Effective dielectric properties of packed mixtures of insulator particles

We present an expression, obtained by following the principles of the effective medium theory (EMT), to compute average dielectric properties of mixtures of random ellipsoids. We show that our formulation is quite general and includes former expressions, valid only for dilute mixtures, as particular cases; moreover it gives accurate predictions when compared with experimental measurements in the whole range of filling factors. The expression can be extended to mixtures of irregularly shaped particles with very little loss of accuracy. Also, our equation is suitable to be used with anisotropic samples. The equation requires an additional parameter, which amounts to a percolation threshold, to the parameters usually employed to describe a binary mixture in EMT, namely, the dielectrical functions of the components and the filling factor. This parameter contains information about the geometry of the particle packing, and approximate values have been found by numerical simulation of different arrangements of spheres in a matrix. Reflectance IR spectra have been measured on pressed pellets of particles of LiF, MgO, α-${\mathrm{Fe}}_2$ ${\mathrm{O}}_3$, and ${\mathrm{MgAl}}_2$ ${\mathrm{O}}_4$ and compared with the spectra predicted by the expression presented in this paper, and other previous formulations.