Magnetic Materials 2

8/8/2019 Magnetic Materials 2

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Magnetic

Materials16th and the LAST !!


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Basic Magnetic Quantities

Magnetic Induction or

Magnetic Flux Density B

BvF v! q

Units: N C-1 m-1 s = Tesla (T) = Wb m-2


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2006: UNESCO Nikola Tesla Year

150th birth Anniversary of Nikola Tesla

AC vs. DC


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Amperes law in free space

id 0. Q! lBi

B

Q0= permeability of freespace

= 4 T 10-7 T m A-1

= 4 T 10-7 H m-1


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Magnetic dipole moment m

i

Area=A

m=iA

Units: A m2


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V

m

M !

Magnetization M of a solid

A solid may have internal magnetic dipolemoments due to electrons

Magnetic dipole moment per unit volumeof a solid is called magnetization

Units: A m2

/m3

= A m-1


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Amperes law in a solid

id 0. Q{ lB

i

B0

! lMlB did .. 00 QQ

id !

l

MB

.0

0

Q

Q

MHB 00 QQ |

id !

lH.

H: magnetic field intensity Units: A m-1


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In free space

HB 0Q!

Inside a solid

MHB 00 QQ !

HB Q!

16.1

16.3

16.2

Q = permeability of solid, H m-1

relative permeability of solid,

dimensionless0Q

QQ !

r


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HM G!

G: magnetic susceptibility of the solid

GType of magnetic solid

dimensionless

diamagnetic -10-5

superconductor -1paramagnetic +10-3

ferromagnetic

(universal)

+103

-105

16.4


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Origin of permanent magnetic moments in

solids:

1. orbital magnetic moment of electrons

2. spin magnetic moment of electrons3. spin magnetic moment of nucleus

We will consider only spin magneticmoment of electrons


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Bohrmagneton QB

The magnetic moment due to spinof a single electron is called theBohr magneton QB

QB= 9.273 x 10-24A m2

Net moment of two electrons ofopposite spins = 0


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Unpaired electrons give rise to

paramagnetism in alkali metals

Na 3s1

Net magnetic moment

1 QB

Fe 3d64s2 4 QB

atom crystal

2.2 QB

Co 3d74s2 3 QB 1.7 QB

Ni 3d84s2 2 QB 0.6 QB


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Example 16.1

The saturation magnetization of bcc Fe is1750 kA m-1. Determine the magneticmoment per Fe atom in the crystal.

a=2.87 V = a3 = 2.873x10-30

Magnetic moment per atom

= 1750x1000x2.873x10-30

= 2.068x10-23A m2

= 2.2 QB


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Ferromagnetic, ferrimagnetic and

antiferromagneticmaterials

Due to quantum mechanical interactionthe magnetic moment of neighbouringatoms are aligned parallel orantiparallel to each other.

ferromagnetic Anti-ferromagnetic

Ferri-magnetic


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ferromagnetic Fe, Co, Ni, Gd

Element

orbitald

atom

d

d

3

Ti Cr Mn Fe Co Ni

1.12 1.18 1.47 1.63 1.82 1.98

Eexchange interaction= Eunmagnetized-Emagnetized

1.5-2.0

Heusler Alloys: Cu2MnSn, Cu2MnAl

Ferromagnetic alloys made of non-ferromagneticelements


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Thermal energy can randomize the spin

Ferromagnetic ParamagneticTcurieheat

Fe 1043 K Co 1400 K Ni 631 K

Gd 298 K Cu2MnAl 710 K


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Ferrimagnetic materials

24

3

2

2OFeMFerrites

M2+: Fe2+, Zn2+, Ni2+, Mg2+, Co2+, Ba2+, Mn2+,

Crystal structure: Inverse spinel

See last paragraph (small print) ofSection 5.4


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Crystal structure: Inverse spinel

2

4

3

2

2OFeFerrites

O2+ FCC packing

4 O2+

8 THV

4 OHV

Antiferromagnetic

coupling

Fe3+

Fe3+ M2+

Net moment due to M2+

ions only.


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If Fe is ferromagnetic with atomicmagnetic moments perfectly aligned

due to positive exchange interactionthen why do we have Fe which is not amagnet?

Answer byPierre Ernest Weiss (1907)

Existence of domains knownas Weiss domains


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Domain walls are regions of high energy(0.002 Jm-2) due to moment misalignment.Then why do the exist?

Ans: Fig. 16.3


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Randomly aligned domains

1. decrease the manetostaticenergy in the field outside themagnet

2. increase the domain wall energyinside the magnet

A magnet will attain a domain structurewhich minimizes the overall energy


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MHB 00 QQ !

16.3

B never saturates

M saturates

The value of B at

the saturation of Mis called thesaturationinduction (~ 1 T)


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Two ways foraligning ofmagneticdomains:

1.Growth offavorably orienteddomains (initially)

2.Rotation ofdomains (finally)

Initial

permeability

Saturation induction


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The hysteresis

Loop

Fig. 16.4

Br residual

induction

Hc coercivefield

Area =hysteresis loss


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Soft magnetic materials

High initial permeability

Low hysteresis loss

Low eddy current losses

For application requiring highfrequency reversal of directionof magnetization

Eg. Tape head

Problem 6.11


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Easily moving domain walls

Low impurity,low non magnetic inclusions,

low dislocation densitylow second phase precipitate

Soft magnetic materials

For low hysteresis loss ( w frequency)

For low eddy current loss ( w frequency2)

Material: high resistivity

Design: Lamination

Choose: Pure, single phase, well-annealed materialof high resistivity


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Table 16.1


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Magnetic anisotropy

Fig. 16.5

easy direction

hard direction

Iron single crystal

Polycrystal: attempt to align easy direction in all grains

Preferred orientation or texture

By rolling and recrystallization

By solidification

By sintering ferrite powder in magnetic field


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Fe-4% Si alloy for low frequency transformers

Wt% Si Wt% Si

resistivity

BsTDBTT

Si enhancesresistivity: low eddycurrent losses

More than 4 wt% Siwill make it too brittle


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T

Stableliquid

log t

Tm

glass

Metallic Glass Fe + 15-25%(Si, B, C)

High solute

High resistivity

Low eddy currentloss

Amorphous Isotropic No hard direction

Amorphous No grain boundary

Easy domain wall movement

Low eddy current loss


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50 Hz Fe-4wt% Si

K Hz Permalloy, SupermalloyMHz Ferrites


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Hard magnetic materials

For permanent magnetsMotors, headphones

High Br, high Hc

Br Hc = energy product

Martensitic high carbon steels (BrHc=3.58 kJm3)Alnico alloys: directionally solidified and annealed in amagnetic field (BrHc=5.85 kJm3)

Mechanically hard c Magnetically hard

Large M phase as elongated particle in low M matrix


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Elongated Single Domain (ESD) magnets

Long particles, thickness < domain wall thickness

Each particle a single domain

No domain growth possible only rotation

Ferrite: BaO 6 Fe2O3 (Br Hc=48-144 kJm3)

Co-Rare Earths (Sm, Pr) (Br Hc=200 kJm3)

Nd2 Fe14 B (Br Hc=400 kJm3)


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For true understanding comprehension

of detail is imperative. Since such

detail is well nigh infinite

our knowledge is alwayssuperficial and

imperfect.

Duc Franccois de la Rochefoucald(1613-1680)

Magnetic Materials 2

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