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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 structure of NaNbO3 has been refined from three-dimensional X-ray data. It is a distorted perovskite, with space group Pbma and 8 formula units in an orthorhombic unit cell about 5.5 x 15 x 5.5/l,.Electron-density projections constructed with only the Nb atoms displaced from their ideal positions gave approximate magnitudes for all the larger displacement parameters. With the help of an additional projection, assuming one oxygen parameter to fix the sense of the y axis, the signs of all these displacement parameters could be found by several different arguments allowing cross-checking. The trial model thus set up proved to be a very good approximation and refined easily both by Fourier difference syntheses and by least-squares.The NbO6 octahedra, which are the asymmetric units, are in fact very regular, though tilted appreciably (,-, 10 °) about both the [010] and the [100] directions. The Nb atoms are off-centre, with their displacement vector inclined at about 20 ° to [100], nearly in the (010) plane. There are thus two short, two long, and two intermediate Nb-O bonds; each O has only one short bond to Nb. Deviations from regularity of the octahedron shape, though of second-order magnitude, are systematic and can be correlated with the Nb displacement. Along any column of octahedra parallel to [010], a pair of Nb displacements related by the (010) mirror plane is followed by an antiparallel pair, but in adjacent columns the displacements are not exactly parallel. The two independent Na atoms have very different environments; Na(1) has 3 very near neighbours in a triangle, and 6 distinctly more distant, while Na(2) has 4 nearest in a tetrahedron and 4 slightly more distant. Thermal vibration amplitudes are in general greatest at right angles to strong bonds. The structure is compared with the ferroelectric phase (Phase Q), and some suggestions are made as to how the Na environment may determine the relative stabilities of the two phases.

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