Flexoelectricity is a property of a
dielectric
In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
material whereby it exhibits a spontaneous electrical polarization induced by a
strain
Strain may refer to:
Science and technology
* Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes
* Strain (chemistry), a chemical stress of a molecule
* Strain (injury), an injury to a mu ...
gradient. Flexoelectricity is closely related to
piezoelectricity
Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ''p ...
, but while piezoelectricity refers to polarization due to uniform strain, flexoelectricity refers specifically to polarization due to strain that changes from point to point in the material. This nonuniform strain breaks
centrosymmetry
In crystallography, a centrosymmetric point group contains an inversion center as one of its symmetry elements. In such a point group, for every point (x, y, z) in the unit cell there is an indistinguishable point (-x, -y, -z). Such point group ...
, meaning that unlike in piezoelectiricty, flexoelectric effects can occur in centrosymmetric crystal structures. Flexoelectricity is not the same as
Ferroelasticity.
Inverse flexoelectricity, quite intuitively can be defined as generation of strain gradient due to polarization. Similarly extending on that, Converse flexoelectricity would refer to the process where a polarization gradient induces strain in a material.
The electric polarization due to mechanical
stress
Stress may refer to:
Science and medicine
* Stress (biology), an organism's response to a stressor such as an environmental condition
* Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
in a dielectric is given by
:
where the first term corresponds to the direct
piezoelectric
Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word '' ...
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.
See also
*
Piezoelectricity
Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ''p ...
*
Ferroelectricity
Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoelectric and pyroelectric, with the a ...
*
Ferroelasticity
References
{{Reflist
External links
Introduction to Flexoelectricity
Electric and magnetic fields in matter
Condensed matter physics