On the mixing rules for astrophysical inhomogeneous grains

We present the computation of effective refractive coefficients for inhomogeneous two-component grains with three kinds of inclusions with m(incl) = 3.0 + 4.0i, 2.0 + 1.0i, 2.5 + 0.0001i and a matrix with m(m) = 1.33 + 0.01i for 11 volume fractions of inclusions from 0 to 50 per cent and wavelengths = 0.5, 1.0, 2.0 and 5.0 mum. The coefficients of extinction for these grains have been computed using a discrete dipole approximation. Computation of the extinction by the same method for grains composed of a matrix material with randomly embedded inclusions has been carried out for different volume fractions of inclusions. A comparison of extinction coefficients obtained for both models of grain material allows one to choose the best mixing rule for a mixture. In cases of inclusions with mincl = 2.0 + 1.0i and 2.5 + 0.0001i the best fit for the whole wavelength range and volume fractions of inclusions from 0 to 50 per cent has been obtained for the Lichtenecker mixing rule. In the case of mincl = 3.0 + 4.0i the fit for the whole wavelength range and volume fractions of inclusions from 0 to 50 per cent is not very significant but the best fit has been obtained for the Hanai rule. For volume fractions of inclusions from 0 to 15 per cent a very good fit has been obtained for the whole wavelength range for Rayleigh and Maxwell-Garnett mixing rules.