  Studying absorption and scattering of X-ray radiation by interstellar dust
grains allows us to access the physical and chemical properties of cosmic
grains even in the densest regions of the Galaxy. We aim at characterising the
dust silicate population which presents clear absorption features in the energy
band covered by the Chandra X-ray Observatory. Through these absorption
features, in principle, it is possible to infer the size distribution,
composition, and structure of silicate in the interstellar medium. In
particular, in this work, we investigate the magnesium and silicon K-edges. By
using newly acquired synchrotron measurements, we build X-ray extinction models
for fifteen dust candidates. These models, adapted for astrophysical analysis,
and implemented in the Spex spectral fitting program, are used to reproduce the
dust absorption features observed in the spectrum of the bright low mass X-ray
binary GX 3+1 which is used as a background source. With the simultaneous
analysis of the two edges we test two different size distributions of dust: one
corresponding to the standard Mathis-Rumpl-Nordsieck model and one considering
larger grains ($n(a) \propto a_i^{-3.5}$ with $0.005<a_1<0.25$ and
$0.05<a_2<0.5$, respectively, with $a$ the grain size). These distributions may
be representative of the complex Galactic region towards this source. We find
that up to $70\%$ of dust is constituted by amorphous olivine. We discuss the
crystallinity of the cosmic dust found along this line of sight. Both magnesium
and silicon are highly depleted into dust ($\delta_{Z} = 0.89\ \rm{and}\ 0.94$,
respectively) while their total abundance does not depart from solar values.
