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

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 ${\alpha }^{\prime }$ phase of Nb${\mathrm{D}}_{0.85}$ at $T=160\mathrm{}°\mathrm{C}$ were fit with a Born—von Kármán 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 $x=0.45\mathrm{}$, $x=0\mathrm{}$, and with the Nb-Mo system. A new dispersionless excitation is observed in Nb${\mathrm{D}}_{0.85}$ at $\hslash \omega =18.4\mathrm{}$ meV. A similar feature is observed in Nb${\mathrm{H}}_{0.82}$ at $\hslash \omega =19.0\mathrm{}$ meV and in Ta${\mathrm{D}}_{0.78}$ at $\hslash \omega =15.0\mathrm{}$ meV. The linewidth of this excitation in Nb${\mathrm{D}}_{0.85}$ decreases as the $\beta$ phase is entered and its position shifts slightly to higher energies. A detailed examination of the dispersion curves within the $\beta$ 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 ${\alpha }^{\prime }$ phase.