Modeling the Electroelastic Moduli of Porous Textured Piezoceramics

A new model for piezoelectric textured ceramics was developed that considers the presence of porosity, which can appear during heat treatment (ceramic sintering). In the long wavelength approximation, a matrix method, which has already been applied to piezoelectric composites, was extended to textured ceramics for three phases [porosity (air), piezoelectric single-crystal (related to the texturation degree), and ceramic] to calculate the effective electroelastic modulus. This method was first compared and validated with finite-element calculations. A computation was applied to two systems with lead-based (PMN-PT) and lead-free (KNN) compositions. The results showed that the introduction of porosity in the whole material promotes electromechanical performance, particularly the electromechanical coupling factor k(t), while limiting the degree of texturation. As an example, for the chosen PMN-PT system, an equivalent k(t) factor of 60% can be obtained with 1% porosity and an 85% single-crystal volume fraction or with 16% porosity and a 40% single-crystal volume fraction. According to the database used, this tradeoff is different. With the chosen lead-free composition, the degree of texture is less important than in the lead-based composition. Consequently, the porosity content is of primary importance for significantly improving the electromechanical coupling factor k(t).