Electrostriction

# Electrostriction

Discussion

Encyclopedia
Electrostriction is a property of all electrical non-conductors, or dielectrics, that causes them to change their shape under the application of an electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

. (Compare with magnetostriction
Magnetostriction
Magnetostriction is a property of ferromagnetic materials that causes them to change their shape or dimensions during the process of magnetization. The variation of material's magnetization due to the applied magnetic field changes the magnetostrictive strain until reaching its saturation value, λ...

.)

## Explanation

Electrostriction is a property of all dielectric materials, and is caused by the presence of randomly-aligned electrical domains within the material. When an electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

is applied to the dielectric, the opposite sides of the domains become differently charged and attract each other, reducing material thickness in the direction of the applied field (and increasing thickness in the orthogonal directions characterized by Poisson's ratio
Poisson's ratio
Poisson's ratio , named after Siméon Poisson, is the ratio, when a sample object is stretched, of the contraction or transverse strain , to the extension or axial strain ....

). The resulting strain
Strain (materials science)
In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal deformations of a continuum body...

(ratio of deformation to the original dimension) is proportional to the square of the polarization
Polarization density
In classical electromagnetism, polarization density is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is...

. Reversal of the electric field does not reverse the direction of the deformation.

More formally, the electrostriction coefficient is a fourth rank tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...

(), relating second order strain () and first order polarization tensors (, ).

The related piezoelectric effect occurs only in a particular class of dielectrics. Electrostriction applies to all crystal symmetries, while the piezoelectric effect only applies to the 20 piezoelectric point groups. Electrostriction is a quadratic
In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms...

effect, unlike piezoelectricity, which is a linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

effect. In addition, unlike piezoelectricity, electrostriction cannot be reversed: deformation will not induce an electric field.

## Materials

Although all dielectrics exhibit some electrostriction, certain engineered ceramics, known as relaxor ferroelectrics, have extraordinarily high electrostrictive constants. The most commonly used are
• lead lanthanum zirconate titanate (PLZT)

## Magnitude of effect

Electrostriction can produce a strain of 0.1 % at a field strength of 2 million volts per meter (2 MV/m) for the material called PMN-15 (TRS website listed in the references below). The effect appears to be quadratic at low field strengths (up to 0.3 MV/m) and roughly linear after that, up to a maximum field strength of 4 MV/m . Therefore, devices made of such materials are normally operated around a bias voltage in order to behave nearly linearly. This will probably cause deformations to lead to a change of electric charge, but this is unconfirmed.

## Applications

• Sonar
Sonar
Sonar is a technique that uses sound propagation to navigate, communicate with or detect other vessels...

projectors for submarines and surface vessels
• Actuator
Actuator
An actuator is a type of motor for moving or controlling a mechanism or system. It is operated by a source of energy, usually in the form of an electric current, hydraulic fluid pressure or pneumatic pressure, and converts that energy into some kind of motion. An actuator is the mechanism by which...

s for small displacements