In-plane ordering in stage-2 graphite intercalation compounds

A theoretical study of the orientational in-plane ordering in stage-2 graphite intercalation compounds is developed with particular emphasis on the role of phonons. Phonon dispersion curves are calculated within a simple phenomenological model. The rotation angle of intercalant layers relative to the graphite layers in the reciprocal-lattice space is shown to be determined predominantly by the transverse-acoustic mode. The rotation angles calculated for Cs${\mathrm{C}}_{24}$, Rb${\mathrm{C}}_{24}$, and K${\mathrm{C}}_{24}$ are in fairly good agreement with experiments. The rotation angle depends also on the lattice constants of the host and guest layers. Our calculations have been carried out assuming a homogeneous triangular lattice structure for the intercalant layer. Comment is, therefore, made on the possibility of having a domain structure in which locally registered domains are bounded by discommensurations.