Skip to main content
SpringerLink
Log in

Theory of the Structure of Coherent Boundaries in ZrO2 Nanoparticles

  • Proceedings of the Topical Meeting of the European Ceramic Society “Nanoparticles, Nanostructures, and Nanocomposites”
  • (St. Petersburg, Russia, July 5–7, 2004)
  • Published:
Glass Physics and Chemistry Aims and scope Submit manuscript

Abstract

A general algorithm is proposed for constructing coherent boundaries. This algorithm is based on the interrelation between the spatial coherence of structural fragments in nanoparticles and the geometric connection in the corresponding associated bundle. A local approach is used to describe the structure of coherent boundaries in zirconia nanoparticles. The inference is made that the models of structures thus obtained should be preferred over the models constructed in terms of the theory of coincident site lattice.

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

Similar content being viewed by others

REFERENCES

  1. Wigner, E. P., The Unreasonable Effectiveness of Mathematics in the Natural Sciences, in Symmetries and Reflections: Scientific Essays of Eugene P. Wigner, Bloomington: Indiana Univ. Press, 1967. Translated under the title Invariantnost’ i zakony sokhraneniya. Etyudy o simmetrii, Moscow: Editorial URSS, 2002.

    Google Scholar 

  2. 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 

  3. 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 

  4. Dubrovin, B.L., Novikov, S.P., and Fomenko, A.T., Sovremennaya geometriya: Metody i prilozheniya. Tom 2. Geometriya i topologiya mnogoobrazii (Modern Geometry: Methods and Applications, vol. 2: Geometry and Topology of Manifolds), Moscow: Editorial URSS, 2001.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  7. 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, no. 19, pp. 2731–2748.

  8. Tran, N.T., Kawano, M., Powell, D.R., and Dahl, L.F., High-Nuclearity [Pd13 Ni13 (CO)34]4− Containing a 26-Atom Pd13Ni13 Core with an Unprecedented Five-Layer Close-Packed Triangular Stacking Geometry: Possible Substitutional Pd/Ni Crystal Disorder at Specific Intralayer Nickel Sites, J. Chem. Soc., Dalton Trans., 2000, no. 18, pp. 4138–4144.

  9. Rossi, G., Rapallo, A., Mattet, C., Fortunelli, A., Baletto, F., and Ferrando, R., Magic Polyicosahedral Core-Shell Clusters, Phys. Rev. Lett., 2004, vol. 93, pp. 105503-1–105503-4.

    Article  Google Scholar 

  10. Gulseren, O., Ercolessi, F., and Tosatti, E., Noncrystalline Structures of Ultrathin Unsupported Nanowires, Phys. Rev. Lett., 1998, vol. 80, no.17, pp. 3775–3778.

    Article  Google Scholar 

  11. Tosatti, E., Prestipino, S., Kostlmeier, S., Dal Corso, A., and Di Tolla, F.D., String Tension and Stability of Magic Tip-Suspended Nanowires, Science (Washington, D.C., 1883-), 2001, vol. 291, no.5502, pp. 288–290.

    Article  PubMed  Google Scholar 

  12. Torres, J.A., Tosatti, E., Dal Corso, A., Ercolessi, F., Kohanoff, J.J., Di Tolla, F.D., and Soler, J.M., The Puzzling Stability of Monatomic Gold Wires, Surf. Sci. Lett., 1999, vol. 426, pp. L441–L446.

    Article  Google Scholar 

  13. 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 

  14. 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, no.5632, pp. 483–487.

    Article  PubMed  Google Scholar 

  15. Harris, P.J.F., Carbon Nanotubes and Related Structures: New Materials for the Twenty-One Century, Cambridge: Cambridge Univ. Press, 1999. Translated under the title Uglerodnye nanotruby i rodstvennye struktury. Novye materialy XXI veka, Moscow: Tekhnosfera, 2003.

    Google Scholar 

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

    Google Scholar 

  17. Shevchenko, V.Ya., Madison, A.E., and Glushkova, V.B., Structure of Nanosized Zirconia Centaur Particles, Fiz. Khim. Stekla, 2001, vol. 27, no.3, pp. 419–428 [Glass Phys. Chem. (Engl. transl.), 2001, vol. 27, no. 4, pp.400–405].

    Google Scholar 

  18. 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 

  19. Talis, A.L., Generalized Crystallography of Diamond-Like Structures: I. Finite Projective Planes and Specific Clusters of Diamond-Like Structures Determined by These Planes, Kristallografiya, 2002, vol. 47, no.4, pp. 583–593.

    Google Scholar 

  20. Talis, A.L., Generalized Crystallography of Diamond-Like Structures: II. Diamond Packing in the Space of a Three-Dimensional Sphere, Subconfigurations of Finite Projective Planes, and Generating Clusters of Diamond-Like Structures, Kristallografiya, 2002, vol. 47, no.5, pp. 775–784.

    Google Scholar 

  21. Kasatkin, I., Girgsdies, F., Ressler, T., Caruso, R.A., Schattka, J.H., Urban, J., and Weiss, K., HRTEM Observation of the Monoclinic-to-Tetragonal (m-t) Phase Transition in Nanocrystalline ZrO2, J. Mater. Sci., 2004, vol. 39, no.6, pp. 2151–2157.

    Article  Google Scholar 

  22. Shevchenko, V.Ya., Samoilovich, M.I., Talis, A.L., and Madison, A.E., On the Structure of a Pd561 Giant Palladium Cluster, Fiz. Khim. Stekla, 2005, vol. 31, no.2, pp. 352–357 [Glass Phys. Chem. (Engl. transl.), 2005, vol. 31, no. 2, pp. 259–263].

    Google Scholar 

  23. Shevchenko, V.Ya., Samoilovich, M.I., Talis, A.L., and Madison, A.E., On the Structure of Icosahedral Keplerates and Their Derivatives, Fiz. Khim. Stekla, 2005, vol. 31, no.3, pp. 541–545 [Glass Phys. Chem. (Engl. transl.), 2005, vol. 31, no. 3, pp. 402–406].

    Google Scholar 

  24. Nyman, H., Hyde, B.G., and Andersson, S., Zircon, Anhydrite, Scheelite, and Some Related Structures Containing Bisdisphenoids, Acta Crystallogr., Sect. B: Struct. Sci., 1984, vol. 40, no.5, pp. 441–447.

    Google Scholar 

  25. Sadoc, J.F. and Rivier, N., Hierarchy and Disorder in Non-Crystalline Structures, Philos. Mag. B., 1987, vol. 5, pp. 537–573.

    Google Scholar 

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

    Google Scholar 

  27. Zheng, C., Hoffman, R., and Nelson, D.R., A Helical Face-Sharing Tetrahedron Chain with Irrational Twist, Stella Quadrangula, and Related Matters, J. Am. Chem. Soc., 1990, vol. 112, pp. 3784–3791.

    Article  Google Scholar 

  28. Nyman, H. and Andersson, S., The Stella Quadrangula as a Structure Building Unit, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr., 1979, vol. 35, no.6, pp. 934–937.

    Google Scholar 

  29. Dickey, E.C., Fan, X., and Pennycook, S.J., Direct Atomic-Scale Imaging of Ceramic Interfaces, Acta Mater., 1999, vol. 47, no.15, pp. 4061–4068.

    Article  Google Scholar 

  30. Shibata, N., Oba, F., Yamamoto, T., Sakuma, T., and Ikuhara, Y., Grain Boundary Faceting at a Σ = 3, [110]/{112} Grain Boundary in a Cubic Zirconia Bicrystal, Philos. Mag., 2003, vol. 83, no.19, pp. 2221–2246.

    Article  Google Scholar 

  31. Buljan, S.T., McKinstry, H.A., and Stubican, V.S., Optical and X-ray Single Crystal Studies of the Monoclinic → Tetragonal Transition in ZrO2, J. Am. Ceram. Soc., 1976, vol. 59, nos.7–8, pp. 351–354.

    Google Scholar 

  32. Bailey, J.E., The Monoclinic-Tetragonal Transformation and Associated Twinning in Thin Films of Zirconia, Proc. R. Soc. London, Ser. A, 1964, vol. 279, pp. 395–412.

    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. E. Madison

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

    M. I. Samoilovich

  3. All-Russia Research Institute of Synthesis of Mineral Raw Materials, Institutskaya ul. 1, Aleksandrov, Vladimirskaya oblast, 601650, Russia

    A. L. Talis

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. Theory of the Structure of Coherent Boundaries in ZrO2 Nanoparticles. Glass Phys Chem 31, 407–419 (2005). https://doi.org/10.1007/s10720-005-0077-x

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10720-005-0077-x

Keywords

Search

Navigation