Critical behaviors of melting and high-temperature structures in stage-1 rubidium-graphite intercalation compounds.

Abstract

The phase diagram, the high-temperature (T) structures of liquid and solids, and the critical behaviors of melting in stage-1 Rb-graphite intercalation compounds have been investigated with use of x-ray diffraction. The (${P}_{\mathrm{Rb}}$,T) phase diagram shows a narrow region of a high-T \ensuremath{\alpha}\ensuremath{\beta} stacking solid with the in-plane (2\ifmmode\times\else\texttimes\fi{}2) structure between the low-T \ensuremath{\alpha}\ensuremath{\beta}\ensuremath{\gamma}\ensuremath{\delta} solid and the high-T liquid. At high temperatures Rb atoms behave as a quasi-two-dimensional liquid with in-plane correlations, and as T approaches ${T}_{m}$ (melting temperature) they have strong in-plane and out-of-plane correlations with the same symmetry as the \ensuremath{\alpha}\ensuremath{\beta} solid; the two-dimensional (2D) to 3D crossover effect is observed. Remarkable features of the continuous melting are observed at ${T}_{m}$: (1) the peak wave number of the in-plane short-range order in the liquid changes continuously to the Bragg peak wave number of the \ensuremath{\alpha}\ensuremath{\beta} solid, (2) the order parameter of the \ensuremath{\alpha}\ensuremath{\beta} solid grows continuously with \ensuremath{\beta}=0.30\ifmmode\pm\else\textpm\fi{}0.06, and (3) the in-plane positional and orientational correlation lengths \ensuremath{\xi} increase in the solid and the liquid and have critical exponents ${\ensuremath{\nu}}_{a}$=0.24\ifmmode\pm\else\textpm\fi{}0.04 and ${\ensuremath{\nu}}_{\ensuremath{\varphi}}$=0.34\ifmmode\pm\else\textpm\fi{}0.04 in the liquid, respectively. All the critical parameters show no appreciable hysteresis at ${T}_{m}$. Contrary to these continuous behaviors, the correlation lengths remain finite at ${T}_{m}$, suggesting the presence of a small but finite first-order gap. These experimental results are discussed in terms of the 3D four-state Potts model. In the low-${P}_{\mathrm{Rb}}$ case, the transition is of first order in contrast to the high-${P}_{\mathrm{Rb}}$ case mentioned above. In some samples, the maximum temperature in \ensuremath{\xi}(T) which is obtained in the off-Bragg scan shifts a few degrees lower than ${T}_{m}$. Some discussions are given. The \ensuremath{\alpha}\ensuremath{\beta} solid at high T shows remarkable in-plane anisotropic Debye-Waller factors.