Acoustic modes of the phonon dispersion relation ofNbDxalloys

Abstract

The acoustic modes of the phonon dispersion relation in Nb, Nb${\mathrm{D}}_{0.15}$, and Nb${\mathrm{D}}_{0.45}$ have been measured at 473 K for phonons with wave vectors along the [100], [110], and [111] axes by coherent neutron scattering. The observed neutron groups for both alloys were well defined, with little or no apparent broadening. The results are compared to similar data for Nb-Mo alloys and with previous lattice-dynamics results for Pd${\mathrm{D}}_{0.63}$. This comparison shows that despite differences in detail, the general features of the dispersion relations of $\mathrm{Nb}{\mathrm{D}}_x$ and Nb-Mo are similar after allowing for the differences in lattice parameters for the two alloys. The measured dispersion curves and derived phonon frequency distributions for the Nb-D alloys are quite different from the analogous results for Pd${\mathrm{D}}_{0.63}$ in that the average acoustic phonon frequencies increase with increasing deuterium concentration and lattice parameter.