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Magnetism Magnetism, the phenomenon by which materials assert an attractive or repulsive force or influence on other materials. Basic Concepts An electrical current in a loop generates a magnetic field. Magnetic fields are generated by moving electrically charged particles. Magnetic field strength - H Earth North Pole is actually the South magnetic pole. Field lines – come out from the north towards the south

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• MagnetismMagnetism, the phenomenon by which materials assert an attractive or repulsive force or influence on other materials.

Basic ConceptsAn electrical current in a loop

generates a magnetic field.Magnetic fields are generated by

moving electrically charged particles.

Magnetic field strength - H

Earth North Pole is actually the South magnetic pole.

Field lines come out from the north towards the south

• Magnetization, Permeability, and the Magnetic Field

(A/m) LnIH =

A current passing through a coil sets up a magnetic field (H). Where n=number of turns; L=length of the coil and I=current. Units for H (A/m) and oersted 31 104.11 = mAoersted

)(weber/m 2HB oo =

When H is applied in vacuum, lines of magnetic flux are inducted. The number of lines of flux, called flux density or inductance B, is related to the applied magnetic filed by the equation

o magnetic permeability of vacuum.

Units:H(oersted), B(gauss), o(gauss/oersted)H(A/m), B(weber/m2 tesla), o(4x10-7weber/A.m henry/m)

• )(weber/m 2HB =When we place a material within the magnetic field, B is determined by the manner in which induced and permanent dipoles interact.

= permeability of the material in the field>o magnetic dipole moments reinforce the field

• Magnetization of a SolidB = oH + oM

field-vacuum dipoles-material

o = permeability under vacuum

M = magnetization of the material

Review of TermsB Magnetic Induction (Tesla or kg/A-s2 or Wb/m2)H Magnetic field (amp-turn/m or C/m-s)M Magnetization (same as magnetic field)o Permeability (henry/m or kg-m/C2)

Magnetic susceptibility (m) 1=

=

rm

m HM

17104 = mhenryO .

M is defined as the magnetic moment per unit volume. It is a property of the material and depends on both the individual magnetic moments of the constituent ions, atoms or molecules and how these dipole moments interact with each other. )1( mo +=

• 17104 = mhenryO .

• Magnetic MaterialsMagnetic behavior is determined primarily by the electronic structure of a material, which provides magnetic dipoles.

Magnetic Dipoles: (Analogous to electric dipoles) They are the result of (a) electrons orbiting around the nucleus and (b) spin of theelectron around its axis.

• These two motions (i.e. orbital and spin) contribute to the magnetic behavior of the material. The interaction between these dipoles determine the type of magnetic behavior of the material.The magnetic behavior can be controlled by composition, microstructure and processing.The magnetic moment of an electron due to its spin is known as the Bohr Magneton (MB Fundamental Constant)q=charge of electron,h=Planck constantme=mass of the electronThen, we can view electrons as small elementary magnets.However, the magnetic moments due to electron do not all line up in the same direction.

224 .10274.94

mAxm

qhMe

B==

• Two mechanisms to cancel magnetic dipole moments:(1) Electron pairs have opposite spins they cancel each other.(2) Orbital moments of the electrons also cancel outThus:Atoms having completely filled electron shells (He, Ne, Ar, etc) are not

capable of being permanently magnetized.Some elements, such as transition elements (3d, 4d, 5d partially filled) have a net magnetic moment since some of their levels have unpaired electrons. Example (Sc to Cu) the electrons in the 3d level do not enter the shells in pairs. Mn has five electrons with the same spin. Transition metals have a permanent magnetic moment, which is related to the number of unpaired electrons.

• Types of magnetism: Ferromagnetism. Property of iron, nickel, neodymium

Strongest type of magnetism. Uncancelled electron spins as a consequence of the electron structure.

Paramagnetism. Exhibited by materials containing transition, rare earth or actinide elements

Diamagnetism Exhibited by all common materials but masked if other two types of magnetism are present

Ferrimagnetism Source of magnetic moment different as ferromagnetic. Incomplete cancellation of spin moments due to atomic position and surrounding. Ceramics (insulators).

Antiferromagnetism Alignment of the spin moments of neighboring atoms or ions in exactly opposite direction.

• DiamagnetismCompletely filled shells or subshells.Total cancellation of orbital and spin momentsCannot be permanently magnetized. Very weakIt is induced by change in orbital motion due to applied fieldThe dipoles induced by the field are aligned opposite to the field direction.Only exists while a field is on. It is found in all materialsVery hard to observe. It is of no practical purposer < 1 (~0.99) H = 0

H

Superconductors:

r=0

• External magnetic field acting on the atoms slightly unbalances their orbiting electrons and creates small magnetic dipoles within the atoms, which oppose the applied field, and this action produces a negative magnetic effect to the applied field.

A weak, negative, repulsive reaction of a material to an applied magnetic field.

is around 10-6to 10-5 . Inert gases, many organic compounds, some metals (Bi, Zn, Ag) and nonmetals (S, P, Si)

Magnetization is negative (

• ParamagnetismIncomplete cancellation of electron spin/orbital magnetic momentsPermanent Dipoles. Randomly oriented when no field is presentParamagnetism. Permanent dipoles align with an external field No interaction between adjacent dipoles. Exists only in a magnetic fieldRandomly oriented permanent dipoles align with field. (Only present

when field is applied)r = 1.00 to 1.01 H = 0

H

• Magnetization is positive (> 0)Applied field aligns the individual magnetic dipoles of the atoms or molecules and slightly increases magnetic induction, B. The magnetic susceptibility ranges from 10-6 to 10-2Temperature reduces the paramagnetic effectsDiamagnetism and paramagnetism are all induced by an applied field, when the field is removed, the effect disappears. Rare earth metals, Li, Na, K, RhA weak, positive, attractive reaction of a material to an applied fieldVery limited engineering applications.

• DiamagneticBismuth -16.6Mercury -2.85Silver -2.38Carbon (diamond) -2.1Gold -3.44Sodium chloride -1.4Copper -1.8ParamagneticIron aluminum alum 66Uranium 40Platinum 26Aluminum 2.07Sodium 0.85Chromium 3.13

Material Susceptibility m(x 10-5)

• FerromagnetismElectron Spins dont cancel outCoupling interactions cause adjacent atoms to align with one anotherFerromagnetism. Permanent magnetic moment in the absence of an external field.

large magnetizationr = up to 106

Permanent dipoles are aligned even in the absence of a magnetic field.

H = 0

• Magnetic susceptibility is positive and very large (101< < 106)Very large magnetization will be created by the material.Relationship between magnetization (M) and applied field (H) is nonlinear and complicated. Repeated magnetization leads to hysteresis.Large magnetic field can be retained after the applied field removed.Most important ferromagnetic elements are: Fe, Co, Ni Great engineering importance.A rare-earth element gadolinium (Gd) is also ferromagnetic below 16oC, but has little engineering application.

• Fe atom has four unpaired 3d electrons; Co has three unpaired 3d electrons; Ni has two unpaired 3d electrons.

Spins of the 3d electrons of adjacent atoms align in a parallel direction by a phenomenon called spontaneous magnetization. This parallel alignment of atomic magnetic dipoles occurs in microscopic regions called magnetic domains. Most critical difference between Ferromagnetism and Paramagnetisim: The former has Spontaneous Magnetization. Randomly oriented domains No net magnetizationDomains aligned in a magnetic field Very strong magnetic induction

• As a whole the materials magnetic domains are oriented randomly and effectively cancel each other out

If H is applied, domains align giving a strong net H field in same direction as H

Net H field partially exists even when Hext is removed

• Fe, Co and Ni ferromagnetic materials

Cr and Mnnot ferromagnetic materials, Why?

(they all have unpaired 3d electrons)

Magnetic exchange interaction energy Energy associated with the coupling of individual magnetic dipoles into a single magnetic domain. Only when this exchange energy is positive material be ferromagnetic. Magnetic exchange energy is related to the ratio of atomic spacing to 3d orbit, must be in the range of 1.4 to 2.7.

• AntiferromagnetismAlignment of neighboring atomsSpin moments are opposite

no net magnetic moment

Antiparallel alignmentCeramic oxides, Manganese (Mn), chromium (Cr), MnO, CrO, and CoOexhibit this behavior M2+ O 2-

A type of magnetism in which the magnetic dipoles of atoms are aligned themselves in opposite directions by an applied field so that there is no net magnetic moment.

• If we place ferromagnetic material (e.g. iron) inside a solenoid with field B0 , increase the total B field inside coil to

BM is magnitude of B field contributed by iron coreBM result of alignment of the domainsBM increases total B by large amount - iron core inside solenoid increases B by typically about 5000 times For the electromagnetic core we use soft iron where the magnetism is not permanent (goes away when the external field isturned off).

The maximum possible magnetization, or saturation magnetization Msrepresents the magnetization that results when all the magnetic dipoles in a solid piece are mutually aligned with the external field. There is also a corresponding saturation flux density Bs

MBBB += 0 HB 00 = MBM 0=

MBHM o>>

• The magnetic moments change direction continuously for ferromagnetic material

B small: Domains with favorable orientation to applied field grow at the expense of others.

B large: Rotation of the domain orientation towards the applied field.

MS: Saturation Magnetization

• 1) Fast stage: The domains with moments parallel to the applied field grow at the expense of those with less favorable orientations. The domain growth takes place by domain wall movement. The magnetization increases rapidly as the applied field increases2) Second stage: When domain wall growth has finished, if the applied field is continuously increased, domain rotation occurs. The magnetization increases slowly with the applied field.

Domain movement during magnetizationWhen an external magnetic field is applied, the magnetic domains will follow two-stage reactions:

• B small: Domains with favorable orientation to applied field grow at expense of others .B large: rotation of the magnetization, B M || BRemanence Mr: remaining magnetization at B = 0 due to irreversible Bloch wall displacements.Coercitivity BC : required field to remove remaining magnetization.Ms: saturation magnetization lim M(B) B

• Example

The maximum magnetization, called saturation magnetization MSAT, in iron is about 1.75x106 Am-1. This corresponds to all possible net spins aligning parallel to each other. Calculate the effective number of Bohr magnetons per atom that would give MSAT, given that the density and relative atomic mass of iron are 7.86g.cm-3 and 55.85g.mol-1respectively.

Solution:

Number of iron atoms per unit volume( )( )

328

13

12333

10488

10855510022610867

=

==

matomsnmolkg

molmkgA

Nn

Fe

Fe

....

...

22.=

=

=

BFe

SAT

BFeSAT

MnM

MnM

The magnetic saturation is given by the expression:

Where is the number of net spins that contribute to magnetization per iron atom

• Fe Co Ni Gd

Crystal structure

BCC

HCP

FCC

HCP

Bohr magnetons per atom 2.22 1.72 0.60 7.1

Msat(0) (MA m-1) 1.75 1.45 0.50 2.0

Bsat = o Msat (T) 2.2 1.82 0.64 2.5

TC 770 C 1043 K

1127 C 1400 K

358 C 631 K

16 C 289 K

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002)http://Materials.Usask.Ca

Table 8.3 Properties of the ferromagnets Fe, Co, Ni and Gd.

• Example

Calculate the maximum, or saturation magnetization and the saturation flux density that we expect in iron. The lattice parameter of BCC iron is 2.866Angstroms. Data Fe (Z=26) Solution

Based on the unpaired electronic spins (see table), we expect each iron atom to have 2.22 electrons that act as magnetic dipoles.

( )28

310

3 10488108662

2=

=

.

.________m

cellperatomsmperatomsironofNumber

The maximum volume magnetization (MSAT) is the total magnetic moment per unit volume

( )( )( )16

224328

10751

2221027910488

=

=

mAMatomMagnetonsBohrmAmatomsM

SAT

SAT

../_.../.

In ferromagnetic materials OM >> OH and therefore B~OM

TeslamWb

mA

AmWbBSAT _....

19219210751104 267 ==

=

• Example

Calculate (a) the saturation magnetization and (b) the saturation flux density for nickel, which has a density of 8.90g.cm-3. Data ANi = 58.69g.mol-1

Solution

(a) Based on the table, we expect each nickel atom to have 0.6 electrons that act as magnetic dipoles. The number of nickel atoms per cubic meter is related to the density of the nickel 32810139 mperatoms

ANNNi

A __. ==

The saturation magnetization is151015600 == mANMagnetonBohrMSAT .._.

(b) Flux density : TeslaMB SATOSAT _.640==

• FerrimagnetismIn some ceramic compounds, different ions have different magnitude of magnetic moments. When these magnetic moments are aligned in an antiparallel manner, there is a net magnetic moment in one direction.

100< < 104These ceramic magnetic materials are called ferrites and have very useful electronic applications.

• FerrimagnetismCeramics. Permanent magnetism(Source of net magnetic moment is

different)Cubic ferrites MFe2O4 (M = Ni, Mn,

Co, Cu)Can adjust composition to get

different propertiesFerrites are usually good electronic

insulators

• Cubic ferrites having other compositions may be produced by adding metallic ions that substitute for some of the iron in the crystal structure. Again, from the ferrite chemical formula, M2+O2(Fe3+)2(O2-)3 , in addition to Fe2+, M2+ may represent divalent ions such as Ni2+, Mn2+, Co2+, and Cu2+, each of which possesses a net spin magnetic moment different from 4; several are listed in Table 18.4.Thus, by adjustment of composition, ferrite compounds having a range of magnetic properties may be produced. For example, nickel ferrite has the formula NiFe2O4 .Other compounds may also be produced containing mixtures of two divalent metal ions such as (Mn,Mg)Fe2O4 , in which the Mn2+:Mg2+ ratio may be varied; these are called mixed ferrites.

• Example

Calculate the saturation magnetization for Fe3O4 given that each cubic unit cell contains 8 Fe2+ and 16 Fe3+ ions and that the lattice parameter is 0.839nm.

Solution

The net magnetization results from the Fe2+ ions only. Since there are 8 Fe2+ ions per unit cell and 4 Bohr magneton per Fe2+ ion, then the number of electron contributing to the dipole magnetization per unit cell is 32 (nB).

3amagnetonBohrnM BSAT

_=

15

39

224

1005108390

1027932

=

=

mAMcellunitperm

magnetonBohrmAcellunitperMagnetonBohrM

SAT

SAT

..__).(

)_/..)(_____(

• Example

Design a cubic mixed-ferrite magnetic material that has a saturation magnetization of 5.25x105A.m-1

Solution

From the previous example the, if all were Fe2+, the saturation magnetization should be 5.0x105A.m-1. Then, some of the iron Fe2+ ions must be replaced by other ions with more than 4 Bohr Magnetons per ions, such as Mn.

cellunitperMagnetonBohrmagnetonBohr

aMn SATB _____._4533

3

=

=

If x represents the fraction of Mn2+ that have substitute for Fe2+, then the remaining unsusbstituted Fe2+ fraction is (1-x)

[ ]1810

45331458.

.)(=

=+x

xx Or 18.1%Mn

• Hysteresis Loops

a) Soft magnetic materials: 0.001 < Hc < 1 A/cmb) Hard magnetic materials: 100 < Hc < 30000 A/cm

Area of hysteresis loop: losses due to reversal of magnetization (dissipated as heat).

Ms: material property.Hc: depends strongly on microstructure.

• Domain structureFerromagnetic sample generally has no net magnetic moment!Reason: domain structure tends to the reduction of magnetostatic energy.Reduction of magnetostatic energy, stored in the magnetic field, by formation of domains of uniform spin orientation. The domains are generated by so-called Bloch walls, where the spin orientation changes gradually within a distance of the order of 40nm (for Fe). Typical domain sizes are 1 - 10 m. There is a competition between reduction in magnetostatic energy and the energy required to form Bloch walls.

Closure domains eliminate the magnetostatic energy but introduce magnetostrictiveenergy.Bloch wall energy limits density of Bloch walls.

• Magnetic AnisotropyA material is called magnetically anisotropic if the magnetization curve of the material depends on the direction to which the material is magnetized. Some directions need only a little energy to be magnetized, while others need more. The direction that is easy to magnetize is called the easy magnetization direction (ED). The direction that needs most energy to be magnetized is called the hard magnetization direction (HD).

• When a magnetic field is applied in a certain direction, the magnetic moments align along the easy axes that are closest to the direction of the applied magnetic field. The other directions along which the magnetic moments do not become aligned as easily are known as the hard axes. The magnetization reaches its saturation value in a comparatively lower applied field along an easy axis as compared to the hard axis.

• Polycrystalline material -different grains approach MSaturation differently. Easy-orientation grains saturate at lower applied fields.

Grains with hard orientations rotate their moment into the field direction at higher fields.

The energy required during the magnetization to rotate the magnetic domains because of crystalline anisotropy magnetocrystalline energyormagnetocrystalline anisotropic energy

• Magnetocrystallineanisotropy is the energy necessary to deflect the magnetic moment in a single crystal from the easy to the hard direction. The easy and hard directions arise from the interaction of the spin magnetic moment with the crystal lattice (spin-orbit coupling).

• In cubic crystals, like magnetite, the magnetocrystalline anisotropy energy is given by a series expansion in terms of the angles between the direction of magnetization and the cube axes. It is sufficient to represent the anisotropy energy in an arbitrary direction by just the first two terms in the series expansion. These two terms each have an empirical constant associated with them called the first- and second order anisotropy constants, or K1 and K2, respectively. At 300 K, K1 = -1.35x105 ergs/cm3 K2 = -0.44 x105 ergs/cm3.

The simplest form of crystal anistropy is uniaxial anisotropy. For cubic crystals the anisotropy energy can be expressed in terms of the direction cosines (cos1, cos2, cos3) of the internal magnetisation with respect to the three cube edges. Due to the high symmetry of the cubic crystal this can be expressed in a simple manner as a polynomial series in the direction cosines.

( ) ( ) ......32221221232322222121 ++++= CosCosCosKCosCosCosCosCosCosKE

• In hexagonal crystals the anisotropy energy is a function of only one parameter, that is the angle between the magnetization and the c-axis. Experiments show, that it is symmetric with respect to the base plane, and so odd powers of Coscan be omitted in a power series expansion for the anisotropy energy density . The typical values of the anisotropy for cobalt K1=4.1x106erg/cm3 and K2=1.0x106erg/cm3

422

1 coscos KKwani +=

• Summary:The dependence of magnetic properties on a preferred direction is called magnetic anisotropy. There are several different types ofanisotropy:Type depends on1. magnetocrystalline- crystal structure2. shape- grain shape3. stress- applied or residual stressesMagnetic anisotropy strongly affects the shape of hysteresis loops and controls the coercivity and remanence. Anisotropy is also of considerable practical importance because it is exploited in the design of most magnetic materials of commercial importance.

• Shape AnisotropyThe second type of anisotropy is due to the shape of a mineral grain. A magnetized body will produce magnetic charges or poles at the surface. This surface charge distribution, acting in isolation, is itself another source of a magnetic field, called the demagnetizing field. It is called the demagnetizing field because it acts in opposition to the magnetization that produces it.

• For example, take a long thin needle shaped grain. The demagnetizing field will be less if the magnetization is along the long axis than if is along one of the short axes. This produces an easy axis of magnetization along the long axis. A sphere, on the other hand, has no shape anisotropy. The magnitude of shape anisotropy is dependent on the saturation magnetization.For magnetite smaller than about 20 microns, shape anisotropy is the dominant form of anisotropy. In larger sized particles, shape anisotropy is less important than magnetocrystalline anisotropy. For hematite, because the saturation magnetization is so low, shape anisotropy is usually never important.

• Stress AnisotropyIn addition to magnetocrystalline anisotropy and shape anisotropy, there is another effect related to spin-orbit coupling called magnetostriction. Magnetostriction arises from the strain dependence of the anisotropy constants. Upon magnetization, a previously demagnetized crystal experiences a strain that can be measured as a function of applied field along the principal crystallographic axes. A magnetic material will therefore change its dimension when magnetized (Joule Magnetostriction). The inverse affect, or the change of magnetization with stress also occurs (Villary Effect). A uniaxial stress can produce a unique easy axis of magnetization if the stress is sufficient to overcome all other anisotropies. The magnitude of the stress anisotropy is described by two more empirical constants known as the magnetostriction constants (111 and 100) and the level of stress.

• Magnetostrictive MaterialsMagnetostriction is a property of ferromagnetic materials that causes them to change their shape when subjected to a magnetic field. The effect was first identified in 1842 by James Joule when observing a sample of nickel. This effect can cause losses due to frictional heating in susceptible ferromagnetic cores. Magnetostriction is a phenomenon observed in all ferromagnetic materials. In normal ferromagnets, such as Fe or Ni, the strain associated with magnetostriction are of the order of 10-4%, while in materials with exceptionally large magnetostriction, such as Tb-Dy-Fe alloys (Terfenol-D) shos strains of the order on 0.1%.

• Magnetostriction is a transduction process in which electrical energy is converted to mechanical energy. It couples elastic, electric, magnetic and in some situations also thermal fields and is of great industrial interest for use in sensors, actuators, adaptive or functional structures, robotics, transducers and MEMS.

Magnetostriction:Reversible strain along the magnetization axis.Anisotropic, because:

Magnetization curve is anisotropic for different orientationsElastic deformation is anisotropic

Magnetostriction and magnetization saturate at the same time.

• A magnetostrictive material develops large mechanical deformations when subjected to an external magnetic field. This phenomenon is attributed to the rotations of small magnetic domains in the material, which are randomly oriented when the material is not exposed to a magnetic field.

The orientation of these small domains by the imposition of the magnetic field creates a strain field. As the intensity of the magnetic field is increased, more and more magnetic domains orientate themselves so that their principal axes of anisotropy are collinear with the magnetic field in each region and finally saturation is achieved.

Taken from: http://esm.neel.cnrs.fr/2007-cluj/questions/magnetostriction.pdf

• Magnetostriction or Joule magnetostriction is a consequence of the magnetoelastic coupling. It pertains to the strain produced along the field direction and is the most commonly used magnetostrictive effect.Joule magnetostriction is the coupling between the magnetic and elastic regimes in a magnetostrictive material. Magnetostriction is an intrinsic property of magnetic materials.

• Magnetostriction refers to magnetically induced shape change in ferromagnetic materials (Joule Effect)Villari effect is a change in magnetization state due to a mechanical stress

Transfers magnetic energy into mechanical energy Experiences a change in strain due to a magnetic field The internal strain causes a change in length which can be controlled by the magnetic field.

First application: First used during WWII in sonar and echolocation

• If a helical magnetic field is applied to a material, then a twisting in the material is observed. This is the Wiedemann effect. The inverse of this is the Matteucci effect, which refers to the creation of a magnetic field when a material is subjected to a torque.

Magnetostrictive materials' ability to convert magnetic energy into mechanical energy and vice versa makes them suitable for building both actuation and sensing devices.

• When an axial magnetic field is applied to a magnetostrictive wire, and a current is passed through the wire, a twisting occurs at the location of the axial magnetic field. The twisting is caused by interaction of the axial magnetic field, usually from a permanent magnet, with the magnetic field along the magnetostrictive wire, which is present due to the current in the wire.The current is applied as a short-duration pulse, 1 or 2 s; the minimum current density is along the center of the wire and the maximum at the wire surface. This is due to the skin effect.The magnetic field intensity is also greatest at the wire surface. This aids in developing the waveguide twist. Since the current is applied as a pulse, the mechanical twisting travels in the wire as an ultrasonic wave. Themagnetostrictive wire is therefore called the waveguide. The wave travels at the speed of sound in the waveguide material, ~ 3000m/s.

• Contactless absolute linear displacement sensor

• Magnetoelastic Effects

• Magnetic Shape Memory EffectA shape memory effect occurs in certain ferromagnetic materials. The parent austemitic phase transforms into the martensitic phase.

The cubic austenitic crystal structure transform into a tetragonal martensiticstructure. The resultant strain is accomodated by the formation of a twin structure. The shape memory effect is based on the motion of the twin boundaries..

When B=0, the magnetic moment of each twin variant points in the direction of the easy magnetization axis.When an external field B is applied, the magnetic moments are aligned with the field by redistributing the twin variants

• Basic Requirements for the Appearance of the MSM Effect.The material should be (ferro)magnetic and exhibit a martensitic transformation.The magnetic anisotropy energy must be higher than the energy required to move a twin boundary.

Two possibilities:

1) Induce the martensitictransformation with the application of a magnetic field

2) Rearrangement of the martensitic variants with the magnetic field

• Example: Ni-Mn-Ga (Heusler Alloy)

Maximum induced deformation ~ 10% with an applied field ~ 10 kOe two orders of magnitude larger than in magnetosrictive Terfenol-D (Tb0.27Dy0.73Fe2).

Heusler alloys Ni-Mn-X (X=Ga, Al, In) ; Co-Ni-Al ; Ni-Fe-Ga

Others: Fe-Pd ; Fe-Pt ; Co-Ni ;

Heusler, L21 (Fm3m)

Ni

Mn

Ga

Ni2MnGa

Ferromagnetic order (Tc~ 370 K)Total magnetic moment: total 4.1 B

per unit cell

( ) BNitotal 3.5x12 +=Non-stoichiometric Ni2Mn1+xGa1-x(Ni 0.3 B per unit cell) Weak magnetic anisotropy

• Compare Superelasticity andShape-memory Effect

With Magnetic superelasticity and magnetic shape memory effect.

H

H

• Magnetically Induced MartensiteThe magnetic field favors the ferromagnetic phase.

J is the magnetization polarization difference between martensite and austenite.

Materials with high J are required.

Materials must have a narrow temperature regime.

High magnetic fields are required for the transformation.

Clausius Clapeyron:

• Magnetically Induced AusteniteInverse transformation.The magnetic field favors the austenite because its ferromagnetism is stronger than that of martensite.Large and negative J.

• Magnetically Induced Reorientation (MIR)There is no phase transition. Twinned martensite of many variants transforms into one variant martensite due to the magnetic field.Only twin boundary movement.

The material must have a high magnetocrystalline anisotropy and easily movable twin boundaries.

• In practice:

The material is biased to a single-variant state by either (a) applying a stress or by applying a static magnetic field.

B is applied along the hard axis (orthogonal to the biasing direction).

The magnetization vector rotates until the SME takes place. It requires B>0.2 or 0.3T.

Twin boundaries will travel in the opposite direction when the direction of B is reversed == reversible process.

• Strength of the MSM devices:

Solenoid: Faster response. Better proportional position control

Servomotor: faster stroke. Simplier; Less moving parts

Piezoactuators: Larger stroke; lower operating voltage

• SonarTransducers

Veryhighpowertransducersatfrequenciesof1kHzandlower.OfinteresttoNavyforlongrangetransmission,towedarrays,andcommunications.

HydraulicValves

Highspeedvalves,operatingatfrequenciesof1kHz,displace3mmat300Hz.

Cangeneratepressurechangesof100psiat2,000psioperatingpressures.

HelicopterRotors

Potentialapplicationinactivecontrolofvibrationintrailingedgeflapsbymodifyingtheirshape.

InchwormMotors

Motorscangenerate12Nmoftorquedirectlyoffitsshaftat0.5rpm.Applicationsinlowfrequencyacoustictransducers,pumps,andmechanicalsystems.

• Applications:Magnetostrictive Torque SensorA magnetostrictive material coating is rigidly attached to the shaft. An easy axis of magnetization is created in the tangential direction by mechanical stresses. The coating is then magnetized by passing a pulsed current through the shaft. Transducer operation is based on the reorientation of the circumferentially directed remanent magnetization in the coating.

The remanent magnetization, the amount of magnetization that remains in a material after an externally applied field has been removed, is initially oriented in the tangential direction, and the magnetic field created by the shaft is zero. When torque is applied to the shaft, the remanent magnetization reorients and becomes increasingly helical as the torque value increases. This reorientation produces a magnetic field, proportional to the torque, to be detected by a nearby magnetic-field sensing device. The output signal from this device is conditioned in associated electronic circuitry to provide a signal that can be used in a control unit. The drawback is that the generated magnetic fields are weak and the orientation of the magnetization in the coating can be affected by an external axial magnetic field-Earth's, for instance.

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