View source for Electrostriction

{{short description|Ability of non-conductive materials to change shape under an electric field}}

In [[electromagnetism]], '''electrostriction''' is a property of all electrical non-[[Electrical conductor|conductor]]s, or [[dielectrics]], that causes them to change their shape under the application of an [[electric field]]. It is the [[Duality (electricity and magnetism)|dual]] property to [[magnetostriction]].

== Explanation ==
Electrostriction is a property of all dielectric materials, and is caused by displacement of [[ion]]s 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 (materials science)|strain]] (ratio of deformation to the original dimension) is proportional to the square of the [[polarization density|polarization]]. Reversal of the electric field does not reverse the direction of the deformation.

More formally, the electrostriction coefficient is a [[Tensor#Tensor rank|rank four]] [[tensor]] (<math>Q_{ijkl}</math>), relating the rank two strain tensor (<math>x_{ij}</math>) and the electric [[polarization density]] vector (i.e. rank one tensor; <math>P_m</math>).

<math>x_{ij} = Q_{ijkl} P_k P_l</math>

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 [[Crystal structure#Point groups|point groups]].  Electrostriction is a [[quadratic function|quadratic]] effect, unlike piezoelectricity, which is a [[linear]] effect.

== Materials ==
Although all dielectrics exhibit some electrostriction, certain engineered ceramics, known as [[relaxor ferroelectric]]s, have extraordinarily high electrostrictive constants.  The most commonly used are
* [[lead magnesium niobate]] (PMN)
* [[lead magnesium niobate-lead titanate]] (PMN-PT)
* [[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 {{Citation needed|date=June 2010}}. 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
* [[Actuator]]s for small displacements

== See also ==
* [[Magnetostriction]]
* [[Photoelasticity]]
* [[Piezomagnetism]]
* [[Piezoelectricity]]
* [[Relaxor ferroelectric]]

==References==
* [http://www.britannica.com/science/electrostriction "Electrostriction." Encyclopædia Britannica.]
* ''Mini dictionary of physics'' (1988) Oxford University Press
* [http://www.trstechnologies.com/Materials/electrostrictive_materials.php "Electrostrictive Materials"] from TRS Technologies
* [http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_3/backbone/r3_6_1.html#_dum_3 "Electronic Materials"] by Prof. Dr. Helmut Föll

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[[Category:Materials science]]
[[Category:Electric and magnetic fields in matter]]