Permittivity of a multiphase and isotropic lattice of spheres at low frequency

A solution methodology is presented in this article to compute the effectiv e permittivity for a multiphase lattice of dielectric and/or conducting sph eres at low frequencies. It is assumed that the lattice is effectively isot ropic. This methodology relies on two central developments. The first is a T-matrix solution for a multiphase lattice of spheres immersed in a uniform electric field. This solution is presented in a succinct matrix-vector not ation and is valid for any lattice type. The second development is a simple and accurate equation for the effective permittivity that incorporates all mutual coupling between the spheres. Results are shown in this article for three situations. The first is a two-phase system of conducting spheres (u sed for verification) and the second is a dielectric-conductor (cermet comp osite) lattice of spheres. The third and final result is from a lattice con taining a cluster of conducting spheres. It is suggested that this last mat erial type displays a behavior in between that of random materials and two- phase lattices due to "permittivity enhancement" at low volume fraction. It is also shown that the Maxwell Garnett formula is not nearly as accurate f or this cluster lattice, also because of this enhancement effect. (C) 2000 American Institute of Physics. [S0021-8979(00)02116-2].