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. 2017 Oct 10;7:12915. doi: 10.1038/s41598-017-13425-w

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Piezoelectric displacement and large-signal $d_{33}^{⁎}$ value of 4-µm-thick PZT film as a function of working cycles, defined from the unipolar D-E loops measured at 200 kV/cm and 10 Hz. The fatigue testing was performed by applying a bipolar triangular field of 100 kV/cm and at 100 kHz.