Colloid Journal

, Volume 78, Issue 3, pp 378–385 | Cite as

On the size dependence of the surface energy of metal nanoclusters



The many-particle tight-binding potential has been employed to calculate the specific surface energy of icosahedral nanoclusters of transition metals. The equimolecular surface has been considered as the dividing surface. The surface energy has been shown to linearly increase with particle size at nanocluster radii smaller than five radii of the first coordination sphere. As the nanocluster radius is further enlarged, the surface energy passes through a maximum and approaches an asymptotic macroscopic value. The coefficients of proportionality between the specific surface energy and nanocluster radius have been found and compared with the data available from the literature.


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  1. 1.
    Gibbs, J.W., Thermodynamics. Statistical Mechanics, New York: Longmans and Green, 1928.Google Scholar
  2. 2.
    Ono, S. and Kondo, S., Molecular Theory of Surface Tension in Liquids, Berlin: Springer, 1960.Google Scholar
  3. 3.
    Rusanov, A.I., Fazovye ravnovesiya i poverkhnostnye yavleniya (Phase Equilibria and Surface Phenomena), Leningrad: Khimiya, 1967.Google Scholar
  4. 4.
    Rowlinson, J. and Widom, B., Molecular Theory of Capillarity, Oxford: Oxford Univ. Press, 1982.Google Scholar
  5. 5.
    Tolman, R.C., J. Chem. Phys., 1949, vol. 17, pp. 333.CrossRefGoogle Scholar
  6. 6.
    Rusanov, A.I., Termodinamika poverkhnostnykh yavlenii (Thermodynamics of Surface Phenomena), Leningrad: Leningr. Gos. Univ., 1960.Google Scholar
  7. 7.
    Vitol’, E.N., Kolloidn. Zh., 1992, vol. 54, no. 3, pp. 21.Google Scholar
  8. 8.
    Fenelonov, V.B., Kodenyov, G.G., and Kostrovsky, V.G., J. Phys. Chem. B, 2001, vol. 105, pp. 1050.CrossRefGoogle Scholar
  9. 9.
    Shcherbakov, L.M., Issledovaniya v oblasti poverkhnostnykh sil (Studies in Surface Forces), Moscow: Nauka, 1964, pp. 17.Google Scholar
  10. 10.
    Samsonov, V.M., Shcherbakov, L.M., Novoselov, A.R., and Lebedev, A.V., Colloids Surf., 1999, vol. 160, pp. 117.CrossRefGoogle Scholar
  11. 11.
    Samsonov, V.M., Rasplavy, 2002, no. 2, p. 62.Google Scholar
  12. 12.
    Samsonov, V.M., Bazulev, A.N., and Sdobnyakov, N.Yu., Centr. Eur. J. Phys., 2003, vol. 1, pp. 474.Google Scholar
  13. 13.
    Sdobnyakov, N.Yu., Centr. Eur. J. Phys., 2005, vol. 1, pp. 474.Google Scholar
  14. 14.
    Samsonov, V.M., Bazulev, A.N., and Sdobnyakov, N.Yu., Russ. J. Phys. Chem. A, 2003, vol. 77, Suppl. 1, p. 158.Google Scholar
  15. 15.
    Baidakov, V.G. and Boltachev, G.Sh., Dokl. Akad. Nauk, 1998, vol. 363, pp. 753.Google Scholar
  16. 16.
    Baidakov, V.G. and Boltachev, G.Sh., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 1997, vol. 59, pp. 5648.Google Scholar
  17. 17.
    Schiff, D., Phys. Rev., 1969, vol. 186, pp. 151.CrossRefGoogle Scholar
  18. 18.
    Samsonov, V.M., Khashin, V.A., and Dronnikov, V.V., Colloid J., 2008, vol. 70, pp. 763.CrossRefGoogle Scholar
  19. 19.
    Samsonov, V.M., Bazulev, A.N., and Sdobnyakov, N.Yu., Dokl. Phys. Chem., 2003, vol. 389, pp. 83.CrossRefGoogle Scholar
  20. 20.
    Samsonov, V.M., Khashin, V.A., and Sdobnyakov, N.Yu., Izv. Vyssh. Uchebn. Zaved., Fiz., 2007, no. 8, p. 55.Google Scholar
  21. 21.
    Bykov, T.V. and Shchekin, A.K., Colloid J., 1999, vol. 61, pp. 144.Google Scholar
  22. 22.
    Bykov, T.V. and Shchekin, A.K., Inorg. Mater., 1999, vol. 35, pp. 641.Google Scholar
  23. 23.
    Malijevsky, A. and Jackson, G., J. Phys.: Condens. Matter, 2012, vol. 24, pp. 464121.Google Scholar
  24. 24.
    Blokhuis, E.M. and Van Giessen, A.E., J. Phys.: Condens. Matter, 2013, vol. 25, pp. 225003.Google Scholar
  25. 25.
    Helfrich, W., Z. Naturforsch. C, 1973, vol. 28, pp. 693.Google Scholar
  26. 26.
    Cleri, F. and Rosato, V., Phys. Rev. B: Condens. Matter, 1993, vol. 40, pp. 22.CrossRefGoogle Scholar
  27. 27.
    Samsonov, V.M., Kharechkin, S.S., Gafner, S.L., Redel’, L.V., and Gafne., Yu.Ya., Kristallografiya, 2009, vol. 54, pp. 530.Google Scholar
  28. 28.
    Gafner, S.L., Redel, L.V., Gafner, Yu.Ya., and Samsonov, V.M., J. Nanopart. Res., 2011, vol. 13, pp. 6419.CrossRefGoogle Scholar
  29. 29.
    Samsonov, V.M., Bembel’, A.G., Shakulo, O.V., and Vasil’ev, S.A., Kristallografiya, 2014, vol. 59, pp. 641.Google Scholar
  30. 30.
    Samsonov, V.M., Vasil’ev, S.A., Bembel’, A.G., Samsonov, T.E., and Skopich, V.L., Fiz. Tverd. Tela (St. Petersburg), 2014, vol. 56, pp. 2289.Google Scholar
  31. 31.
    Wingrave, J.A., Schechter, R.S., and Wade, W.H., The Modern Theory of Capillarity: The Centennial Gibbs Theory of Capillarity, Leningrad: Khimiya, 1980.Google Scholar
  32. 32.
    Morokhov, I.D., Trusov, L.I., and Lapavok, V.N., Fizicheskie yavleniya v ul’tradispersnykh sredakh (Physical Phenomena in Ultradisperse Media), Moscow: Energoatomizdat, 1984.Google Scholar
  33. 33.
    Tomanek, D., Mukherjee, S., and Bennemann, K.H., Phys. Rev. B: Condens. Matter, 1983, vol. 28, pp. 665.CrossRefGoogle Scholar
  34. 34.
    Gafner, S.L., Redel’, L.V., Goloven’ko, Zh.V., Gafner, Yu.Ya., Samsonov, V.M., and Kharechkin, S.S., JETP Lett., 2009, vol. 89, pp. 364.CrossRefGoogle Scholar
  35. 35.
    Kittel, C., Introduction to Solid State Physics, New York: Wiley, 1974.Google Scholar
  36. 36.
    Samsonov, V.M., Zh. Fiz. Khim., 2002, vol. 76, pp. 2063.Google Scholar
  37. 37.
    Alchagirov, A.B., Alchagirov, B.B., Taova, T.M., and Khokonov, K.B., Trans. J. WRI, 2001, vol. 30, pp. 287.Google Scholar
  38. 38.
    Shebzukhov, Z.A., Shebzukhova, M.A., and Shebzukhov, A.A., Bull. Russ. Acad. Sci.: Phys., 2009, vol. 73, pp. 928.CrossRefGoogle Scholar

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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Tver State UniversityTverRussia

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