Journal of Materials Science

, Volume 41, Issue 19, pp 6193–6197 | Cite as

Temperature dependence of fractal dimension of grain boundary region in SnO2 based ceramics

  • Goran BrankovićEmail author
  • Zorica Branković
  • Daniela Russo Leite
  • José Arana Varela


Fractal dimensions of grain boundary region in doped SnO2 ceramics were determined based on previously derived fractal model. This model considers fractal dimension as a measure of homogeneity of distribution of charge carriers. Application of the derived fractal model enables calculation of fractal dimension using results of impedance spectroscopy. The model was verified by experimentally determined temperature dependence of the fractal dimension of SnO2 ceramics. Obtained results confirm that the non-Debye response of the grain boundary region is connected with distribution of defects and consequently with a homogeneity of a distribution of the charge carriers. Also, it was found that CT−1 function has maximum at temperature at which the change in dominant type of defects takes place. This effect could be considered as a third-order transition.


SnO2 Charge Carrier Fractal Dimension Boundary Region Fractal Model 



This work was financially supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) through the projects number 99/06470-0, 00/09818-6 and 02/01403-7, and by the Ministry for Science and Environmental Protection of Republic of Serbia.


  1. 1.
    Smith A, Baumard JF, Abélard P, Denanot MF (1989) J Appl Phys 65:5119CrossRefGoogle Scholar
  2. 2.
    Jiang SP, Love JG, Badwal SPS (1997) In: Nowotny J, Sorrell CC (eds) Key engineering materials, vol. 125–126, Electrical properties of oxide materials, Trans Tech Publications, Switzerland, p 81Google Scholar
  3. 3.
    Kirkpatrick KS, Mason TO, Balachandran U, Poeppel RB (1994) J Am Ceram Soc 77:1493CrossRefGoogle Scholar
  4. 4.
    Sletson LS, Potter ME, Alim MA (1988) J Am Ceram Soc 71:909CrossRefGoogle Scholar
  5. 5.
    Alim MA (1989) J Am Ceram Soc 72:28CrossRefGoogle Scholar
  6. 6.
    Modine FA, Major RW, Choi S-I, Bergman LB, Silver MN (1989) In: Levinson LM (ed) Ceramic transactions, vol. 3, Advances in varistor technology, The American Ceramic Society, Westerville, OH, p 176Google Scholar
  7. 7.
    Raistrick ID (1987) In: Macdonald JR (ed) Impedance spectroscopy: emphasizing solid materials and systems, John Wiley & Sons, p 27Google Scholar
  8. 8.
    Lindsey CP, Patterson GD (1980) J Chem Phys 73:3348CrossRefGoogle Scholar
  9. 9.
    Jonscher AK (1975) Phys Stat Sol (a) 32:665CrossRefGoogle Scholar
  10. 10.
    Kaplan T, Gray LJ (1985) Phys Rev B 32:7360CrossRefGoogle Scholar
  11. 11.
    Kaplan T, Gray LJ, Liu SH (1987) Phys Rev B 35:5379CrossRefGoogle Scholar
  12. 12.
    Liu SH, (1985) Phys Rev Lett 55:529CrossRefGoogle Scholar
  13. 13.
    Branković G, Branković Z, Jović V, Varela JA (2001) J Electroceramics 7:89Google Scholar
  14. 14.
    Macdonald JR (1987) Impedance spectroscopy: emphasizing solid materials and systems, John Wiley & SonsGoogle Scholar
  15. 15.
    Lee J, Hwang J-H, Mashek JJ, Mason TO, Miller AE, Siegel RW (1995) J Mater Res 10:2295CrossRefGoogle Scholar
  16. 16.
    Strobl G, (2004) Condensed matter physics Springer-Verlag Berlin HeidelbergCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Goran Branković
    • 1
    Email author
  • Zorica Branković
    • 1
  • Daniela Russo Leite
    • 2
  • José Arana Varela
    • 2
  1. 1.Center for Multidisciplinary, Studies of University of BelgradeBelgradeSerbia
  2. 2.Instituto de QuimicaUNESPAraraquaraBrasil

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