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.
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