Ferroelectricity and Antiferroelectricity of a Crystal Containing Rotatable Polar Molecules

Abstract

We have investigated the dielectric properties of a CsCl type crystal made up by insertion of ions into the body center sites of a simple cubic array of rotatable polar molecules. Owing to the Lorentz field exerted by the dipoles themselves, a non-uniform distribution in orientation of the polar molecules is predicted below a certain critical temperature. The main results obtained are as follows: (1) It is shown that the crystal is antiferroelectric so long as the polarizability of the central ions is small, half of the dipoles being partially oriented parallel to and the other half antiparallel to one of the cube edges. On the other hand, if the polarizability of the ions is larger than a certain threshold value, the crystal is ferroelectric, all the dipoles being partially oriented parallel to each other. (2) The dielectric constant-temperature curves calculated for antiferroelectric cases show a variety of forms according to the polarizabilities of both components. For some specimens they are almost flat throughout the region around their own critical temperatures, while for other specimens they can show such sharp peaks that they are hardly discernible from those of ferroelectric crystals, which always show very sharp peaks tending to infinity. (3) Below their respective critical temperatures, the dielectric constant should decrease with increasing dc bias in a ferroelectric crystal, while in an antiferroelectric crystal it should increase slightly under the same condition. (4) If a sufficiently strong field is applied to an antiferroelectric crystal at just below its critical temperature, it will be forced to make a momentary transition to a ferroelectric one, the change being accompanied by an abrupt increase of polarization.It is suggested that most of the phenomenological predictions derived with this model may, qualitatively at least, be valid also for other models which have ions capable of displacement instead of freely rotatable dipoles, as is really the case with the well-known BaTi${\mathrm{O}}_{3}$ and the like.