Low-frequency vibrational properties of nanocrystalline materials: Molecular dynamics simulations of two-dimensional systems

The low-frequency vibrational density of states (VDOS) of two-dimensional nanocrystalline materials is studied within the framework of molecular-dynamics simulations. The partial VDOS for different categories of atoms (as determined from their local environments), as well as the local (on-site) VDOS, is calculated. It is shown that the low-frequency spectrum exhibits a sequence of three distinct regimes below a critical density ρ*, a direct consequence of the length-scale separation in the material: a first regime, at the lowest frequencies, corresponding to the elastic limit; a second (intermediate) regime, associated with the weak connectivity of the material under ρ* and which does not necessarily show a two-dimensional behavior; a third regime, associated with grain modes and characteristic of a usual Debye solid. The intermediate regime is found to disappear above ρ*. It is further demonstrated that the excess vibrational modes in the upper low-frequency regime arise mainly from grain-boundary atoms, while the other two regimes are related to the presence of pores in the materials.