A dielectric mixing law for porous ceramics based on fractal boundaries

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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.