Variation of Permittivity with Electric Field in Perovskite-Like Ferroelectrics

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Abstract
A model is considered for the case of polycrystalline ferroelectrics in which each crystallite is presumed to behave according to a free‐energy function of the type formulated by A. F. Devonshire [Advances in Phys. 3, 85 (1954)] for BaTiO3. The Curie temperatures for the individual grains are taken in a Gaussian distribution about some chosen temperature. The permittivity is obtained by averaging with this distribution over all of the crystallites. In accordance with the free‐energy function, it is assumed that the electric field induces a ferroelectric axis in those crystallites of the distribution which are not ferroelectric at a given temperature. On the basis of experimental evidence, 90° reorientation of domains in the ferroelectric part of the distribution is presumed to be negligible for semistatic and dynamic fields. Despite the seemingly severe restriction imposed by the latter assumption, a large field sensitivity is predicted. Agreement between the theory and experimental data is excellent for both parallel and transverse fields. It is concluded that the variation of incremental permittivity is associated with an induced ferroelectric state rather than being directly a property of domain processes, and that a large variation with field must necessarily be accompanied by strong thermal sensitivity.