Neutron scattering investigation of layer-bending modes in alkali-metal—graphite intercalation compounds

Abstract

Phonon dispersion curves for low-frequency transverse modes propagating in the basal plane have been measured in the alkali-metal—graphite intercalation compounds K${\mathrm{C}}_8$, Cs${\mathrm{C}}_8$, K${\mathrm{C}}_{24}$, and Rb${\mathrm{C}}_{24}$ by means of neutron spectroscopy. The acoustic branches show an almost quadratic dispersion relation at small $q$, characteristic of strongly layered materials. The optical branches of stage-1 compounds can be classified as either graphitelike branches showing dispersion, or as almost dispersionless alkali-metal-like modes. Macroscopic shear constants ${\mathrm{C}}_{44}$ and layer-bending moduli have been obtained for the intercalation compounds by analyzing the data in terms of a simple semicontinuum model. In stage-2 compounds, a dramatic softening of the shear constant by about a factor of 8 compared with pure graphite has been observed. Low-temperature results on K${\mathrm{C}}_{24}$ indicate the opening of a frequency gap near the alkali-metal Brillouin-zone boundary, possibly due to the formation of the alkali-metal superstructure.