Phonon dispersion of nano-graphite ribbons

Based on the classical force constant models, we study numerically and analytically out-of-plane phonon-dispersion relations for two types of nano-graphite ribbons confined by the armchair- and zigzag-shaped edges. We demonstrate for two ribbons how the edge-localized vibrational modes, i.e., edge phonon modes, behave depending on edge environment by means of altering the effective mass of the edge sites. Special emphasis is placed on the qualitative difference in the phonon modes which are localized near two types of edges. q1998 Elsevier Science B.V. All rights reserved.