Order-disorder in higher-stage (n=3, 4) potassium graphites

The disordered and ordered states in stages-3 and -4 potassium graphite (∼${\mathrm{C}}_{36}$K and ${\mathrm{C}}_{48}$K) have been studied with x-ray diffraction on highly oriented pyrolytic graphite samples. The disordered state of both is similar and is confirmed to consist of independent (uncorrelated) layers of intercalant with a liquidlike in-plane structure, incommensurate with the graphite-net planes. The in-plane ordered structures of the two are essentially identical to each other and quite similar to, but somewhat expanded over, the stage-2 structure. The transition to some form of two-dimensional (2D) modulated or ordered state in ${\mathrm{C}}_{36}$K occurs smoothly on cooling with an apparent onset at ∼190 K of ordering reflections similar to those observed in stage 2. This is characterized as well by a continuous shift and sharpening of the 2D pattern below the ordering onset and a concomitant development of weak three-dimensional (3D) order at $T<\mathrm{}131\mathrm{}$ K. This behavior is to be contrasted with the sharp, apparently second-order, transition in stage 2 (∼ ${\mathrm{C}}_{24}$K) in which the modulation peaks and 3D order set in at the same temperature.