Finite-wavelength effects in composite media

Abstract

We report wavelength- ($\ensuremath{\lambda}\ensuremath{-}$) and size-dependent measurements of the dielectric functions ($\ensuremath{\epsilon}$) of macroscopically uniform samples pressed from ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ powders of different particle sizes. The data agree with effective medium (mean-field) theories for particle diameters less than about $0.25\ensuremath{\lambda}$. For particle diameters larger than about $0.5\ensuremath{\lambda}$, measured values of $\ensuremath{\epsilon}$ exceed allowable quasistatic limits for known volume fractions, and finite-wavelength effects must be considered. We show that finite-wavelength theories are more sensitive to microstructural parameters than quasistatic theories, which suggests that finite-wavelength models should be useful for microstructural or materials characterization and could also have predictive value. Finally, we show that the recent perturbation model of Bosi, Girouard, and Truong, that includes dynamic terms as additions to a quasistatic theory, predicts rates of increase of $\ensuremath{\epsilon}$ with particle size that greatly exceed those of experiment or other model calculations. Thus dynamic terms cannot in general be incorporated as additions to quasistatic theories but must be included in the initial formulation of the effective-medium problem.