Editing Magnetostriction (section)

== Magnetostrictive materials ==
[[Image:Magnetostrictive transducer.PNG|thumb|Cut-away of a transducer comprising: magnetostrictive material (inside), magnetising coil, and magnetic enclosure completing the magnetic circuit (outside)]]

Magnetostrictive materials can convert magnetic energy into [[kinetic energy]], or the reverse, and are used to build [[actuator]]s and [[sensor]]s.  The property can be quantified by the magnetostrictive coefficient, λ, which may be positive or negative and is defined as the fractional change in length as the magnetization of the material increases from zero to the [[saturation (magnetic)|saturation]] value. The effect is responsible for the familiar "[[mains hum|electric hum]]" ({{Audio|Mains hum 60 Hz.ogg|Listen}}) which can be heard near [[transformer]]s and high power electrical devices.

Cobalt exhibits the largest room-temperature magnetostriction of a pure element at 60 [[wikt:microstrain|microstrain]]s. Among alloys, the highest known magnetostriction is exhibited by [[Terfenol-D]], (Ter for [[terbium]], Fe for [[iron]], NOL for [[Naval Ordnance Laboratory]], and D for [[dysprosium]]). Terfenol-D, {{chem2|Tb_{''x''}Dy_{1−''x''}Fe2}}, exhibits about 2,000 microstrains in a field of 160 kA/m (2 kOe) at room temperature and is the most commonly used engineering magnetostrictive material.<ref>{{Cite web |url=http://aml.seas.ucla.edu/research/areas/magnetostrictive/mag-composites/Magnetostriction%20and%20Magnetostrictive%20Materials.htm |title=Magnetostriction and Magnetostrictive Materials |website=Active Material Laboratory |publisher=[[UCLA]] |archive-url=https://web.archive.org/web/20060202050523/http://aml.seas.ucla.edu/research/areas/magnetostrictive/mag-composites/Magnetostriction%20and%20Magnetostrictive%20Materials.htm |archive-date=2006-02-02}}</ref> [[Galfenol]], {{chem2|Fe_{''x''}Ga_{1−''x''}|auto=1}}, and [[Alfer]], {{chem2|Fe_{''x''}Al_{1−''x''} }}, are newer alloys that exhibit 200-400 microstrains at lower applied fields (~200 Oe) and have enhanced mechanical properties from the brittle Terfenol-D. Both of these alloys have <100> easy axes for magnetostriction and demonstrate sufficient ductility for sensor and actuator applications.<ref>{{cite journal|last1=Park|first1=Jung Jin|last2=Na|first2=Suok-Min|last3=Raghunath|first3=Ganesh|last4=Flatau|first4=Alison B.|author4-link=Alison Flatau|date=March 2016|title=Stress-anneal-induced magnetic anisotropy in highly textured Fe-Ga and Fe-Al magnetostrictive strips for bending-mode vibrational energy harvesters|journal=AIP Advances|volume=6|issue=5|pages=056221|doi= 10.1063/1.4944772|bibcode=2016AIPA....6e6221P|doi-access=free}}</ref>

[[File:Magnetostrictive flow sensor.png|thumb|Schematic of a whisker flow sensor developed using thin-sheet magnetostrictive alloys.]]

Another very common magnetostrictive composite is the amorphous alloy {{chem2|Fe81Si_{3.5}B_{13.5}C2|auto=1}} with its trade name [[Metglas]] 2605SC. Favourable properties of this material are its high saturation-magnetostriction constant, λ, of about 20 [[wikt:microstrain|microstrain]]s and more, coupled with a low [[magnetic anisotropy|magnetic-anisotropy]] field strength, H<sub>A</sub>, of less than 1 kA/m (to reach [[magnetic saturation]]). [[Metglas]] 2605SC also exhibits a very strong ΔE-effect with reductions in the effective [[Young's modulus]] up to about 80% in bulk. This helps build energy-efficient magnetic [[Microelectromechanical systems|MEMS]].{{Citation needed|reason=source needed for this whole paragraph on Metglas 2605SC information|date=September 2012}}

Cobalt [[ferrite (magnet)|ferrite]], {{chem2|CoFe2O4}} (CoO·Fe<sub>2</sub>O<sub>3</sub>), is also mainly used for its magnetostrictive applications like sensors and actuators, thanks to its high saturation magnetostriction (~200 parts per million).<ref>{{cite journal|last1=Olabi|first1=A.G.|last2=Grunwald|first2=A.|title=Design and application of magnetostrictive materials|journal=Materials & Design|date=January 2008|volume=29|issue=2|pages=469–483|doi=10.1016/j.matdes.2006.12.016|url=http://doras.dcu.ie/15063/1/Olabi-MS-paper-12-09-06.pdf}}</ref> In the absence of [[rare-earth]] elements, it is a good substitute for [[Terfenol-D]].<ref>{{cite journal|last1=Turtelli|first1=R Sato|last2=Kriegisch|first2=M|last3=Atif|first3=M|last4=Grössinger|first4=R|title=Co-ferrite – A material with interesting magnetic properties|journal=IOP Conference Series: Materials Science and Engineering|date=17 June 2014|volume=60|issue=1|pages=012020|doi=10.1088/1757-899X/60/1/012020|bibcode=2014MS&E...60a2020T|doi-access=free}}</ref> Moreover, its magnetostrictive properties can be tuned by inducing a magnetic uniaxial anisotropy.<ref>{{cite journal|last1=Slonczewski|first1=J. C.|title=Origin of Magnetic Anisotropy in Cobalt-Substituted Magnetite|journal=Physical Review|date=15 June 1958|volume=110|issue=6|pages=1341–1348|doi=10.1103/PhysRev.110.1341|bibcode=1958PhRv..110.1341S}}</ref> This can be done by magnetic annealing,<ref>{{cite journal|last1=Lo|first1=C.C.H.|last2=Ring|first2=A.P.|last3=Snyder|first3=J.E.|last4=Jiles|first4=D.C.|title=Improvement of magnetomechanical properties of cobalt ferrite by magnetic annealing|journal=IEEE Transactions on Magnetics|date=October 2005|volume=41|issue=10|pages=3676–3678|doi=10.1109/TMAG.2005.854790|bibcode=2005ITM....41.3676L|s2cid=45873667}}</ref> magnetic field assisted compaction,<ref>{{cite journal|last1=Wang|first1=Jiquan|last2=Gao|first2=Xuexu|last3=Yuan|first3=Chao|last4=Li|first4=Jiheng|last5=Bao|first5=Xiaoqian|title=Magnetostriction properties of oriented polycrystalline CoFe 2 O 4|journal=Journal of Magnetism and Magnetic Materials|date=March 2016|volume=401|pages=662–666|doi=10.1016/j.jmmm.2015.10.073|bibcode=2016JMMM..401..662W}}</ref> or reaction under uniaxial pressure.<ref>{{cite journal|last1=Aubert|first1=A.|last2=Loyau|first2=V.|last3=Mazaleyrat|first3=F.|last4=LoBue|first4=M.|date=August 2017|title=Uniaxial anisotropy and enhanced magnetostriction of CoFe 2 O 4 induced by reaction under uniaxial pressure with SPS|url=https://hal.archives-ouvertes.fr/hal-01636264|journal=Journal of the European Ceramic Society|volume=37|issue=9|pages=3101–3105|doi=10.1016/j.jeurceramsoc.2017.03.036|arxiv=1803.09656|s2cid=118914808}}</ref> This last solution has the advantage of being ultrafast (20 min), thanks to the use of [[spark plasma sintering]].

In early [[sonar]] transducers during World War II, [[nickel]] was used as a magnetostrictive material. To alleviate the shortage of nickel, the Japanese navy used an [[iron]]-[[aluminium]] alloy from the [[Alperm]] family.

===Mechanical behaviors of magnetostrictive alloys===

====Effect of microstructure on elastic strain alloys==== 
[[Single crystal|Single-crystal]] alloys exhibit superior microstrain, but are vulnerable to yielding due to the anisotropic mechanical properties of most metals. It has been observed that for [[polycrystalline]] alloys with a high area coverage of preferential grains for microstrain, the mechanical properties ([[ductility]]) of magnetostrictive alloys can be significantly improved. Targeted metallurgical processing steps promote [[abnormal grain growth]] of {011} grains in [[galfenol]] and [[alperm|alfenol]] thin sheets, which contain two easy axes for magnetic domain alignment during magnetostriction. This can be accomplished by adding particles such as [[boride]] species <ref>{{cite journal|last1=Li|first1=J.H.|last2=Gao|first2=X.X.|last3=Xie|first3=J.X.|last4=Yuan|first4=C.|last5=Zhu|first5=J.|last6=Yu|first6=R.B.|date=July 2012|title=Recrystallization behavior and magnetostriction under pre-compressive stress of Fe–Ga–B sheets|journal=Intermetallics|volume=26|pages=66–71|doi= 10.1016/j.intermet.2012.02.019}}</ref> and [[niobium]] carbide ({{chem2|NbC}}) <ref>{{cite journal|last1=Na|first1=S-M.|last2=Flatau|first2=A.B.|author2-link=Alison Flatau|date=May 2014|title=Texture evolution and probability distribution of Goss orientation in magnetostrictive Fe–Ga alloy sheets|journal=Journal of Materials Science|volume=49|issue=22|pages=7697–7706|doi= 10.1007/s10853-014-8478-7|bibcode=2014JMatS..49.7697N|s2cid=136709323}}</ref> during initial chill casting of the [[ingot]].

For a polycrystalline alloy, an established formula for the magnetostriction, λ, from known directional microstrain measurements is:<ref>{{cite journal|last1=Grössinger|first1=R.|last2=Turtelli|first2=R. Sato|last3=Mahmood|first3=N.|date=2014|title=Materials with high magnetostriction|journal=IOP Conference Series: Materials Science and Engineering|volume=60|issue=1|pages=012002|doi= 10.1088/1757-899X/60/1/012002|bibcode=2014MS&E...60a2002G|doi-access=free}}</ref>

λ<sub>s</sub> = 1/5(2λ<sub>100</sub>+3λ<sub>111</sub>)

[[File:Tensiletestgallium.png|thumb|Magnetostrictive alloy deformed to fracture]]

During subsequent [[hot rolling]] and [[Recrystallization (metallurgy)|recrystallization]] steps, particle strengthening occurs in which the particles introduce a “pinning” force at [[grain boundaries]] that hinders normal ([[stochastic]]) grain growth in an annealing step assisted by a {{chem2|H2S|link=hydrogen sulfide}} atmosphere. Thus, single-crystal-like texture (~90% {011} grain coverage) is attainable, reducing the interference with [[magnetic domain]] alignment and increasing microstrain attainable for polycrystalline alloys as measured by semiconducting [[strain gauges]].<ref>{{cite journal|last1=Na|first1=S-M.|last2=Flatau|first2=A.B.|author2-link=Alison Flatau|date=May 2014|title=Texture evolution and probability distribution of Goss orientation in magnetostrictive Fe–Ga alloy sheets|journal=Journal of Materials Science|volume=49|issue=22|pages=7697–7706|doi= 10.1007/s10853-014-8478-7|bibcode=2014JMatS..49.7697N|s2cid=136709323}}</ref> These surface textures can be visualized using [[electron backscatter diffraction]] (EBSD) or related diffraction techniques.

====Compressive stress to induce domain alignment====
For actuator applications, maximum rotation of magnetic moments leads to the highest possible magnetostriction output. This can be achieved by processing techniques such as stress annealing and field annealing. However, mechanical pre-stresses can also be applied to thin sheets to induce alignment perpendicular to actuation as long as the stress is below the buckling limit. For example, it has been demonstrated that applied compressive pre-stress of up to ~50 MPa can result in an increase of magnetostriction by ~90%. This is hypothesized to be due to a "jump" in initial alignment of domains perpendicular to applied stress and improved final alignment parallel to applied stress.<ref>
{{cite journal|title=Compressive pre-stress effects on magnetostrictive behaviors of highly textured Galfenol and Alfenol thin sheets|journal=AIP Advances|date=January 2017|first1=J|last1=Downing|first2=S-M|last2=Na|first3=A|last3=Flatau|author3-link=Alison Flatau|volume=7|issue=5|pages=056420|id=056420|doi=10.1063/1.4974064|bibcode=2017AIPA....7e6420D|doi-access=free}}</ref>

===Constitutive behavior of magnetostrictive materials===
These materials generally show non-linear behavior with a change in applied magnetic field or stress. For small magnetic fields, linear piezomagnetic constitutive<ref>{{Cite book|last=Isaak D|first=Mayergoyz|title=Handbook of giant magnetostrictive materials|publisher=Elsevier|year=1999|isbn=|location=|pages=}}</ref> behavior is enough. Non-linear magnetic behavior is captured using a classical macroscopic model such as the [[Preisach model of hysteresis|Preisach model]]<ref>{{Cite journal|last=Preisach|first=F.|date=May 1935|title=Über die magnetische Nachwirkung|url=http://link.springer.com/10.1007/BF01349418|journal=Zeitschrift für Physik|language=de|volume=94|issue=5–6|pages=277–302|doi=10.1007/BF01349418|bibcode=1935ZPhy...94..277P |s2cid=122409841|issn=1434-6001|via=}}</ref> and Jiles-Atherton model.<ref>{{Cite journal|last1=Jiles|first1=D. C.|last2=Atherton|first2=D. L.|date=1984-03-15|title=Theory of ferromagnetic hysteresis (invited)|url=http://aip.scitation.org/doi/10.1063/1.333582|journal=Journal of Applied Physics|language=en|volume=55|issue=6|pages=2115–2120|doi=10.1063/1.333582|bibcode=1984JAP....55.2115J|issn=0021-8979}}</ref> For capturing magneto-mechanical behavior, Armstrong<ref>{{Cite journal|last=Armstrong|first=William D.|date=1997-04-15|title=Burst magnetostriction in Tb0.3Dy0.7Fe1.9|url=http://aip.scitation.org/doi/10.1063/1.364992|journal=Journal of Applied Physics|language=en|volume=81|issue=8|pages=3548–3554|doi=10.1063/1.364992|bibcode=1997JAP....81.3548A|issn=0021-8979}}</ref> proposed an "energy average" approach. More recently, Wahi ''et al.''<ref>{{Cite journal|last1=Wahi|first1=Sajan K.|last2=Kumar|first2=Manik|last3=Santapuri|first3=Sushma|last4=Dapino|first4=Marcelo J.|date=2019-06-07|title=Computationally efficient locally linearized constitutive model for magnetostrictive materials|journal=Journal of Applied Physics|language=en|volume=125|issue=21|pages=215108|doi=10.1063/1.5086953|bibcode=2019JAP...125u5108W|s2cid=189954942 |issn=0021-8979|doi-access=free}}</ref> have proposed a computationally efficient [[constitutive equation|constitutive]] model wherein constitutive behavior is captured using a "locally linearizing" scheme.