Flexoelectricity was investigated as a function of temperature in paraelectric and ferroelectric phases of barium titanate ceramic. The flexoelectric coefficient μ12 was measured dynamically at small level of strain gradients. μ12 is around 5μC∕m in orthorhombic phase, rises to about 10μC∕m at room temperature, and peaks at ∼50μC∕m near tetragonal-cubic phase transition point. The coupling effect between mechanical strain gradient and electric polarization is found to be nonlinearly enhanced by high dielectric permittivity and domain contribution in barium titanate. In inhomogeneously strained ferroelectrics, mechanical gradient field may impact electric polarization in a way analogous to electric field.

The strain-gradient-induced polarization (flexoelectric effect) was investigated in Ba0.67Sr0.33TiO3 (BST) ceramic at temperatures above the 21 °C Curie point. At 23 °C the flexoelectric coefficient μ12 was more than one order of magnitude greater than the highest value measured in lead magnesium niobate ceramic. Over the temperature range of linear Curie–Weiss behavior, the coefficient μ12 was roughly proportional to the dielectric permittivity; however, the constant of proportionality was higher than predicted for simple ionic solids. The unexpected behavior in the BST ceramic suggests the need for a broader database of flexoelectric coefficients.

Flexoelectric coefficient μ12 is greatly enhanced in the relaxor ferroelectric lead magnesium niobate ceramic. Phenomenological analysis suggests the high dielectric permittivity is inadequate to explain the great enhancement. Temperature dependent measurement reveals a close relation between the flexoelectric polarization and the preexisting polar microregions in this relaxor ferroelectrics. It is proposed that the strain gradient might change the Gibbs free energy of the relaxor system and easily reorient the already existing polar microregions, leading to the greatly enhanced flexoelectric effect.

Strain-gradient-induced polarization or flexoelectricity was investigated in unpoled soft lead zirconate titanate ͑PZT͒ ceramic where the texture symmetry ϱϱ m forbids macropiezoelectricity. Even under high strain gradient (1 m Ϫ1) the induced polarization is small (1.6 C/m 2) at 20°C. Higher strain gradients induce ferroelastic poling and an additional extrinsic contribution to the flexoelectric coefficient 12 raising the value from 0.5 to 2.0 C/m. Cooling through the Curie point (T C) under maximum stress ͑80 MPa͒ where the peak permittivity (ϳ20 000) could raise 12 to 20 C/m, the equivalent electric field is still only ϳ1 kV/m, inadequate to achieve significant ferroelectric poling. The situation may be different in thin PZT films where much larger strain gradients can occur.

Mechanical strain gradient generated electric polarization or flexoelectric effect was investigated in unpoled lead zirconate titanate (PZT) ceramics in the ferroelectric state by using a cantilevered beam based approach. Flexoelectric coefficient μ12 at room temperature was measured to be 1.4μC∕m in the PZT ceramic at small level of strain gradient. Temperature-dependent experimental investigations clearly showed that high dielectric permittivity in the ferroelectrics enhanced flexoelectric polarization: essentially a linear relation was found to exist between μ12 and dielectric susceptibility χ at lower permittivity level (2100–2800), while μ12 versus χ curve started to deviate from the straight line at the χ∼2800 and nonlinear enhancement of μ12 with χ was observed, with μ12 value reaching 9.5 at χ∼11000. The nonlinearity in the flexoelectric effect was associated with domain-related processes. It is suggested that flexoelectric effect can have a significant impact on epitaxial ferroelectric thin films and mesoscopic structures.