Dielectric nonlinearity of ferroelectrics

The ac field dependence of the dielectric constant and first order reversal curves (FORC) distribution were employed to quantify the effect of dielectric thickness, grain size, oxygen vacancy concentration, and microstructural heterogeneity on the dielectric nonlinearity of PbZr0.52Ti0.48O 3 thin films and BaTiO3-based ceramics on a wide electric field range. With the FORC distribution, the dielectric properties were calculated using Preisach model.;The FORC distribution of PbZr0.52Ti0.48O3 thin films was characterized as a function of film thickness. It was found that the thickness dependence of the small field dielectric constant is due primarily to differences in the domain wall contributions to the properties. The irreversible FORC distribution decreased and the switching fields increased as the thickness decreased. Prediction of the polarization-electric field curves and the ac field dependence of the dielectric constant were found to give a good fit to the experimental results. Some discrepancies remain in the high field dielectric constant, probably caused by its definition.;The dielectric nonlinearity of BaTiO3 ceramics with grain sizes from 1.2 to 76 microm was investigated. Defect dipoles in samples with large grains led to pinching of minor polarization-electric field loops as well as a threshold field in the ac field dependence of the dielectric constant and loss. For samples with small grains, a sublinear ac field dependence was observed. The irreversible FORC distributions characterizing the responses showed two strong and narrow peaks for large-grained samples and a weak, broad peak centered near the origin for samples with small grains. As the grain size decreased, the reversible FORC distribution at zero-bias field increased. No grain size dependence of the reversible FORC distributions was observed at high dc electric fields. These results indicate that the grain size dependence of the small field dielectric constant is attributable to a domain wall contribution and long-range domain wall motion suppressed while short-range domain wall motion enhanced as the grain size decreased.;The effect of the oxygen vacancies on the dielectric nonlinearity of formulated and undoped BaTiO3 ceramics was investigated by changing oxygen partial pressure during firing. For the formulated ceramics, the dielectric constant of both oxygen and air fired samples increased almost linearly with the amplitude of the ac driving field. Formulated BaTiO3 samples sintered in a reducing atmosphere produced a sub-linear increase in the permittivity with the ac field amplitude. For undoped BaTiO3 ceramics, the dielectric constant increased sub-linearly over a wide range of oxygen partial pressures during firing. It is proposed for the formulated ceramics that the dopant-oxygen vacancy defect dipoles in the shell region accounted for the curvature in the field dependence of the permittivity. These defects appear to add a concentration of weak pinning centers to the potential energy profile through which domain walls move.;FORC distributions as well as the ac field dependence of the dielectric constant were investigated for model BaTiO3-based multilayer ceramic capacitors with dielectric layer thicknesses from 2.2 microm to 8.6 microm and those in which the grain size of the dielectrics varied from 0.28 microm to 0.39 microm while the layer thickness was held constant. In both cases, core-shell microstructures were observed. It was found that as the dielectric thickness decreased, the small and high electric field dielectric constants decreased, as did the peaks near the origin in the irreversible and reversible parts of the FORC distribution. The reversible FORC distributions of all the parts did not converge at high bias. These results indicate that the thickness dependence is attributable to a low dielectric constant interfacial layer and/or Schottky depletion layer at dielectric-electrode interfaces.;It was also found that the high field dielectric constant, the peak in the irreversible FORC distribution at the origin, and the reversible FORC distribution at zero bias decreased as grain size decreased, as was observed for the undoped ceramics. The reversible FORC distribution of all the parts converged at high biases, indicating the grain size dependence was influenced by domain wall contributions. Dielectric contributions from the core and shell were estimated based on the temperature dependence of the permittivity. Not unexpectedly, the relative response of the core decreased while that of the shell increased as the grain size decreased. A Preisach model using the measured FORC distribution gave a good fit to the experimental polarization-electric field loops as a function of grain size and dielectric layer thickness.