Micromechanical models of porous ferroelectric ceramics have often assumed that the material is fully polarized in a particular direction and/or consists of a single isolated pore. In this work the polarization state in three-dimensional porous polycrystalline ferroelectric networks has been modelled to eradicate the oversimplification of these idealized unit cells. This work reveals that microstructural network models more closely represent a porous ferroelectric microstructure since they are able to take into account the complex polarization distribution in the material due to the presence of high and low permittivity regions. The modelling approach enables the prediction of the distribution of poled and unpoled material within the structure. The hydrostatic figures of merit and permittivity were determined for a variety of porous lead zirconate titanate microstructures and found to be in good agreement with experimental data. The decrease in piezoelectric activity with porosity was observed to be associated with the complex polarization state within the material. Model results were shown to be much improved when compared to a model assuming a fully polarized model.
Lewis, R. W. C., Dent, A. C. E., Stevens, R., & Bowen, C. R. (2011). Microstructural modelling of the polarization and properties of porous ferroelectrics. Smart Materials and Structures, 20(8), . https://doi.org/10.1088/0964-1726/20/8/085002