The rhombohedral perovskites are of interest in lattice dynamics (e.g. LaA103, PrA103) and for their ferroelectric properties (e.g. LiNbO3, PbZr/TiO3). In this paper, data scattered through the literature are correlated, with correction of some misleading mistakes of calculation. Geometrical descriptions are put in a form allowing comparisons. The structures, classified by their space groups, are described in terms of four structural parameters, the octahedron tilt co, octahedron distortion d, and A-and B-cation displacements s and t, together with an elongation or flattening ~ of the octahedron, deducible with the help of co from the interaxial angle a,h. Attention is drawn to the variety of physical causes underlying these departures from ideal perovskite. In the R-3e structures a correlation not previously noted in the literature is found between the tilt angle co and a flattening of the octahedron, and some tentative suggestions are made as to its cause. In the R3m and R3e structures, a lack of general correlation between B-cation displacement and the other parameters is noted, in contradiction to earlier reports.
The high-temperature phases of the perovskites sodium niobate, NaNbO(3), and sodium tantalate, NaTaO(3), have been re-examined using the high-resolution powder diffractometer HRPD at the ISIS neutron spallation source; the two materials show the same sequence of phases with tilted octahedra. Diffraction patterns were measured every 5 K allowing structural changes with temperature within a single phase to be determined for the first time. Previous structure determinations within one phase had been performed at a single temperature only. The octahedra are tilted about pseudocubic <100> directions and are also deformed; the magnitude of the deformation is shown to be proportional to the square of the angle of tilt as expected from a phenomenological theory applied to such transitions. The structures of NaNbO(3) between 753 and 793 K and of NaTaO(3) below 758 K are not as reported in the literature.
Sodium niobate undergoes an antiferroelectric-ferroelectric transition (P ~ N) at temperatures below about -110°C. The ferroelectric low-temperature phase (N) is rhombohedral, with space group R3c.Though a perovskite structure, it is isostructural with LiNbO3. Using pseudocubic axes of reference, a=2 × 3"9083 (5) ~, ~= 89 ° 13 (1)' at -150°C. The NbO6 octahedra remain nearly regular, but are tilted about the triad axis; displacements of Nb atoms from the centres of octahedra are parallel to this axis. The temperature dependence of the lattice parameters of both phases, N and P, below room temperature is reported, and also that of the magnitude of the Nb displacement in the antiferroelectric phase P. Experimental details of the low-temperature work are given. Evidence used in the structure determination comes from the juxtaposition of high-angle reflexions from twin components in phase N, and the orientation of domains of phase N relative to the parent phase P. The transformation is more rapid and more complete if the parent crystal is single-domain; if it is twinned, both phases coexist for long periods down to the lowest temperatures studied. The relation of the structure to that of other niobates is discussed, and some general principles are put forward from which the occurrence of different structures and the transitions between them can be understood.
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