The phonon density of states of nanocrystalline bcc Fe and nanocrystalline fcc ${\mathrm{N}\mathrm{i}}_3\mathrm{F}\mathrm{e}$ were measured by inelastic neutron scattering in two different ranges of energy. As has been reported previously, the nanocrystalline materials showed enhancements in their phonon density of states at energies from 2 to 15 meV, compared to control samples composed of large crystals. The present measurements were extended to energies in the micro-eV range, and showed significant, but smaller, enhancements in the number of modes in the energy range from 5 to $18\mu \mathrm{e}\mathrm{V}$. These modes of micro-eV energies provide a long-wavelength limit that bounds the fraction of modes at milli-eV energies originating with the cooperative dynamics of the nanocrystalline microstructure.

• Received 27 April 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.205501