| With the rapid development of modern electronic information industry, ferroelectric materials are wildly used in electronics and micromanipulation industries and usual utilized to fabricate capacitors, sensors and precise actuators. The miniaturization and integration of micro-electromechanical systems(MEMS) required ferroelectric materials to be smaller in size. Meanwhile, due to the progress of nano preparation technology, the grain size of materials continuously decreases. However, the characteristics of the ferroelectric materials will change with grain size. In addition, because the working environment of MEMS is not static, the ferroelectric material will work under dynamic external field. But the properties of ferroelectric materials can change with the different field frequency. Therefore, in order to guarantee the performance of components, it is very significant to study frequency and grain size effect of barium titanate ceramic characteristics.In this paper, with phase field method, the effects of field frequency and grain size on barium titanate ceramic characteristics are studied. A two-dimensional phase field model with grain boundary is established. The time dependent Ginzburg–Landau kinetic equation is used to evaluate the evolution of polarization vectors. In order to achieve the standard electric hysteresis loop, a sinusoidal electric field of large amplitude is conducted on the model for polarization flip, and the ferroelectric, dielectric and piezoelectric properties of barium titanate ceramics is analyzed. But in experiment, smaller voltage is usually used in order to measure dielectric constant of ferroelectric materials. Therefore, electric field of small amplitude is also applied to the model to calculate dielectric constant in the numerical simulation.In this article, we assume that frequency dependence of ferroelectric hysteresis is a result of direct competition between the speed of polarization evolution and the speed of external loading. Based on this assumption, the numerical simulation of microstructure evolution is carried out by phase field method under different frequency of electric field. First of all, electric field of large amplitude is applied to barium titanate ceramics of 100 nm grain size, and the frequency of electric field is from 10 Hz to 2500 Hz. The results show that, as the frequency increases, the coercive field increases, while the tangent dielectric constant and tangent of piezoelectric constant decrease. Besides, the polarization shows a complete 180°reversal at low frequencies, but stop mostly at 90° at high frequencies. Secondly, the effect of electric field of small amplitude is studied, and the frequency changes from 10 Hz to 200 Hz. The dielectric constant is found decreasing with the increase of frequency. At last, the influence of the kinetic coe?cient is also examined. The results show that it has an opposite effect on barium titanate ceramics with frequency proving the correctness of assumption.Moreover, it is also found that grain size effect will not be reflected if grain boundary is not included in the model. This suggests that grain boundary plays a very important role in grain size effect. Large amplitude electric field of 100 Hz is applied to barium titanate ceramics with grain size from 10 nm to 170 nm. The change law of hysteresis and butterfly loops with grain size is obtained, and the remnant polarization, coercive field, tangent dielectric constant, tangent piezoelectric constant and dielectric constant at small amplitude electric field are measured. The results show that both the “dilution effect” of grain boundary and domain structures are important factors to the changing of barium titanate ceramics properties. |
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