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Engineering 45
Magnetic
Properties
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
[email protected]
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Learning Goals – Magnetic Props
 How to measure magnetic properties
 Atom-scale sources of magnetism
 How to Classify Magnetic Materials
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Properties of Solid Materials
 Mechanical: Characteristics of
materials displayed when forces and or
torques are applied to them.
 Physical: Characteristics of materials
that relate to the interaction of materials
with various forms of energy.
 Chemical: Material characteristics that
relate to the structure of a material.
 Dimensional: Size, shape, and finish
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Material Properties
Chemical
Composition
Microstructure
Phases
Grain Size
Corrosion
Crystallinity
Molecular Weight
Flammability
Physical
Melting Point
Thermal
Magnetic
Electrical
Optical
Acoustic
Gravimetric
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Mechanical
Dimensional
Tensile properties
Toughness
Ductility
Fatigue
Hardness
Standard Shapes
Standard Sizes
Surface Texture
Stability
Mfg. Tolerances
Creep
Compression
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Magnetic Field Strength
 Consider a Tightly
Coiled Wire Carrying
an Electric Current, I
I
B
 This SOLENOID
Configuration
Generates a Magnetic
Field with Strength, H
H  NI / L
• where
Engineering-45: Materials of Engineering
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L
– N  Number of Coils
(turns)
– I  Current (Amps)
– L  Coil Length (m)
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Magnetic Field Strength cont
 H has the unusual
Units of Amp-Turns
per Meter (A/m)
I
B
H  NI / L
 H induces Magnetic
Flux, B as
B  µH  µNI L
L
Think:
C = ε(A/L)
• where
– µ  the Magnetic
PERMEABILITY
(Henry per meter, or
H/m)
Engineering-45: Materials of Engineering
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 Units for B = Tesla
• 1 Tesla = 1 Amp-Henry
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Magnetization
 B = µH applies to
the General Case
where some
Material Occupies
the Center of the
Coil
 BaseLine Case →
Coil in a VACUUM
B0  µ0 H
Engineering-45: Materials of Engineering
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I
B
B  µH
L
 µ0 is a Universal
Constant
• µ0 = 1.257x10-6 H/m
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Magnetization cont.
 The Presence of
Material in the
Coil-Core Changes
the Magnetic Flux
• The Intensity of the
Materal-Filled Coil
Relative to the
Baseline
B
µH
µ


 µr
B0 µ0 H µ0
Engineering-45: Materials of Engineering
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B = Magnetic Induction
inside the material
B  µH
current I
Material
μ (H/m)
μr (H/m)
Ferrite U 60
Ferrite M33
Nickel (99% pure)
Ferrite N41
Iron (99.8% pure)
Ferrite T38
Silicon GO steel
supermalloy
1.00E-05
9.42E-04
7.54E-04
3.77E-03
6.28E-03
1.26E-02
5.03E-02
1.26E+00
8
750
600
3000
5000
10000
40000
1000000
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Magnetization cont.2
M  m H
 Alternatively
Describe the
Magnetic Field
Strengthening by
B  B0  B  µ0 H  µ0 M
• Where M 
MAGNETIZATION
– A Material Property
– Units → Amp/m
 Define Magnetic
SUSCEPTIBILITY
Engineering-45: Materials of Engineering
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• m is A Unitless
Material Property
 So B
B  µ0 H  µ0  m H
B  µ0 H 1   m 
 Then µr vs m
B
µ

 µr  1   m
B0 µ0
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Magnetic Susceptibility Origins
 Measures the response of electrons
to an Electric field
 Electrons Produce Electric Fields Due to
• Orbit about a the Nucleus (a tiny current)
• Electron Spin (recall spin-↑ & spin-↓)
magnetic moments
electron
 The Magnetic Analog to
the Electronic charge, q,
electron is the Bohr Magneton:
• µB = 9.27x10-24 J/Tesla
nucleus
Engineering-45: Materials of Engineering
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spin
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Types of Magnetism
 Magnetism arises from e- Orbit & Spin
• NET MAGNETIC MOMENT = Sum of all individual
Magnetic moments from both Orbit & Spin
 The Form of the Magnetic Sums Yields Three
Types of Magnetism
• DiaMagnetism
– DECREASES B
• ParaMagnetism
– Weakly Enhances B
• FerroMagnetism
– STONGLY Enhances B
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
The 3 Types of Magnetism
B  (1  )oH
permeability of a vacuum:
(1.26 x 10-6 Henrys/m)
Magnetic induction
B (tesla)
(3) ferromagnetic e.g. Fe3O4, NiFe2O4
ferrimagnetic e.g. ferrite(), Co, Ni, Gd
(  as large as 106 )
(2) paramagnetic (  ~ 10 -4)
e.g., Al, Cr, Mo, Na, Ti, Zr
vacuum ( = 0)
(1) diamagnetic (  ~ −10-5)
e.g., Al 2 O3 , Cu, Au, Si, Ag, Zn
Strength of applied magnetic field (H)
(ampere-turns/m)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
DiaMagnetism
 NonPermanent and Weak
• m ~–10-5 (recall Ni  600)
 Exists Only When H-Field Applied
• Atoms have NO permanent
Magnetic DiPoles
• When Field Applied, the
Generated Dipoles COUNTER
the Field → B<B0 Thus
– ur <1 (i.e., a %-age)
– m <0m (i.e., NEGATIVE)
Engineering-45: Materials of Engineering
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Material m (10-5)
Ammonia
Bismuth
Copper
Hydrogen
Oxygen
Silicon
Water
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
-1.1
-16.7
-0.9
0.0
0.2
-0.4
-0.9
ParaMagnetism
 Each Atom DOES Possess a
Permanent DiPole
 Atomic Dipoles are RANDOMLY
Arranged
•  A “Chunk” of Material has NO Net
Macroscopic Magnetism
 However, Dipoles Do Align to an Applied
Field, Strengthening it
• Yields a Small & Positive m: 10-5 -10-3
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
FerroMagnetism
 Material is Magnetic, Even
withOUT an Applied H-Field
• Relatively Rare in Nature
• Large Susceptibility Caused by Parallel
Alignment of Domains due to Coupled
Spin Moments of UnPaired Electrons
• Yeilds Large & Positive m: 102 -105
– Recall Field Strength Eqn
B  µ0 H 1   m 
if  m  1 then
B  µ0  m H  µ0 M
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Magnetization vs H
 M for
Ferromagnetics is a
Function of the
Applied Field, H
 As H increases, B
approaches a
Maximum Value
• i.e., the
Magnetization
SATURATES
 Msat for FerroMags
Engineering-45: Materials of Engineering
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M sat  nB µB N
• Where
– nB  Bohr Magnetons
per atom
– µB  Bohr Mageton Value
– N  atomic Density
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
AntiFerroMagnetism
 Atoms Contain a Permanent DiPole,
but There are equal Quantities of
Oppositely Directed Dipoles
• Therefore, the magnetic field cancels out
and the material appears to behave in the
same way as a paramagnetic material
 Dipoles will Align somewhat to an
Applied Field thus
• Yields a Small & Positive m: 10-5 -10-3
– Similar to Paramagnetics
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
FerriMagnetism
 Arises in Ceramics Where The Oxidant (the
metal) Exists in More than One Valence State
 Example = Ferrite (Lodestone), Fe3O4
• Fe Exists in Two Valence States: +2 & +3
2
2

Fe3O4  Fe O  Fe
3
 O 
2
2
3
– The Fe DiValent:TriValent Ratio = 1:2
• Note that The Divalent & TriValent Iron Ions have
Bohr Magneton Ratios of 4 & 5 respectively
• O2- ions are Magnetically Neutral
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
FerriMagnetism cont
 The Atoms in Lodestone
Arrange in A
Xtal Structure that
can be Represented as
X
X
X
X
X
X
 Note that Magnetic Spin
Moments for the
TRIVALENT ions Cancel
 This Leaves a Net Ferrimagnetic Form
due to the DiValent Fe2+ ions
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Magnet Types Summarized
Magnetism
Susceptibility
Example /
Susceptibility
Atomic / Magnetic Behavior
Small & negative.
Atoms have no
magnetic moment
Au
Cu
-2.74x10-6
-0.77x10-6
Paramagnetism
Small & positive.
Atoms have
randomly oriented
magnetic moments
β-Sn
Pt
Mn
0.19x10-6
21.04x10-6
66.10x10-6
Ferromagnetism
Large & positive,
function of applied Atoms have parallel
field,
aligned magnetic
microstructure
moments
dependent.
Fe
~100,000
Cr
3.6x10-6
Ba
ferrite
~3
Diamagnetism
Antiferromagnetism Small & positive.
Ferrimagnetism
Large & positive,
function of applied Atoms have antifield,
parallel aligned
microstructure
magnetic moments
dependent
Engineering-45: Materials of Engineering
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Atoms have mixed
parallel and antiparallel aligned
magnetic moments
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Temperature Affects
 Even though electronic
exchange forces in
ferromagnets are very large,
thermal energy eventually
overcomes the exchange
and produces a randomizing
effect.
 This occurs at a particular
temperature called the Curie
temperature (TC).
 Below the Curie
temperature, the
ferromagnet is ordered
 Above TC the FerroMagnet is
DISordered.
Engineering-45: Materials of Engineering
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(ºC)
 The saturation magnetization
goes to zero at the Curie
temperature.
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Magnetic Domains
 In Ferr(o/i)Magnetic Materials There
Exist Small PHYSICAL volumes of
Well Aligned Magnetic Dipoles
called DOMAINS
 The Domains are MicroScopic, and,
in polyXtal Materials a Grain May
contain More than one Domain
 The Magnitude of M for a Macroscopic Piece
of Material is the VECTOR sum of all
Magnetization for all Domains
• This is a VOLUME-Weighted Integration
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Magnetization vs H Revisited
H
H
Magnetic
induction (B)
 For Ferr(o/i)Magnetics
Bsat
as H↑ the Overall Dipole
Alignment becomes
Stronger.
 In other Words, The
Favorably-Aligned
Domains GROW at the
Expense of the less
favorably Aligned
0
Domains
 Thus Domain Structure
can overcome Grain
(Physical) Structure
Engineering-45: Materials of Engineering
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H
H
H
Applied Mag Field (H)
H=0
 c.f. cool photos on
text pg W19 Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Permanent Magnets
 Permanent Magnets Exhibit Hysteresis in their B-H
Curves Due to B-Lags in the Aligning & Unaligning
processes
• An Outline of the Process
3. Bring H to Zero, some
Alignment remains
(Remnance, Br). Have
Permanent Magnet
B
2. Apply H, Cause
Domain
Alignment &
Growth
Applied H Field
4. To Reach B=0 Must
Apply NEGATIVE H
(Coercivity, HC)
Magnet is Still Perm.
Engineering-45: Materials of Engineering
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1. Initial (Unmagnetized)
State
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Soft & Hard Magnet Materials
 The Area within the B-H Curve is
Proportional to Energy Absorbed by
the Permanent Magnet
• This will be Dissipated as Heat
 “Soft” Materials Have Small
Hysteresis Areas, but
Lower Magnetizations
• Good for Devices Where High H-Field
Reversal Rates and hence Heat dissipation is as issue; e.g.,
Electric Motors
 “Hard” have Large Hysteresis Areas,
but Higher Remnance
• The High Remnance, and resistance to demagnetization,
Makes Hard Materials well suited for
Permanent Magnet applications
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
B-H Energy Density
 Consider a Hard Material
Hysteresis Curve at right
 The Area Under the Curve has
units of Energy Density:
kg
C
kg
BH 


C  s s  m m  s2
 Now Mult by m2/m2:
kg m 2 kg  m 2
BH 
 2  3 2
2
ms m
m s
kg  m 2 s 2
J

 3 
3
m
m


Engineering-45: Materials of Engineering
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 (BH)max as measured in the
2nd Quadrant is the
Industry Standard metric for
Resistance by a PM to
Demagnetization
• PM material Microstructure is
adjusted to impede Domain
Wall motion, enhancing
(BH)max
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Application  Magnetic Storage
• Information is stored by magnetizing material.
• Head can...
Tape recording medium
--apply magnetic field H &
align domains (i.e.,
magnetize the medium).
--detect a change in the
magnetization of the
Simulation of hard drive
medium.
courtesy Martin Chen.
• Two media types:
Reprinted with permission
from International Business
Machines Corporation.
--Particulate: needle-shaped
g-Fe2O3. +/- mag. moment
along axis. (tape, floppy)
Adapted from Fig.
20.19, Callister
6e. (Fig. 20.19
courtesy P.
Rayner and N.L.
Head, IBM
Corporation.)
Engineering-45: Materials of Engineering
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~2.5m
recording head
Adapted from Fig. 20.18, Callister 6e.
(Fig. 20.18 from J.U. Lemke, MRS
Bulletin, Vol. XV, No. 3, p. 31, 1990.)
--Thin film: CoPtCr or CoCrTa
alloy. Domains are ~ 10-30nm!
(hard drive)
Adapted from Fig.
20.20(a), Callister 6e.
(Fig. 20.20(a) from M.R.
Kim, S. Guruswamy, and
K.E. Johnson, J. Appl.
Phys., Vol. 74 (7), p.
4646, 1993. )
Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
9
Summary  Magnetics
 A magnetic field can be produced by
• Running a current through a coil
 Magnetic induction
• Occurs When A Material Is Subjected
To A Magnetic Field
• Is A Change In Magnetic Moment From Electrons
 Types of material-response to a Mag-field are
• Ferri- Or Ferro-magnetic (Large Magnetic
Induction)
• Paramagnetic (Poor Magnetic Induction)
• Diamagnetic (Opposing Magnetic Moment)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
Summary cont.
 HARD magnets → LARGE Coercivity.
 SOFT magnets → SMALL Coercivity.
 Magnetic storage media:
• Particulate g-Fe2O3 in Polymeric Film
(Tape Or Floppy)
• Thin Film CoPtCr or CoCrTa On Glass or
Aluminum Disk (Hard Drive)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt
WhiteBoard Work - Magnetics
A bar of an Fe-Si Allow has
B-H characteristics shown at
Left. A bar of this Material
inserted into a wire coil 0.2 m
long, and having 60 turns,
thru which passes a
current of 100 mA.
1.35
For This arrangement:
(a) What is the B-Field within
the bar?
(b) At this magnetic field find:
 Remember
the 1.35
Tesla Value
1) The Permeability
2) The Relative Permeability
3) The Susceptibility
4) The Magnetization
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-12_Magnetic_Prop.ppt