Skip to main content
Log in

Thermodynamic model of crystallization and melting of small particles

  • Published:
Central European Journal of Physics

Abstract

The size dependence of the nanocrystal melting temperature has been investigated based on a nonequilibrium thermodynamics approach. An expression has been derived for the melting temperature that, contrary to the classical Tomson formula, takes into account the metastable character of the crystal nucleus-melt shell equilibrium. Quantitative estimations have been carried out for small spherical particles of aluminum, tin, and lead.

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. P. Pawlov: “Uber die Abhangigkeit des Schmelzpunctes von der Oberflachenenergie eines festen Korpers”, Z. Phys. Chem., Bd. 65, (1909), Vol. 1, pp. 1–35, Vol. 5, pp.545–548.

    Google Scholar 

  2. Yu.I. Petrov: Physics of small particles, Nauka, Pub., Moskow, 1982 (in Russian).

    Google Scholar 

  3. V.P. Skripov and V.P. Koverda: Spontaneous crystallization of liquids, Nauka. Pub., Moskow, 1984 (in Russian).

    Google Scholar 

  4. L.M. Shcherbakov, V.M. Samsonov, V.A. Lavrov and O.A. Rybalchenko: “Principles of similarity in thermodynamics of microgeterogenious systems”, Colloid Journal, Vol. 61, (1999), pp. 1–6.

    Google Scholar 

  5. B. Wunderlich: Macromolecular Physics, Vol. 2, Academic Press, New York, San Francisco, London A Subsidiary of Harcourt Brace Jovanovich, Publishers, 1974.

    Google Scholar 

  6. M. Schmidt, R. Kusche, H. Haberland and B. von Issendorff “Irregular variation in the melting point of size-selected atomic clusters”, Nature, Vol. 393, (1998), pp. 238–240.

    Article  ADS  Google Scholar 

  7. K.F. Peters, J.B. Cohen and Ch. Yip-Wah.: “Melting of Pb nanocrystals.”, Phys. Rev. B., Vol. 57, (1998), pp. 13430–13438.

    Article  ADS  Google Scholar 

  8. A. Adamson: Physical chemistry of third edition, 2nd Ed., John Willey and sons, New York, London, Sidney, Toronto, 1967, pp. 113–116.

    Google Scholar 

  9. Yu.V. Naidich, V.M. Perevertailo and N.F. Grigorenco: Capillary fenomena in processes of crystal growth and melting, Naukova dumka, Kiev, 1983.

    Google Scholar 

  10. R. Good: “Contact Angles and Surface Free Energy of Solid”, Surface and Coloid Science, Vol. 11, (1979), pp. 1–30.

    MathSciNet  Google Scholar 

  11. N. Eustatopolous: “Energetics of solid/liquid interfaces of metals and alloys”, International Metals Reviews, Vol. 28(4), (1983), pp. 189–210.

    Google Scholar 

  12. G. Kaptay: “A Model for the Solid Liquid Interfacial Energies of Pure Metals” Transactions Toining and Welding Research Institute, Vol. 30, (2001), pp. 245–250.

    Google Scholar 

  13. Ph. Buffat and J.P. Borel: “Size effect on the melting temperature of gold particles” Phys. Rev., Vol. 13(6), (1976), pp. 2287–2298.

    Article  ADS  Google Scholar 

  14. R. Haase: Thermodinamik der Irreversiblen Pozesse, Dr. Dietrich Steinkopff Verlag, Darmstadt, 1963.

    Google Scholar 

  15. Gyarmati: Non-equilibrium thermodynamics spinger, Verlag, Berlin-Heidelberg-New York, 1970.

  16. I. Prigogine: Introduction to thermodynamics of irreversible processes, Charles C. Thomas, Springfild, Illinois, 1955.

    MATH  Google Scholar 

  17. P. Chambadal: Evolution et applications du concept d'entropie, Dunod, Paris, 1963.

    Google Scholar 

  18. A.I. Rusanov: Phasengleichgewichte und Grenzflaechen erscheinungen, Academie-Verlag, Berlin, 1978.

    Google Scholar 

  19. C.R.W. Wronski: “The size dependence of the melting point of small particles of tin”, Brit. J. Appl. Phys., Vol. 18(12), (1967), pp. 1731–1737.

    Article  ADS  Google Scholar 

  20. A.A. Dic, V.N. Skokov and V.P. Koverda: Size dependence of the melting temperature of aluminium island films. Thermodinamic properties of metastable systems and kinetics of phase transitions, Ural scientific center, Sverdlovsk, 1985, pp. 27–29.

    Google Scholar 

  21. V.P. Koverda, V.N. Skokov and V.P. Skripov: “Influence of fluctuations and nonequilibrium facing on the melting of small metallic crystals”, Physics of metals and metal sience, Vol. 51, (1981), pp. 1238–1244. (in Russian).

    Google Scholar 

  22. A.R. Regel and V.M. Glasov: Periodic low and physical properties of electronic melts, Nauka. Pub., Moskow, 1978 (in Russian).

    Google Scholar 

  23. S.I. Popel: Surface Phenomena in Melts, Ural'sk State Technical University, 1994.

  24. Ch. Kittel: Introduction to solid state physics, 4th Ed., John Wiley and Sons Inc., New York, London, Sydney, Toronto, 1972.

    MATH  Google Scholar 

  25. Kh.B. Khokonov: “The measurement methods of the surface energy and tension of metals and alloys in the solid state”, Surface phenomena in melts and solid phases, Shtiintsa, Kishinev, (1974), pp. 190–261.

    Google Scholar 

  26. V.M. Samsonov: “Conditions for applicability of a thermodynamic description of highly disperse and microheterogeneous systems”, Russian Journal of Physical Chemistry, Vol. 76, (2002), pp. 1863–1867.

    Google Scholar 

  27. A.N. Basulev, V.M. Samsonov, N.Yu. Sdobnyakov: “Thermodynamic perturbation theory calculations of interpose tension in small objects”, Russian Journal of Physical Chemistry, Vol. 76, (2002), pp. 1872–1876.

    Google Scholar 

  28. V.M. Samsonov, A.N. Basulev, N.Yu. Sdobnyakov: “On applicability of the Gibbs thermodynamic to nanoparticles”, Central European Journal of Physics, (2003), (in print).

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Samsonov, V.M., Malkov, O.A. Thermodynamic model of crystallization and melting of small particles. centr.eur.j.phys. 2, 90–103 (2004). https://doi.org/10.2478/BF02476274

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.2478/BF02476274

Keywords

PACS (200)

Navigation