R. Upthegrove:Trans. ASM, 1966, vol. 59, p. 479.

    CAS  Google Scholar 

  42. B. Okkerse:Acta Met., 1954, vol. 2, p. 555.

    Article  Google Scholar 

  43. D. Turnbull and R. E. Hoffman:Acta Met., 1954, vol. 2, p. 419.

    Article  CAS  Google Scholar 

  44. Hsun Hu and B. B. Rath:Met. Trans., 1970, vol. 1, p. 3181.

    Google Scholar 

  45. K. Lücke and H. P. Stüwe:Acta Met., 1971, vol. 19, p. 1087.

    Article  Google Scholar 

  46. J. W. Cahn, W. B. Hillig, and G. W. Sears:Acta Met., 1964, vol. 12, p. 1421.

    Article  CAS  Google Scholar 

  47. J. C. M. Li:Trans. TMS-AIME, 1969, vol. 245, p. 1591.

    Google Scholar 

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BRUCE E. SUNDQUIST, formely with the U.S. Steel Corp., E. C. Bain Laboratory for Fundamental Research

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Sundquist, B.E. Cellular precipitation. Metall Trans 4, 1919–1934 (1973). https://doi.org/10.1007/BF02665420

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  • DOI: https://doi.org/10.1007/BF02665420

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