Ferroelectricity in tetragonal polycrystalline ceramics: matrix transformation of electric dipoles

Abstract

Ferroelectricity is closely related to the switching of electric dipoles in ferroelectric materials. The ferroelectric performances, such as polarization, hysteresis, etc., are fundamentally decided by the orientation, reversal, and coercivity of electric dipoles. However, the constitutive relationship between microscopic electric dipoles at the unit cell scale and macroscopic ferroelectricity is seldom revealed. Also, the evolution of microscopic electric dipoles with respect to the applied electric field is not clearly figured out. Here, we propose a matrix transformation model for investigating the electric dipole evolution in tetragonal 0.367BiScO₃–0.633PbTiO₃ (abbreviated as BS–PT) polycrystalline ferroelectric ceramics, where the relationships between the macroscopic ferroelectric properties and microscopic electric dipole structures are correlatively established. The electric field induced electric dipole evolution results in the variations of polarization and strain in polarization–electric field (P–E) and strain–electric field (S–E) loops. The theoretical values of saturated polarization P_m in the P–E loop, remanent polarization P_r in the P–E loop, and maximum strain in the S–E loop are, respectively, 47.225 μC cm⁻², 38.087 μC cm⁻², and 0.2257%, in good accordance with the experimental values, where P_m, P_r, and the maximum strain are 45.676 μC cm⁻², 36.962 μC cm⁻², and 0.222%, respectively. The proposed matrix transformation model provides an explicit insight into the relationship between the electric dipoles and ferroelectricity, demonstrating great potential for performance evaluation, manipulation, and improvement of ferroelectric devices.