▎ 摘　　要

The phonon dispersion and the vibrational density of states (VDOS) of graphene nanoribbons (GNR) of various widths and edge shapes are calculated using the force constant model including the fifth-nearest neighbor atoms. Among typical graphene peaks like E2g (or G) and D peaks, several distinctive ribbon peaks are identified in the VDOS depending on the edge shape. According to our calculation, the edge nature of a GNR can be identified by several characteristic peaks in the VDOS:many out-of-plane edge localized modes are detected at about 630 cm(-1) in armchair GNRs and many in-plane edge modes are detected at about 480 cm(-1) in zigzag GNRs. In mixed-edge GNRs the intensity of these peaks is strongly correlated to the armchair-to-zigzag edge ratio. (C) 2011 American Institute of Physics. [doi:10.1063/1.3552293]