Hydrogen-rich scandium compounds at high pressures

Scandium hydrides at high pressures have been investigated by using ab initio density functional calculations. Although the stable scandium hydride so far known to have the highest content rate of hydrogen is ${\mathrm{ScH}}_3$, other more hydrogen-rich compounds are found to be possible at high pressures. These are ${\mathrm{ScH}}_4$ in the $I4/mmm$ structure above 160 GPa, ${\mathrm{ScH}}_6$ in the $P{6}_3/mmc$ structure from 135 to 265 GPa, and ${\mathrm{ScH}}_6$ in the $Im\overline{3}m$ structure above 265 GPa. The three phases are all metallic, and the superconducting transition temperatures estimated from the extended McMillan equation are 67 K in the $I4/mmm{\mathrm{ScH}}_4$ at 195 GPa, 63 K in the $P{6}_3/mmc{\mathrm{ScH}}_6$ at 145 GPa, and 130 K in the $Im\overline{3}m{\mathrm{ScH}}_6$ at 285 GPa. While the $I4/mmm$ tetrahydride and the $Im\overline{3}m$ hexahydride were similarly predicted for yttrium (another group-3 element), the $P{6}_3/mmc$ hexahydride is possible only for scandium. The smaller atomic size of scandium stabilizes the $P{6}_3/mmc$ structure, and other nearby $d$-block elements, whose atomic sizes are smaller or comparable, might be likewise capable of forming such polyhydrides.

Figure 1

Enthalpy per atom of ${\mathrm{Sc}}_{1-x}{\mathrm{H}}_x$ as a function of $x$. The enthalpy is given relative to that of the system consisting of ${\mathrm{ScH}}_3$ and H phases. In the top (bottom) panel, the ionic system is treated as a static (dynamic) one. The ${\mathrm{ScH}}_4$ has $I4/mmm$ symmetry; the ${\mathrm{ScH}}_5$ has $C2/m$ symmetry; the ${\mathrm{ScH}}_6$ has $P{6}_3/mmc$ symmetry below 325 (265) GPa and $Im\overline{3}m$ symmetry above 325 (265) GPa for the static (dynamic) ionic system. The enthalpy of ${\mathrm{ScH}}_3$ is calculated for the $Fm\overline{3}m$ structure [39], and that of H for the $C2/c$ [54], the $Cmca$-12 [54], the $Cmca$ [48], and the Cs-IV ($I{4}_1/amd$) [51] structures. As a guide to the eye, stable phases are connected with solid lines.

Figure 2

The $I4/mmm$ structure for ${\mathrm{ScH}}_4$ (above 160 GPa), the $P{6}_3/mmc$ structure for ${\mathrm{ScH}}_6$ (from 135 to 265 GPa), and the $Im\overline{3}m$ structure for ${\mathrm{ScH}}_6$ (above 265 GPa). The detailed structural parameters are as follows. The $I4/mmm{\mathrm{ScH}}_4$ (195 GPa): $a=2.605\AA ,c=4.767\AA$; Sc at 2b sites (0, 0, 1/2); H at 4d sites (0, 1/2, 1/4) and 4e sites (0, 0, 0.125). The $P{6}_3/mmc{\mathrm{ScH}}_6\left(145\mathrm{GPa}\right):a=3.419\AA ,c=4.271\AA ;\mathrm{Sc}$ at 2c sites (1/3, 2/3, 1/4); H at 12k sites (0.166, 0.332, 0.630). The $Im\overline{3}m{\mathrm{ScH}}_6$ (285 GPa): $a=3.242\AA$; Sc at 2a sites (0, 0, 0); H at 12d sites (1/4, 0, 1/2).

Figure 3

DOS projected onto each element: (a) the $Fm\overline{3}m{\mathrm{ScH}}_3$ at $r_s=1.65$ (135 GPa); (b) the $I4/mmm{\mathrm{ScH}}_4$ at $r_s=1.55$ (195 GPa); (c) the $P{6}_3/mmc{\mathrm{ScH}}_6$ at $r_s=1.57$ (145 GPa); (d) the $Im\overline{3}m{\mathrm{ScH}}_6$ at $r_s=1.45$ (285 GPa).

Figure 4

Total DOS of scandium hydrides in comparison with those of yttrium and calcium hydrides: (a) the $I4/mmm$ tetrahydrides at $\sim 195$ GPa; (b) the $P{6}_3/mmc$ hexahydrides at $\sim 145$ GPa; (c) the $Im\overline{3}m$ hexahydrides at $\sim 285$ GPa. The asterisks mean that the phases are unstable all over the pressure regime considered here.

Figure 5

Eliashberg function ${\alpha }^{2}F$ multiplied by $2/\omega$ (i.e. $2{\alpha }^{2}F/\omega$) and the density of phonon modes $D_{\mathrm{ph}}$ for the $Fm\overline{3}m{\mathrm{ScH}}_3$ at $r_s=1.65$ (135 GPa), the $I4/mmm{\mathrm{ScH}}_4$ at $r_s=1.55$ (195 GPa), the $P{6}_3/mmc{\mathrm{ScH}}_6$ at $r_s=1.57$ (145 GPa), and the $Im\overline{3}m{\mathrm{ScH}}_6$ at $r_s=1.45$ (285 GPa).