Hello Jiawang,

We recently found domain-like nanoregions (DLNRs) up to an extreme temperature of 800 °C in a NBT-25ST core–shell nanoparticles by TEM. By applying electric field to the nanoparticles in temperature-dependent in-situ TEM, the change of DLNRs indicates a polorizaiton-switching-like behavior. By combing the TEM observation and phase-field simulation including flexoelectricity, we found that the DLNRs at extreme temperature is possibly attributed to the flexoelectricity which is originated from the strain gradient induced by the diffusion of strontium cations at high temperatures.

Ref:

Enabling nanoscale flexoelectricity at extreme temperature by tuning cation diffusion. Nature Communicationsvolume 9, Article number: 4445 (2018)

https://www.nature.com/articles/s41467-018-06959-8

All the best,

Min

Dear Jiawang,

Thank you for your interest on our works. I would also like to share our recent work published in Physical Review Letters. In this paper, we have shown that piezoelectricity can indeed imitate flexoelectricity on the condition that the piezoelectric coefficient is inhomogeneously and asymmetrically distributed across the sample. If this condition is met, asymmetric piezoelectricity becomes indistinguishable from intrinsic flexoelectricity in single cantilever-bending experiments. Our calculations show that, for standard perovskite ferroelectrics, even a tiny gradient of piezoelectricity (1% variation of piezoelectric coefficient across 1 mm) is sufficient to yield a giant effective flexoelectric coefficient of 1 μC/m, three orders of magnitude larger than the intrinsic expectation value. This mimicry complicates the task of interpreting experimental results although we have suggested some approaches to separate inhomogeneous piezoelectricity from flexoelectricity.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.205502

Dear Amir,

Thank you very much for bringing attention of your recent works on computational modeling of flexoelectricity and its applications. They are very nice works! Your work shows the previous simplified model may cause one order of magnitude overestimation of the flexoelectric coefficient. Including this effect (1 order of magnitude), surface effect, as well as the different electric boundary condition used in theory and experiment (2-3 order of magnitude), it would be expected that the large discrepancy (3-4 orders of magnitude) between theory and experiment will be small or even disappear.

Best,

Jiawang

Dear Jiawang,

Thank you for sharing this very nice review. I would like to bring to attention some of our recent works on computational modeling of flexoelectricity and its applications.

Mathematically, the self-consistent electromechanical field equations of flexoelectricity are a coupled system of fourth-order partial differential equations. Despite that analytical solutions are starting to emerge for simple geometries and loads [1,2], most of the field operates with approximate solutions that are valid under very restrictive assumptions [3,4]. Furthermore, to interpret experiments, the two-way flexoelectric coupling is often ignored [5]. To go beyond these simple approximate solutions, one can resort to computational methods, but because the equations involve high-order spatial derivatives, flexible methods such as conventional finite elements cannot be used. On rectangular or brick geometries, finite difference calculations have been applied to flexoelectricity [6-8]. To deal with more general geometries with nonuniform grid refinement, we have recently resorted to mesh-free methods, relying on smooth basis functions, to solve numerically the continuum equations of flexoelectricity in two [9] and three dimensions [10]. Surprisingly, we found that previous simplified calculations on beam and truncated triangle configurations provided only rough order-of-magnitude estimations of the flexoelectric response. These observations can partially explain the discrepancy between different experimental measurements and theoretical estimates [11]. We have also employed this computational model to study the manifestations of flexoelectricity in the fracture mechanics of piezoelectrics [12] and constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators [13].

[1] M. C. Ray, J. Appl. Mech. 81, 091002 (2014).

[2] S. Mao and P. K. Purohit, J. Appl. Mech. 81, 081004 (2014).

[3] Z. Yan and L. Y. Jiang, J. Appl. Phys. 113, 194102 (2013).

[4] M. S. Majdoub, P. Sharma, and T. Cagin, Phys. Rev. B 79, 119904 (2009).

[5] P. Zubko, G. Catalan, P. R. L. Welche, A. Buckley, and J. F. Scott, Phys. Rev. Lett. 99, 167601 (2007).

[6] R. Ahluwalia, A. K. Tagantsev, P. Yudin, N. Setter, N. Ng, and D. J. Srolovitz, Phys. Rev. B 89, 174105 (2014).

[7] Y. Gu, M. Li, A. N. Morozovska, Y. Wang, E. A. Eliseev, V. Gopalan, and L.-Q. Chen, Phys. Rev. B 89, 174111 (2014).

[8] H. Chen, A. Soh, and Y. Ni, Acta Mech. 225, 1323 (2014).

[9] A. Abdollahi, C. Peco, D. Millan, M. Arroyo, and I. Arias, J. Appl. Phys. 116, 093502 (2014).

[10] A. Abdollahi, D. Millan, C. Peco, M. Arroyo, and I. Arias, Phys. Rev. B 91, 104103 (2015).

[11] P. Zubko, G. Catalan, and A. K. Tagantsev, Annu. Rev. Mater. Res. 43, 387 (2013).

[12] A. Abdollahi and I. Arias, Phys. Rev. B 92, 094101 (2015).

[13] A. Abdollahi and I. Arias, J. Appl. Mech. 82, 121003 (2015).