Low-frequency vibrational properties of nanocrystalline materials.

The vibrational density of states (VDOS) of bulk nanocrystalline Ni and Cu (model) samples with grain diameters between 5 and 12 nm are derived from molecular-dynamics simulations. The results show an enhancement of the density of states at low and high energies. Because of large system sizes and a decomposition of the VDOS into grain and grain-boundary components, the low-frequency region can be investigated for the first time. It is found that the anomalous increase of the VDOS is mainly caused by the high number of grain-boundary atoms and that a power-law behavior of the low-frequency grain-boundary VDOS exists, which suggests a reduced dimensionality effect.