Divergent synthesis routes and superconductivity of ternary hydride MgSiH 6 at high pressure

We predict a new ternary hydride ${\mathrm{MgSiH}}_{6}$ under high pressures, which is a metal with an ionic feature and takes on a simple cubic structure with space group $Pm\text{\ensuremath{-}}3$ above 250 GPa. Our first-principles calculations show that the cubic ${\mathrm{MgSiH}}_{6}$ is a potential high-temperature superconductor with a superconducting transition temperature ${T}_{\mathrm{c}}$ of $\ensuremath{\sim}63$ K at 250 GPa. Further analysis suggests that phonon softening along mainly $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}X$ and $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}M$ directions induced by Fermi surface nesting plays a crucial role in the high-temperature superconductivity. Herein we propose the ``triangle straight-line method'' which provides a clear guide to determine the specific A + B \ensuremath{\rightarrow} D type formation routes for ternary hydrides of the Mg-Si-H system and it effectively reveals two divergent paths to obtain ${\mathrm{MgSiH}}_{6}$ under high pressures: ${\mathrm{MgH}}_{2}+{\mathrm{SiH}}_{4}\ensuremath{\rightarrow}{\mathrm{MgSiH}}_{6}$ and MgSi + $3{\mathrm{H}}_{2}\ensuremath{\rightarrow}{\mathrm{MgSiH}}_{6}$. This method might be applicable to all ternary compounds, which will be very significant for further experimental synthesis.