Theory of interlayer spacing in ternary graphite intercalation compounds

The composition dependence of interlayer spacing in stage-1 ternary graphite intercalation compounds is studied within two theoretical models and by computer simulation. Both the theoretical models neglect the energy associated with the transverse distortion of the graphite layers but include the difference in the ionic size and compressibility of the intercalant species. The first is a bilayer model which assumes that intercalants are randomly distributed in each layer but takes into account the correlation between intercalant ions in neighboring layers. The second is a monolayer model which assumes that the intercalants are randomly distributed in a rigid layer. Different conditions under which one sees a Vegard’s-law behavior are discussed. The intercalant-composition (x) dependence of the average interlayer spacing and its deviation from the Vegard’s-law behavior for different compressibility ratios are presented. Finally, we explore layer distortions in systems with finite transverse rigidity and compare our theoretical results with experimental data in ${\mathrm{Rb}}_{\mathrm{x}}$ ${\mathrm{K}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{C}}_8$ systems.