Hydrogen vibration excitations of ZrH1.8 and TiH1.84 up to 21 GPa by incoherent inelastic neutron scattering

Abstract

Hydrogen vibration excitations of fluorite-type $\mathrm{Zr}{\mathrm{H}}_{1.8}$ and $\mathrm{Ti}{\mathrm{H}}_{1.84}$ were investigated at pressures up to 21 and 4 GPa, respectively, by incoherent inelastic neutron scattering experiments. The excitations of both the samples were well described by quantum harmonic oscillator (QHO) over the entire pressure region of this study. The first excitation energies increased with increasing pressure, as described by the equations ${E}_{1}(\mathrm{meV})=141.4(2)+1.02(2)P$ (GPa) and ${E}_{1}\phantom{\rule{0.16em}{0ex}}(\mathrm{meV})=149.4(1)+1.21(8)P$ (GPa) for $\mathrm{Zr}{\mathrm{H}}_{1.8}$ and $\mathrm{Ti}{\mathrm{H}}_{1.84}$, respectively. Coupling with pressure dependence of lattice parameters determined by diffraction experiments, the relations between metal-hydrogen distance $({d}_{\mathrm{M}\text{\ensuremath{-}}\mathrm{H}})$ and ${E}_{1}$ of $\mathrm{Zr}{\mathrm{H}}_{1.8}$ and $\mathrm{Ti}{\mathrm{H}}_{1.84}$ at high pressures are found to be well described by the equations ${E}_{1}(\mathrm{meV})=1.62(9)\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.16em}{0ex}}{d}_{\mathrm{M}\text{\ensuremath{-}}\mathrm{H}}^{\ensuremath{-}3.32\phantom{\rule{0.16em}{0ex}}(7)}(\AA{})$ and ${E}_{1} (\mathrm{meV})=1.47(21)\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.16em}{0ex}}{d}_{\mathrm{M}\text{\ensuremath{-}}\mathrm{H}}^{\ensuremath{-}3.5(2)}(\AA{})$, respectively. The slopes of these curves are very steep compared to the previously reported trend in various fluorite-type metal hydrides at ambient pressure, suggesting that pressure and chemical substitution affect the hydrogen vibration excitations differently. The hydrogen wave function spreading estimated from the ${E}_{1}$ value assuming the QHO model showed the preferential shrinkage of the wave function to the tetrahedral sites, suggesting that the local potential field for a hydrogen atom shrinks more intensively than the tetrahedral site. The preferential shrinkage of the hydrogen wave function and the steep rise in the ${E}_{1}$ at a small ${d}_{\mathrm{M}\text{\ensuremath{-}}\mathrm{H}}$ under pressure are likely caused by the rigid metal ion core compared to hydrogen atoms and the resulting confinement of the hydrogen atom in the narrower potential field at high pressures.