Skip to main content
Log in

Thermodynamics of the phase equilibrium of multicomponent solid solutions containing nano-sized precipitates of the second phase

  • Surface Physics and Thin Films
  • Published:
Physics of the Solid State Aims and scope Submit manuscript

Abstract

Based on the theory of regular solutions, the interphase boundary model for the case of an arbitrary number of components is developed. General relations for the calculation of the phase composition of multicomponent solutions containing nano-sized precipitates of the second phase are derived. By the example of binary and ternary solutions, it is shown that a considerable mutual enrichment of the conjugated phases by atoms of components dissolved in them occurs in the case if precipitates of the second phase are characterized by the sizes of the order of several nanometers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. B. Sonderegger, I. Holzer, and E. Kozeschnik, Mater. Sci. Forum 638–642, 2730 (2010).

    Article  Google Scholar 

  2. G. Bonny, D. Terentyev, and L. Malerba, Comput. Mater. Sci. 42, 107 (2008).

    Article  Google Scholar 

  3. J. Wallenius, P. Olsson, C. Lagerstedt, N. Sandberg, R. Chakarova, and V. Pontikis, Phys. Rev. B: Condens. Matter 69, 094103 (2004).

    Article  ADS  Google Scholar 

  4. D. Forsa and G. Wahnstrom, J. Appl. Phys. 109, 113709 (2011).

    Article  ADS  Google Scholar 

  5. D. Terentyev, G. Bonny, C. Domain, and R. C. Pasianot, Phys. Rev. B: Condens. Matter 81, 214106 (2010).

    Article  ADS  Google Scholar 

  6. K. Berland, T. Andersson, and P. Hyldgaard, Phys. Rev. B: Condens. Matter 84, 245313 (2011).

    Article  ADS  Google Scholar 

  7. J. Ulloa, P. Koenraad, and M. Hopkinson, Appl. Phys. Lett. 93, 083103 (2008).

    Article  ADS  Google Scholar 

  8. V. Liuolia, S. Marcinkevicius, D. Billingsley, M. Shatalov, J. Yang, R. Gaska, and M. Shur, Appl. Phys. Lett. 100, 242104 (2012).

    Article  ADS  Google Scholar 

  9. F. Sommer, R. Singh, and E. Mittemeijer, J. Alloys Compd. 467, 142 (2009).

    Article  Google Scholar 

  10. R. A. Swalin, Thermodynamics of Solids (Metallurgiya, Moscow, 1968) [in Russian].

    Google Scholar 

  11. J. Frenkel, Kinetic Theory of Liquids (Dover, New York, 1954; Nauka, Leningrad, 1975).

    Google Scholar 

  12. D. Perez and L. Lewis, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 74, 031609 (2006).

    Article  ADS  Google Scholar 

  13. M. Strobel, K.-H. Heinig, and W. Moller, Phys. Rev. B: Condens. Matter 64, 031609 (2001).

    Article  Google Scholar 

  14. P. Maugis, F. Soisson, and L. Lae, Diffus. Defect Data, Pt. A 237–240, 671 (2005).

    Article  Google Scholar 

  15. V. V. Svetukhin and P. E. L’vov, Tech. Phys. Lett. 26(11), 986 (2000).

    Article  ADS  Google Scholar 

  16. S. Novy, P. Pareige, and C. Pareige, J. Nucl. Mater. 384, 96 (2009).

    Article  ADS  Google Scholar 

  17. P. E. L’vov, V. V. Svetukhin, and A. V. Obukhov, Phys. Solid State 53(2), 421 (2011).

    Article  ADS  Google Scholar 

  18. S. Goodman, S. Brenner, and J. Low, Jr., Metall. Trans. 4, 2363 (1973).

    Article  Google Scholar 

  19. S. Goodman, S. Brenner, and J. Low, Jr., Metall. Trans. 4, 2371 (1973).

    Article  Google Scholar 

  20. S. He, N. van Dijk, M. Paladugu, H. Schut, J. Kohlbrecher, F. Tichelaar, and S. van der Zwaag, Phys. Rev. B: Condens. Matter 82, 174111 (2010).

    Article  ADS  Google Scholar 

  21. R. Becker, Ann. Phys. (Leipzig) 32, 128 (1938).

    Article  ADS  Google Scholar 

  22. J. Schmelzer and G. Boltachev. J. Chem. Phys. 124, 194503 (2006).

    Article  ADS  Google Scholar 

  23. A. Abyzov and J. Schmelzer, J. Chem. Phys. 127, 114504 (2007).

    Article  ADS  Google Scholar 

  24. V. Slezov, Kinetics of First-Order Phase Transitions (Wiley, New York, 2009).

    Book  Google Scholar 

  25. V. Svetukhin, P. L’vov, E. Gaganidze, M. Tikhonchev, and C. Dethloff, J. Nucl. Mater. 415, 205 (2011).

    Article  ADS  Google Scholar 

  26. V. Svetukhin, P. L’vov, M. Tikhonchev, E. Gaganidze, and N. Krestina, J. Nucl. Mater. 437 (2013) (in press) doi 10.1016/j.jnucmat.2013.03.030.

  27. J. W. Cahn and J. E. Hilliard, J. Chem. Phys. 28, 258 (1958).

    Article  ADS  Google Scholar 

  28. J. W. Cahn, J. Chem. Phys. 30, 1121 (1959).

    Article  ADS  Google Scholar 

  29. J. W. Cahn and J. E. Hilliard, J. Chem. Phys. 31, 688 (1959).

    Article  ADS  Google Scholar 

  30. A. G. Khachaturyan, Theory of Phase Transitions and Structure of Solid Solutions (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  31. V. P. Skripov and A. V. Skripov, Sov. Phys.-Usp. 22(6), 389 (1979).

    Article  ADS  Google Scholar 

  32. J. Schmelzer, V. Baidakov, and G. Boltachev, J. Chem. Phys. 119, 6166 (2003).

    Article  ADS  Google Scholar 

  33. P. E. L’vov and V. V. Svetukhin, Phys. Solid State 54(11), 2285 (2012).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. E. L’vov.

Additional information

Original Russian Text © P.E. L’vov, V.V. Svetukhin, 2013, published in Fizika Tverdogo Tela, 2013, Vol. 55, No. 11, pp. 2256–2261.

Rights and permissions

Reprints and permissions

About this article

Cite this article

L’vov, P.E., Svetukhin, V.V. Thermodynamics of the phase equilibrium of multicomponent solid solutions containing nano-sized precipitates of the second phase. Phys. Solid State 55, 2374–2380 (2013). https://doi.org/10.1134/S1063783413110140

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063783413110140

Keywords

Navigation