On the computation of optical properties of heterogeneous grains

Abstract

The Maxwell-Garnet (MG) expression for the effective dielectric function of a composite medium consisting of small spherical inclusions embedded in a homogeneous matrix is derived. It is shown that the MG theory accounts for dipole-dipole interactions among the inclusions and that the validity of the theory does not depend on the matrix being non-absorbing. Moreover, by comparing the Mie theory with the MG theory it is shown that the MG dielectric function is correct at least to terms linear in the volume fraction of inclusions. For a sphere ‘carved out’ of such a medium we then have a prescription for calculating cross sections and scattering phase functions. The scattering properties of a small heterogeneous sphere described by the MG dielectric function are identical to those of a small layered sphere with the same outer radius and volumes of the two constituents. In the small particle (Rayleigh) limit we discuss two illustrative examples: (a) a porous sphere, (b) spherical inclusions in a ‘waxy’ dielectric matrix. In both cases we obtain the conditions for resonance absorption. Finally, we apply these results to evaluate the role of porosity in individual graphite grains, and of a waxy matrix containing small spherical graphite inclusion, on the graphite particle resonance absorption at 2200 Å. Increasing porosity and increasing the volume fraction of matrix material have similar effects in shifting the resonance to longer wavelengths.