Magnetic Materials

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Magnetic Materials
16th and the LAST !!
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Basic Magnetic Quantities
Magnetic Induction or Magnetic Flux Density B
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
i
?0 permeability of free space 4 ? 10-7 T
m A-1 4 ? 10-7 H m-1
B
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Magnetic dipole moment m
miA
Units A m2
AreaA
i
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Magnetization M of a solid
A solid may have internal magnetic dipole moments
due to electrons
Magnetic dipole moment per unit volume of a solid
is called magnetization
Units A m2/m3 A m-1
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Amperes law in a solid
i
B0
H magnetic field intensity
Units A m-1
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In free space
16.1
Inside a solid
16.3
16.2
? permeability of solid, H m-1
relative permeability of solid, dimensionless
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16.4
? magnetic susceptibility of the solid
dimensionless
?
Type of magnetic solid
diamagnetic
-10-5
(universal)
superconductor
-1
paramagnetic
10-3
ferromagnetic
103-105
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Origin of permanent magnetic moments in
solids 1. orbital magnetic moment of
electrons 2. spin magnetic moment of
electrons 3. spin magnetic moment of nucleus
We will consider only spin magnetic moment of
electrons
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Bohr magneton ?B
The magnetic moment due to spin of a single
electron is called the Bohr magneton ?B
?B 9.273 x 10-24 A m2
Net moment of two electrons of opposite spins 0
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Unpaired electrons give rise to paramagnetism in
alkali metals
Net magnetic moment
atom
crystal
Na 3s1
1 ?B
4 ?B
2.2 ?B
Fe 3d64s2
3 ?B
1.7 ?B
Co 3d74s2
Ni 3d84s2
0.6 ?B
2 ?B
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Example 16.1 The saturation magnetization of bcc
Fe is 1750 kA m-1. Determine the magnetic moment
per Fe atom in the crystal.
a2.87 Å
V a3 2.873x10-30
Magnetic moment per atom
1750x1000x2.873x10-30 2.068x10-23 A m2 2.2
?B
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Ferromagnetic, ferrimagnetic and
antiferromagnetic materials
Due to quantum mechanical interaction the
magnetic moment of neighbouring atoms are aligned
parallel or antiparallel to each other.
ferromagnetic
Anti-ferromagnetic
Ferri-magnetic
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Fe, Co, Ni, Gd
ferromagnetic
Eexchange interaction Eunmagnetized-Emagnetized
Element
Ti Cr Mn Fe Co Ni
1.12 1.18 1.47 1.63 1.82 1.98
1.5-2.0
Heusler Alloys Cu2MnSn, Cu2MnAl Ferromagnetic
alloys made of non-ferromagnetic elements
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Thermal energy can randomize the spin
Tcurie
Ferromagnetic
Paramagnetic
heat
Fe 1043 K Co 1400 K Ni 631 K Gd 298
K Cu2MnAl 710 K
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Ferrimagnetic materials
Ferrites
M2 Fe2, Zn2, Ni2, Mg2, Co2, Ba2, Mn2,
Crystal structure Inverse spinel
See last paragraph (small print) of Section 5.4
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Ferrites
Crystal structure Inverse spinel
O2 FCC packing
8 THV
Fe3
4 O2
Antiferromagnetic coupling
4 OHV
M2
Fe3
Net moment due to M2 ions only.
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If Fe is ferromagnetic with atomic magnetic
moments perfectly aligned due to positive
exchange interaction then why do we have Fe which
is not a magnet?
Answer by Pierre Ernest Weiss (1907)
Existence of domains known as 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
manetostatic energy in the field outside the
magnet 2. increase the domain wall energy
inside the magnet
A magnet will attain a domain structure which
minimizes the overall energy
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16.3
B never saturates M saturates The value of B at
the saturation of M is called the saturation
induction ( 1 T)
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Saturation induction

• Two ways for aligning of magnetic domains
• Growth of favorably oriented domains (initially)
• Rotation of domains (finally)

Initial permeability
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The hysteresis Loop
Br residual induction
Hc coercive field
Area hysteresis loss
Fig. 16.4
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Soft magnetic materials
For application requiring high frequency reversal
of direction of magnetization Eg. Tape head
High initial permeability Low hysteresis
loss Low eddy current losses
Problem 6.11
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Soft magnetic materials
For low hysteresis loss ( ? frequency)
Easily moving domain walls
Low impurity, low non magnetic inclusions, low
dislocation densitylow second phase precipitate
For low eddy current loss ( ? frequency2)
Material high resistivity Design Lamination
Choose Pure, single phase, well-annealed
material of high resistivity
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Table 16.1
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Magnetic anisotropy Fig. 16.5
Iron single crystal
lt100gt easy direction lt111gt hard direction
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
Si enhances resistivity low eddy current losses
resistivity
More than 4 wt Si will make it too brittle
TDBTT
Bs
Wt Si
Wt Si
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Metallic Glass Fe 15-25(Si, B, C)
T
Stable liquid
Tm
High solute
L?
High resistivity
glass
Low eddy current loss
log t
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,
Supermalloy MHz Ferrites
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Hard magnetic materials
For permanent magnets
Motors, headphones
High Br, high Hc
Br Hc energy product
Mechanically hard
Magnetically hard
c
Martensitic high carbon steels (Br Hc3.58 kJm3)
Alnico alloys directionally solidified and
annealed in a magnetic field (Br Hc5.85 kJm3)
Large M phase as elongated particle in low M
matrix
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Elongated Single Domain (ESD) magnets
Long particles, thickness lt domain wall thickness
Each particle a single domain
No domain growth possible only rotation
Ferrite BaO 6 Fe2O3 (Br Hc48-144 kJm3)
Co-Rare Earths (Sm, Pr) (Br Hc200 kJm3)
Nd2 Fe14 B (Br Hc400 kJm3)
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For true understanding comprehension of detail
is imperative. Since such detail is well nigh
infinite our knowledge is always superficial
and imperfect. Duc Franccois de la
Rochefoucald(1613-1680)