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.