Neutron vibrational spectroscopy and first-principles calculations of the ternary hydrides ${\mathrm{Li}}_4{\mathrm{Si}}_2\mathrm{H}\left(\mathrm{D}\right)$ and ${\mathrm{Li}}_4{\mathrm{Ge}}_2\mathrm{H}\left(\mathrm{D}\right)$: Electronic structure and lattice dynamics

Using combined neutron spectroscopy and first-principles calculations, we investigated the electronic structure and vibrational dynamics of the recently discovered class of ternary hydrides ${\mathrm{Li}}_4{\mathit{Tt}}_2\mathrm{H}$ ($\mathit{Tt}=\mathrm{Si}$ and Ge). In these compounds, all hydrogen atoms are located in a single type of ${\mathrm{Li}}_6$-defined octahedral site. The $\mathit{Tt}$ atoms form long-range $\mathit{Tt}\text{−}\mathit{Tt}$ chains sandwiched between each ${\mathrm{Li}}_6$-octahedra layer. The Li-H interactions are strongly ionic, with bond lengths comparable to those in LiH. Our density functional theory calculations indicate that Li atoms transfer their electrons to both H and $\mathit{Tt}$ atoms. $\mathit{Tt}$ atoms within the $\mathit{Tt}\text{−}\mathit{Tt}$ chain are bonded covalently. The electronic density of states reveals that both hydrides exhibit metallic behavior. The observed vibrational spectra of these hydrides are in good overall agreement with the calculated phonon modes. There is evidence of dispersion induced splitting in the optical phonon peaks that can be ascribed to the coupling of H vibrations within the ${\mathrm{Li}}_6$-octahedra layers.

Figure 1

(Color online) An off-[001] view of the orthorhombic ${\mathrm{Li}}_4{\mathit{Tt}}_2\mathrm{H}$ crystal structure with centered octahedral interstices. The large blue and small pink spheres represent $Tt$ ($=\mathrm{Si}$, Ge) and Li, respectively, and the interstitial H atoms (small white) are centered in the shaded ${\mathrm{Li}}_6$ octahedra

Figure 2

(Color online) Total electronic DOS of (a) ${\mathrm{Li}}_4{\mathrm{Si}}_2\mathrm{H}$ and (b) ${\mathrm{Li}}_4{\mathrm{Ge}}_2\mathrm{H}$ and projection around the different atomic sites. $E_F$ is taken as the zero of energy and shown as the dashed line.

Figure 3

(Color online) Characteristic charge-density maps on (a) (100), (b) (001), (c) (002), (d) (010), and (e) (020) planes. The values of the contours in all maps are from $0\text{to}0.57e∕{\mathrm{\AA }}^2$. The atoms (H, small white; Li, medium pink; Si, large blue spheres) on the corresponding crystallographic planes are also shown underneath the transparent charge-density maps for clarity.

Figure 4

NV spectra of (a) ${\mathrm{Li}}_4{\mathrm{Si}}_2\mathrm{H}\left(\mathrm{D}\right)$ and (b) ${\mathrm{Li}}_4{\mathrm{Ge}}_2\mathrm{H}\left(\mathrm{D}\right)$ at $10\mathrm{K}$. The ratio of corresponding energy-loss scales for hydrides and deuterides is $\sqrt{2}$. The spectra for hydrides and deuterides are plotted using the bottom and the top $x$ axes, respectively.

Figure 5

(Color online) Comparison of observed NV spectra of ${\mathrm{Li}}_4{\mathrm{Si}}_2\mathrm{H}$ (bottom panel) and ${\mathrm{Li}}_4{\mathrm{Ge}}_2\mathrm{H}$ (top panel) with the calculated spectra. The inset schemes the assigned H phonon modes corresponding to their observed peaks in the NV spectra (solid, dot, and dash-dot arrows indicate the H phonon modes in ${\mathrm{Li}}_6$-octahedron and the corresponding observed peaks in NV spectra, respectively), which are well correlated with the Li-H bond lengths.