Flexoelectric properties of ferroelectrics and the nanoindentation size-effect

Abstract

a b s t r a c tRecent works have established the critical role of flexoelectricity in a variety of size-dependent physical phenomena related to ferroelectrics including giant piezoelectricity at the nanoscale, dead-layer effect in nanocapacitors, dielectric properties of nanostructures among others. Flexoelectricity couples strain gradients to polarization in both ordinary and piezoelectric dielectrics. Relatively few experimental works exist that have determined flexoelectric properties and they all generally involve some sort of bending tests on micro-specimens. In this work, we present a straightforward method based on nanoindentation that allows the evaluation of flexoelectric properties in a facile manner. The key contribution is the development of an analytical model that, in conjunction with indentation load-displacement data, allows an estimate of the flexoelectric constants. In particular, we confirm the experimental results of other groups on BaTiO 3 which differ by three orders of magnitude from atomistic predictions. Our analytical model predicts (duly confirmed by our experiments) a strong indentation size-effect due to flexoelectricity.

Flexoelectric Effect in Solids

“…In particular, the electrostatic cost of generating flexoelectric charge causes a depth-dependent stiffening in nanoindentation experiments, owing to the very inhomogeneous nature of the stress introduced by a nanoindenter. This effect was studied both experimentally and theoretically for several materials by the Texas group [78][79][80]. By measuring the curvature ζ induced by the electric field E, one can also get an estimate of the flexoelectric coefficient which is given bỹ…”

Dynamic piezoresponse force microscopy: Spatially resolved probing of polarization dynamics in time and voltage domains

“…Note that in all locations the offset component shows pronounced hysteresis with an "ideal" loop shape. However, the hysteresis loops are significantly shifted in the vertical direction, either due to the presence of frozen polarization layers, 84,85,108 non-uniform stress effects, 106,[109][110][111][112] or contribution of nonlocal bimorph modes. 113 The relaxing part shows almost complete lack of hysteresis, similar to the tip-electrode data in Sec.…”

Analysis of flexoelectric response in nanobeams using nonlocal theory of elasticity

“…The continuum theory incorporating the effects of flexoelectricity identified some unexpected manifestations of this phenomenon. For example, Gharbi et al (2011) identified an important role of flexoelectricity in the hardening of ferroelectrics at nano-indentation. Morozovska et al (2011) showed that the flexoelectric effect can play an important role in the electromechanical properties of moderate conductors.…”