Journal of Materials Science

, Volume 43, Issue 22, pp 7102–7114 | Cite as

A model kinetics for nucleation and diffusion-controlled growth of immiscible alloys

  • Massimo TomelliniEmail author


A system of mean field rate equations is employed for describing the kinetics of solid-solid phase separation within the immiscibility gap of binary alloys. The system allows us to study the time evolution of both supersaturation and diffusion length of the components in the metastable phase. It is shown that in the case of simultaneous nucleation the system of differential equations leads to a simple formula for the characteristic time of the transformation in terms of material parameters and initial supersaturation. The nucleation rate is computed on the basis of the classical nucleation theory and the alloy is assumed to behave as a regular solution. It turns out that for low values of the initial supersaturation the nucleation process can be considered as simultaneous. It is also found that thermally activated nucleation takes place for supersaturation values lower than about 0.21. The assumption of a concentration-independent diffusion coefficient and the effect of nucleus curvature on interface composition have been analyzed and discussed.


Supersaturation Nucleation Rate Planar Interface Nucleation Density Volumetric Fraction 



The author is grateful to Dr. N. Downer for the critical reading of the manuscript.


  1. 1.
    Kolmogorov AN (1937) Bull Acad Sci URSS (Cl Sci Math Nat) 3:355Google Scholar
  2. 2.
    Johnson WA, Mehl RF (1939) Trans Am Inst Min Metall Pet Eng 135:416Google Scholar
  3. 3.
    Avrami M (1939) J Chem Phys 7:1103CrossRefGoogle Scholar
  4. 4.
    Avrami M (1940) J Chem Phys 8:212CrossRefGoogle Scholar
  5. 5.
    Zener C (1949) J Appl Phys 21:950CrossRefGoogle Scholar
  6. 6.
    Hermann H, Mattern N, Roth S, Uebele P (1997) Phys Rev B 56:13888CrossRefGoogle Scholar
  7. 7.
    Svoboda J, Fischer FD, Fratzl P, Gamsjäger E, Simha NK (2001) Acta Mater 49:1249CrossRefGoogle Scholar
  8. 8.
    Nagase T, Yamauchi I, Ohnaka I (2001) J Alloys Compd 316:212CrossRefGoogle Scholar
  9. 9.
    Schmidt U, Schmidt B (2000) Mater Sci Forum 331:889CrossRefGoogle Scholar
  10. 10.
    Starink MJ, Zahra A-M (1999) J Mater Sci 34:1117CrossRefGoogle Scholar
  11. 11.
    Starink MJ (2004) Int Mater Rev 49:191CrossRefGoogle Scholar
  12. 12.
    Fanfoni M, Tomellini M, Volpe M (2002) Phys Rev B 65:172301CrossRefGoogle Scholar
  13. 13.
    Rios PR, Oliveira JCPT, Oliveira VT, Castro JA (2006) Mater Res 9:165CrossRefGoogle Scholar
  14. 14.
    Birnie DP III, Weinberg MC (1995) J Chem Phys 103:3742CrossRefGoogle Scholar
  15. 15.
    Burbelko AA, Fraś E, Kapturkiewicz W (2005) Mater Sci Eng A 413:429CrossRefGoogle Scholar
  16. 16.
    Shepilov MP, Baik BS (1994) J Non-Cryst Solids 171:141CrossRefGoogle Scholar
  17. 17.
    Shepilov MP (2004) Glass Phys Chem 30:291CrossRefGoogle Scholar
  18. 18.
    Farjas J, Roura P (2007) Phys Rev B 75:184112CrossRefGoogle Scholar
  19. 19.
    Pusztai T, Gránásy L (1998) Phys Rev B 57:14110CrossRefGoogle Scholar
  20. 20.
    Kooi BJ (2004) Phys Rev B 70:224108CrossRefGoogle Scholar
  21. 21.
    Bruna P, Crespo D, Gonzalez-Cinca R (2006) J Appl Phys 100:054907CrossRefGoogle Scholar
  22. 22.
    Pradell T, Crespo D, Clavaguera N, Clavaguera-Mora MT (1998) J Phys Condens Matter 10:3833CrossRefGoogle Scholar
  23. 23.
    Zhao J, Li H, Wang Q, He J (2008) Comput Mater Sci. doi: CrossRefGoogle Scholar
  24. 24.
    Zhao J, Li H, Zhang X, He J (2008) Mater Lett 62:3779CrossRefGoogle Scholar
  25. 25.
    Tomellini M (2003) J Alloys Compd 348:189CrossRefGoogle Scholar
  26. 26.
    Bales GS, Chrzan DC (1994) Phys Rev B 50:6057CrossRefGoogle Scholar
  27. 27.
    Grabke HJ (1998) Mater Corr 49:303CrossRefGoogle Scholar
  28. 28.
    Grabke HJ (2003) Mater Corr 54:736CrossRefGoogle Scholar
  29. 29.
    Szakálos P (2003) Mater Corr 10:54Google Scholar
  30. 30.
    Hillert M (1999) Acta Mater 47:4181CrossRefGoogle Scholar
  31. 31.
    Raghavan V, Cohen M (1975) In: Bruce Hannay N (ed) Treatise on solid state chemistry, vol 5, chap 2. Plenum Press, New York, p 67Google Scholar
  32. 32.
    Pineda E, Crespo D (2003) J Non-Cryst Solids 317:85CrossRefGoogle Scholar
  33. 33.
    Ham FS (1958) J Phys Chem Solids 6:335CrossRefGoogle Scholar
  34. 34.
    Bulyarskii SV, Svetukhin VV, Agafonova OV, Grishin AG, Ilin PA (2002) Phys Status Solidi 231:237CrossRefGoogle Scholar
  35. 35.
    Mutaftschiev B (2001) The atomistic nature of crystal growth. Springer-Verlag, BerlinCrossRefGoogle Scholar
  36. 36.
    Qian M (2002) Metall Mater Trans A 33:1283CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Dipartimento di Scienze e Tecnologie ChimicheUniversità di Roma “Tor Vergata”RomeItaly

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