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LECTURE #21
Chapter 18: Magnetic Properties
Learning Objectives...
• What are the important magnetic properties? Recognize
the connection between electrical current and magnetism
• How do we explain magnetic phenomena?
• How are magnetic materials classified?
• Materials applications that utilize magnetism….
Magnetic information storage
Magnetism for cancer therapy
Etc.
Relevant Reading for this Lecture...
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• Pages 751-785
Magnetism
magnetic flux lines
Magnitude (strength) & direction of magnetic field produced is a vector H
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Generation of a Magnetic Field - Vacuum
• Can be created by current passing through a coil:
B0
N = total number of turns
 = length
g of turns ((m))
H

I
I = current (ampere)
H = applied magnetic field (ampere-turns/m)
B0 = magnetic flux density in a vacuum
(tesla)
• Computation of the strength of magnetic field produced, H:
NI
H


• Computation of the magnetic flux density in a vacuum, B0:
B0 = 0H
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permeability of a vacuum
(1.257 x 10-6 Henry/m)
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Generation of a Magnetic Field -within a Solid Material
• A magnetic
ti fi
field
ld iis iinduced
d
d iin th
the material
t i l
B
applied
magnetic
field H
B = Magnetic Induction (tesla)
inside the material
B = H
permeability of a solid
currentt I
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RESPONSE TO A MAGNETIC FIELD
• Without passing a current, a continually varying
magnetic field will cause a current to flow
For zero applied
pp
current
B
applied
magnetic
field H
B = Magnetic Induction (tesla)
Let B vary continuously like this.
current I
“Wiggling” the magnetic field H induces an electric current
inside the wire!
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Electricity and Magnetism are Related!
Compass near a current-carrying wire
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Basic Physics of Magnetism
B  o H
B  H
There is a parallel between this
equation & Ohm’s Law.
V  IR
RA

L
1


8
B, magnetic induction,
is analogous to current
density
current
density
(A/cm2)
voltage
gradient
(V/cm)
I
V

A
L
BH
H is magnetic field
gradient analogous to
voltage gradient (V/cm)
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The presence of a solid changes the induction B.
B   H  o  H  M   o H  o M
(o·M) represents the “extra” magnetic
induction resulting
g from the solid
r 

0
relative permeability r is a measure of the ease
with which a B field can be induced inside a
material.
Diamagnetic
g
materials have r slightly
g y<1
e.g. Cu, Au, electronic structure sets up a slight opposing field.
These materials are relatively unaffected by magnetic fields.
Paramagnetic materials have r slightly > 1
e.g. Al, Cs, W, Mg, electronic structure sets up a reinforcing field.
These materials are “weakly attracted” to magnetic fields.
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More magnetic quantities
If a material has internal magnetic moments, then the field generated
by those moments must be added to the induced field:
B = 0 (H+M)
M is known as the magnetization of the material, and is essentially
the dipole moment per unit volume. (same units as H)
The magnetization is proportional to the applied field: M = m H
m is the magnetic susceptibility [dimensionless] m = r - 1
B
m > 0
vacuum m = 0
m < 0
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m is a measure of a material’s
magnetic response relative to a
vacuum
H
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Let’s look at a couple of example problems
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Example Problem 1
A magnetic-field strength of 2.0  105 amperes/m (provided by an ordinary bar magnet) is
applied to a paramagnetic material with a relative permeability of 1.01. Calculate the values
of induction B and magnetization M.
B   H  0 ( H  M )
B B ,M  M
r 

0
 H  0 ( H  M )
 H  0 H  0 M

H H M
0

B   H  r 0 H  (1.01)(4  107 henry / m)(2  105 amperes / m)
 0.254 henry  amperes / m 2
 0.254 weber / m 2  B


M    1 H  ( r  1) H

 0 
 (1.01  1)(2  105 amperes / m)
 2  103 amperes / m  M
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Example Problem 2
A coil of copper wire, 200 mm long and having 200 turns carries a current of 10 A. (a)
What is the magnitude of the magnetic field strength H? (b) Compute the flux density B if
the coil is in vacuum. (c) Compute the flux density inside a bar titanium that is positioned
inside the coil. (d) What is the magnetization? The magnetic susceptibility, χm, for titanium
is 1.81  10-4.
NI (200)(10 A)
=
= 10,000 A/m
l
0.20 m
(a)
H =
(b)
B0 = 0 H = (1.257  10-6 H/m)(10,000 A/m) = 1.257  10-2 tesla
(c)
B =  0 H +  0 M =  0 H +  0  m H =  0 H (1 +  m )
= (1.257  10-6 H/m) (10,000 A/m)(1 + 1.81  10-4 )
=1.257  10-2 tesla
(d)
M =  m H = (1.81  10-4 )(10,000 A/m) = 1.81 A/m
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Origins of Magnetic Moments
• Magnetic moments arise from: (1) electron motions and (2) the
spins on electrons.
magnetic moments
electron
electron
spin
nucleus
electron orbital
motion
ti
electron
spin
i
Adapted from Fig. 18.4, Callister & Rethwisch 4e.
• Net atomic magnetic moment:
-- sum of moments from all electrons.
• Four
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types of response...
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Magnetic Responses for 4 Types
none
e
oppossing
(2) paramagnetic
random
aligned
Adapted from Fig.
18.5(b), Callister &
Rethwisch 4e.
(3) ferromagnetic
(4) ferrimagnetic
aligned
Dipole
alignment
relative to H
Adapted from Fig.
18.5(a), Callister &
Rethwisch 4e.
Adapted from Fig.
18.7, Callister &
Rethwisch 4e.
(1) diamagnetic
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Applied
Magnetic Field (H)
aligned
No Applied
Magnetic Field (H = 0)
Permanent magnetism is a result of the magnetic moment due to uncanceled electron spins
(wither the electronic structure for ferro or the incomplete spin cancellation in ferri (e.g. MFe2O4)]
B (tesla)
4 Types of Magnetism
(3) ferromagnetic e.g. Fe3O4, NiFe2O4
(4) ferrimagnetic e.g. ferrite(), Co, Ni, Gd
( m as large as 106 !)
(2) paramagnetic ( m ~ 10-4)
e.g., Al, Cr, Mo, Na, Ti, Zr
vacuum (m = 0)
(1) diamagnetic (m ~ -10-5)
e g Al2O3, Cu,
e.g.,
Cu Au
Au, Si
Si, Ag
Ag, Zn
H (ampere-turns/m)
Plot adapted from Fig. 18.6, Callister & Rethwisch 4e.
Values and materials from Table 18.2 and discussion in
Section 18.4, Callister & Rethwisch 4e.
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Diamagnetics and Paramagnetics
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Influence of Temperature on
Magnetic Behavior
Spin coupling is
destroyed at Tc
d tto iincreased
due
d
atomic thermal
motions
With increasing temperature, the saturation magnetization diminishes gradually
and then abruptly drops to zero at Curie Temperature, Tc.
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Magnetic Domains in Ferromagnets
Schematic depiction of domains in a ferromagnetic
or ferrimagnetic material. Arrows represent atomic
magnetic dipoles. Within each domain, all dipoles
are aligned, whereas the direction of alignment
varies from one domain to another.
The gradual change in magnetic dipole
orientation across a domain wall.
(From W.D. Kingery, H.K. Bowen, and
D.R. Uhlmann,, Introduction to
Cermaics, 2nd Edition, (John Wiley &
Sons, New York, 1976).
Various magnetic domain structures observed in
Fe-Pd; L. Wang and D. E. Laughlin
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Domains in Ferromagnetic &
Ferrimagnetic Materials
• As the applied field (H) increases the magnetic domains
change shape and size by movement of domain boundaries.
B satt
H
Magnetic
duction (B)
ind
H
H
H
H
0
Adapted from Fig. 18.13,
Callister & Rethwisch
4e. (Fig. 18.13 adapted
from O.H. Wyatt and D.
Dew-Hughes, Metals,
Ceramics, and
Polymers, Cambridge
University Press, 1974.)
• “Domains” with
aligned magnetic
moment grow at
expense of poorly
aligned ones!
Applied Magnetic Field (H)
H=0
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Hysteresis and Permanent
Magnetization
• The magnetic hysteresis phenomenon
Stage 3.
St
3 Remove
R
H alignment
H,
li
t
remains! Remanent Magnetization
=> permanent magnet!
B
Stage 2. Apply H,
align domains
Adapted from Fig. 18.14,
Callister & Rethwisch 4e.
H
Stage 4. Coercivity, HC
Negative H needed to
demagnetize!
Stage 1. Initial (unmagnetized state)
Stage 5. Apply -H,
align domains
Stage 6. Close the
hysteresis loop
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Hard and Soft Magnetic Materials
B
-- large coercivities
-- used for permanent magnets
-- add particles/voids to
inhibit domain wall motion
-- example: tungsten steel -Hc = 5900 amp-turn/m)
Soft
Hard magnetic materials:
H
Soft magnetic materials:
-- small coercivities
-- easy to “write”
write over
-- used for electric motors
-- example: commercial iron 99.95 Fe
Adapted from Fig. 18.19, Callister & Rethwisch
4e. (Fig. 18.19 from K.M. Ralls, T.H. Courtney,
and J. Wulff, Introduction to Materials Science
and Engineering, John Wiley and Sons, Inc.,
1976.)
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Magnetic Anisotropy
Easy (flips at low applied field)
Easy magnetization direction:
Ni- [111], Fe- [100], Co- [0001].
Hard (higher
field to flip)
Hard magnetization direction:
Ni- [100], Fe- [111],
Co- [10-10], [11-20]
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Iron-Silicon Alloy (97 wt% Fe – 3 wt% Si) in Transformer Cores
used for stepping up/down voltages
Transformer cores require soft magnetic materials, which are easily magnetized
and de-magnetized, and have high electrical resistivity.
A transformer is a power converter that transfers electrical energy from one
circuit to another through inductively coupled conductors—the transformer's
coils. A varying current in the primary winding creates a varying magnetic flux
in the transformer's core and thus a varying magnetic field through the
secondary winding. This varying magnetic field induces a varying
electromotive force (EMF) or voltage in the secondary winding. This effect is
called inductive coupling.
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Energy losses in transformers could be minimized if their cores were
fabricated such that the easy magnetization direction is parallel to the
direction of the applied magnetic field.
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Growth in areal densities of hard disk drives
(from IBM web site)
Information Storage
Equivalent
All written books in Library
off Congress
C
stored
t d on size
i
of a quarter
 Original IBM RAMAC hard-drive = 2,000 bits/in2 (1956), size
of a refrigerator, $20/MByte
 Modern memory is 100Gbits/in2, 3x5 inches in size,
$0.30/MByte
: $35B sales industry
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Magnetic Storage:
Information is stored by magnetizing material
• Head can...
--Apply magnetic field H
& align domains (i.e.,
(i e
magnetize the medium).
-- “write” or record data by
applying a magnetic field that
aligns domains in small regions
of the recording medium
--Detect a field,, or change
g
in magnetization H of the
material (i.e. detect 1 or 0).
-- “read” or retrieve data from
medium by sensing changes
in magnetization
Require hard magnetic materials, which
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are resistant to de-magnetization
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GMR Head
Giant Magneto-Resistance (GMR) Effect
The 2007 Nobel Prize was awarded to Albert Fert and Peter Grunberg for
the discovery of GMR.
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Audio Speakers
Loudspeakers - the signal (or voltage) from an amplifier causes a
current to flow in the voice coil which is in a B field as shown
shown. The
current experiences a force along the axis of the coil. If the signal is
an AC signal of a certain frequency the coil will vibrate back and
forth at that frequency causing the speaker cone to vibrate and put out
a sound wave.
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Ferro-fluids
•
Ferro-fluids are colloidal suspension of magnetic nanoparticles that
respond to a magnetic field.
Applications:
Loud speakers: A loudspeaker works by passing a current that
goes though the coil and creates a magnetic field. The magnetic
field moves the diaphragm back and forth creating sound waves.
waves
A ferrofluid is held in place by a magnet next to the voice coil.
The vibrating coils produces sound and heat which the ferrofluid
removes improving unwanted resonance.
Rotary seals: A ferrofluidic seal
provides a hermetic seal against gas,
vapor and other contaminants under
both static and dynamic conditions
while providing virtually no friction
between the rotating and stationary
components.
Shocks: controlled damping of vibrations
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Superconductivity
Found in 26 metals and hundreds of alloys & compounds
Mercury
Copper
(normal)
Fig. 18.26, Callister &
Rethwisch 4e.
• TC = critical temperature
= temperature below which material is superconductive
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Critical Properties of
Superconductive Materials
TC = critical temperature - if T > TC not superconducting
JC = critical current density - if J > JC not superconducting
HC = critical magnetic field - if H > HC not superconducting
 T 2 
HC (T )  HC (0)1  2 
 TC 
Fig. 18.27, Callister &
Rethwisch 4e.
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Meissner Effect
• Superconductors expel magnetic fields (diamagnetic)
normal
superconductor
p
Fig. 18.28, Callister &
Rethwisch 4e.
• This is why a superconductor will float above a magnet
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Fantastic Voyage
Novel by Isaac Asimov and motion picture
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A Multifunctional Nanoplatform
for Cancer Targeting, Imaging and Therapy
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Nano-magnetism for Cancer Therapy
Targeting
The adenovirus is genetically engineered to
target cancer cells
Imaging
The magnetic nanoparticle enhances MRI
contrast for sensitive imagining
Therapy
Hyperthermia Therapy – an external radio
frequency magnetic field heats the
magnetic particles heats the cancerous
tissue thereby killing it.
Triggered Drug Release – magnetic field
heating of the magnetic particles causes a
phase transition in a temperature sensitive
polymer allowing a cancer drug to be
released.
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Magnetic Fluid Hyperthermia (MFH)
• Oscillating magnetic fields at the proper
frequency will heat the magnetic particles,
killing the cell.
• Benign and deep penetration of magnetic
fields has advantage over other
hyperthermia methods.
A
B
C
D
Magnetic hyperthermia coils and infrared images of nanoparticle solutions
A. 4-turn test tube coil B. Infrared image of a cobalt ferrite nanoparticle solution
heated in a centrifuge tube C. Petri dish coil D. Infrared image of a cobalt ferrite
nanoparticle solution in a Petri dish
The particles are heated by
magnetic induction
Healthy tissue
Healthy
tissue
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Alternating
magnetic field Diseased tissue with
magnetic particles
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Implantable, Magnetically Triggered Drug Delivery
• Magnetic nanoparticles and a cancer drug in a polymer gel
matrix
• Heating
g causes the polymer
p y
gel
g to open
p pores
p
that allow the
cancer drug to escape
Matrix with
magnetic particles
and dispersed drug
Heat dissipation from
Molecular response:
magnets after exposure
Thermoresponsive grafts
to magnetic energy
collapse; pores open
Drug releases until
local temperature falls
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Summary
•
A magnetic field is produced when a current flows
through a wire coil.
• Magnetic induction (B):
-- an internal magnetic field is induced in a material that is
situated within an external magnetic field (H).
(H)
-- magnetic moments result from electron interactions with
the applied magnetic field
• Types of material responses to magnetic fields are:
-- ferrimagnetic and ferromagnetic (large magnetic susceptibilities)
-- paramagnetic (small and positive magnetic susceptibilities)
-- diamagnetic (small and negative magnetic susceptibilities)
• Types
ypes o
of ferrimagnetic
e
ag et c a
and
d ferromagnetic
e o ag et c materials:
ate a s
-- Hard: large coercivities
-- Soft: small coercivities
• Magnetic applications:
-- Hard drives
-- Ferrofluids
-- Cancer treatments
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