Flexoelectricity
Encyclopedia
Flexoelectricity is a property of a dielectric
Dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...

 material whereby it exhibits a spontaneous electrical polarization induced by a strain gradient. Flexoelectricity is not the same as Ferroelasticity
Ferroelasticity
Ferroelasticity is a phenomenon in which a material may exhibit a spontaneous strain. In ferroics, ferroelasticity is the mechanical equivalent of ferroelectricity and ferromagnetism. When a stress is applied to a ferroelastic material, a phase change will occur in the material from one phase to an...

.

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

where the first term corresponds to the direct piezoelectric
Piezoelectricity
Piezoelectricity is the charge which accumulates in certain solid materials in response to applied mechanical stress. The word piezoelectricity means electricity resulting from pressure...

effect and the second term corresponds to the flexoelectric polarization induced by the strain gradient.

Here, the flexoelectric coefficient, , is a fourth-rank polar tensor and is the coefficient corresponding to the direct piezoelectric effect.

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