Download Magnetism

Magnetism
MSE 630
Fall, 2008
MSE-630
Magnetic field strength = H
H = Ni/l
(amp-turns/m)
N = # turns
i = current, amps
l = conductor length
B = Magnetic Induction or
Magnetic flux density
(Wb/m2)
Magnetic field lines of
force around a current
loop and a bar magnet
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B = mH
m is the “permeability”
In a vacuum,
Bo = moH
where
mo is the permeability in a vacuum
=4p x 10-7 (1.257 x 10-6) H/m or T-m/A
Units:
T: Tesla
1T = 1 V-s/m2
Analogous to dielectrics, the “relative permeability” is
mr = m/mo
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The Magnetization is another field
quantity defined by the equation:
B = moH + moM
And
M = cmH
B = mH = moH + moM
Or
M = (m-mo)/mo * H
Thus
cm = (m-mo)/mo
cm is called the
magnetic susceptibility,
and is a measure of how
easily a material is
magnetized
Thus
B = mo(1+cm)H
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The Origin of Magnetic Moments
Magnetic moments come
both from the electrons
orbiting the nucleus and its
spin
The most fundamental
magnetic moment is the
Bohr magnetron, mB
mB = 9.27 x 10-24 A-m2
For each electron, the spin magnetic moment
is ±mB
Furthermore, the orbital magnetic moment
contribution is equal to ml*mB, where ml is the
magnetic quantum number
Only unpaired electrons contribute to
the total magnetic moment in an atom
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Diamagnetism and Paramagnetism
Diamagnetism is
extremely small,
nonpermanent,
opposes external
field, and only
persists while the
external field is
applied
The atomic dipole configuration for a diamagnetic material
with and without a magnetic field. In the absence of an
external field, no dipoles exist; in the presence of a field,
dipoles are induced that are aligned opposite to the field
direction. (b) Atomic dipole configuration with and without an
external magnetic field for a paramagnetic material
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Ferromagnetism
Ferromagnetism is displayed by large and
permanent magnetizations.
These occur in transition metals (BCC iron,
nickel, and cobalt) and some rare earth
elements
Susceptibility is as high as 106 – thus, H<<M,
and
Schematic illustration of the mutual
alignment of atomic dipoles for a
ferromagnetic material, which will
exist even in the absence of an
external magnetic field
B = moM
In ferromagnets, magnetic moments remain
aligned when external fields are removed,
resulting in permanent magnetization
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Example:
The maximum possible magnetization, or
Calculate the saturation
magnetic saturation, Ms of a ferromagnetic magnetization and saturation
material represents the magnetization that
flux density for nickel, which
results when all the magnetic dipoles in a solid has a density of 8.9 g/cm3:
piece are mutually aligned to the external field.
Ms = 0.60mBN
There is a corresponding saturation flux
N = rNA/ANi
density, B .
s
The saturation magnetization is equal to the
product of the net magnetic moment for each
atom and the number of atoms present. For
iron, cobalt and nickel, the net magnetic
moments per atom are 2.22, 1.2 and 0.60
Bohr magnetrons, respectively
= (8.90 g/cm3)*(6.023 x 1023
atoms/mol)/58.71 g/mol
= 9.13 x 1028 atoms/m3
Ms = 0.60 x (9.27 x 10-24) x
(9.13 x 1028)
= 5.1 x 105 A/m
Bs = moMs = 4p x 10-7 H/m * 5.1
x 105 A/m
= 0.64 Tesla
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Antiferromagnetism
Antiparallel alignment of spin magnetic
moments in antiferromagnetic manganese
oxide results in complete cancellation of
magnetic moments and no net magnetism
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Ferrimagnetism
Some ceramics can show
permanent magnetism called
Ferrimagnetism.
Ferrimagnetism is similar to
ferromagnetism, though the
source of the net magnetic
moments is different
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Example:
Saturation Magnetization determination for Fe3O4
Calculate the saturation magnetization for Fe3O4 given that each cubic unit cell
contains 8 Fe2+ and 16 Fe3+ ions, and that the unit cell edge length is 0.839 nm
The saturation magnetization is equal to the product of the number, N’, of Bohr
magnetrons per cubic meter of Fe3O4 and the magnetic moment per Bohr
magnetron, mB: Ms = N’mB
N’ is the number of Bohr magnetrons per unit cell nB divided by the unit cell
volume Vc, or: N’ = nB/Vc
Net magnetization results from the Fe2+ ions only. Each cell has 8 Fe2+ , and
each Fe2+ has 4 Bohr magnetrons, thus nB = 32, and Vc = a3, thus
Ms = (32 Bohr magnetrons/unit cell * 9.27 x 10-24 A/-m2/Bohr magnetron)/(0.839
x 10-9 m)3/unit cell
Ms = 5.0 x 105 A/m
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Temperature and Magnetization
Elevated temperatures
cause magnetic dipoles to
become unaligned.
Magnetism is completely
destroyed at the Curie
Temperature, Tc
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Domains and Hysteresis
There is a gradual
change in magnetic
dipole orientation
across a domain
wall, as shown
below:
Dipoles are
aligned in each
domain, but vary
from one domain
to the other
The B-versus-H behavior
for a ferromagnetic or
ferrimagnetic material that
was initially unmagnetized.
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Hysteresis
H increases until Bs and Ms
are reached. Upon removal,
some magnetism, call
remanence, remains at Br. H
field must be reversed to –Hc
to eliminate residual
magnetism. This is called the
coercivity.
The area in the hysteresis
loop represents work or
energy expended in going
from (+) to (-) H and back.
The product of B*H is
measured in kJ/m3 or gaussoersted (MGOe)
1 MGOe = 7.96 kJ/m3
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Magnetization and crystal alignment
Magnetization curves for single
crystals of iron and nickel.
Magnetization varies with
crystallographic directions
Magnetization curves for
single crystals of cobalt.
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Hard vs. Soft magnets
Hard magnetic materials retain magnetism
after field is removed; soft magnetic materials
do not.
Soft magnetic materials require small H to
reach Bs, and Hc is small. This means less
energy is wasted in hysteresis loop. Soft
magnetic materials are desirable in
transformer cores and other applications
where residual magnetization is undesirable
Defects, such as nonmagnetic phases and
voids restrict easy movement of domain walls
and are to be avoided in soft magnetic
materials. Sometimes Si or Ni is added to Fe
to minimize eddy currents that rob energy in
hysteresis loops
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Magnetic storage
Small domains in materials can
be magnetically aligned in one
of two ways, corresponding to a
0 or a 1 in digital storage.
This same technique of
magnetic alignment being
“written” and “read” is used in
recording tapes, VCR and other
media
Hysteresis loops for particulate magnetic
storage media. Saturation flux density is
typically 0.4-0.6 Tesla, and the
hysteresis loop should be relatively large
and square, to ensure that storage will
be permanent and magnetization
reversal will occur over a narrow range
of applied field strengths. For coercivity
is typically ~2 x 105 A/m.
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Scanning electron micrograph
showing the microstructure of a
magnetic storage disk. Needleshaped particles of g-Fe2O3 are
oriented and embedded within an
epoxy phenolic resin. 8000X
Each particle is a single domain that
may be magnetized only with its
magnetic moment lying along this axis.
Only two states are allowed,
corresponding to digital storage of 1’s
and 0’s
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CoPtCr or CoCrTa alloy are applied to a
substrate as a “thin film” for magnetic
storage. This provides higher storage
capacity than g-Fe2O3 at lower cost.
The film is usually 10 – 50-nm thick, and is
applied over a layer of pure chromium or a Cr
alloy. The thin film is polycrystalline, with a
grain size o ~10 – 30-nm. Each grain is a
single magnetic domain.
Storage density in particulate media is ~1.5 x
105 bits/mm2, while storage density for thin
films exceeds 108 bits/mm2.
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