Crystal stability and the theory of ferroelectricity

Abstract The phenomenon of ferroelectricity in pseudo-cubic crystals is discussed in terms of the normal modes of vibration. It is shown that the parameters which determine the lattice vibrations of a diatomic ionic crystal may be chosen in such a way that the crystal will exhibit ferroelectric properties, and that ferroelectric or anti-ferroelectric transitions may be regarded as the result of an instability of the crystal for a certain normal mode of vibration. The theory is extended to apply to other cubic crystals, including barium titanate, and the concepts of ‘ionic polarizability’ and ‘a polarizability catastrophe’ are discussed in terms of lattice dynamics. Certain of the parameters which appear in Devonshire's phenomenological theory of ferroelectricity are found to be expressible in terms of atomic parameters. Values for the latter which are physically reasonable are found to account quite well for the dielectric properties of barium titanate and for the relative movements of the atoms which occur at the cubic-tetragonal transition. The lowest dielectric dispersion frequency is calculated to be about 3 × 1011 c.p.s. for barium titanate, and to be a function of temperature in the cubic phase. Other predictions of the theory are discussed.