Upper bounds for flexoelectric coefficients in ferroelectrics

Abstract

Flexoelectric effect is the response of electric polarization to the mechanical strain gradient. At the nano-scale, where large strain gradients are expected, the flexoelectric effect becomes appreciable and may substitute piezoelectric effect in centrosymmetric materials. These features make flexoelectricity of growing interest during the last decade. At the same time, the available theoretical and experimental results are rather contradictory. In particular, experimentally measured flexoelectric coefficients in some ferroelectric materials largely exceed theoretically predicted values. Here, we determine the upper limits for the magnitude of the static bulk contribution to the flexoelectric effect in ferroelectrics, the contribution which was customarily considered as the dominating one. The magnitude of the upper bounds obtained suggests that the anomalously high flexoelectric coupling documented for perovskite ceramics can hardly be attributed to a manifestation of the static bulk effect. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4865208] Flexoelectric effect is the response of electric polarization to the mechanical strain gradient. It can be viewed as higher-order effect with respect to piezoelectricity, which is the response of polarization to strain itself. However at the nano-scale, where large strain gradients are expected, the flexoelectric effect becomes appreciable. Besides, in contrast to piezoelectric effect, flexoelectricity is allowed by symmetry in any material. Due to these features flexoelectricity has attracted growing interest during the last decade. On the other hand, the available theoretical and experimental results are rather contradictory, attesting to a limited understanding in the field. In particular, often experimentally measured flexoelectric coefficients largely exceed theoretically predicted values. It is important to distinguish different contributions to the effect: bulk and surface contributions; static and dynamic contributions. The relative magnitude of these contributions is discussed in a recent review article.

Revisiting pyramid compression to quantify flexoelectricity: A three-dimensional simulation study

“…It has been found that flexoelectric coefficients are particularly large in materials with high dielectric constants, such as ferroelectrics 9,11,[13][14][15] . However, the magnitude of these coefficients greatly exceeds theoretical estimates 1, 16,17 . This discrepancy has lead to a controversy in the field of flexoelectricity, demanding further investigations into the quantification of the flexoelectric response 18 .…”

Lattice dynamics and antiferroelectricity inPbZrO3tested by x-ray and Brillouin light scattering

“…According to order-of-magnitude estimates 30,34,35 and ab initio calculations in perovskites 36 , the values of the components of the f tensor in perovskites are expected to be about 1 − 10 V. Thus, we see that ferroelectric perovskites are not far from the modulation instability. The fact that the apparent "pushing down", or renormalizing of the TA mode in PZO is much more pronounced than in other studied systems suggests that it could be the prime candidate in the search for materials where the modulation instability "would be found".…”

“…For typical perovskite ferroelectrics BaTiO 3 and SrTiO 3 , using experimental data [31][32][33] , these criteria can be substantialized 30 as |f 44 | < 3.3 V, |f 11 − f 12 | < 7 V and |f 44 | < 2.4 V, |f 11 − f 12 | < 10 V, respectively. According to order-of-magnitude estimates 30,34,35 and ab initio calculations in perovskites 36 , the values of the components of the f tensor in perovskites are expected to be about 1 − 10 V. Thus, we see that ferroelectric perovskites are not far from the modulation instability.…”

Pseudo Jahn–Teller effect in the origin of enhanced flexoelectricity

“…In a recent paper, 8 it is concluded that this is approximately the upper limit of the flexoelectricity strength that can be achieved in ionic crystals.…”

“…12 Some of the above-cited authors state that the origin of this big discrepancy between the theory and experiment is at present not understood; others relate it to crystal imperfections assuming that in the paraelectric BaTiO 3 , there are polar islands that are reoriented by the strain gradient. An expert conclusion 8 states that "The magnitude of upper bonds obtained suggest that the anomalously high flexoelectricity coupling documented for perovskites ceramics can hardly be attributed to a manifestation of the static bulk effect." But in a more recent paper, 13 using a variety of experimental procedures including pyroelectric current, it is shown that the effect is intrinsic (bulk), and it is due to some polar formations in dielectric solids that exist beyond (and independent of) the external strain.…”