# Flexoelectricity

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Flexoelectricity is a property of a dielectric material whereby it exhibits a spontaneous electrical polarization induced by a strain gradient. Flexoelectricity is not the same as Ferroelasticity.

The electric polarization due to mechanical stress in a dielectric is given by

${\displaystyle P_{i}=d_{ijk}\sigma _{jk}+\mu _{ijkl}{\frac {\partial \epsilon _{jk}}{\partial x_{l}}}}$

where the first term corresponds to the direct piezoelectric effect and the second term corresponds to the flexoelectric polarization induced by the strain gradient.

Here, the flexoelectric coefficient, ${\displaystyle \mu _{ijkl}}$, is a fourth-rank polar tensor and ${\displaystyle d_{ijk}}$ is the coefficient corresponding to the direct piezoelectric effect.