Abnormal Electromechanical Property of Nonlinearly Graded Lead‐Free Ferroelectric Thin Films

A phase field model for nonlinearly graded ferroelectric thin films is developed based on the Ginzburg–Landau theory. The developed phase field model is validated by comparing simulated results and available experiment data. Via phase field simulations, effects of gradient index on polarization field and electromechanical response are systematically investigated. Anomalously large electromechanical responses are explored in nonlinearly graded ferroelectric thin films made of Ba1−x$_{1-x}$SrxTiO3, where SrTiO3 mole fraction varies across the film thickness according to power‐law relationships. In addition, a large gradient of polarization can be stabilized in graded ferroelectric thin films, where both magnitude and gradient of polarization can be manipulated by controlling the gradient index of thin films. The remarkable enhancement of electromechanical properties originates from the large gradient of polarization in thin films, which makes the polarization field more susceptible to external excitation. An optimal gradient index for maximizing the electromechanical response is also identified. Furthermore, a consideration of energy properties of graded thin films suggests that both energy storage density and charge–discharge efficiency increase with increasing gradient index of thin films. Anomalously large electromechanical responses are found in nonlinearly graded ferroelectric thin films. A large gradient of polarization in graded films, which can be manipulated by gradient index, makes polarization field more susceptible to external excitation, and thereby, is responsible for the remarkable enhancement of electromechanical properties. In addition, energy storage density and charge–discharge efficiency strongly depend on gradient index.