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

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.