Modern data of the extinction curve from the ultraviolet to the near infrared are revisited to study properties of dust grains in the Milky Way ( MW ) and the Small Magellanic Cloud ( SMC ) .
We confirm that the graphite-silicate mixture of grains yields the observed extinction curve with the simple power-law distribution of the grain size but with a cutoff at some maximal size : the parameters are tightly constrained to be q = 3.5 \pm 0.2 for the size distribution a ^ { - q } and the maximum radius a _ { max } = 0.24 \pm 0.05 \mu m , for both MW and SMC .
The abundance of grains , and hence the elemental abundance , is constrained from the reddening versus hydrogen column density , E ( B - V ) / N _ { H } .
If we take the solar elemental abundance as the standard for the MW , > 56 % of carbon should be in graphite dust , while it is < 40 % in the SMC using its available abundance estimate .
This disparity and the relative abundance of C to Si explain the difference of the two curves .
We find that 50–60 % of carbon may not necessarily be in graphite but in the amorphous or glassy phase .
Iron may also be in the metallic phase or up to \sim 80 % in magnetite rather than in silicates , so that the Mg/Fe ratio in astronomical olivine is arbitrary .
With these substitutions the parameters of the grain size remain unchanged .
The mass density of dust grains relative to hydrogen is \rho _ { dust } / \rho _ { H } = 1 / ( 120 { +10 \atop - 16 } ) for the MW and 1 / ( 760 { +70 \atop - 90 } ) for the SMC under the elemental abundance constraints .
We underline the importance of the wavelength-dependence of the extinction curve in the near infrared in constructing the dust model : if A _ { \lambda } \propto \lambda ^ { - \gamma } with \gamma \simeq 1.6 , the power-law grain-size model fails , whereas it works if \gamma \simeq 1.8–2.0 .