Properties of Dust Grains Probed with Extinction Curves
  Modern data of the extinction curve from the ultraviolet to the near infrared
are revisited to study the property 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 $a_{max} = 0.24 \pm 0.05$ um, 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 the glassy phase. Iron
may also be in the metallic phase or up to ~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
some abundance constraints. We underline the importance of the
wavelength-dependence slope of the extinction curve in the near infrared in
constructing the dust model: if $A_{\lambda} \propto \lambda^{-gamma}$ with
gamma ~ 1.6, the power-law grain-size model fails, whereas it works if gamma ~
1.8-2.0.
