Flexoelectricity is a property of a
dielectric
In electromagnetism, a dielectric (or dielectric medium) is an Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electric ...
material where there is coupling between electrical polarization and a
strain gradient. This phenomenon 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 piezoel ...
, but while piezoelectricity refers to polarization due to uniform strain, flexoelectricity specifically involves polarization due to strain that varies 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 piezoelectricity, flexoelectric effects occur in both centrosymmetric and asymmetric crystal structures. This property is not the same as
ferroelasticity. It plays a critical role in explaining many interesting electromechanical behaviors in hard crystalline materials and core mechanoelectric transduction phenomena in soft biomaterials. Additionally, it is a size-dependent effect that becomes more significant in nanoscale systems, such as crack tips.
In common usage, flexoelectricity is the generation of polarization due to a strain gradient; inverse flexoelectricity is when polarization, often due to an applied electric field, generates a strain gradient. Converse flexoelectricity is where a polarization gradient induces strain in a material.
The electric polarization
due to mechanical
strain of
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 stress (mechanics), mechanical s ...
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 piezoel ...
*
Ferroelectricity
In physics and materials science, 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 piezoel ...
*
Ferroelasticity
*
Triboelectric effect
The triboelectric effect (also known as triboelectricity, triboelectric charging, triboelectrification, or tribocharging) describes electric charge transfer between two objects when they contact or slide against each other. It can occur with d ...
References
External links
Introduction to Flexoelectricity {{Webarchive, url=https://web.archive.org/web/20090306042324/http://cmt.dur.ac.uk/sjc/thesis_dlc/node130.html , date=2009-03-06
Electric and magnetic fields in matter
Condensed matter physics