The octahedron tilt transitions of ABX_3 perovskite-structure materials lead
to an anti-polar (or antiferroelectric) arrangement of dipoles, with the low
temperature structure having six sublattices polarized along various
crystallographic directions. It is shown that an important mechanism driving
the transition is long range dipole-dipole forces acting on both displacive and
induced parts of the anion dipole. This acts in concert with short range
repulsion, allowing a gain of electrostatic (Madelung) energy, both
dipole-dipole and charge-charge, because the unit cell shrinks when the hard
ionic spheres of the rigid octahedron tilt out of linear alignment.Comment: 4 page with 3 figures included; new version updates references and
clarifies the argument
