Understanding the role of aligned porosity on the intrinsic and extrinsic contributions to the dielectric permittivity of freeze-cast ferroelectrics

Ferroelectric ceramics are widely used as actuators, sensors, and energy harvesters. Their coupled electromechanical properties arise from intrinsic polarisation at the lattice scale, with a significant proportion of their bulk properties originating from the mobility of ferroelectric and ferroelastic domains. Separating the intrinsic from the extrinsic contributions to the dielectric properties using Rayleigh analysis is an important characterisation tool for optimising ferroelectric ceramics. This technique is typically conducted on monolithic ceramics with a relative density (ρrel) greater than 0.95, where the effects of porosity on the measured permittivity are neglected, and the local electric field during the measurement of ferroelectric and dielectric properties is assumed to be homogeneously distributed. This study proposes an adjustment to the Rayleigh analysis for porous ferroelectric composites formed using directional freeze-casting, where these assumptions for monolithic ceramics no longer hold. Our experimental results show that the apparent intrinsic contribution scales linearly with the fraction of aligned porosity (1 - ρrel) due to the reduction of the active ferroelectric volume, despite no significant structural transformations being observed. To address this, a relative density adjustment was introduced, which decouples the intrinsic contribution from ρrel. The adjusted extrinsic contribution increases with decreasing ρrel, which is attributed to the reduction in intragranular stress due to the introduction of porosity. The proposed adjustment provides a more accurate characterisation of the intrinsic and extrinsic contributions in freeze-cast porous ferroelectric ceramics, enabling the optimisation of ferroelectric devices with enhanced and reliable properties.