Phonon modes in graphite,C60, andC60-based fibers

The influence of curvature on the radial vibrational modes in ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{60}$-based fibers is considered and is shown to lead to a softening of these modes in comparison with the out-of-plane phonon mode in graphite. The effect on the restoring force constants of doping these systems with an alkali metal is then considered. In graphite, intercalation with an alkali metal leads to mode softening: in ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{60}$-based fibers, on the other hand, it is shown that doping softens the tangential modes, while the curvature stiffens the radial modes.