Skip to main content
SpringerLink
Log in

Structure of Icosahedral Nanoobjects

  • Letters to the Editor
  • Published:
Glass Physics and Chemistry Aims and scope Submit manuscript

Abstract

The structure of nanoparticles is probably the most important problem for physicists and chemists dealing with the nanostate of matter. The structure of many nanoparticles synthesized over the last decade is so unusual from the standpoint of classical crystallography that many authors describe it in literary rather than in rigorous scientific terms. The basic structural (for the most part, geometric) principles of the nanostate are formulated. The nanoparticle structure is determined in the framework of the local approach, which includes the paradigm of structural blocks with the use of non-Euclidean geometry concepts (the curved-space approximation) and locally minimal manifolds and takes into account the possibility of coherently joining fragments with different (incompatible in crystals) symmetry elements. The formulated principles are used to explain the structure of nanoparticles of different types, in particular, icosahedral nanoparticles.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  1. Fedorov, E.S., Symmetry of Regular Systems of Figures, Zap. S.-Peterb. Mineral. O-va, Ser. 2, 1891, no. 4, pp. 1–227.

  2. Schoenflies, A., Kristallsysteme und Kristallstruktur, Leipzig: Teubner, 1891.

    Google Scholar 

  3. Wigner, E.P., The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Commun. Pure Appl. Math., 1960, vol. 13, no.1, pp. 1–14.

    Google Scholar 

  4. Bernal, J.D. and Carlisle, C.H., Fields of Application of Generalized Crystallography, Kristallografiya, 1968, vol. 13, no.5, pp. 927–951.

    CAS  Google Scholar 

  5. Mackay, A.L., Generalized Crystallography, J. Mol. Struct. (THEOCHEM), 1995, vol. 336, nos.2–3, pp. 293–303.

    Google Scholar 

  6. Mackay, A.L., Generalized Crystallography, Struct. Chem., 2002, vol. 13, nos.3–4, pp. 215–220.

    Google Scholar 

  7. Manoharan, V.N., Elsesser, M.T., and Pine, D.J., Dense Packing and Symmetry in Small Clusters of Microspheres, Science (Washington, D.C., 1883-), 2003, vol. 301, pp. 483–487.

    Article  CAS  Google Scholar 

  8. Rossi, G., Rapallo, A., Mottet, C., Fortunelli, A., Baletto, F., and Ferrando, R., Magic Polyicosahedral Core-Shell Clusters, Phys. Rev. Lett., 2004, vol. 93, p. 105503.

    Article  CAS  Google Scholar 

  9. Tran, N.T., Kawano, M., and Dahl, L.W., High-Nuclearity Palladium Carbonyl Trimethylphosphine Clusters Containing Unprecedented Face-Condensed Icosahedral-Based Transition-Metal Core Geometries: Proposed Growth Patterns from a Centered Pd13 Icosahedron, J. Chem. Soc., Dalton Trans., 2001, pp. 2731–2748.

  10. Kondo, K. and Takayannagi, K., Synthesis and Characterization of Helical Multi-Shell Gold Nanowires, Science (Washington, D.C., 1883-), 2000, vol. 289, pp. 606–608.

    CAS  Google Scholar 

  11. Gulseren, O., Ercolessi, F., and Tosatti, E., Non-Crystalline Structures of Ultrathin Unsupported Nanowires, Phys. Rev. Lett., 1998, vol. 80, pp. 3775–3778.

    CAS  Google Scholar 

  12. Dress, A.W.M. and Brinkmann, G., Phantasmagorical Fulleroids, Match, 1996, vol. 33, pp. 87–100.

    CAS  Google Scholar 

  13. Delgado Friedrichs, O. and Deza, M., More Icosahedral Fulleroids, in Discrete Mathematical Chemistry, Hausen, P., Fowler, P., and Zheng, M., Eds., DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 2000, vol. 51, pp. 97–115.

  14. Hervieu, M., Mellene, B., Retoux, R., Boudin, S., and Raveau, B., The Route to Fullerenoid Oxides, Nature Mater., 2004, vol. 3, pp. 269–273.

    Article  CAS  Google Scholar 

  15. Ugarte, D., Curling and Closure of Graphitic Networks under Electron-Beam Irradiation, Nature (London), 1992, vol. 359, pp. 707–709.

    Article  CAS  Google Scholar 

  16. Liu, T., Diemann, E., Li, H., Dress, A.W.M., and Muller, A., Self-Assembly in Aqueous Solution of Wheel-Shaped Mo154 Oxide Clusters into Vesicles, Nature (London), 2003, vol. 426, pp. 59–62.

    Article  CAS  Google Scholar 

  17. Colomer, J.F., Henrard, L., Van Tendeloo, G., Lucas, A., and Lambin, P., Study of the Packing of Double-Walled Carbon Nanotubes onto Boundless by Transmission Electron Microscopy and Electron Diffraction, J. Mater. Sci., 2004, vol. 14, pp. 603–606.

    CAS  Google Scholar 

  18. Conway, J.H., Hardin, R.H., and Sloane, N.J.A., Packing Lines, Planes, Etc.: Packings in Grassmannian Spaces, Exp. Math., 1996, vol. 5, pp. 139–159.

    Google Scholar 

  19. Shevchenko, V.Ya., Khasanov, O.L., Yur'ev, G.S., and Ivanov, Yu.F., Coexistence of Cubic and Tetragonal Structures in an Yttria-Stabilized Zirconia Nanoparticle, Neorg. Mater., 2001, vol. 37, pp. 950–952.

    CAS  Google Scholar 

  20. Shevchenko, V.Ya., Khasanov, O.L., Madison, A.E., and Lee, J.Y., Investigation of the Structure of Zirconia Nanoparticles by High-Resolution Transmission Electron Microscopy, Fiz. Khim. Stekla, 2002, vol. 28, no.5, pp. 459–464 [Glass Phys. Chem. (Engl. transl.), 2002, vol. 28, no. 5, pp. 322–325].

    Google Scholar 

  21. Alok Singh and Tsai, A.P., On the Cubic W Phase and Its Relationship to the Icosahedral Phase in Mg-Zn-Y Alloys, Scr. Mater., 2003, vol. 49, no.2, pp. 143–148.

    Article  CAS  Google Scholar 

  22. Sun, W. and Hiraga, K., Al-Ni-Ru Icosahedral Quasicrystal and Coexisting Decagonal Quasicrystals with 0.4 nm Periodicity, Studied by Atomic-Resolution Electron Microscopy Observations, J. Non-Cryst. Solids, 2004, vols. 334–335, pp. 194–197.

    Google Scholar 

  23. O'Keeffe, M., Eddaoudi, M., Li, H., Reineke, T., and Yaghi, O.M., Frameworks for Extended Solids: Geometrical Design Principles, J. Solid State Chem., 2000, vol. 152, pp. 3–20.

    Article  Google Scholar 

  24. Yaghi, O.M., O'Keeffe, M., Ockwig, N.W., Chae, H.K., Eddaoudi, M., and Kim, J., Reticular Synthesis and the Design of New Materials, Nature (London), 2003, vol. 423, pp. 705–714.

    Article  CAS  Google Scholar 

  25. Ferey, G., Mellot-Draznieks, C., and Loiseau, T., Real, Virtual, and Not Yet Discovered Porous Structures Using Scale Chemistry and/or Simulation: A Tribute to Sten Andersson, Solid State Sci., 2003, vol. 5, no.1, pp. 79–94.

    CAS  Google Scholar 

  26. Dubrovin, B.A., Fomenko, A.T., and Novikov, S.P., Modern Geometry: Methods and Applications, Part 2: The Geometry and Topology of Manifolds, Graduate Texts in Mathematics, New York: Springer-Verlag, 1985, vol. 104.

    Google Scholar 

  27. Shevchenko, V.Ya., Samoilovich, M.I., Talis, A.L., and Madison, A.E., Nanostructures with Coherent Boundaries and the Local Approach, Fiz. Khim. Stekla, 2004, vol. 30, no.6, pp. 732–749 [Glass Phys. Chem. (Engl. transl.), 2004, vol. 30, no. 6, pp. 537–550].

    Google Scholar 

  28. Shevchenko, V.Ya., Samoilovich, M.I., Talis, A.L., Madison, A.E., and Shudegov, V.E., Geometrical Structural Complexes of ZrO2 Nanoparticles, Fiz. Khim. Stekla, 2005, vol. 31, no.2, pp. 252–269 [Glass Phys. Chem. (Engl. transl.), 2005, vol. 31, no. 2, pp. 187–200].

    Google Scholar 

  29. Volkov, V.V., Van Tendeloo, G., Tsirkov, G.A., Cherkashina, N.V., Vargaftik, M.N., Moiseev, I.I., Novotortsev, V.M., Kvit, A.V., and Chuvilin, A.L., Long-and Short-Distance Ordering of the Metal Cores of Giant Pd Clusters, J. Cryst. Growth, 1996, vol. 163, pp. 377–387.

    Article  CAS  Google Scholar 

  30. Mackay, A.L., A Dense Non-Crystallographic Packing of Equal Spheres, Acta Crystallogr., 1962, vol. 15, pp. 916–918.

    CAS  Google Scholar 

  31. Coxeter, H.S.M., Regular Polytopes, New York: Dower, 1973.

    Google Scholar 

  32. Pearson, W.B., The Crystal Chemistry and Physics of Metals and Alloys, New York: Wiley, 1972.

    Google Scholar 

  33. Puyraimond, F., Quiquandon, M., Gratias, D., Tillard, M., Belin, C., Quivy, A., and Calvayrac, Y., Atomic Structure of the (Al,Si)CuFe Cubic Approximant Phase, Acta Crystallogr., Sect. A: Found. Crystallogr., 2002, vol. 58, pp. 391–403.

    Article  CAS  Google Scholar 

  34. Abe, E., Yan, Y., and Pennycook, S.J., Quasicrystals as Cluster Aggregates, Nature Mater., 2004, vol. 3, pp. 759–767.

    Article  CAS  Google Scholar 

  35. Fuller, R.B., Synergetics: Explorations in the Geometry of Thinking, New York: Macmillan, 1975.

    Google Scholar 

  36. Fuller, R.B., Synergetics 2: Further Explorations in the Geometry of Thinking, New York: Macmillan, 1979.

    Google Scholar 

  37. Sadoc, J.F. and Rivier, N., Hierarchy and Disorder in Non-Crystalline Structures, Philos. Mag. B., 1987, vol. 55, pp. 537–573.

    CAS  Google Scholar 

  38. Sadoc, J.F. and Mosseri, R., Icosahedral Order, Space, and Quasicrystals, in Aperiodicity and Order, Jaric, M.V. and Gratias, D., Eds., Boston: Academic, 1989, vol. 3, pp. 163–189.

    Google Scholar 

  39. Sadoc, J.F. and Rivier, N., Boerdijk-Coxeter Helix and Biological Helices, Eur. Phys. J. B, 1999, vol. 12, pp. 309–318.

    Article  CAS  Google Scholar 

  40. Sadoc, J.F., Helices and Helix Packings Derived from the {3, 3, 5} Polytope, Eur. Phys. J. E, 2001, vol. 5, pp. 575–582.

    Article  CAS  Google Scholar 

  41. Lord, E.A. and Ranganathan, S., Sphere Packing, Helices and the Polytope {3, 3, 5}, Eur. Phys. J. D, 2001, vol. 15, pp. 335–343.

    Article  CAS  Google Scholar 

  42. Conway, J.H. and Sloane, N.J.A., Sphere Packings, Lattices and Groups, Comprehensive Studies in Mathematics, vol. 290, New York: Springer-Verlag 1999, 3rd ed.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences, ul. Odoevskogo 24/2, St. Petersburg, 199155, Russia

    V. Ya. Shevchenko, A. L. Talis & A. E. Madison

  2. OAO Central Research Technological Institute “Tekhnomash”, ul. Ivana Franko 4, Moscow, 121108, Russia

    M. I. Samoilovich

Authors
  1. V. Ya. Shevchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. I. Samoilovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. L. Talis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. E. Madison
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text Copyright © 2005 by Fizika i Khimiya Stekla, Shevchenko, Samoilovich, Talis, Madison.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shevchenko, V.Y., Samoilovich, M.I., Talis, A.L. et al. Structure of Icosahedral Nanoobjects. Glass Phys Chem 31, 823–828 (2005). https://doi.org/10.1007/s10720-005-0132-7

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10720-005-0132-7

Keywords

Search

Navigation