Skip to main content
Log in

Generalized Lifshits-Slezov-Wagner distribution

  • Order, Disorder, and Phase Transition in Condensed Systems
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The particle (cluster) size distribution function and the temporal variation of the middle (critical) and maximum particle dimensions have been calculated assuming that two mechanisms of mass transfer—those controlled by (i) the volume diffusion and (ii) the rate of chemical bond formation on the particle surface—are simultaneously operative. A comparison of the theoretical curves to experimental histograms shows that the proposed mechanism of particle growth can be realized in practice in the course of the Ostwald ripening.

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. W. Ostwald, Z. Phys. Chem. 34, 495 (1900).

    Google Scholar 

  2. V. V. Slezov and V. V. Sagalovich, Usp. Fiz. Nauk 151, 67 (1987) [Sov. Phys. Usp. 30, 23 (1987)].

    Google Scholar 

  3. S. A. Kukushkin and A. V. Osipov, Usp. Fiz. Nauk 168, 1083 (1998) [Phys. Usp. 41, 983 (1998)].

    Article  Google Scholar 

  4. I. M. Lifshits and V. V. Slezov, Zh. Éksp. Teor. Fiz. 35, 479 (1958) [Sov. Phys. JETP 8, 331 (1959)].

    Google Scholar 

  5. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961).

    Article  ADS  Google Scholar 

  6. C. Wagner, Z. Elektrochem. 65, 581 (1961).

    Google Scholar 

  7. V. V. Slezov, Fiz. Tverd. Tela (Leningrad) 9, 1187 (1967) [Sov. Phys. Solid State 9, 927 (1967)].

    Google Scholar 

  8. H. O. K. Kirchner, Metall. Trans. 2, 2861 (1971).

    Google Scholar 

  9. B. K. Chakraverty, J. Phys. Chem. Solids 28, 2401 (1967).

    Article  ADS  Google Scholar 

  10. R. D. Vengrenovich, Ukr. Fiz. Zh. 22, 219 (1977).

    ADS  Google Scholar 

  11. H. Kreye, Z. Metallkd. 61, 108 (1970).

    Google Scholar 

  12. A. J. Ardell, Acta Metall. 20, 602 (1972).

    Google Scholar 

  13. R. D. Vengrenovich, Fiz. Met. Metalloved. 39, 435 (1975).

    Google Scholar 

  14. R. D. Vengrenovitch, Acta Metall. 30, 1079 (1982).

    Article  Google Scholar 

  15. R. D. Vengrenovich, Yu. V. Gudyma, and S. V. Yarema, Fiz. Met. Metalloved. 91(3), 16 (2001) [Phys. Met. Metallogr. 91, 228 (2001)].

    Google Scholar 

  16. R. D. Vengrenovich, Yu. V. Gudyma, and S. V. Yarema, Scr. Mater. 46, 363 (2002).

    Article  Google Scholar 

  17. M. C. Bartelt and J. W. Evans, Phys. Rev. B 46, 12675 (1992).

    Google Scholar 

  18. N. C. Bartelt, W. Theis, and R. M. Tromp, Phys. Rev. B 54, 11741 (1996).

    Google Scholar 

  19. I. Goldfarb, P. T. Hayden, J. H. G. Owen, and G. A. D. Briggs, Phys. Rev. Lett. 78, 3959 (1997); Phys. Rev. B 56, 10459 (1997).

    Article  ADS  Google Scholar 

  20. B. A. Joyce, D. D. Vvedensky, A. R. Avery, et al., Appl. Surf. Sci. 130–132, 357 (1998).

    Article  Google Scholar 

  21. T. I. Kamins, G. Medeiros-Ribeiro, D. A. A. Ohlberg, and R. Stanley Williams, J. Appl. Phys. 85, 1159 (1999).

    Article  ADS  Google Scholar 

  22. R. D. Vengrenovich, Yu. V. Gudyma, and S. V. Yarema, Fiz. Tekh. Poluprovodn. (St. Petersburg) 35, 1440 (2001) [Semiconductors 35, 1378 (2001)].

    Google Scholar 

  23. R. D. Vengrenovich, Yu. V. Gudyma, and S. V. Yarema, Phys. Status Solidi B 242, 881 (2005).

    Article  ADS  Google Scholar 

  24. O. P. Pchelyakov, Yu. B. Bolkhovityanov, A. V. Dvurechenskiĭ, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 34, 1281 (2000) [Semiconductors 34, 1229 (2000)].

    Google Scholar 

  25. N. N. Ledentsov, V. M. Ustinov, V. A. Shchukin, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 32, 385 (1998) [Semiconductors 32, 343 (1998)].

    Google Scholar 

  26. R. D. Vengrenovich and Yu. V. Gudyma, Fiz. Tverd. Tela (St. Petersburg) 43, 1171 (2001) [Phys. Solid State 43, 1214 (2001)].

    Google Scholar 

  27. R. D. Vengrenovich, Yu. V. Gudyma, and D. D. Nikirsa, J. Phys.: Condens. Matter 13, 2947 (2001).

    Article  ADS  Google Scholar 

  28. S. N. Sleptsov, V. V. Slezov, and V. V. Sagalovich, Preprint KhFTI No. 82-72 (Kharkov Physics and Technology Inst., Kharkov, 1982).

    Google Scholar 

  29. E. A. Marquis and D. N. Seidman, Acta Mater. 49, 1909 (2001).

    Article  Google Scholar 

  30. H. Nitsche, F. Sommer, and E. J. Mittemeijer, J. Non-Cryst. Solids 351, 3760 (2005).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © R.D. Vengrenovich, B.V. Ivanskiĭ, A.V. Moskalyuk, 2007, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 131, No. 6, pp. 1040–1047.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vengrenovich, R.D., Ivanskiĭ, B.V. & Moskalyuk, A.V. Generalized Lifshits-Slezov-Wagner distribution. J. Exp. Theor. Phys. 104, 906–912 (2007). https://doi.org/10.1134/S1063776107060088

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776107060088

PACS numbers

Navigation