Articles
All articles | Recent articles
Higher Electronics Circuit Integrations within the Fractal Electronics Frontiers
V.V. Mitic1,2, V. Paunovic1, Lj. Kocic1
1 University of Niš, Faculty of Electronic Engineering, Niš, Serbia
2 Institute of Technical Sciences of SASA, Belgrade, Serbia
received July 15, 2016, received in revised form November 21, 2016, accepted November 24, 2016
Vol. 7, No. 4, Pages 365-378 DOI: 10.4416/JCST2016-00047
Abstract
Knowledge of the morphology of ceramic grains and pores facilitates understanding of the sintering process. The real intergrain contact surfaces, as highly irregular objects, can only be adequately described by using fractal models. Both micro- and nanostructured shapes of grains and intergranular contacts can be easily reconstructed by using fractal analysis/modeling. Several variations of Coble's two-sphere model are reviewed in this paper. Further, the intergranular capacity model has been reexamined from the perspective of intergranular fractal formations. The area of grains' surface is calculated using fractal correction and fractal dimension. This results in a more precise numerical interpretation of the parameters and related properties of electronic ceramics. In particular, the role of the dielectric constant, being correlated with the fractal nature of intergranular morphology, causes corrections to the Heywang model and Curie-Weiss law. In order to obtain an equivalent circuit model, an intergranular contacts model is determined and implemented for characterization of the electrical properties of barium titanate. The improved material prognosis electronic properties can be given on the basis of micro-/nanostructure fractal relations. Considering the obtained results, new frontiers are established for deeper and higher level of microelectronic integration of electronic circuits, which practically results in a new framework for fractal electronics.
Download Full Article (PDF)
Keywords
Ceramics, Coble's model, Heywang model, Curie-Weiss law
References
1 Coble, R.L.: Effects of particle-size distribution in initial-stage sintering, J. Am. Ceram. Soc., 56, [9], 461 – 466 (1973)
2 Coble, R.L.: Sintering of crystalline solids. I. Intermediate and final state diffusion models, J. Appl. Phys., 32, 789 – 92, (1961).
3 Gibbs, J.W.: Collected works, Longmans, New York, 1928.
4 Wulff, G.: On the question of the speed of growth and the resolution of crystal surfaces (in German), Z. Kristallogr., 34, 449 – 530, (1901).
5 Mitić, V.V.: Structures and elektrical properties of BaTiO3 ceramics, Begrade: Zadužbina Andrejević (in Serbian), 2001.
6 Kang, S.J.L.: Sintering. Densification, Grain Growth, and Microstructure, Elsevier 2005.
7 DeJonge L., Rahman M.N.: Sintering of Ceramics, Handbook of Advanced Ceramics, S.Sowmya et al. (Eds.), Elsevier (78s), 2003
8 Cho, Y.K., Kang, S.L., Yoon, D.Y.: Dependence of grain growth and grain-boundary structure on the Ba/Ti ratio in BaTiO3, J. Am. Ceram. Soc., 87, 119 – 124, (2004).
9 Zhang, D., Weng, G., Gong, S., Zhou D.: The kinetics of initial stage in sintering process of BaTiO3 based PTCR ceramics and its computer simulation, Mater. Sci. Eng. B, 99, [1 – 3], 88 – 92, (2003).
10 Mitic, V.V., Paunovic,V., Mancic, D., Kocic, Lj., Zivkovic, Lj., Pavlovic, V.B.: Dielectric properties of BaTiO3 doped with Er2O3 and Yb2O3 based on intergranular contacts model. In Advances in electroceramic materials, ed. K. M. Nair, D. Suvorov, R. W. Schwartz, and R. Guo, 137 – 144. John Wiley & Sons, Inc. 2009.
11 Mitic, V.V., Pavlovic, V., Paunovic, V., Purenovic, J., Kocic, Lj., Jankovic, S., Antolovic, I., Rancic, D.: Intergranular properties and structural fractal analysis of BaTiO3-ceramics doped by rare earth additives. In: Advanced processing and manufacturing technologies for structural and multifunctional materials V, ed. Tatsuki Ohji, Mrityunjay Singh, Sujanto Widjaja, and Dileep Singh, 121 – 132., 2011
12 Mitrovic, I., Mitic, V.V.: BaTiO3-ceramics electrical model based on intergranular contacts, J. Eur. Ceram. Soc., 21, [15], 2771 – 2775, (2001).
13 Mitić, V.V., Kocić, Lj. M., Ristić, M.M.: The Fractals and BaTiO3-ceramics sintering, 1997, Key Eng. Mat., 136, 1060 – 1063, (2001).
14 Mitić, V.V., Petković, P., Kocić, Lj.: BaTiO3-ceramics capacitance in terms of consolidation parameters, Proc. of Micro Materials Conference and Exhibition Micro Mat 97, Berlin, 1103 – 1105, 1997.
15 Mitić,V., Živković, Lj.: Effect of nonstoichiometry on the microstructure and electrical properties of BaTiO3-ceramics, Proc. of the 12th Conference on glass and ceramics, Bulgarian Ceramic Society, Varna, Bulgaria, 479 – 484, 1997.
16 Mitić, V.V., Kocić, Lj. M., Mitrović, I.: BaTiO3-ceramics structure and consolidation process, extended abstracts of the 5th Conference and Exhibition of the European Ceramic Society, Euro Ceramics V, Part 2, Versailles, France, 924 – 927, 1997.
17 Mitić, V.V., Kocić, Lj.M., Ristić, M.M.: The fractals and structure, extended abstracts of the 5th Conference and Exhibition of the European Ceramic Society, Euro Ceramics V, Part 2, Versailles, France,. 1060 – 1063, 1997.
18 Nikolić, Z.S., Mitrović, I., Mitić, V.V.: Computer simulation of neck growth during sintering process, Proc. of the IX World Round Table Conference on Sintering held in Belgrade: Advanced Science and Technology of Sintering, edited by Stojanović et al., Kluwer Academic/Plenum Publishers, New York, pp. 61 – 66, 1999.
19 Mitić, V.V., Kocić, Lj. M., Mitrović, I.Z.: Fractals in ceramic structure, Proc. of the IX World Round Table Conference on Sintering" held in Belgrade:Advanced Science and Technology of Sintering, edited by Stojanović et al., Kluwer Academic/Plenum Publishers, New York, pp. 397 – 402, 1999.
20 Mitić, V.V., Mitrović, I.Z.: BaTiO3 structure prognosis, Proc. of the IX World Round Table Conference on Sintering held in Belgrade: Advanced Science and Technology of Sintering, edited by Stojanović et al., Kluwer Academic/Plenum Publishers, New York, pp. 431 – 436, 1999.
21 Mitic, V.V., Pavlovic, V.B., Kocic, Lj., Paunovic, V., Mancic, D.: Application of the intergranular impedance model in correlating microstructure and electrical properties of doped BaTiO3, Sci. Sinter., 41, [3], 247 – 256, (2009).
22 Mitić, V., Paunović, V., Mancic, D., Kocic, Lj.,. Zivković, Lj., Pavlović, V.B.: Dielectric properties of BaTiO3 doped with Er2O3, Yb2O3 based on intergranular contacts model, Ceram. Trans., 204, 137 – 144, (2009).
23 Mancic, D., Paunovic, V., Vijatović, M., Stojanović, B. Zivković, Lj., Electrical characterization and impedance response of lanthanum doped barium titanate ceramics, Science of Sintering, 40 [3], 283 – 294, (2008).
24 Chen, J.H. Johnson, P.F.: Computer simulation of initial stage sintering in two-dimensional particulate systems, P.E. Russell, Ed., Microbeam Analysis- 405 – 409, 1989,
25 W. Heywang, H. Thomann, Electronic Ceramics, London and New York, 1991.
26 Pontes, F.M., Pontes, D.S.L., Leite, E.R., Longo, E., Chiquito, A.J., Pizani, P.S., Varela, J.A.: Electrical conduction mechanism and phase transition studies using dielectric properties and Raman spectroscopy in ferroelectric Pb0.76Ca0.24TiO3 thin films, J. App. Phy., 94, [11], 7256. (2003).
27 Frenkel, Y.I.: On the surface crawling particles in crystals and the natural roughness of natural faces, JETP, 16, [1], (1948).
28 Mitić, V.V., Fecht, H.J., Kocić,Lj.: Materials science and energy fractal nature new frontiers, Contemporary Materials (Renewable energy sources), VI, 2 (2015), 190 – 203.
29 Mitić, V.V., Paunović, V., Kocić, Lj.: Fractal approach to BaTiO3-ceramics micro-impedances, Ceram. Int., 41 – 5, 6566 – 657, (2015).
30 Mandelbrot, B.B., The fractal geometry of nature, W. H. Freeman, New York 1983.
31 Boyd D.W.: The osculatory packing of a three dimensional sphere, Canad. J. Math., 25, 303 – 322, (1973).
32 Borkovec M. et al.: The fractal dimension of the apollonian sphere packing, Fractals, 2, [4], 521 – 526 (1994).
Copyright
Göller Verlag GmbH