Lattice dynamics and low-frequency excitations of transition-metal hydrides:NbDx,NbHx, andTaDx

Abstract

Phonon dispersion curves have been measured on single crystals of Nb${\mathrm{D}}_{0.85}$ along the [100], [011], and [111] directions. The dispersion curves of the ${\ensuremath{\alpha}}^{\ensuremath{'}}$ phase of Nb${\mathrm{D}}_{0.85}$ at $T=160\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ were fit with a Born---von K\'arm\'an model of the interatomic force constants out to the seventh neighbors. From these constants the acoustic-phonon density of states is calculated. The results are compared with previous measurements on $\mathrm{Nb}{\mathrm{D}}_{x}$ with $x=0.45$, $x=0$, and with the Nb-Mo system. A new dispersionless excitation is observed in Nb${\mathrm{D}}_{0.85}$ at $\ensuremath{\hbar}\ensuremath{\omega}=18.4$ meV. A similar feature is observed in Nb${\mathrm{H}}_{0.82}$ at $\ensuremath{\hbar}\ensuremath{\omega}=19.0$ meV and in Ta${\mathrm{D}}_{0.78}$ at $\ensuremath{\hbar}\ensuremath{\omega}=15.0$ meV. The linewidth of this excitation in Nb${\mathrm{D}}_{0.85}$ decreases as the $\ensuremath{\beta}$ phase is entered and its position shifts slightly to higher energies. A detailed examination of the dispersion curves within the $\ensuremath{\beta}$ phase reveals interaction between the acoustic modes and this dispersionless excitation. Possible origins of this new feature are discussed. Also observed is an anomalous broadening of the [110] zone-boundary LA phonon with the ${\ensuremath{\alpha}}^{\ensuremath{'}}$ phase.