Editing Electrostriction

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

{{Sources exist|date=June 2024}}
In [[electromagnetism]], '''electrostriction''' is a property of all electrical non-[[Electrical conductor|conductor]] or [[dielectrics]].{{citation needed|date=August 2024}} Electrostriction causes these materials to change their shape under the application of an [[electric field]].<ref name="smart2013">{{cite book | title=Smart Structures Theory | chapter=Magnetostrictives and Electrostrictives | publisher=Cambridge University Press | date=2013-12-30 | doi=10.1017/cbo9781139025164.007 | pages=581–684| isbn=978-0-521-86657-6 }}</ref>{{rp|662}} It is the [[Duality (electricity and magnetism)|dual]] property to [[magnetostriction]].

== Explanation ==
Electrostriction is a property of all dielectric materials,<ref name="giant2022"/> and is caused by displacement of [[ion]]s in the crystal lattice upon being exposed to an external electric field. The cause of electrostrictive is linked to anharmonic effects.<ref name="giant2022"/> 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.{{citation needed|date=August 2024}}

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.<ref name="smart2013"/>{{rp|664}}<ref name="giant2022"/>

More formally, the electrostriction coefficient is a [[Tensor#Tensor rank|rank four]] [[tensor]] (<math>Q_{ijkl}</math>), relating the rank two strain tensor (<math>\varepsilon_{ij}</math>) and the electric [[polarization density]] vector (i.e. rank one tensor; <math>P_k</math>)<ref name="giant2022">{{cite journal | last1=Yu | first1=Jiacheng | last2=Janolin | first2=Pierre-Eymeric | title=Defining "giant" electrostriction | journal=Journal of Applied Physics | publisher=AIP Publishing | volume=131 | issue=17 | date=2022-05-05 | issn=0021-8979 | doi=10.1063/5.0079510 | page=| arxiv=2110.11304 | bibcode=2022JAP...131q0701Y }}</ref>

:<math>\varepsilon_{ij} = Q_{ijkl}P_k P_l.</math>

The electrostrictive tensor satisfies<ref name="smart2013"/>{{rp|666}}

:<math>Q_{ijkl} = \frac{1}{2}\frac{\partial^2\varepsilon_{ij}}{\partial P_k \partial 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]].  Piezoelectricity is a result of electrostrictive in ferroelectric materials.<ref name="giant2022"/> Electrostriction is a [[quadratic function|quadratic]] effect, unlike piezoelectricity, which is a [[linear]] effect.<ref name="smart2013"/>{{rp|665}}<ref name="giant2022"/>

== Materials ==
Although all dielectrics exhibit some electrostriction, certain engineered ceramics, known as [[relaxor ferroelectric]]s, have extraordinarily high electrostrictive constants.<ref name="giant2022"/> 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 on the order of 0.1% for some materials.<ref name="smart2013"/>{{rp|662}} This occurs at a field strength of 2 million volts per meter (2 MV/m) for the material PMN-15.<ref name="e896">{{cite web | title=Electrostrictive Ceramics | website=TRS Ceramics | url=https://www.trstechnologies.com/Materials/Electrostrictive-Ceramics | access-date=2024-08-09}}</ref> Electrostriction exists in all materials, but is generally negligible.<ref name="smart2013"/>{{rp|662}}

== Applications ==

* [[Sonar]] projectors for submarines and surface vessels
* [[Actuator]]s for small displacements <ref name="giant2022"/>
* Sensors, provided a bias electric field or pre-stress is present.<ref name="giant2022"/>

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

==References==
{{reflist}}

==Further reading==
* [http://www.britannica.com/science/electrostriction "Electrostriction." Encyclopædia Britannica.]
* ''Mini dictionary of physics'' (1988) Oxford University Press
* [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

{{Authority control}}

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