Structure of high-stage potassium-intercalated graphite

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Abstract
We have used x-ray diffraction to study the structure of stage-4 through stage-11 potassium-intercalated graphite as a function of temperature. The (00.L) diffraction patterns are analyzed in terms of the Hendricks-Teller model for a disordered one-dimensional crystal. Stage 4–5 samples are best described by phase separation of two different stages, while higher-stage samples are best described by a broad distribution of many stages. In plane, all samples show a high-temperature two-dimensional fluid structure of the potassium atoms. In the stage 4–6 samples, the fluid peak gradually sharpens on cooling and increases in intensity to form a two-dimensional incommensurate superlattice. This evolution is consistent with a second-order transition. By contrast, the higher-stage samples show a strongly first order, hysteretic transition to a commensurate √7 × √7 superlattice at 235 K. In all cases, the expansion of the two-dimensional lattice upon freezing agrees within experimental error with the 2–4?increase in out-of-plane density of potassium layers.