Journal of Materials Science

, Volume 45, Issue 3, pp 733–743 | Cite as

On the kinetics of nucleation and growth reactions in inhomogeneous systems

  • Massimo TomelliniEmail author


Nucleation and growth kinetics in systems with a small degree of inhomogeneity are usually modeled through the KJMA (Kolmogorov–Johnson–Mehl–Avrami) theory, that is by using the local values of the nucleation and growth rates which are proper to the region where the transition takes place. In this study, a general expression for the kinetics is derived which applies, in principle, to any degree of inhomogeneity and conforms to previous approaches. The model is employed to study, analytically, first order corrections to the KJMA formula in the case of simultaneous nucleation and interface-limited growth. It is shown that under these circumstances, the nucleus shape is a circle (two-dimensional) whose center is displaced with respect to the point where the nucleation event occurs. The displacement of the center and the radius of the nucleus are both functions of time. The behavior of the Avrami exponent and the impingement factor as a function of the fraction of transformed volume is investigated and discussed.


Cementite Avrami Exponent Nucleus Shape Birth Time Site Saturation 


  1. 1.
    Schmalzried H (1974) Solid state reactions. Academic Press, INC, New York, LondonGoogle Scholar
  2. 2.
    Cahn RW Haasen P (1983) In: Cahn RW, Haasen P (eds) Physical metallurgy part II. North Holland Physics Publishing, Amsterdam, Oxford, New York, TokyoGoogle Scholar
  3. 3.
    Crespo D, Pradell T (1996) Phys Rev B 54:3101CrossRefGoogle Scholar
  4. 4.
    Rickman JM, Tong WS, Barmak K (1997) Acta Mater 45:1153CrossRefGoogle Scholar
  5. 5.
    Pineda E, Pradell T, Crespo D (2001) J Non-Cryst Solids 287:88CrossRefGoogle Scholar
  6. 6.
    Farjas J, Roura P (2008) Phys Rev B 78:144101CrossRefGoogle Scholar
  7. 7.
    Klikovits J, Schmid M, Gustafson J, Mikkelsen A, Resta A, Lundgren E, Andersen JN, Varga P (2006) J Phys Chem B 110Google Scholar
  8. 8.
    Kolmogorov AN (1937) Bull Acad Sci URSS 3:355Google Scholar
  9. 9.
    Johnson WA, Mehl RF (1939) Trans Am Inst Min Metall Pet Eng 135:416Google Scholar
  10. 10.
    Avrami M (1939) J Chem Phys 7:1103CrossRefGoogle Scholar
  11. 11.
    Avrami M (1940) J Chem Phys 8:212CrossRefGoogle Scholar
  12. 12.
    Fanfoni M, Tomellini M (2005) J Phys Condens Matter 17:R571CrossRefGoogle Scholar
  13. 13.
    Rios PR, Oliveira JCPT, Oliveira VT, Castro JA (2006) Mater Res 9:165CrossRefGoogle Scholar
  14. 14.
    Uebele P, Hermann H (1996) Model Simul Mater Sci Eng 4:203CrossRefGoogle Scholar
  15. 15.
    Birnie DP, Weinberg MC (1995) J Chem Phys 103:3742CrossRefGoogle Scholar
  16. 16.
    Weinberg MC, Birnie DP (1996) J Non-Cryst Solids 202:290CrossRefGoogle Scholar
  17. 17.
    Pusztai T, Gránásy L (1998) Phys Rev B 57:141CrossRefGoogle Scholar
  18. 18.
    Kooi BJ (2004) Phys Rev B 70:224108CrossRefGoogle Scholar
  19. 19.
    Burbelko AA, Fraś E, Kapturkiewicz W (2005) Mater Sci Eng A 413:429CrossRefGoogle Scholar
  20. 20.
    Shepilov MP (2004) Glass Phys Chem 30:291CrossRefGoogle Scholar
  21. 21.
    Shepilov MP, Baik BS (1994) J Non-Cryst Solids 171:141CrossRefGoogle Scholar
  22. 22.
    Farjas J, Roura P (2007) Phys Rev B 75:184112CrossRefGoogle Scholar
  23. 23.
    Levine LE, Lakshmi Narayan K, Kelton KF (1997) J Mater Res 12:124CrossRefGoogle Scholar
  24. 24.
    Berg BA, Dubey S (2008) Phys Rev Lett 100:165702CrossRefGoogle Scholar
  25. 25.
    Todinov MT (2000) Acta Mater 48:4217CrossRefGoogle Scholar
  26. 26.
    Alekseeckin NV (2001) J Phys Condens Matter 13:3083CrossRefGoogle Scholar
  27. 27.
    Grabke HJ (2003) Mater Corros 54:736CrossRefGoogle Scholar
  28. 28.
    Starink MJ (2001) J Mater Sci 36:4433. doi: CrossRefGoogle Scholar
  29. 29.
    Starink MJ (2004) Int Mater Rev 49:191CrossRefGoogle Scholar
  30. 30.
    Sun NX, Liu XD, Lu K (1996) Scripta Mater 34:1201CrossRefGoogle Scholar
  31. 31.
    Avrami M (1941) J Chem Phys 9:177CrossRefGoogle Scholar
  32. 32.
    Fanfoni M, Tomellini M (1998) Il Nuovo Cimento 20:1171CrossRefGoogle Scholar
  33. 33.
    Asahi N, Miyashita A (1988) Jpn J Appl Phys 27:875CrossRefGoogle Scholar
  34. 34.
    Pradell T, Crespo D, Clavaguera N, Clavaguera-Mora MT (1998) J Phys Condens Matter 10:3833CrossRefGoogle Scholar
  35. 35.
    Zhou F, He K, Sui M, Lai Z (1994) Mater Sci Eng A 181/182:1419CrossRefGoogle Scholar
  36. 36.
    Saada S, Barrat S, Bauer-Grosse E (2000) Diam Relat Mater 9:300CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Dipartimento di Scienze e Tecnologie ChimicheUniversità di Roma Tor Vergata, Via della Ricerca ScientificaRomeItaly

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