The frequency dependence of electromechanical behaviors of columnar-grained BaTiO₃ nanofilms

The frequency-dependent behaviors of columnar-grained ferroelectric nanofilms are rarely studied under strong AC field. We report a phase-field investigation of such problem for columnar-grained BaTiO₃ nanofilms under high-strength AC field with the frequency from 0.1 to 100 kHz. The influences from the film-substrate misfit strain, microdefects, low-permittivity surface layer and grain boundaries are taken into account. A noticeable transition from the low-frequency behavior to the high-frequency one was confirmed by observing the obtained hysteresis and butterfly loops and the change of the physical properties. The mechanism for such frequency dependence was discovered via the study of the microstructural dynamics.