On the mixing rules for interstellar inhomogeneous grains

We present the computation of effective refractive coefficients for inhomogeneous two-component grains with 3 kinds of inclusions with ${\rm m_{incl}=3.0+4.0i, 2.0+1.0i, 2.5+0.0001i}$ and a matrix with ${\rm m_m=1.33+0.01i}$ for 11 volume fractions of inclusions from 0% to 50% and wavelengths ${\rm\lambda}$=0.5, 1.0, 2.0 and 5.0 ${\rm \mu m}$. The coefficients of extinction for these grains have been computed using a discrete dipole approximation (DDA). 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 materials allows to choose the best mixing rule for a mixture. In cases of inclusions with ${\rm m_{incl}}$=2.0+1.0i and 2.5+0.0001i the best fit for the whole wavelengths range and volume fractions of inclusions from 0 to 50% has been obtained for Lichtenecker mixing rule. In case of ${\rm m_{incl}=3.0+4.0i}$ the fit for the whole wavelength range and volume fractions of inclusions from 0 to 50% is not very significant but the best has been obtained for Hanai rule. For volume fractions of inclusion from 0 to 15% a very good fit has been obtained for the whole wavelength range for Rayleigh and Maxwell-Garnett mixing rules.