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    Universal Theoretical Elucidation of Electrobending Deformation in Piezoelectrics

    Zhi Tan*, Xiang Lv, Laiming Jiang, Xing Huang, and Jie Xing†

    Shaoxiong Xie

    Hui Zhang‡

    Jianguo Zhu§

    • Shaanxi Key Laboratory of High-Orbits-Electron Materials and Protection Technology for Aerospace, School of Advanced Materials and Nanotechnology, Xidian University, Xi’an 710126, China

    • *Contact author: tanzhi0838@scu.edu.cn
    • †Contact author: xingjie@scu.edu.cn
    • ‡Contact author: zhanghui@xidian.edu.cn
    • §Contact author: nic0400@scu.edu.cn

    Phys. Rev. Lett. 134, 226801 – Published 4 June, 2025

    DOI: https://doi.org/10.1103/f9y4-lh2m

    Abstract

    The origin of frequently observed ultrahigh electro-induced longitudinal strain, ranging from 1% to 26%, remains an open question. While recent studies have associated this phenomenon with bending deformation, the underlying mechanisms and the pronounced thickness dependence of the nominal strain have yet to be fully elucidated. Here, we demonstrate that the bending in piezoelectrics can be induced by a nonzero gradient of d31 across thickness direction. A scaling law (η3,nom∝L2E3∇zd31/t) is derived to quantify the size dependence, thereby resolving longstanding ambiguities surrounding reported “giant” electrostrains. Simulations reveal that in standard perovskite piezoceramics, such as KNbO3, a 0.69% concentration of oxygen vacancies can induce a 6.3  pC/N variation in d31 by suppressing polarization rotation, being sufficient to produce ultrahigh nominal strain in thin samples. Numerous factors, including gradients in defect concentration, composition, and stress, may lead to sufficient inhomogeneity in the distribution of d31, suggesting electrobending may be a widespread phenomenon. This Letter presents a unified framework for understanding electrobending deformation, offering deeper insight into the mechanisms behind abnormally giant electrostrain responses in diverse piezoelectric systems and may encourage new engineering applications.

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