Criteria for mixing rules application for inhomogeneous astrophysical grains

The analysis presented in this paper verifies which of the mixing rules are best for real components of interstellar dust in possible wide range of wavelengths.The DDA method with elements of different components with various volume fractions has been used. We have considered 6 materials: ice, amorphous carbon, graphite, SiC, silicates and iron, and the following mixing rules: Maxwell-Garnett, Bruggeman, Looyenga, Hanay and Lichtenecker which must satisfy rigorous bounds. The porous materials have also been considered. We have assumed simplified spatial distribution, shape and size of inclusions. The criteria given by \citet{draine1988} have been used to determine the range of wavelengths for the considered mixtures in order to calculate the ${\rm Q_{ext}}$ using the DDA. From all chosen mixing rules for the examined materials in majority of cases (13 out of 20) the best results have been obtained using the Lichtenecker mixing rule. In 5 cases this rule is better for some volume fraction of inclusions.