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Research Article | Open Access

Distinguishing electrotensile strain and electrobending strain

Shuo Tian, Bin Li(), Yejing Dai()

School of Materials, Sun Yat-sen University, Shenzhen 518107, China

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Abstract

Electrobending, an emerging phenomenon in electroactive ceramics, has recently attracted significant interest; however, existing measurement methods often confound electrotensile and electrobending strains, leading to ambiguity. This study distinguishes electrotensile and electrobending strains in K_0.5Na_0.5NbO₃ (KNN) ceramics by examining their thickness, frequency, temperature, and directional dependency, identifying a critical thickness threshold of 600 μm for electrobending in samples of 8.5 mm diameter. This threshold establishes a clear distinction between electrotensile and electrobending within the KNN system and provides a benchmark that can be applied to other systems through similar methodologies. Additionally, new electrobending parameters have been defined to assess bending deformation, addressing recent misinterpretations of “giant strain” and advancing electrostrain research by introducing an electrobending framework.

Keywords

electrobending electrostrain deformation piezoceramics

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Journal of Advanced Ceramics

Volume 14 Issue 3,
March 2025

Article number: 9221048

DOI: 10.26599/JAC.2025.9221048

Cite this article:

Tian S, Li B, Dai Y. Distinguishing electrotensile strain and electrobending strain. Journal of Advanced Ceramics, 2025, 14(3): 9221048. https://doi.org/10.26599/JAC.2025.9221048

Fig. 1Comparison of mechanisms of electrotensile strain and electrobending strain in KNN ceramics: (a) spontaneous polarization in KNN ceramics; (b) schematic diagram of electrotensile strain; (c) ( $V_{A}^{^{'}} - V_{O}^{\cdot \cdot}$ ) defect dipoles in KNN ceramics; (d) schematic diagram of electrobending strain.
Fig. 2Investigation of thickness dependence: (a) schematic diagram of measurement holder; (b) illustration of asymmetric S–E curves due to electrobending-induced deformation; (c, d) Bipolar S–E curves with varying thicknesses; (e, f) unipolar S–E curves with varying thicknesses; (g) variation in apparent strain values (bipolar and unipolar) with thickness in KNN ceramics; (h) P–E hysteresis loops with varying thicknesses.
Fig. 3Comparison of electrotensile and electrobending strain characteristics: deformation response of (a) electrotensile strain and (b) electrobending strain at different frequencies; deformation responses of (c) electrotensile strain and (d) electrobending strain at different temperatures; (e) S–E curves of poled-aged KNN ceramics with ( ${C u}_{N b}^{^{'}^{'}^{'}} - V_{O}^{\cdot \cdot}$ ) defect dipoles measured along different sample thickness directions; (f) S–E curves of KNN ceramics without a poling–aging process measured along different sample thickness directions.
Fig. 4Definitions and measurement methods for parameters related to electrotensile strain and electrobending strain: measurement methods for (a) electrotensile strain and (b) electrobending strain; (c) definitions and calculation of inverse piezoelectric coefficient and hysteresis with respect to electrotensile strain; (d) definitions and calculation of bending coefficient and hysteresis in electrobending strain.

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Table 1Theoretical maximum achievable strain values for various ferroelectric crystal systems

Crystalsystem	Prototypephase	Ferroelasticphase	[hkl*]	$S_{l a t t i c e}^{0}$	MaximumferroelasticMRD, f_[hkl*]	MaximumferroelectricMRD (g)	S_ZZ/ $S_{l a t t i c e}^{0}$ (tension)
R	Cubic	Rhombohedral	[111]	( $d_{111} - d_{11 \bar{1}}$ )/ $d_{11 \bar{1}}$	4	8	0.424(0)
T	Cubic	Tetragonal	[001]	(c − a)/a	3	6	0.367(0)
O	Tetragonal	Orthorhombic	[010]	(b − a)/a	2	4	0.212(1)

Table 2Parameters, bending coefficients, and hysteresis for samples of different thicknesses

Thickness (μm)	r (mm)	d (μm)	C_m (m⁻¹)	E_m (kV·cm⁻¹)	$Δ C_{1 / 2 E_{m}}$ (m⁻¹)	b_c (MV⁻¹)	Hysteresis
600	1.5	0.54	0.480	50	0.128	0.096	26.6%
500	1.5	0.80	0.711	50	0.215	0.142	30.3%
400	1.5	0.44	0.391	50	0.050	0.078	12.7%
300	1.5	1.17	1.040	50	0.311	0.208	29.9%
200	1.5	3.12	2.773	50	0.553	0.555	19.9%

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