Intercalate structure, melting, and the commensurate-incommensurate transition in bromine-intercalated graphite

Abstract

In situ high-resolution x-ray scattering experiments have been carried out to study in-plane intercalate structure and phase transitions as a function of temperature in a single crystal graphite host. For the case of bromine-intercalated graphite the intercalate plane has three sublattices and each sublattice has a centered ($\sqrt{3}\ifmmode\times\else\texttimes\fi{}7$) rectangular structure with four ${\mathrm{Br}}_{2}$ molecules per two-dimensional unit cell in the commensurate phase. The coherently ordered in-plane bromine regions exceed 10 000 \AA{} in size. Above the commensurate-incommensurate transition (342.20\ifmmode\pm\else\textpm\fi{}0.05 K), a stripe domain phase becomes established in a single domain of a sublattice along the sevenfold direction. The incommensurability as a function of reduced temperature exhibits a power law with an exponent of 0.50\ifmmode\pm\else\textpm\fi{}0.02, confirming the existing theories. The relative shifts observed for the various harmonics are accurately predicted by a sharp-domain-wall model with $\frac{4\ensuremath{\pi}}{7}$ phase shifts. A power-law line shape is observed for the incommensurate intercalate layer, yielding values for the exponent $\ensuremath{\eta}$ consistent with model calculations. Results on the temperature dependence of the intensities, linewidths, and line shapes of several Bragg peaks around the melting transition are presented. The intercalate layer exhibits a continuous melting transition from a two-dimensional solid phase to an anisotropic fluid phase, occurring at 373.41\ifmmode\pm\else\textpm\fi{}0.10 K for a stage-4 compound.