Decorated-latticed structure factors: Applications to intercalation compounds

The structure factors $S\left(k\right)\mathrm{}$ of several randomly decorated triangular lattices are compared with those measured in disordered alkali-metal graphite intercalation compounds (GIC's). The intralayer short-range order in GIC's is modeled under the assumption that the intercalant ions occupy only sites of high symmetry in the graphite host. An intralayer structure with clusters of predominantly third-nearest-neighbor ($2\times 2$) correlations and mean grain size ∼25 Å reproduces the main features of the measured $S\left(k\right)\mathrm{}$ in partially desorbed stage-1 cesium-graphite. The higher-stage alkali metal GIC's, on the other hand, are not well modeled by a simple lattice gas description. A hexagonally modulated fluid structure is proposed with $\sqrt{7}\times \sqrt{7}$ short-range order. Maximum packing fractions are determined for the various decorated lattices. The experimentally observed intercalant density is approximately reproduced for the disordered stage-1 case. We find no evidence for the supposedly fixed 12:1 layer stoichiometry of the higher-stage GIC's.