Editing Electrostriction (section)

== 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"/>