Deciphering the commensurately modulated monoclinic phase of Rb$_2$ZnCl$_4$ at low temperatures

The ferroelectric phase III of Rb$_2$ZnCl$_4$ is stable below $T_c$ = 192 K. It is known to be a threefold superstructure of the centrosymmetric high-temperature structure, with space group $P2_1 cn$. Below $T_L$ = 70 K, phase IV exists as a sixfold superstructure. We report the crystal structure of phase IV with monoclinic symmetry $Cc$ (b unique), while a structure model with symmetry $Pn$ (c unique) leads to an almost equally good, yet significantly worse fit to the diffraction data. Employing the superspace approach to these commensurately modulated structures results in modulation waves that follow the two-dimensional irreducible representation $T_1$ of $P2_1 cn$, albeit with different order parameter directions defining $Cc$ and $Pn$ symmetries, consistent with the literature. Standard tools of crystal-chemical analysis indicate that the sixfold superstructure is more stable than the threefold superstructure of phase III. However, crystal-chemical arguments cannot distinguish between the correct superstructure model with space group $Cc$ ($b$ unique) and the incorrect superstructure model with symmetry $Pn$ ($c$ unique) for phase IV. New crystal chemical tools are required, in order to attain a meaningful understanding of superstructure formation.