Template:Sources exist In electromagnetism, electrostriction is a property of all electrical non-conductor or dielectrics.Template:Citation needed Electrostriction causes these materials to change their shape under the application of an electric field.<ref name="smart2013">Template:Cite book</ref>Template:Rp It is the dual property to magnetostriction.
ExplanationEdit
Electrostriction is a property of all dielectric materials,<ref name="giant2022"/> and is caused by displacement of ions 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.Template:Citation needed
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.<ref name="smart2013"/>Template:Rp<ref name="giant2022"/>
More formally, the electrostriction coefficient is a 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">Template:Cite journal</ref>
- <math>\varepsilon_{ij} = Q_{ijkl}P_k P_l.</math>
The electrostrictive tensor satisfies<ref name="smart2013"/>Template:Rp
- <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 point groups. Piezoelectricity is a result of electrostrictive in ferroelectric materials.<ref name="giant2022"/> Electrostriction is a quadratic effect, unlike piezoelectricity, which is a linear effect.<ref name="smart2013"/>Template:Rp<ref name="giant2022"/>
MaterialsEdit
Although all dielectrics exhibit some electrostriction, certain engineered ceramics, known as relaxor ferroelectrics, 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 effectEdit
Electrostriction can produce a strain on the order of 0.1% for some materials.<ref name="smart2013"/>Template:Rp This occurs at a field strength of 2 million volts per meter (2 MV/m) for the material PMN-15.<ref name="e896">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Electrostriction exists in all materials, but is generally negligible.<ref name="smart2013"/>Template:Rp
ApplicationsEdit
- Sonar projectors for submarines and surface vessels
- Actuators for small displacements <ref name="giant2022"/>
- Sensors, provided a bias electric field or pre-stress is present.<ref name="giant2022"/>
See alsoEdit
ReferencesEdit
Further readingEdit
- "Electrostriction." Encyclopædia Britannica.
- Mini dictionary of physics (1988) Oxford University Press
- "Electronic Materials" by Prof. Dr. Helmut Föll