# Electrostriction

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## Electrostriction

A form of elastic deformation of a dielectric induced by an electric field; specifically, the term applies to those components of strain which are independent of reversal of the field direction. Electrostriction is a property of all dielectrics and is thus distinguished from the converse piezoelectric effect, a field-induced strain which changes sign upon field reversal and which occurs only in piezoelectric materials. *See* Dielectric materials, Piezoelectricity

The electrostrictive effect in certain ceramics is employed for commercial purposes in electromechanical transducers for sonic and ultrasonic applications.

## Electrostriction

(also electrostrictive strain), a deformation of dielectrics in an electric field **E**. Electrostrictive strain is proportional to the square of electric field strength *E*^{2} and is independent of reversal of the direction of the field E. Electrostriction is caused by dielectric polarization in an electric field and occurs in all dielectrics, whether solid, liquid, or gaseous. In solid dielectrics, electrostriction is very small and is of no practical importance.

Electrostriction should be distinguished from the converse piezoelectric effect, which is linear in electric field strength, in several orders of magnitude greater than electrostriction, and can be observed only in dielectric crystals with a particular symmetry (*see*PIEZOELECTRICITY). A large electrostrictive strain in ferroelectrics is sometimes reported. In fact, the phenomenon observed is the converse piezoelectric effect. However, owing to the possibility of a change in the direction of the spontaneous polarization of ferroelectric domains upon field reversal, the strain is independent of field direction.

In anisotropic crystals, electrostriction may be described by a relation between two tensors of rank two, namely, a tensor of the square of electric field strength and a strain tensor. The relation is

where *r _{ij}* is a component of the strain tensor and

*E*are components of the electric field. The coefficient

_{m}E_{n}*R*is called an electrostrictive strain coefficient. The number of independent electrostrictive strain coefficients depends on the crystal symmetry. For example, electrostrictive strain tensors have 36 independent coefficients for triclinic crystals and two independent coefficients for isotropic dielectrics. The value of

_{ij}*R*is ~ 10

_{ij}^{–14}–10

^{–10}. In a field of

*E*~ 300 volts/cm,

*r*~ 10

_{ij}^{–6}.

In isotropic media, including gases and liquids, electrostriction is observed as a change in density under the action of an electric field. It is described by the equation Δ*VIV = AE ^{2}*, where Δ

*V*/

*V*is the relative volume strain and

*A*is the electrostrictive strain constant. The constant

*A*is equal to

where β is the compressibility, p is the density, and ∊ is the dielectric constant. For organic liquids, such as xylene, toluene, and nitrobenzene, A ~ 10^{–2}.

Under the action of an alternating electric field with a frequency of ω, a dielectric vibrates at a frequency of 2ω as a result of electrostriction; such behavior is characteristic of quadratic effects. Therefore, electrostriction may be used to convert electric oscillations into sound vibrations.

### REFERENCES

Zheludev, I. S., and A. A. Fotchenkov. “Elektrostriktsiia lineinykh dielektrikov.”*Kristallografiia*, 1958, vol. 3, issue 3.

Jona, F., and G. Shirane.

*Segnetoelektricheskie kristally.*Moscow, 1965. (Translated from English.)

Zheludev, I. S.

*Osnovy segnetoelektrichestva.*Moscow, 1973.

I. S. ZHELUDEV