A self-consistent constitutive model for switching in polycrystalline barium titanate

A self-consistent model for the constitutive behavior of polycrystalline barium titanate is presented. More generally, the model is valid for any ferroelectric material that changes its remanent polarization state primarily due to 180° switching, i.e. switching with no change in the remanent strain state. We will assume that the polycrystal is made up of spherical grains or crystallites. Each crystallite contains many domains and domain wall motion proceeds in a manner that effectively produces 180° switching. The constitutive behavior of the single crystal is derived on the assumption that the work done by applied stresses and electric fields must be balanced by the dissipation due to domain wall motion and by changes in the stored elastic, piezoelectric and dielectric energy of the crystallite. Once the single crystallite behavior is determined, a self-consistent scheme is implemented to ascertain the polycrystalline constitutive behavior. To demonstrate the theory, the model material is subjected to uniaxial poling and depoling by an electric field to generate the standard electric displacement versus electric field hysteresis loops, axial strain versus electric field butterfly loops and the evolution of the “switching surface” with increasing poling field. Comparison to experiments on fine grained barium titanate show that the model loops match the qualitative features of experimental loops remarkably well.