Abstract
Effective dielectric constants of diphase composite dielectrics are simulated by Monte Carlo-finite element method on three-dimensional lattice. Effective dielectric constants with coefficients of variation less than 5.5% are obtained for different ratios of dielectric constants of the two phases, ranging from 10 to 700. Various mixing rules and equations are fitted to these data and the accuracy and relevance of the fits are thoroughly examined. Modified logarithmic rule loses its physical basis when fitted to three-dimensional data. As the ratio of dielectric constants of the two phases increases, the parameters in general Lichterecker mixing rule, general Bruggeman's symmetric equation, general effective media equation and its modified form all increase or decrease monotonously. General effective media equation and its modified form give the best fits to the effective dielectric constants simulated. The simulation results for the dielectric constants of some composite systems are in good agreement with experimental data.
Similar content being viewed by others
References
T.R. Shrout and A. Halliyal, Am. Ceram. Soc. Bull., 66, 704 (1987).
J. Chen, Microstructure-Property Relations in the Complex Perovskite Lead Magnesium Niobate, Ph.D. Thesis, Leigh University, Pennsylvania State, USA (1991).
A. Nakano, D.P. Cann, and T.R. Shrout, Jpn. J. Appl. Phys. A, 36, 1136 (1997).
J. Wu and D.S. McLachlan, Phys. Rev. B, 56, 1236 (1997).
J. Wu and D.S. McLachlan, Phys. Rev. B, 58, 14880 (1998).
D.S. McLachlan, J. Phys. C: Solid State Phys., 20, 865 (1987).
D.J. Bergman and D. Strout, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull (Academic, San Diego, 1992), p. 147.
D.S. McLanchlan, M. Blaszkiewicz, and R. E. Newnham, J. Am. Ceram. Soc., 73, 2187 (1990).
P.C. Sturman and R.L. McCullough, J. Appl. Phys., 72, 2883 (1992).
H.E. Roman, A. Bunde, and W. Dieterich, Phys. Rev. B., 34, 3439 (1986).
M. Bartkowiak, G.D. Mahan, F.A. Modine et al., J. Appl. Phys., 80, 6516 (1996).
K. Wakino, T. Okada, N. Yoshida et al., J. Am. Ceram. Soc., 76, 2588 (1993).
X. Zhao and Y. Wu, J. Mater. Sci., 39, 291 (2004).
E. Tuncer, Y.V. Serdyuk, and S.M. Gubanski, IEEE Transactions on Dielectrics and Electrical Insulation, 9, 809 (2002).
B. Sareni, L. Krahenbuhl, and A. Beroual, J. Appl. Phys., 80, 1688 (1996).
K. Lichtenecker, Phys. Z., 27, 115 (1926).
Z. Hashin and S. Shtrikman, J. Appl. Phys., 33, 3125 (1962).
D.S. McLanchlan, J.H. Hwang, and T.O. Mason, Journal of Electroceramics, 5, 37 (2000).
D.S. McLanchlan, Journal of Electroceramics, 5, 93 (2000).
I. Webman, J. Jortner, and M.H. Cohen, Phys. Rev. B, 15, 5712 (1977).
F. Brouers, J. Phys. C: Solid State Phys., 19, 7183 (1987).
A. Bunde and W. Dieterich, Journal of Electroceramics, 5, 81 (2000).
D.S. McLachlan and J. Chen, J. Phys.: Condens. Matter, 4, 4557 (1992).
J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, Inc., New York, 1993), p. 256.
Y. Yuan, Numerical Method For Nonlinear Programming (Shanghai Scientific & Technical Publishers, Shanghai, 1993), p. 207.
D.S. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1994).
C. Chiteme and D.S. McLachlan, Phys. Rev. B, 67, 024206 (2003).
J.H.Hwang, D.S. McLanchlan, and T.O. Mason, Journal of Electroceramics, 3, 7 (1999).
J. Chen and M.P. Harmer, J. Amer. Ceram. Soc., 73, 68 (1990)
K. Huh, J. Kim, and S. Cho, in Proc. of Fulrath Memorial Int'l Symp. on Advanced Cera., edited by N. Ichinose (CNT Inc., Tokyo, 1993), p. 61.
W.D. Kingery, Introduction to Ceramics (Wiley, New York, 1976).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, Y., Zhao, X., Li, F. et al. Evaluation of Mixing Rules for Dielectric Constants of Composite Dielectrics by MC-FEM Calculation on 3D Cubic Lattice. Journal of Electroceramics 11, 227–239 (2003). https://doi.org/10.1023/B:JECR.0000026377.48598.4d
Issue Date:
DOI: https://doi.org/10.1023/B:JECR.0000026377.48598.4d