A dielectric mixing law for porous ceramics based on fractal boundaries

Abstract

The effect of porosity on the complex dielectric permittivity of microwave sintered zinc oxide at room temperature and 2.45 GHz is reported. The predictions of conventional Maxwell–Garnet theory and the effective medium approximation are in poor agreement with the experimental results. Various methods are employed to investigate the system in an effort to come up with new mixing laws, including combinations of these two analytic theories and finite difference electromagnetic simulations of representative microstructures. A model that assumes the existence of dielectrically inactive, fractal-geometry boundaries between ceramic grains provides an excellent description of the results with no free parameters. It gives physical insight into the experimentally observed mixing law.

Electrical conductivity of synthetic iron-bearing olivine

“…Multiple arcs imply that there are additional, time delayed, responses from the material to the electrical conduction, out of phase to the applied voltage. Factors that can cause additional effects like these are grain interiors, grain boundaries and porosity (Calame et al 1996). Figure 3 shows the electrical impedance data at 1,100°C and at fO 2 = 5.5 9 10 -5 Pa. ZView model parameters for arc fitting are shown in the Appendix (Table 5).…”

“…Although minor porosity (as shown in Fig. 2) may influence existing arc shapes or conductivity (Calame et al 1996), the likelihood that porosity can induce an additional impedance arc is debatable (Barsoukov and Macdonald 2005, p. 218). While pore surfaces may offer additional surface conduction pathways, these will be in parallel with grain boundary conductivity.…”

Broadband Spectral Analysis of Non-Debye Dielectric Relaxation in Percolating Heterostructures

“…, the best fit of our data using maximum likelihood method yields 0 τ ≈ 10 -8 s, 267 ≤ T 0 ≤ 292 °C which is an ordering temperature lower than T g whose significance has remained unclear (there is no microscopic [12][13]18 The value of 0 τ is almost 3 orders of magnitude larger than 0 τ ≈ 10 -11 s, commonly used for the preexponential factor. A possible interpretation of this pre-exponential factor is to assume that a dipole on average visits So far, we have only discussed the Cole-Cole phenomenology.…”

“…dielectric spectroscopy experiments [8][9] and computer simulations, e.g. Monte Carlo and finite element calculations 6,7,[10][11][12][13] have progressed in parallel. Models for dielectric relaxation in heterostructures can be broadly placed in two groups.…”

Microwave Heating Behavior of Blast Furnace Slag Bearing High Titanium

“…In the present case, CaTiO 3 has volume fraction of about 10-20 %. There are many theories 18) to evaluate the average permittivity of the composite materials. Although the permittivity of CaTiO 3 is much larger than the other oxides, it is possible to predict the measured permittivity roughly, using the MaxwellGarnet theory, 19) for example.…”