Grain size effect of the flexoelectric response in BaTiO₃ ceramics

Size effect is a fundamental phenomenon in ferroelectric materials and grain size dependence of the dielectric and piezoelectric properties of BaTiO₃ (BTO) ceramics has been observed. However, the dependence of flexoelectric response on grain size has not been reported, thus far. In this work, BTO ceramics with grain sizes ranging from 0.59 to 8.90 μm were prepared by a two-step sintering method. We found that with increasing grain size, the flexoelectric coefficient of BTO ceramics increases from less than 20 μC/m (grain size 0.59-0.69 μm) to more than 300 μC/m (grain size 8.90 μm), but the grain size dependence of the flexoelectric response is different from that of the dielectric and piezoelectric properties. Observation by piezoresponse force microscopy reveals that the surface regions of BTO ceramics are spontaneously polarized. Strong inhomogeneous strain is measured by grazing incidence x-ray diffraction and the resultant flexoelectric effect is enough to polarize the surface regions. Fitting of the flexoelectric data indicates that the grain size effect of the flexoelectric response can be well explained by the polarized surface layer mechanism.