  The family of binary compounds composed of magnesium and silicon is rather
rich. In addition to the well-known magnesium silicide Mg$_2$Si, other
compounds, including MgSi$_2$, Mg$_4$Si$_7$, Mg$_5$Si$_6$, MgSi, and
Mg$_9$Si$_5$, have also been identified and/or proposed in precipitated
Al-Mg-Si solid solutions. Nevertheless, computational studies show that only
Mg$_2$Si is thermodynamically stable at ambient conditions while certain
non-zero hydrostatic pressure can stabilize Mg$_9$Si$_5$ so that it can
co-exist with Mg$_2$Si. We conduct a comprehensive search for viable binary
compounds of Mg$_x$Si$_{1-x}$ ($1/3\leq x \leq 2/3$), discovering numerous new
structures for all the compounds. On the one hand, we find that MgSi$_2$, MgSi,
and Mg$_9$Si$_5$ are likely pressure-stabilized materials, while, on the other
hand, supporting previous studies, raising doubt on the existence of
Mg$_5$Si$_6$, and claiming that the existence of Mg$_4$Si$_7$ remains an open
question. Therefore, we recommend that (hydrostatic and/or non-hydrostatic)
pressure should be explicitly considered when discussing the stability of these
solids (and maybe other solids as well) by computations. We also find that
MgSi$_2$ can potentially exhibit superconducting behaviors within a wide range
of pressure with the critical temperature of up to $7$ K.
