Vibrational modes and quantum zero-point energy of hydrogen in ZrH_0.0155 and ZrH₂

We report on an inelastic neutron scattering study of the proton dynamics in ZrH_0.0155 and ε-ZrH₂. In particular, we present measurements of the incoherent dynamic structure factor, generalized vibrational density of states, and proton momentum distribution of these two materials. Our results are generally consistent with theoretical predictions of Elsässer et al. [Mat. Res. Soc. Symp. Proc. 453 221-226 (1997)]. They argued that the effective Born-Oppenheimer potential experienced by the hydrogen atoms in ε-ZrH₂ is nearly isotropic and harmonic at energies below 0.3 eV, but becomes anisotropic and anharmonic for higher energies. At low temperatures, the proton momentum distribution is dominated by the quantum-mechanical ground state of the protons. We find that it assumes a Gaussian shape, consistent with the concept that the potential surface is approximately harmonic for small displacements of the hydrogen atoms. However, the anharmonicity of the potential becomes readily apparent in the excited states of the hydrogen atoms, as the harmonic approximation breaks down in the description of the multiphonon bands.