Dispersion relations in graphite intercalation compounds: Phonon dispersion curves

A phenomenological model based on staging periodicity and in-plane superlattice symmetry is developed for the phonon dispersion relations of graphite intercalation compounds, analogous to the formalism developed for the electronic dispersion relations. The formalism, based on the zone folding of the graphite dynamical matrix required by symmetry, gives with a minimum number of parameters the only available calculation for the phonon dispersion relations for high-stage compounds. Specific application of the model to a ${\mathrm{C}}_{2n}X$ structure yields results in good agreement with the stage dependence of the lattice mode spectra, indicating that the staging periodicity is the dominant effect in these compounds. Implications on the velocity of sound, second-order Raman spectrum, and specific-heat measurements are discussed.