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A comparative study of the phase-field approach in modeling the frequency-dependent characteristics of ferroelectric materials

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Abstract

In this work, the electromechanical behaviors of ferroelectric materials are numerically studied with selected electric field frequency varying from 10 to 1000 Hz. The material under investigation is barium titanate (\(\hbox {BaTiO}_{3})\). We take the view that the frequency dependency is a result of direct competition between the speed of the microstructural evolution and the speed of the external field. Three phase-field models were established to investigate the frequency-dependent characteristics, namely the single-crystal model (Model-I), the polycrystal model with zero thickness of grain-grain interface (Model-II), and the polycrystal model with the grain boundary affected zone (Model-III). The frequency-dependent ferroelectric properties, e.g., the coercive electric field, the remnant polarization and the actuation strain, are numerically examined based on these three models. The phase-field results show that the frequency dependence becomes more remarkable as the level of the complexity of the crystalline microstructure gets higher. The results based on Model-I and Model-II confirm that the resistance to the domain switching mostly comes from the dipole–dipole interaction and the resistance gets stronger with higher field frequency. High-frequency characteristics were observed in the results based on Model-III, in the form of elliptic hysteresis loop and kidney-shaped butterfly loop. It was further revealed that smaller grain size causes stronger grain-boundary effect and tends to promote the influence of the dynamic field. As a result, the high-frequency characteristics can be more easily attained with smaller grain size. More interestingly, a new very-high-frequency response can be observed with the enhanced grain-boundary effect: the hysteresis ellipse completely shifts to the positive-polarization zone, and the kidney-shaped butterfly loop evolves to a tilted ellipse. Such frequency-dependent characteristics are discussed based on the underlying domain-switching dynamics.

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Authors and Affiliations

  1. Department of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Ning Liu & Yu Su

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  1. Ning Liu
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  2. Yu Su
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Correspondence to Yu Su.

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Liu, N., Su, Y. A comparative study of the phase-field approach in modeling the frequency-dependent characteristics of ferroelectric materials. Acta Mech 227, 2671–2682 (2016). https://doi.org/10.1007/s00707-016-1638-x

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  • DOI: https://doi.org/10.1007/s00707-016-1638-x

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