Divergent synthesis routes and superconductivity of ternary hydride ${\mathrm{MgSiH}}_6$ 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 $Pm\text{−}3$ 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 $\sim 63$ K at 250 GPa. Further analysis suggests that phonon softening along mainly $\mathrm{\Gamma }\text{−}X$ and $\mathrm{\Gamma }\text{−}M$ 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 → 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: ${\mathrm{MgH}}_2+{\mathrm{SiH}}_4\to {\mathrm{MgSiH}}_6$ and MgSi + $3{\mathrm{H}}_2\to {\mathrm{MgSiH}}_6$. This method might be applicable to all ternary compounds, which will be very significant for further experimental synthesis.

Figure 1

Trigonal phase diagrams of the Mg-Si-H system at 200, 250, and 300 GPa, respectively. Solid symbols denote stable stoichiometries. Four different color lines stand for different synthesis routes for ternary hydrides.

Figure 2

(a)–(c) The formation enthalpies of Mg-Si-H compounds with respect to decomposition into ${\mathrm{MgH}}_2$ and ${\mathrm{SiH}}_4$ at different pressures. (d)–(f) The enthalpies of formation with respect to decomposition into MgSi alloy and H at different pressures. These solid lines stand for the convex hull, and solid symbols located on the convex hull represent stable stoichiometries. Open symbols connected by dashed lines indicate unstable species.

Figure 3

The enthalpies per formula unit of $R\text{−}3$ and $C2/m$ phases as a function of pressure, referenced to $Pm\text{−}3$ phase of ${\mathrm{MgSiH}}_6$. Illustration: The enthalpies of $R\text{−}3$ and $C2/m$ relative to $Pm\text{−}3$ phase with the zero-point motion corrections from 250 to 300 GPa.

Figure 4

(a), (c), (d), and (e) Some perspectives of $Pm\text{−}3$ ${\mathrm{MgSiH}}_6$ at 250 GPa. (a) Crystal structure. The lattice parameters are $a=2.851\AA$ with H at 6g (0.255, 0.500, 0.00), Mg at 1b (0.500, 0.500, 0.500), and Si at 1a (0.000, 0.000, 0.000). (b) Crystal structure of Pm-$3n$ ${\mathrm{AlH}}_3$. (c) The electronic band structure and density of electronic states (DOS) of ${\mathrm{MgSiH}}_6$. The electron localization function (ELF) of Mg-H (d) and Si-H (e) planes.

Figure 5

Phonon band structure (a) and projected density of states (PHDOS) (b) of $Pm\text{−}3$ ${\mathrm{MgSiH}}_6$ at 250 GPa. These red solid circles with black borders overlapping with band show mode-resolved electron phonon coupling constants ${\lambda }_{q,v}$ and the sizes of the circles are proportional to EPC strength.

Figure 6

Some planes for ${\mathrm{MgSiH}}_6$ at 250 GPa. (a) The calculated nesting function ξ$\left(Q\right)$ along some special $Q$ trajectories. The calculation employs $5225k$ points and 658350 k + Q points to attain their respective energy eigenvalues. (b) The Eliashberg phonon spectral function ${\alpha }^{2}F\left(\omega \right)$ and the electron-phonon integral λ.

Figure 7

Fermi surface for ${\mathrm{MgSiH}}_6$ at 250 GPa. (a) Three-dimensional (3D) Fermi surface calculated with $60\times 60\times 60k$ mesh. (b) 2D Fermi surface along Γ-$X$ and Γ-$M$ directions calculated with 216 $000k$ points. The solid line represents the boundary of first Brillouin zone and possible nesting vectors in (b) are indicated by dashed lines.

Figure 8

(a) EPC parameter (λ), the phonon frequency logarithmic average $\left({\omega }_{log}\right)$ in Kelvin (K), the electronic DOS at Fermi level $N\left({\varepsilon }_F\right)$ in states/spin/Ry/cell, and superconducting transition temperature $T_c({\mu }^{*}=0.1)$ in Kelvin (K) for $Pm\text{−}3n$ ${\mathrm{Al}}_2{\mathrm{H}}_6,Pm\text{−}3$ ${\mathrm{AlSiH}}_6$, and $Pm\text{−}3$ ${\mathrm{MgSiH}}_6$ at 250 GPa. (b) The pressure evolution of λ, ${\omega }_{log},N\left({\varepsilon }_F\right)$, and $T_c({\mu }^{*}=0.1)$ for ${\mathrm{MgSiH}}_6$ at selected pressures.