Geometrical and structural relations in the rhombohedral perovskites

The rhombohedral perovskites are of interest in lattice dynamics (e.g. LaAlO₃, PrAlO₃) 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 ω, octahedron distortion d, and A- and B-cation displacements s and t, together with an elongation or flattening ζ of the octahedron, deducible with the help of ω from the interaxial angle α_rh. Attention is drawn to the variety of physical causes underlying these departures from ideal perovskite. In the Rc structures a correlation not previously noted in the literature is found between the tilt angle ω and a flattening of the octahedron, and some tentative suggestions are made as to its cause. In the R3m and R3c structures, a lack of general correlation between B-cation displacement and the other parameters is noted, in contradiction to earlier reports.