Magnetic Materials
Basic Magnetic Quantities
Magnetic Induction or
Magnetic Flux Density B
BvF q
Units: N C-1 m-1 s = Tesla (T) = Wb m-2
2006: UNESCO Nikola Tesla Year
150th birth Anniversary of Nikola Tesla
AC vs. DC
Ampere’s law in free space
id 0. lB
i
B
0= permeability of free space
= 4 10-7 T m A-1
= 4 10-7 H m-1
Magnetic dipole moment m
i
Area=A
m=iA
Units: A m2
V
mM
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
Ampere’s law in a solid
id 0. lB
i
B0
lMlB did .. 00
id
l
MB.
0
0
MHB 00
id lH.
H: magnetic field intensity or field strength Units: A m-1
In free space
HB 0
Inside a solid
MHB 00
HB
16.1
16.3
16.2
= permeability of solid, H m-1
relative permeability of solid, dimensionless 0
r
HM : magnetic susceptibility of the solid
Types of magnetic solid
Dimensionless
diamagnetic -10-5
superconductor -1
paramagnetic +10-3
ferromagnetic
(universal)
+103-105
16.4
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
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
Unpaired electrons give rise to paramagnetism in alkali metals
Na 3s1
Net magnetic moment
1 B
Fe 3d64s2 4 B
atom crystal
2.2 B
Co 3d74s2 3 B 1.7 B
Ni 3d84s2 2 B 0.6 B
Example 16.1
The saturation magnetization of bcc Fe is 1750 kA m-1. Determine the magnetic moment per Fe atom in the crystal.
a=2.87 Å V = a3 = 2.873x10-30
Magnetic moment per atom
=1750 x 1000 x 2.873 x 10-30 x 1/2
=2.068x10-23 A m2
=2.2 B
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
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-ferromagnetic elements
Thermal energy can randomize the spin
Ferromagnetic ParamagneticTcurie
heat
Fe 1043 K Co 1400 K Ni 631 K
Gd 298 K Cu2MnAl 710 K
Ferrimagnetic materials
24
32
2 OFeMFerrites
M2+: Fe2+, Zn2+, Ni2+, Mg2+, Co2+, Ba2+, Mn2+,
Crystal structure: Inverse spinel
See last paragraph (small print) of Section 5.4
Crystal structure: Inverse spinel
24
32
2 OFeMFerrites
O2+ FCC packing
4 O2+
8 THV
4 OHV
Antiferromagnetic coupling
Fe3+
Fe3+ M2+
Net moment due to M2+ ions only.
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
Domain walls are regions of high energy (0.002 Jm-2) due to moment misalignment. Then why do the exist?
Ans: Fig. 16.3
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
MHB 00
16.3
B never saturates
M saturates
The value of B at the saturation of M is called the saturation induction (~ 1 T)
Two ways for aligning of magnetic domains:
1.Growth of favorably oriented domains (initially)
2.Rotation of domains (finally)
Initial permeability
Saturation induction
The hysteresis Loop
Fig. 16.4
Br residual induction
Hc coercive field
Area = hysteresis loss
Soft magnetic materials
High initial permeability
Low hysteresis loss
Low eddy current losses
For application requiring high frequency reversal of direction of magnetization
Eg. Tape head
Problem 16.11
Easily moving domain walls
Low impurity, low non magnetic inclusions, low dislocation densitylow second phase precipitate
Soft magnetic materials
For low hysteresis loss ( frequency)
For low eddy current loss ( frequency2)
Material: high resistivity
Design: Lamination
Choose: Pure, single phase, well-annealed material of high resistivity
Table 16.1
Material Init. Rel. Hysteresis Saturation Resistivity
Perm. Loss (Jm-3) Induction (T) (10-6 m)
Com. Fe 250 500 2.2 0.1
Fe-4%Si 500 100 2.0 0.6
Fe-Si oriented 1500 90 2.0 0.6
Permalloy 2700 120 1.6 0.55 (45%Ni)
Supermalloy 100,000 21 0.8 0.65(79%Ni, 5%Mo)
Ni-Zn Ferrite 200-1000 35 0.4 1
Mn-Zn Ferrite 2000 40 0.3 1
Magnetic anisotropy Fig. 16.5
<100> easy direction
<111> 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
Fe-4% Si alloy for low frequency transformers
Wt% Si Wt% Si
resistivity
BsTDBTT
Si enhances resistivity: low eddy current losses
More than 4 wt% Si will make it too brittle
L+
TStable liquid
log t
Tm
glass
Metallic Glass Fe + 15-25%(Si, B, C)
High solute
High resistivity
Low eddy current loss
Amorphous Isotropic No hard direction
Amorphous No grain boundary
Easy domain wall movement
Low eddy current loss
50 Hz Fe-4wt% Si
K Hz Permalloy, Supermalloy
MHz Ferrites
Hard magnetic materials
For permanent magnets
Motors, headphones
High Br, high Hc
Br Hc = energy product
Martensitic high carbon steels (Br Hc=3.58 kJm3)
Alnico alloys: directionally solidified and annealed in a magnetic field (Br Hc=5.85 kJm3)
Mechanically hard c Magnetically hard
Large M phase as elongated particle in low M matrix
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)
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)
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