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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)