Analysis of switching properties of porous ferroelectric ceramics by means of first-order reversal curve diagrams

Particular aspects of the switching properties of the Nb-PZT ceramics with anisotropic porosity (40% relative porosity) were investigated by comparison with the dense ceramics (5% relative porosity) of the same composition by means of the first-order reversal curve (FORC) analysis. The reversible/irreversible components give different contributions to the total polarization: A sharp FORC distribution with an almost negligible reversible component is characteristic to the dense material, while a broad distribution with an important reversible component is characteristic for the porous one. The coercivity corresponding to the maximum of the irreversible component is the same irrespective to the sample density and pore's configuration with respect to the electrodes: E(c,M)=1.5 kV/mm, while the bias fields are zero for the dense ceramic, small and positive; E(bias,M)=50 V/mm, when the major axis of the elongated pores is parallel with the electrodes and negative; E(bias,M)=-100 V/mm, when this axis is perpendicular to the electrodes. The influence of the dipolar coupling leading to such bias fields is explained by considering that the particular microstructure is causing a symmetry breaking, decoupling the dipolar interaction (forward or laterally). A dipolar (discrete) model with random orientations of the dipoles' directions was used to simulate this confinement effect. The calculated FORC diagrams lead to the same type of bias as the experimental ones, proving that the lateral confinement gives an intrinsic contribution to the biased P(E) loops observed for the porous ceramics. In addition with other possible extrinsic contributions, this dipolar coupling can be a source of the built-in field in confined ferroelectric structures. The experimental FORC distribution was used as input in a Preisach-type model to recompose the major and symmetric minor hysteresis loops and a remarkable agreement with the experimental data was obtained. The FORC method proves to be an excellent tool in describing the ferroelectric systems, simulating polarization experiments, and predicting outputs of the circuits with ferroelectric capacitors. In the particular case of the porous anisotropic ceramics, the combined experimental and analytical FORC analysis allowed us to probe and to describe qualitatively the presence of the bias field as a result of the geometrical confinement.