Colloid Journal

, Volume 70, Issue 3, pp 284–296 | Cite as

Structure of silver clusters with magic numbers of atoms by data of molecular dynamics

  • V. I. Kuzmin
  • D. L. Tytik
  • D. K. Belashchenko
  • A. N. Sirenko


The behavior of silver clusters (cubic octahedron habit) with magic numbers of atoms N = 13, 55, 146, 309, 561, 923, 1415, and 2057 in the 0–1300 K temperature range is studied for the embeded atom model by the molecular dynamics method. The structural method for the analysis of the dynamics of local configurations of atoms based on the construction of angular characteristics of simplexes of the Delone partition of a cluster is proposed. Structural transitions of clusters with a cubic octahedron habit to the stable clusters with an icosahedron habit are revealed. Motions of atoms in clusters with an icosahedron habit are transformed into the stationary vibration mode. Middle positions of atoms in clusters tend to form shells with a regular structure. At N = 561, there are 15 such shells. The cluster with N = 561 at 650 K is characterized by a reduced density close to that of silver melt.


Colloid Journal Magic Number Silver Cluster Molecular Dynamic Trajectory Cluster Mass 
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  1. 1.
    Rehbinder, P.A., Izbrannye trudy. Poverkhnostnye yavleniya v dispersnykh sistemakh. Kolloidnaya khimiya (Selected Works. Surface Phenomena in Disperse Systems. Colloid Chemistry), Moscow: Nauka, 1978.Google Scholar
  2. 2.
    Derjaguin, B.V., Churaev, N.V., and Muller, V.M., Surface Forces, New York: Consultants Bureau, 1987.CrossRefGoogle Scholar
  3. 3.
    Makkei, A., Kristallografiya, 2001, vol. 46, p. 587.Google Scholar
  4. 4.
    Sadovsky, M.A., Izbrannye trudy. Geofizika i fizika vzryva (Selected Works. Geophysics and Explosion Physics), Moscow: Nauka, 1999.Google Scholar
  5. 5.
    Kuzmin, V.I. and Galusha, N.A., in Sistemnye issledovaniya. Metodologicheskie problemy. Ezhegodnik 2000 (System Researches. Methodology Problems. Yearbook 2000), Moscow: URSS, 2002.Google Scholar
  6. 6.
    Gusev, A.I., Nanomaterialy, nanostruktury, nanotekhnologii (Nanomaterials, Nanostructures, Nanotechnologies), Moscow: Fizmatlit, 2005.Google Scholar
  7. 7.
    Suzdalev, I.P., Nanotekhnologiya. Fizikokhimiya nanoklasterov, nanostruktur i nanomaterialov (Nanotechnology. Physical Chemistry of Nanoclusters, Nanostructures and Nanomaterials), Moscow: URSS, 2006.Google Scholar
  8. 8.
    Chini, P., Gazz. Chim. Ital., 1979, vol. 109, p. 225.Google Scholar
  9. 9.
    Rosch, N. and Pacchioni, G., in Clusters and Colloids. From Theory to Applications, Schmid, G., Ed., Weinheim: VCH, 1994, p. 5.CrossRefGoogle Scholar
  10. 10.
    Martin, T.P., Phys. Rep., 1996, vol. 273, p. 199.CrossRefGoogle Scholar
  11. 11.
    De Heer, W.A., Rev. Mod. Phys., 1993, vol. 65, p. 611.CrossRefGoogle Scholar
  12. 12.
    Sergeev, G.B., Nanokhimiya (Nanochemistry), Moscow: Mosk. Gos. Univ., 2003.Google Scholar
  13. 13.
    Ershov, B.G., Usp. Khim., 1997, vol. 66, p. 93.Google Scholar
  14. 14.
    Ershov, B.G., Izv. Akad. Nauk, Ser. Khim., 1999, vol. 48, no. 1, p. 1.Google Scholar
  15. 15.
    Plaksin, O.A., Amekura, H., and Kishimoto, N., J. Appl. Phys., 2006, vol. 99, p. 044307–10.CrossRefGoogle Scholar
  16. 16.
    Plaksin, O.A., Takeda, Y., Amekura, H., and Kishimoto, N., Appl. Phys. Lett., 2006, vol. 88, p. 201915-1–3.CrossRefGoogle Scholar
  17. 17.
    Bulienkov, N.A., Vestn. Nizhegorod. Univ., Ser. Fiz. Tverd. Tela, 1998, no. 1, p. 19.Google Scholar
  18. 18.
    Bulienkov, N.A, in Quasicrystals and Discrete Geometry. The Fields Institute Monographs, Patera, J., Ed., Providence: American Mathematical Society, 1998, vol. 10, p. 67.Google Scholar
  19. 19.
    Bulienkov, N.A. and Tytik, D.L., Izv. Akad. Nauk, Ser. Khim., 2001, vol. 50, no. 1, p. 1.Google Scholar
  20. 20.
    Brack, M., Rev. Mod. Phys., 1993, vol. 65, p. 677.CrossRefGoogle Scholar
  21. 21.
    Brechignac, C, in Clusters of Atoms and Molecules, Haberland, H., Ed., Berlin: Springer, 1994, p. 255.Google Scholar
  22. 22.
    Teo, B.K. and Sloane, N.J.A., Inorg.Chem., 1985, vol. 24, p. 4545.CrossRefGoogle Scholar
  23. 23.
    Schommers, W., Phys. Lett. A, 1973, vol. 43, p. 157.CrossRefGoogle Scholar
  24. 24.
    Schommers, W., Phys. Rev. A: Gen. Phys., 1983, vol. 28, p. 3599.CrossRefGoogle Scholar
  25. 25.
    Belashchenko, D.K., Komp’yuternoe modelirovanie zhidkikh i amorfnykh veshchestv (Computer Simulation of Liquid and Amorphous Substances), Moscow: MISiS, 2005.Google Scholar
  26. 26.
    Doyama, M. and Kogure, Y., Comput. Mater. Sci., 1999, vol. 14, p. 80.CrossRefGoogle Scholar
  27. 27.
    Tytik, D.L., Belashchenko, D.K., and Sirenko, A.N., Abstracts of Papers, IX Mezhdunar. seminar “Strukturnye osnovy modifikatsii materialov metodami netraditsionnykh tekhnologii” (IX Int. Workshop “Structural Fundamentals of Material Modification Using Nontraditional Technologies”), Obninsk, 2007, p. 57.Google Scholar
  28. 28.
    Tytik, D.L., Belashchenko, D.K., and Sirenko, A.N., Zh. Strukt. Khim., 2008, vol. 49, no. 1, p. 130.Google Scholar
  29. 29.
    Konovalov, O.V., Crystallographically Proper Partitions of Euclidean Space into Semiproper Isogonals, Preprint of Inst. of Crystallography, USSR Acad. Sci., Moscow, 1988, no. 7.Google Scholar
  30. 30.
    Medvedev, N.N. and Naberukhin, Yu.I., J. Non-Cryst. Solids, 1987, vol. 94, p. 402.CrossRefGoogle Scholar
  31. 31.
    Medvedev, N.N., Metod Voronogo-Delone v issledovanii struktury nekristallicheskikh sistem (The Voronoi-Delone Method in Studying Structure of Noncrystalline Systems), Novosibirsk: Sib. Otd. Ross. Akad. Nauk, 2000.Google Scholar
  32. 32.
    Nieto, M., The Titius-Bode Law of Planetary Distances: Its History and Theory, Oxford: Pergamon, 1972.Google Scholar
  33. 33.
    Wenninger, M., Polyhedron Models, Cambridge: Cambridge Univ. Press, 1971.Google Scholar
  34. 34.
    Spreadborough, J. and Christian, J.W., J. Sci. Instrum., 1959, vol. 36, p. 116.CrossRefGoogle Scholar
  35. 35.
    Bleecker, D.D., J. Diffus. Geom., 1996, vol. 43, p. 505.Google Scholar
  36. 36.
    Pak, I., Inflating Polyhedral Surfaces, Preprint of Department of Mathematics, Massachusetts Inst. of Technology, Cambridge, 2006,
  37. 37.
    Mendeleev, D.I., Rastvory (Solutions), Leningrad: Akad. Nauk SSSR, 1959.Google Scholar
  38. 38.
    Zhirmunsky, A.V. and Kuzmin, V.I., Critical Levels in the Development of Natural Systems, Berlin: Springer, 1988.Google Scholar
  39. 39.
    Zhirmunskii, A.V. and Kuzmin, V.I., Kriticheskie urovni v razvitii prirodnykh sistem (The Critical Levels in Evolution of Nature Systems), Leningrad: Nauka, 1990.Google Scholar
  40. 40.
    Bethe, H., Lektsii po teorii yadra (Lectures on the Nuclear Theory), Moscow: Inostrannaya Literatura, 1949.Google Scholar
  41. 41.
    Schmidt-Nielsen, K., Scaling: Why is Animal Size So Important, Cambridge: Cambridge Univ. Press, 1984.Google Scholar

Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  • V. I. Kuzmin
    • 1
  • D. L. Tytik
    • 2
  • D. K. Belashchenko
    • 3
  • A. N. Sirenko
    • 3
  1. 1.Moscow State Institute of Radio Engineering, Electronics, and AutomationMoscowRussia
  2. 2.Frumkin Institute of Physical Chemistry and ElectrochemistryMoscowRussia
  3. 3.Moscow State Institute of Steel and AlloysMoscowRussia

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