M. E. Huster, P. A. Heiney, V. B. Cajipe, and J. E. Fischer, Phys. Rev. B35 , 3311-3326 (1987).
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 sqrt(7)Xsqrt(7) superlattice at 235 K. In all cases, the expansion of the two-dimension lattice upon freezing agrees within experimental error with the 2-4% increase in out-of-plane density of potassium layers.
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