Reports about the ferroelectric ordering temperatures in the multiferroic hexagonal RMnO 3 system are controversial: transition temperatures varying between Ϸ900 K and Ϸ1300 K are reported for the same material. To elucidate the structural changes leading to ferroelectric distortions in hexagonal manganites, we calculate the irreducible representations of the distortions from the possible high-temperature symmetry P6 3 /mmc to the low-temperature symmetry P6 3 cm. There are four different orthogonal modes, of which only one allows a spontaneous electric polarization. Structure refinements and an accurate statistical analysis of neutron powder-diffraction data of TmMnO 3 , based on this group-theoretical analysis, reveal two phase transitions: We extrapolate a polar to nonpolar transition temperature of T npt ϭ1433(27) K, where the hexagonal bitetrahedra start to tilt, while the ferroelectric distortion appears at T FE ϭ1050(50) K. For RϭLu, Yb the tilt of the bitetrahedra and the buckling of the R layers as well as the ferroelectric distortion were extrapolated to comparable temperatures.

Crystal optical and x-ray diffraction studies show that the high-temperature phase I of the perovskite-type layer compounds (C,I.12,,1NH,),CuC1, with n = 1, 2, 3 is Jahn-Teller distorted orthorhombic with space group Bbcm (Dif). As a consequence, the order of the CnH2n+ INH3 group leads to two configurations, realised in a monoclinic phase I1 with space group P2,/c (C&) and an orthorhombic phase I11 with Pbca (D::). The transition sequences found above 300 K depend on n: I +-T,, = 348 K+ I1 for n = 1; I + T,, = 364 K-+ I1 +-T& = 356 K, Te2 = 338K+ I11 forn = 2; and I +-T,, = 434K+ I11 forn = 3. The domain phenomena at T,, and T,, point to a subtle balance between the tilt and order configurations of phases I1 and 111. Birefringence and lattice constants indicate a very loose inter-layer contact in phase I.