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Energmaterials.co.uk Magnetism and Magnetostriction

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2.0) Origin of magnetism

The intrinsic principle behind magnetism is that any moving charge produces both a

magnetic field and changes its motion in response to an external magnetic field.

Examples include electrons in a television tube or current flowing in a wire. Electrons

within atoms also possess a property known as spin; quantum mechanics has shown

that spin can behave in two ways, either spin up or spin down. When there is a net

spin imbalance of spins up and spins down within an atom a magnetic dipole exists.

Magnetic dipoles give rise to a magnetic exchange energy, which is a measure of

retained magnetic moment; at room temperature the magnetic exchange energy is

high in elements such as Fe, Co and Ni.

2.1) Magnetism and magnetic units

The scientific study of magnetism dates from ~1600 with William Gilbert (1544-

1603), and over the years several systems of units have been used. The CGS

(centimeters-grams-seconds) system was introduced formally by the British

Association for the Advancement of Science in 1874 and the later SI (Système

International d'Unités) system was introduced in 1960 by the International Office of

Weights and Measures.

The commonly used SI unit of magnetism is the Tesla, which is named in honour of

the Serbian-American inventor Nikola Tesla. It is defined as:

HB 0 (Equ 2.1)

where magnetic induction (B) is measured in Tesla or Webers per square meter, µ0 is

the permeability of free space ( 7104 Hm-1(in vacuum)) and H the applied field (Am-

1).

The Weber is defined as the amount of magnetic flux, if removed or introduced

steadily into a region bound by a conductor in 1 second, will induce an emf of 1 volt

in the conductor during the activity, which can be expressed as:

Weber [Vs]= Tesla [NA-1m-1] x area [m2] = ampéres [A] x Henrys [VsA-1]

The definition of a Henry is the inductance which will deliver 1 volt of back emf

when the current in it changes at a rate of 1 ampére per second, thus:


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dt

dILemf (Equ 2.2)

Where L represents the inductance and dI and dt are the change in current and time

respectively. The inducted emf obeys Lenz’s law; when a current is increasing, the

induced emf is negative and opposes the supply voltage, i.e. back emf and hence the

negative sign.

The magnetic induction can be intensified many times, depending on what type of

material is present, which can be expressed as:

)(0 MHB (Equ 2.3)

Where M is the magnetic moment of the material present within an applied field (H).

The degree to which a magnetic material affects B depends on the susceptibility of the

material, which is defined as:

HM (Equ 2.4)

Where χ is the susceptibility of the material, which is a dimensionless constant, thus

Equ 1.3 becomes:

HB )1(0 (Equ 2.5)

The magnetic permeability of a material, is defined as:

H

B (Equ 2.6)

Where µ is the permeability, which can also be written as )1( , thus equ 2.5

can be simplified to:

HB 0 (Equ 2.7)

[1-2] For ease of comparison with previous work, the relationship between commonly used

magnetic units in C.G.S and SI are shown in table 2.1.


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Quantity C.G.S units

S.I. Units Conversion factor (C.G.S to S.I)

Magnetic Field (H) Oe Am-1 103/4π Flux Density (B) G T 10-4

Magnetization (M) G or Oe Am-1 103 Energy product

(BH)max MGOe kJm-3 102/4π

Table 2.1, Relationship between C.G.S and S.I units

2.2 Magnetism within materials

All elements and materials show some form of magnetic behaviour, as shown in the

periodic table in figure 2.1. This behaviour can be categorized as either:

Diamagnetism, Paramagnetism, Ferromagnetism, Antiferromagnetism or

Ferrimagnetism depending on the interaction of the material with an applied field.

These states are explored below and summarised in figure 2.2

Figure 2.1, magnetic classification of elements within the periodic table

2.2.1 Diamagnetism

Diamagnetism is a weak non-permanent form of magnetism. Under the effect of an

applied magnetic field, a torque is created on the atomic magnetic dipole causing it to

rotate about the field direction, creating a magnetic field in the opposite direction,

opposing the applied field. Such a material is said to exhibit a negative susceptibility

or relative permeability. Superconductors are considered to be perfect diamagnets

with a susceptibility of –1, while Bismuth is the most diamagnetic element with a

susceptibility at room temperature of –170x10-6.


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2.2.2 Paramagnetism

As noted above, applying a field can cause atomic moments to rotate. In paramagnets,

these atomic moments line up with the externally applied field direction. The net

magnetization of the material depends linearly on the applied field and is temperature

dependent. Usually paramagnetism decreases with increasing temperature (possibly

due to thermal agitation). As is described by the Curie-Weiss law ()( cTT

C

)

where C is the Curie constant for the material and T is temperature and Tc is constant

with the same units as temperature, which can be positive or negative, and marks the

state between the paramagnetic and ferromagnetic state. When Tc is set to 0 the

behaviour is described as the Curie law.

2.2.3 Ferromagnetism

Ferromagnetic materials exhibit a parallel alignment of atomic moments whereby the

material is spontaneously magnetized without the need for an external field. This

parallel arrangement can be disturbed by thermal agitation, with the spontaneous

magnetism decreasing with increasing temperature. The temperature at which the

spontaneous magnetisation is reduced to zero is known as the Curie temperature TC.

Above this point ferromagnetic materials loose their ferromagnetism and behave like

paramagnetic materials. The only elements which are ferromagnetic at room

temperature are Fe, Co and Ni, while other examples of common ferromagnetic

materials include permanent magnets based on NdFeB or Alnico.

2.2.4 Antiferromagnetism

Antiferromagnetic materials exhibit a positive susceptibility and a temperature

dependence of susceptibility that is characterized by a kink in the curve at the Néel

temperature. Below the Néel temperature the atomic moments are arranged in an

antiparallel arrangement whereby the atomic moments cancel each other out resulting

in zero net moment. Above the Néel temperature the arrangement of moments is

random due to thermal agitation and the material shows paramagnetic behaviour.

Examples of antiferromagnetic materials include chromium, manganese and iron

manganese (FeMn).


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2.2.5 Ferrimagnetism

Ferrimagnetism is a form of magnetism which involve complex ordering of moments

within the crystal structure. An example of a ferromagnetic material is BaO.6Fe2O3

where the unit cell contains 64 atoms or ions with 16 Fe3+ ions orientated parallel to

an applied field and 8 Fe3+ ions orientated antiparallel to the applied field, giving a net

magnetic moment parallel to the applied field (there is no magnetic contribution from

the barium or oxygen atoms). Therefore there exists an unequal balance in atomic

moments resulting in spontaneous magnetism.

Type of Magnetism Susceptibility Atomic / Magnetic Behaviour Example /

Susceptibility

Diamagnetism Small & negative.

Atoms have no magnetic moment

Au Cu

-2.74x10-6

-0.77x10-6

Paramagnetism Small & positive.

Atoms have randomly oriented magnetic moments

β-Sn Pt Mn

0.19x10-6

21.04x10

-6

66.10x10-6

Ferromagnetism

Large & positive, function of applied field, microstructure dependent.

Atoms have parallel aligned magnetic moments

Fe ~100,000

Antiferromagnetism Small & positive.

Atoms have mixed parallel and anti-parallel aligned magnetic moments

Cr 3.6x10-6

Ferrimagnetism

Large & positive, function of applied field, microstructure dependent

Atoms have anti-parallel aligned magnetic moments

Ba ferrite ~3


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Figure 2.2 Summary of different types of magnetic behaviour.

2.3 Magnetic Anisotropy

Magnetic anisotropy refers to the ease of which a material can be magnetised in any

given direction. The three main mechanisms that contribute to magnetic anisotropy

include: crystal, shape and stress anisotropy. Other anisotropy mechanisms can

include, magnetic annealing, plastic deformation and/ or irradiation.

Crystal anisotropy (or magnetocrystalline anisotropy) is an intrinsic material property

and depends on the composition and on the crystallographic structure. The energy

required in a cubic crystal to rotate the magnetic vector away from an easy direction is

expressed by:

...)()( 23

22

212

21

23

23

22

22

2110 KKKE

Where E is the energy stored in crystal when the magnetic moment points in a non

easy direction, K0 is an anisotropy constant (measured in Jm-3) independent of angle,

K1+ is dependent on the direction of the magnetic moment with respect to α1, α2, α3,

which are the cosines of the moment angles with respect to the crystal axes. Therefore

the higher the anisotropy constants the more difficult it is to rotate a magnetic moment

away from an easy direction. Examples of crystal anisotropy are shown in figure 2.3

as magnetization curves for single crystals of cobalt and iron. The magnetization of

hexagonal cobalt shows the easy axis to be along the <0001> (c-axis) and for cubic

iron along the <100> direction, which is why efficient transformers are made from

laminated iron which is grain orientated with the <100> direction parallel to the field

direction for ease of magnetization.

CobaltJ (T)

H (kA/m)

<1010>

<0001>

IronJ (T)

H (kA/m)

<100>

<110>

<111>

Figure 2.3, magnetisation curves along different crystal axis for cobalt and iron


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Shape anisotropy arises from internal demagnetizing fields within a material when

there is no suitable flux return path. Sample geometry can play an important roll, as in

the case of fine needle like structures with high aspect ratios within heat treated alnico

magnets.

The amount of internal field generated in a material from an external field can depend

on the demagnetizing factor, which is strongly related to shape anisotropy and given

by the following equation:

H int = H app - Nd M

Where H int represents the internal magnetic field, Happ is the applied magnetic field,

M is the magnetization and Nd is the demagnetizing factor (Nd = one third for spheres

and zero for a toroid, in essence this means a toroid can be more easily magnetized by

an externally applied field).

Stress anisotropy is discussed later alongside the effects of stress on magnetostriction.

2.4 Magnetic domains

Although Ferromagnetic materials are spontaneously magnetized due to exchange

interactions, it is possible to find these materials in a demagnetised state. Weiss

postulated in 1910 that this was because the material is divided up into regions called

domains where each domain is a region in which all the magnetic moments are

orientated in the same direction. A ferromagnetic material exhibits zero external

magnetism when these magnetic domains are orientated in a manner such as to cancel

each other out, as shown in figure 2.4. When a material with randomly orientated

domains is subject to an increasing magnetic field, favorably orientated magnetic

domains grow into surrounding domains (depending on the anisotropy), then begin to

rotate towards the direction of the applied field. There exists a domain wall between

each domain that allows space for the magnetic moment to rotate from the direction of

one domain to another and so reduce the overall energy of the system. The width of a

domain wall depends on a combination of the anisotropy and the exchange energy;

magnetic systems with a high exchange energy and anisotropy will have narrow

domain walls compared with systems with a low anisotropy.


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(a) (b) (c) (d)

Figure 2.4 Schematic illustration of the break up of magnetisation into domains and the external field pattern for a (a) single domain, (b) two domains,(c) four domains and (d) closure domains.

It is possible for a closure domain to exist, which is a state where a closed magnetic

circuit exists within the bulk of the magnetic material, which results in little external

magnetic field, thus lowering the overall magnetostatic energy of the system.

2.5 Hysteresis

Ferromagnetic materials can be further categorized as either hard or soft magnetic

materials, depending on how easy they are to magnetise and demagnetise. This

behaviour can be illustrated in the magnetization curves, shown in figure 2.5, which

features a BH loop (with magnetic induction on the vertical axis and applied field on

the horizontal) and a MH loop (with magnetization on the vertical axis and applied

field on the horizontal axis). The key locations on such hysteresis loops are as

follows: intrinsic coercivity (iHc), which is the applied field needed to reduce the

magnetization to zero. Magnetic saturation (Ms), which is the saturation field, that

corresponds to the maximum level of magnetization beyond which no further

magnetisation occurs. Remanence (Br), which is the retained magnetism without an

externally applied field, energy produce (BHmax), which is the maximum product of

the induction and the applied field and represents the amount of material required to

produce a given amount of magnetic energy. Very different properties are sought for

hard and soft magnetic materials; an ideal hard magnetic material will have a very

square loop on its hysteresis curve (particularly in the second quadrant with respect to

demagnetisation) with a high remanence and coercivity, whereas an ideal soft

magnetic material is one with little or no remanence or coercivity, but with a high


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permeability and saturation magnetization. A comparison between some hard and soft

magnetic materials is shown in table 2.2 (Note the difference in units of coercivity).

-22

-17

-12

-7

-2

3

8

13

18

-15 -10 -5 0 5 10 15

Applied field (H)

M vs H -Loop

B vs H -Loop

2nd 1st

3rd 4th

Saturation

magnetisation

(Ms)

Remanent

magnetisation

(Br)

Intrinsic coercivity

(iHc)

Inductive coercivity

(bHc)

Energy product

(BH)max

Figure 2.5, Simplified hysteresis loop showing behaviour in all 4 quadrants

Hard magnetic

materials

Coercivity

(kA/m)

Remanence

(Tesla)

Energy Product

(kJ/m3)

Curie

Temperature (ºC)

Sintered

Nd2Fe14B 955 1.3 320 330

Sintered

samarium cobalt

(Sm2Co17)

1160 1.03 183 800

Alnico 5 45 1.26 37 860

Barium ferrite

(BaO.6Fe2O3) 255 0.390 28 450

Table 2.2, Examples of some hard and soft magnetic materials [3]


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Soft magnetic

materials

Coercivity

(A/m)

Relative

permeability

Saturation flux

(Tesla)

Iron 80 5,000 2.15

Grain orientated

silicon iron

(Fe+3%Si)

8 40,000 2

Permendur

(Fe+50%Co) 160 5,000 2.45

Supermalloy

(Ni+16%Fe+5%Mo) 0.16 1,000,000 0.79

Table 2.2 continued, Examples of some hard and soft magnetic materials [3]

2.6 History of Magnetostriction

James Prescott Joule discovered the phenomenon of magnetostriction in 1842, when

he observed that an iron rod changed shape when placed in a static magnetic field.

Joule used a series of mechanical levers to make his observation of the relatively

small magnetostrictive strain associated with iron. Soon afterwards it was discovered

that all ferromagnetic materials exhibit magnetostriction to some degree, as illustrated

in table 2.3.

Material Magnetostrictive

strain/ ppm

Material Magnetostrictive

strain/ ppm

Fe -14 SmFe2 -2340

Co -93 TbFe2 2630

Ni -50 DyFe2 650

Fe3O4 40 TbFe3 693

Table 2.3, Magnetostriction parallel to the applied field for some ferromagnetic materials carried out at room temperature [4] [5] [6]

From table 2.3 it is apparent that some magnetostrictive materials expand parallel to

an applied field, while others contract. Terfenol, which has the formula TbFe2,

currently demonstrates the largest positive magnetostrictive strain of any known

material at room temperature, whereas Samfenol, with the formula SmFe2, exhibits the

largest negative magnetostrictive strain at room temperature.


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Although magnetostriction was discovered in 1842, it is only comparatively recently

that magnetostrictive materials have found practical applications. Historically, the

first major application was in the use of sonar, which was developed during the

Second World War, where pure nickel was used to produce the low frequency sonar

pulses. Today, magnetostrictive materials are still used for sonar, but rather than using

nickel a new range of giant magnetostrictive materials (GMM) were developed during

the 1960’s, based on Terfenol [5].

2.7 Magneto elastic coupling

Magneto elastic coupling, which is defined as the tendency of neighbouring ions to

shift their positions in response to the rotation of the magnetic moment, is where

magnetostriction originates. Two obvious mechanisms to explain magneto elastic

coupling are explored below, namely Joule and volume magnetostriction:

2.7.1 Joule magnetostriction

Joule magnetostriction is associated with a change in sample length due to the

application of an external magnetic field. This is an anisotropic change as it depends

on the magneto crystalline anisotropy, which determines how the neighboring

moments interact with each other.

A pictorial representation of the Joule effect is shown in figure 2.6. An external

magnetic field causes a magneto elastic coupling effect as the domains rearrange

themselves, according to the field direction, and this results in a change in

dimensions. This dimensional change can be positive or negative, parallel to the

applied field, depending on the material.

Figure 2.6, domain rotation brought about by an externally applied magnetic field [6]


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A typical magnetostrictive strain curve is shown in figure 2.7 for a rod of Terfenol-

based material. From the figure it is clear that positively or negatively applied fields

yield similar strains (this has been referred to as a butterfly curve due to its

symmetry). While an ideal magnetostrictive material would behave like a soft

magnetic material, with a high permeability and low coercivity, in reality most strain

curves exhibit some evidence of hysteresis.

One of the desirable features of a magnetostrictive strain curve is a high gradient of

strain within the direction of the applied field, which is denoted as the

magnetostrictive constant and given the symbol d33, with units of nm/A.

Figure 2.7, Typical magnetostrictive strain-field curve for a zoned rod of a Terfenol- based material [7]

2.7.2) Volume magnetostriction As mentioned previously, temperature affects the internal magnetization in

ferromagnetic materials. For example, cooling a ferromagnetic material below its

Curie point causes a coupling between the magnetic moment and volume, which

results in a small magnetostrictive strain. This effect can be noticed by observing the

thermal expansion of a ferromagnetic material as it is heated through its Curie point,

when the expansion deviates from linear behaviour and a rapid change in volume

occurs due to the change in order of the magnetic moments.

Volume magnetostriction, however, is generally a very small contribution to the

overall magnetostriction, although a series of alloys, known as the Invar alloys, based

on iron-nickel, use volume magnetostriction to control thermal expansion over a range

of temperatures.


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2.7.3) Effects of stress on magnetostriction

The interaction of an applied stress can induce anisotropy into a magnetic system. The

type of stress required to increase the anisotropy field depends on the sign of

magnetostriction, according to Le Chatelier’s principle. If a material has a positive

magnetostrictive constant, it will elongate in the direction of an applied field. Thus a

tensile stresses will help elongate such a magnetostrictive material and reduce the

anisotropy field required to magnetically saturate the material in the direction of the

tensile stress. Similarly, a magnetostrictive material that exhibits a negative strain

with an applied field will have a reduced saturation field in the direction of an

externally applied compressive stress.

2.8 Magnetostrictive units and terminology

The maximum total magnetostrictive strain is obtained from fully rotating a magnetic

domain from a perpendicular to a parallel direction in a magnetic field. This can be

measured by bonding strain gauges at right angles and measuring strain parallel and

perpendicular to the magnetizing direction. The total magnetostrictive strain is then

calculated from the difference in the two directions, thus for isotropic crystals this is

given by:

esssssII 2

3

2

1 [3]

The variation in saturation stain of an isotropic material with angle of applied field

relative to the measuring direction is given by:

)3

1(

2

3)( 2 COSss

Where λs is the saturation magnetostriction along the direction of the magnetization.

Functional materials, for example piezo electrics and magnetostrictive materials

change properties in all directions when one direction is altered, for example stressing

in one axis will affect the permeability in another direction; therefore, it can be

helpful to consider the magnetostrictive components as vectors that can be

represented using a stress tensor with a six-component vector, this is illustrated below.


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333231

232221

131211

TTT

TTT

TTT

Tij

Tensor notation 11 22 33 23/32 31/13 12/21 Vector notation 1 2 3 4 5 6

Commonly referred to magnetostrictive parameters include:

H

ij

Hj

i sT

S

elastic compliances at constant H (field)

T

mk

Tk

m

H

B

Magnetic permeabilities at constant T (temperature)

33

3

3

3

3 ddT

B

H

S

HT

Magnetostrictive constant in the longitudinal mode

The efficiency of transferring magnetic energy into mechanical energy is known as

the magneto-mechanical coupling coefficient, and given the symbol k. Magneto

mechanical coupling is a ratio of the magnetoelastic energy to the geometric mean of

the elastic and magnetic energy, thus:

me

me

UU

Uk

Where Ume corresponds to the mutual magnetoelastic energy, Ue the elastic energy

and Um corresponding to the magnetic energy.


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In the longitudinal case, in which the applied field and stresses act only in the x3

direction, this becomes:

HTs

dk

3333

2

332

33

An ideal magnetostrictive material would have a magneto mechanical coupling

coefficient of unity; however, in practice this is impossible to achieve due to inherent

core and eddy current losses. k33 is often derived from detecting resonance and anti-

resonance frequencies in a magnetostrictive rod and calculated using the equation

shown below (for a cylindrical rod):

22

2

338

1

a

r

F

Fk

Where Fr and Fa are the resonance and anti-resonance frequencies respectively.

The method often used to calculate the magneto mechanical coupling coefficient uses

the three-parameter resonance technique. This technique applies an oscillating field to

produce a magnetically induced mechanical resonance in a magnetostrictive sample,

the resonance being detected either on the drive coil or on a pick up coil wound

around the sample, which monitors a change in the permeability.

To determine how the efficiency of the sample changes with applied bias field, a DC

bias field is often applied by an additional fixed current power supply energizing over

the drive coil or an outer coil.

2.8.1 Energy density

The mechanical work performed by a magnetostrictive material can be expressed as

an energy density. The mechanical strain energy per unit volume or strain energy

density U0 is given by:

EE

U xx

xx2

2

02

1

2

1

2

1

(For linear behaviour)

Where U0 represents the strain energy density, x represents stress in the in the x axis,

x represents strain in the x axis and E represents Young’s modulus

This is equal to the area ( d ) under a magnetostrictive strain curve, assuming that

the pre-stress provides a constant stress; see below (figure 2.8)


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Figure 2.8, calculation of energy density under a 0.5Tesla field for 10 and 20MPa.

Figure 2.8 shows a greater amount of work done with a 20MPa pre-stress compared

with 10MPa. The energy density of a magnetostrictive material allows designers to

calculate the overall displacement and force of an actuator. With mechanical or

hydraulic amplification built into the actuator it is possible to increase the

displacement achieved (for example by incorporating a lever into the actuator),

although this will be achieved at the expense of available force output from the

actuator.

2.9 REFe2 compounds

The discovery and early development of magnetostriction in REFe2 compounds

occurred during the 1960’s with TbFe2 and SmFe2. It was found that the exchange

energy of elemental terbium and samarium could be largely maintained at room

temperature by forming an intermetallic with iron, since the rare earth-iron exchange

is large, helping to keep the rare earth sublattice magnetization nearly intact at room

temperature. REFe2 compounds form in a cubic laves C15 phase structure (or

commonly referred to as the MgCu2 structure), that is shown in figure 2.9 and possess

the largest magnetic anisotropies of any known cubic crystal; for example, k1(10-3Jm-

3) for TbFe2 and SmFe2 is -7600 and 2100 respectively compared with 45 and –5 for

iron and nickel [8] [9].


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Figure 2.9, C15 laves phase, with the green spheres representing a rare earth atom (Tb or Dy) and the

red spheres represent iron atoms.

The sign and amount of magnetostriction depends on the interaction of the 4f-electron

charge distribution. For samarium the 4f-electron charge distribution is prolate in

form and for terbium the distribution is oblate. When the 4f-electron charge

distribution is prolate, the charge distribution elongates along the moment direction

and when oblate the charge distribution expands perpendicular to the moment

direction [10].

2.9.1) Magnetostriction in Terfenol

A single crystal of Terfenol currently holds the record for room temperature

magnetostriction. However, Terfenol has a high magneto crystalline anisotropy

energy (>106Jm-3) and a high anisotropy field (>100kOe), which results in a well-

defined easy axis along the [111] direction. This means that when the domains are

rotated through 180° they must travel through a hard axis. In the case of a

magnetostrictive vibrating actuator however, it is preferable to have easy rotation of

domains from one direction to another in order to reduce the amount of magnetic

energy supplied, and hence increase the efficiency of converting magnetic energy into

mechanical energy. Therefore although pure TbFe2 is suitable for thin film actuators,

it is rarely used for bulk actuators.

1.9.2) Magnetostriction in the case of Terfenol-D


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The high magneto crystalline anisotropy of Terfenol has led to the development of

materials in which some of the terbium in Terfenol is substituted by dysprosium or

holmium, or put another way, TbFe2 is mixed with DyFe2 or HoFe2. These materials

are known as Terfenol-D & Terfenol-H; the name, “Terfenol-D” originates from the

development of the material, Ter –from terbium, fe- from iron, nol- from navel

ordnance laboratory and D- from dysprosium [11]

Such substitutions do not affect the C15 structure but have the effect of reducing the

anisotropy energy and increasing the magneto mechanical coupling coefficient.

Ideally, the substitution will be with a compound with the same crystal structure, with

different signs of anisotropy and the same sign of magnetostrictive strain to maximize

the magnetostriction and minimize the anisotropy. DyFe2 and HoFe2, which have easy

directions lying in the [100] direction allowing easier rotation of domains from <111>

to <100> [3]. However, this is achieved at the expense of magnetostrictive strain as

DyFe2 and HoFe2 exhibit less magnetostrictive strain, as shown in figure 2.9.

Figure 2.9, Effect of substituting terbium with dysprosium in the ReFe2 compound with measurements

performed at room temperature. [3]

Figure 2.9 shows that dysprosium substitution has a more profound effect on

minimizing anisotropy energy than holmium, with k33 reaching a maximum with a 73

atomic percent substitution for terbium. While the anisotropy energy may be

minimized for Terfenol-D at room temperature, heating or cooling above or below

room temperature will cause a change in the anisotropy energy, and hence a spin

reorientation. This spin reorientation occurs as TbFe2 and DyFe2 possess different


21

anisotropy values, both in sign and magnitude; therefore TbFe2 and DyFe2 compounds

respond differently to a change in temperature.

The spin reorientation with temperature has been measured experimentally using X-

ray diffraction to detect the splitting of an XRD, as shown in figure 2.10

Figure 2.10, Temperature dependence of Spin reorientation (Atmony et al (1973))

From figure 2.10 it is possible to see that a 73 at% substitution for terbium with

dysprosium has no defined easy axis at room temperature, i.e. 298K. However,

heating above room temperature the [111] axis dominates and below room

temperature the [100] axis dominates as the easy direction of magnetization. This may

give the opportunity to magnetically align powdered Terfenol-D along the <111>

direction with a composition based on Tb.27Dy.27Fex, (which minimises anisotropy at

room temperature) by heating above room temperature.

It is known that an applied compressive stress can improve magnetostrictive

performance in Terfenol-D, in that it can enhance magnetostrictive strain, both

saturation and the proportion of the linear magnetostrictive strain curve with field.

Since Terfenol-D exhibits positive magnetostriction, applying a compressive load

does increase the required field for saturation; but the dramatic improvement in

magnetostrictive properties can far out weigh the small additions in field required for

saturation. This is shown in figures 2.11-2.12 which show the dramatic effect of

applying a compressive stress on Terfenol-D and the resulting increase in the

proportion of usable magnetostriction obtained.

The optimum value of compressive stress required for magnetostrictive enhancement

of Terfenol-D has been found to be ~7MPa [12].


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Figure 2.11, showing domain behavior with no applied field and (a) no applied force (b) with an applied compressive stress and (c-d) domain behavior in an applied magnetic field.

The effect of domain behaviour, applied stress and strain can be appreciated by

investigating the magnetoelastic modulus for Terfenol-D when measured in

magnetically blocked conditions, i.e. constant B can result in a modulus of 20-50 GPa

whereas with magnetically free conditions, i.e. constant field, the modulus ranges 3-5

GPa [b3]. Magnetostrictive dampers are being developed to take advantage of this

large ΔE effect to potentially provide systems with an intelligent electronic feed back

control system to control oscillations [13].

Figure 2.12, effect of compressive loading on strain performance. [12]

2.9.3 Samfenol

Samfenol is the name given to the SmFe2 intermetallic compound that exhibits the

greatest negative magnetostriction at room temperature parallel to an applied

magnetic field. The phase diagram for Sm-Fe is broadly similar to the Tb-Fe system,

although, the peritectic reaction occurs at a lower temperature. Solidification of the


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SmFe2 phase proceeds by the following reaction, with the phase diagram shown in

figure 2.13

Fe + Liquid → Sm2Fe17 + Liquid (~1280ºC) Sm2Fe17 + Liquid → SmFe3 + Liquid (~1010ºC)

Sm2Fe2 + Sm2Fe3 → SmFe2 (~900ºC)

Not surprisingly, given the phase diagram, single phase SmFe2 has been shown to be

difficult to prepare when compared to TbFe2 and the peritectic reaction often does not

go to completion. Consequently there is often found to be a lot of entrapped SmFe3

phase within the microstructure, this phase being detrimental to magnetostriction due

to its low magnetostrictive strains.

The SmFe2 phase possesses a high degree of anisotropy at room temperature, and as

with TbFe2, the anisotropy is decreased at room temperature by partially substituting

samarium with dysprosium or holmium, which have different signs of anisotropy

when compared to that of SmFe2. X-ray spin reorientation measurements show the

compounds Sm1-xDyxFe2 and Sm1-xHoxFe2 are compensated around room temperature

with x values of 0.15 and 0.3 respectively. The magnetostriction is anisotropic within

both of these compounds with maximum magnetostrictive strain occurring along the

[111] direction, i.e. λ111>> λ100.

Figure 2.13, Iron- samarium binary phase diagram [14]


24

Previous work has shown it necessary to anneal as-melted samples to produce a

single phase microstructure; however, the high vapour pressure of samarium can

cause problems, often leaving voids where samarium has volatilised. Indeed the high

vapour pressure of samarium (4mbar at its melting point) hinders preparation of

samarium compounds through conventional routes.

Samfenol-D is crystallographicaly identical to Terfenol-D, i.e. same C15 laves phase

(MgCu2); however, it is a negative magnetostrictive material and contracts parallel to

an applied magnetic field. Spin compensation is again obtained by substituting with

dysprosium. The optimum composition being Sm0.86Dy0.14Fe2 for low anisotropy and

good magnetostrictive performance at room temperature.

References [1] P. Beckley, Electrical steels for rotating machines, The institution of electrical engineers, 2002, 14 [2] J.P. Jakabovics, Magnetism and magnetic materials, The institute of materials, 1994 [3] D. Jiles, Introduction to magnetism and magnetic materials, Chapman and Hall, 1991. pg 99- [4] Etienne du Tremolet, “Magnetostriction Theory and applications of magnetoelasticity”, CRC press inc, 1993 [5] A.E.Clark, Ferromagnetic materials, vol1, North-Holland publishing Co, 1980, 533-587 [6] Goran Engdahl, “Handbook of giant magnetostrictive materials” ,Academic press, 2000, 52-121 [7] Etrema Products, inc, 2500 North Loop Dr, Ames, USA, www.etrema-usa.com [8] A Clark, Applied physics letters, 11, 642 (1973) [9] U. Hoffman, Z. Angew, Phys, 22, 106 (1967) [10] K.H.J.Buschow, N.H.Luong and J.J.M.Franse, Handbook of magnetic properties, volume 8, Elsevier, 1995, Pg 442. [11] Butler, John L, 1988, “Application manual for the design of Etrema Terfenol-D magnetostrictive transducers”, Image Acoustics Inc, N.Marshfield, MA 02059 [12] R. Kellogg, A. Flatau, “Blocked-force characteristics of Terfenol-D transducers”, Journal of intelligent material systems and structures, 15 (2), 117-128 (2004) [13] W. Qian, G. R. Liu, L. Chun, Y. K. Lam, “Active vibration control of composite laminated cylindrical shells via surface-bonded magnetostrictive layers”, Smart material & structures, 12, (6), 889-897 (2003) [14] Thaddeus Massalski, “Binary alloy phase diagrams”, ASM international, 1990, 1519 & 1779


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[15] V. Neu, S. Melcher, U. Hannenman, S. Fahler, and L. Schultz, “Growth, microstructure and magnetic properties of highly textured and highly coercive Nd-Fe-B films”, Physical review B,70, 1444418 (2004) [16] A.E. Clark, J.B. Restorff and M.Wun-Fogle, Magnetoelastic coupling and ΔE effect in TbxDy1-x single crystals, J. Appl. Phys, 73 (1993), 6150

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