Estimation of grain sizes and mixing ratios of fine powder mixtures of common geologic minerals

Two different approaches for modeling reflectance spectra of intimate mixtures, Hapke's model and the isograin model, are used to estimate grain sizes and mixing ratios of powder mixtures of three geologic minerals: olivine, orthopyroxene, and plagioclase. In Hapke's model, scattering and extinction effiencies are mixed separately, and both models employ semiempirical refractive index spectra for component minerals. Mixing ratios of mixtures of grain size 45-75 micrometers are well estimated by both models assuming a common grain size of 60 micrometers and optimizing the constants for the single-particle scattering. For each model, effective grain size ratios for mineral constituents in mixtures of grain size less than 25 micrometers, are derived successfully that allows mineral abundances to be accurately predicted within approximately 4 wt percent. On the other hand, neither model can accurately predict mineral reflectance spectra for its smaller grain sizes less than 25 and 25-45 micrometers using an absorption coefficient spectrum derived from a larger grain size (45-75 micrometers). The errors in both models are significantly reduced if surface roughness effects of the smaller grain-size fractions are modeled.