The R{overline{3}} c to R{overline{3}} m transition in nitratine, NaNO3, and implications for calcite, CaCO3

The temperature dependences of the crystal structure and superstructure intensities in sodium nitrate, mineral name nitratine, NaNO₃, were studied using Rietveld structure refinements based on synchrotron powder X-ray diffraction. Nitratine transforms from $R{overline{3}} c;hbox{to};R{overline{3}} m$ at T _c = 552(1) K. A NO₃ 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 NO₃ group is rotated by 60° or 180° with respect to the other. The occupancy of the two orientations in the $R{overline{3}} c$ phase is obtained from the occupancy factor, x, for the O1 site and gives rise to the order parameter, S = 2x ? 1, where S is 0 at T _c and 1 at 0 K. The NO₃ groups rotate in a rapid process from about 541 to T _c, where the a axis contracts. Using a modified Bragg–Williams model, a good fit was obtained for the normalized intensities (that is, normalized, NI^1/2) for the (113) and (211) reflections in $R{overline{3}} chbox {,NaNO}_{3},$ and indicates a second-order transition. Using the same model, a reasonable fit was obtained for the order parameter, S, and also supports a second-order transition.