In situ study of the $R\overline{3} c \to R\overline{3} m$ orientational disorder in calcite

Abstract

The temperature dependences of the crystal structure and intensities of the (113) and (211) reflections in calcite, CaCO₃, were studied using Rietveld structure refinements based on synchrotron powder X-ray diffraction data. Calcite transforms from $R\overline{3} c$ to $R\overline{3} m$ at about T _c = 1,240 K. A CO₃ group occupies, statistically, two positions with equal frequency in the disordered $R\overline{3} m$ phase, but with unequal frequency in the partially ordered $R\overline{3} c$ phase. One position for the CO₃ group is rotated by 180° with respect to the other. The unequal occupancy of the two orientations in the partially ordered $R\overline{3} c$ phase is obtained directly from the occupancy factor, x, for the O1 site and gives rise to the order parameter, S = 2x − 1. The a cell parameter shows a negative thermal expansion at low T, followed by a plateau region at higher T, then a steeper contraction towards T _c, where the CO₃ groups disorder in a rapid process. Using a modified Bragg–Williams model, fits were obtained for the order parameter S, and for the intensities of the (113) and (211) reflections.