The Mie theory is used to find the in situ electric dipole polarizability of a sphere of arbitrary size and material. This size-dependent polarizability, together with the Clausius-Mossotti equation, yields an effective dipole generalization of the Maxwell Garnett equation for spheres of nonzero size. Calculated effective optical constants are used to find the reAectance from a suspension of Ag spheres. The results are in good agreement with the recent reflectance measurements of Lee et al. [Phys. Rev. B 37, 2918(1988] on porous glass media containing Ag particles.

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The numerical solution of the Clausius-Mossotti problem for the permittivity of a suspension of perfectly conducting spheres in a cubic array is presented for sc, fcc, and bcc lattices. The results apply to electrical permittivity, magnetic permeability, electrical and thermal conductivity, and particle diffusivity. The calculations are compared with the Clausius-Mossotti relation. Rayleigh’s equation is corrected and compared with the numerical results. A simple interpolation formula for the permittivity of a medium of perfectly conducting spheres in a simple cubic lattice is found to give an excellent approximation at all volume ratios.

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Disordered suspensions of conducting particles exhibit substantial permittivity enhancements beyond the predictions of the Clausius–Mossotti equation and other purely dipolar approximations. The magnitude of the enhancement depends upon the shape of the particles. A recently developed effective cluster model for spherical particles [Phys. Rev. B 42, 9319 (1990)] that treats a disordered suspension as a mixture, or mesosuspension, of isolated spheres and close-packed spherical clusters of arbitrary size is in excellent agreement with experiments on well-stirred suspensions of spheres over the entire accessible range of volume loading. In this paper, the effective cluster model is extended to be applicable to disordered suspensions of arbitrarily shaped conducting particles. Two physical parameters are used to characterize a general suspension: the angular average polarizability of an isolated particle, and the volume loading at closest packing of the suspension. Multipole interactions within the clusters are treated exactly. External particle-shape-dependent interactions between clusters and isolated particles are treated in the dipole approximation in two ways: explicitly, using the Clausius–Mossotti equation, and implicitly, using the Wiener equation. Both versions of the model are used to find the permittivity of a monodisperse suspension of conducting spheroids, for which the model parameters can be determined independently. The two versions are in good agreement when the axial ratio of the particles is not extreme. The Clausius–Mossotti version of the model yields a mesoscopic analogue of the dielectric virial expansion. It is limited to small volume loadings when the particles have an extremely nonspherical shape. The Wiener equation version of the model holds at all volume loadings for particles of arbitrary shape. Comparison of the two versions of the model leads to a simple physical interpretation of Wiener’s equation. The models are compared with experiments of Kelly, Stenoien, and Isbell [J. Appl. Phys. 24, 258 (1953)] on aluminum and zinc particles in paraffin, with Nasuhoglu’s experiments on iron particles in oil [Commun. Fac. Sci. Univ. Ankara 4, 108 (1952)], and with new X-band and Kα-band permittivity measurements on Ni-Cr alloy particles in a polyurethane binder.