Finite size corrections for the Johnson-Mehl-Avrami-Kolmogorov equation

Abstract

The Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation is frequently used to describe phase transformations involving nucleation and growth. The assumptions used in the derivation of this equation, however, are frequently violated when making experimental measurements; use of the JMAK equation for analyzing such data can often produce invalid results. Finite-size effects are among the most serious of these problems. We present modified analytic JMAK equations that correct for the finite-size effects and are roughly independent of both the sample shape and the shape of the growing nuclei. A comparison with computer simulations shows that these modified JMAK equations accurately reproduce the growth behavior over a wide range of conditions.

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References

  1. 1.

    A. N. Kolmogorov, Isz. Akad. Nauk SSR, Ser. Fiz. 3, 355 (1937).

    Google Scholar 

  2. 2.

    W. A. Johnson and R. Mehl, Trans. AIME 135, 416 (1939).

    Google Scholar 

  3. 3.

    M. Avrami, J. Chem. Phys. 7, 1103 (1939).

    CAS  Article  Google Scholar 

  4. 4.

    M. Avrami, J. Chem. Phys. 8, 212 (1940).

    CAS  Article  Google Scholar 

  5. 5.

    M. Avrami, J. Chem. Phys. 9, 177 (1941).

    CAS  Article  Google Scholar 

  6. 6.

    C. Wert and C. Zener, J. Appl. Phys. 21, 5 (1950).

    CAS  Article  Google Scholar 

  7. 7.

    J. W. Cahn, Acta Metall. 4, 449 (1956).

    CAS  Article  Google Scholar 

  8. 8.

    K. F. Kelton and F. Spaepen, Acta Metall. 33, 455 (1985).

    CAS  Article  Google Scholar 

  9. 9.

    E. D. Zanotto and A. C. Galhardi, Anais do VI CBECI-MAT, T-7, PUC/RJ, December 1984, p. 30.

  10. 10.

    M. C. Weinberg, J. Non-Cryst. Solids 82, 779 (1987).

    CAS  Google Scholar 

  11. 11.

    M. C. Weinberg, J. Non-Cryst. Solids 202, 290 (1996).

    CAS  Article  Google Scholar 

  12. 12.

    J. C. Holzer and K. F. Kelton, Acta Metall. Mater. 39, 1833 (1991).

    CAS  Google Scholar 

  13. 13.

    H. Yinnon and D. R. Uhlmann, J. Non-Cryst. Solids 54, 253 (1983).

    CAS  Article  Google Scholar 

  14. 14.

    K. F. Kelton, J. Non-Cryst. Solids 163, 283 (1993).

    CAS  Article  Google Scholar 

  15. 15.

    M. C. Weinberg, J. Non-Cryst. Solids 142, 126 (1992).

    Article  Google Scholar 

  16. 16.

    K. F. Kelton, K. Lakshmi Narayan, T. S. Cull, and C. S. Ray, J. Non-Cryst. Solids (in press).

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Correspondence to L. E. Levine.

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Levine, L.E., Narayan, K.L. & Kelton, K.F. Finite size corrections for the Johnson-Mehl-Avrami-Kolmogorov equation. Journal of Materials Research 12, 124–132 (1997). https://doi.org/10.1557/JMR.1997.0020

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