A model for switching and hysteresis in ferroelectric ceramics

In ferroelectric ceramics every grain has an average polarization arising from the spontaneous polarization of all domains. Since the domain configuration is known in fine grained as well as in coarse grained perovskite ceramics the average polarization can be easily determined. An electric field can invert the average polarization by 180 degrees if it exceeds a critical field strength E(2crit). At fields above E(2crit) a new 90 degrees domain wall being perpendicular to the regular 90 degrees domain walls nucleates at the boundary of the grain. It traverses the grain driven by the external field and disappears at the opposite grain boundary where its energy is dissipated. This transient domain wall is highly mobile, because, on its passage through the grain it does not change the gross shape of the grain. The calculated values of the critical electric field and its temperature dependence are in good agreement with observations. In addition, the new domain wall is the origin of dielectric nonlinearities in ferroelectric ceramics for large signal ac-fields or for de-biased fields. The very high permittivity which is observed in fine grained ceramics can also be ascribed to the presence of these easily movable walls. Internal depolarization fields in this case cause the generation of the new walls. The electric hysteresis curve P(E) is described by a progress parameter delta such that P(delta) and E(delta) are separate hysteresis curves. A model for the determination of P(delta) and E(delta) is presented. The final hysteresis curve results from the elimination of delta.