Abstract
It is useful to distinguish hard and soft structure-building units : the soft are those which vary easily with temperature or composition, while the hard stay constant. In perovskites, the O6 octahedra themselves are hard, their tilts relative to one another, and the displacement of the B-cation from its centre, may be soft. Tilts are often determined by the A-cation environment ; displacements are primarily determined by the B-cation, but may be modified by other factors. Tilts and displacements, though independent in origin, interact. Each may be resolved into three components associated with the tetrad axes of the octahedron ; they may be doubly or triply degenerate (equivalent to diad or triad axes), and they may be coupled by symmetry. The tilt systems throw light on possible lattice modes. Only when they are coupled with B-cation displacements do the tilts affect the ferroelectric properties significantly. Reversal of tilts between adjacent layers of octahedra tends to be difficult. Illustrations include the rare-earth orthoferrites and various phases of NaNbO3 including the low-temperature phase N and the highest non-cubic phase T2