# Electrostriction

Electrostriction (cf. magnetostriction) is a property of all electrical non-conductors, or dielectrics, that causes them to change their shape under the application of an electric field.

## Explanation

Electrostriction is a property of all dielectric materials, and is caused by a slight displacement of ions in the crystal lattice upon being exposed to an external electric field. Positive ions will be displaced in the direction of the field, while negative ions will be displaced in the opposite direction. This displacement will accumulate throughout the bulk material and result in an overall strain (elongation) in the direction of the field. The thickness will be reduced in the orthogonal directions characterized by Poisson's ratio. All insulating materials consisting of more than one type of atom will be ionic to some extent due to the difference of electronegativity of the atoms, and therefore exhibit electrostriction.

The resulting strain (ratio of deformation to the original dimension) is proportional to the square of the polarization. Reversal of the electric field does not reverse the direction of the deformation.

More formally, the electrostriction coefficient is a fourth rank tensor (${\displaystyle Q_{ijkl}}$), relating second order strain (${\displaystyle x_{ij}}$) and first order polarization tensors (${\displaystyle P_{k}}$, ${\displaystyle P_{l}}$).

${\displaystyle x_{ij}=Q_{ijkl}\times P_{k}\times P_{l}}$

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 effect, unlike piezoelectricity, which is a linear effect.

## Materials

Although all dielectrics exhibit some electrostriction, certain engineered ceramics, known as relaxor ferroelectrics, have extraordinarily high electrostrictive constants. The most commonly used are

## 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[citation needed]. 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 projectors for submarines and surface vessels
• Actuators for small displacements