Metallization of magnesium polyhydrides under pressure

Evolutionary structure searches are used to predict stable phases with unique stoichiometries in the hydrogen-rich region of the magnesium/hydrogen phase diagram under pressure. MgH${}_4$, MgH${}_{12}$, and MgH${}_{16}$ are found to be thermodynamically stable with respect to decomposition into MgH${}_2$ and H${}_2$ near 100 GPa, and all lie on the convex hull by 200 GPa. MgH${}_4$ contains two H${}^{-}$ anions and one H${}_2$ molecule per Mg${}^{2+}$ cation, whereas the hydrogenic sublattices of MgH${}_{12}$ and MgH${}_{16}$ are composed solely of H${}_2^{\delta -}$ molecules. The high-hydrogen content stoichiometries have a large density of states at the Fermi level, and the $T_c$ of MgH${}_{12}$ at 140 GPa is calculated to be nearly three times greater than that of the classic hydride, MgH${}_2$, at 180 GPa.

Figure 1

The electronic band structure of $\zeta$-MgH${}_2$ at 180 GPa. The character of the bands which cross the Fermi level is highlighted. The Fermi energy is set to zero in all of the plots. A side and top view of $\zeta$-MgH${}_2$ is shown on the right, with the Mg/H atoms colored in red/white.

Figure 2

Phonon band structure, phonon density of states, and the Eliashberg spectral function, ${\alpha }^2$F($\omega$), of $\zeta$-MgH${}_2$ at 180 GPa. Circles indicate the phonon linewidth with a radius proportional to the strength. At this pressure, $\lambda =0.58$, ${\omega }_{ln}=1111$ K, and $T_c=16–23$ K assuming ${\mu }^{*}=0.13–0.1$.

Figure 3

$\Delta H_F$ of the MgH${}_4$, MgH${}_{12}$, and MgH${}_{16}$ phases as a function of pressure. The plot also illustrates the enthalpy of the various MgH${}_2$ phases with respect to the most stable structure at a given pressure, with the region below 15 GPa magnified in the inset.

Figure 4

(a) A schematic illustration of the structural similarity between $Cmcm$-MgH${}_4$ (right) and the $I4/mmm$-symmetry CaH${}_4$ structure from Ref. 20 (left). The hydride cages around Mg${}^{2+}$/Ca${}^{2+}$ and the H${}_2$ molecules are colored red and blue, respectively.[57] (b) The PBE electronic band structure of MgH${}_4$ at 100 GPa. The character of the bands which cross the Fermi level is highlighted. Also shown on the right are the total electronic and hydrogen site-projected densities of states (DOS).

Figure 5

(a) A $2\times 2\times 2$ supercell of $R3$–MgH${}_{12}$ where the polyhedral units are highlighted to emphasize the $ABCABC$$\cdots$ close-packed arrangement. The MgH${}_{12}$ building blocks are colored such that the red polyhedra all lie in the same plane. (b) A supercell of $P$-1-MgH${}_{16}$. The MgH${}_{12}$ building blocks are colored to emphasize the similarity to the structure in (a). The blocks colored red or green lie in the same plane, and the hydrogens colored in blue do not belong to an MgH${}_{12}$ building block.[57]

Figure 6

The PBE valence densities of states of (a) MgH${}_{12}$ and (b) MgH${}_{16}$. Note that the Fermi level lies just below (directly after) a sharp peak in the DOS in MgH${}_{12}$ at 140 GPa (MgH${}_{16}$ at 130 GPa).

Figure 7

(a) Calculated molecular orbital level diagram of an MgH${}_{12}$ cluster when optimized in the gas phase at 1 atm (left) and in the geometry which it adopts in the $R3$-MgH${}_{12}$ solid at 5 GPa (center) and 140 GPa (right). The energies of the MOs at 140 GPa are given to the right in electron volts. (b) Calculated site-projected densities of states of $R3$-MgH${}_{12}$ at 5 and 140 GPa.

Figure 8

Phonon band structure, phonon density of states and the Eliashberg spectral function, ${\alpha }^2$F($\omega$), of MgH${}_4$ at 100 GPa. Circles indicate the phonon linewidth with a radius proportional to the strength. At this pressure, $\lambda =0.74$, ${\omega }_{ln}=941$ K, and $T_c=29–37$ K assuming ${\mu }^{*}=0.13–0.1$.

Figure 9

Phonon band structure, phonon density of states, and the Eliashberg spectral function, ${\alpha }^2$F($\omega$), of MgH${}_{12}$ at 140 GPa. Circles indicate the phonon linewidth with a radius proportional to the strength. At this pressure, $\lambda =0.73$, ${\omega }_{ln}=1554$ K, and $T_c=47–60$ K assuming ${\mu }^{*}=0.13–0.1$.