Temperature and hydrogen-concentration dependence of hydrogen optic vibrational frequencies inα- andα′-phase niobium hydride: Static lattice strain and anharmonicity effects

Abstract

We calculate the shift and broadening of hydrogen optic vibrational frequencies in the $\ensuremath{\alpha}$ (lattice-gas) and ${\ensuremath{\alpha}}^{\ensuremath{'}}$ (lattice-liquid) phases of $\mathrm{Nb}{\mathrm{H}}_{c}$ as a function of temperature $T$ and hydrogen concentration $c$ (H-Nb ratio). We assume the H's vibrate in local modes and linearly relate their vibrational frequencies to the static local lattice dilation through an anharmonicity parameter $\ensuremath{\gamma}$ estimated from inelastic neutron scattering data. The static local lattice dilations are obtained from a grand-canonical Monte Carlo calculation. The H lattice-gas or lattice-liquid model used in the Monte Carlo calculation is an approximation of that of Horner and Wagner, which involves a lattice-mediated H-H strain interaction and H-H hard core. Our calculatins are done in that part of the region described by $0.1<c<0.5$ and $400 <T<600$ K which lies outside the $\ensuremath{\alpha}\ensuremath{-}{\ensuremath{\alpha}}^{\ensuremath{'}}$ coexistence region. Our calculated $c$- and $T$-dependent frequency shifts are roughly consistent with the available data. The calculated broadenings are too small. We estimate that the addition of thermal lattice fluctuations to the model would yield realistic broadenings.