Depending on the heterogeneous system various effective medium models are used for description of experimental dielectric spectra [1]. The dielectric response is often described by the well-known mixing rules such as Wiener, Maxwell-Garnett, Bruggemann, Hashin-Shtrikman, Lichtenecker or logarithmic, among which the last two are essentially empirical. The 2-component composites and uniaxial polycrystals (ceramics) can be also modeled within the general concept of the Bergman spectral representation [2] together with the numerical simulations, e. g., the finite element method [1].
It is shown that the general properties of the effective permittivity of polycrystals or multi-component composites depend on the various structural characteristics such as macroscopic symmetry or percolation strengths, and consequently it also allows estimation of the asymptotic behaviour of the permittivity. Further, an analytically solvable model of polycrystal is considered, which provides various mixing formulas. The laminar structure is composed of the layers, which are rotated anisotropic crystallites. The effective dielectric response of such structure is much complex comparing with the response of the layered structure built up of the isotropic materials. The latter serves either parallel or serial capacities only, depending on the direction of the electric field. In case of the polycrystal the effective permittivity tensor depends on the particular distribution of crystallite orientations. Several distributions are analyzed, and in particular, a distribution of orientations is found that results in the exact logarithmic law.
[1] D. Nuzhnyy, J. Petzelt, I. Rychetsky, and G. Trefalt: Phys. Rev. B 89, 214307 (2014).
[2] D. J. Bergman and D. Stroud: Sol. State Phys. 46 (1992), pp. 147–269.
[3] I. Rychetský, A. Klíč: J. Eur. Ceram. Soc. (2017), https://doi.org/10.1016/j.jeurceramsoc.2017.12.048
[4] I. Rychetský, A. Klíč, J. Hlinka: Phase Transitions 89, 740 (2016)
