The Electromagnetic Properties of
Materials
•
Electrical conduction
•
Magnetic materials
•
Photonic Materials (optical)
–
–
–
–
Metals
Semiconductors
Insulators (dielectrics)
Superconductors
–  Ferromagnetic materials
–  Others
–  Transmission of light
–  Photoactive materials
•  Photodetectors and photoconductors
•  Light emitters: LED, lasers
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Magnetic Materials
•  Sources of magnetism
–  Unpaired electrons
•  Inner core: transition metals and rare earth elements
•  Electron bands (secondary)
–  Electron orbit (secondary)
•  Types of magnetism
–  Diamagnetism:
•  Electron orbit changed in magnetic field
–  Paramagnetism:
•  Disordered, unpaired spins align in magnetic field
–  Magnetic order:
•  Unpaired atomic moments spontaneously order at low T
•  Adjacent moments parallel: ferromagnets
•  Adjacent moments antiparallel: antiferromagnets (ferrimagnets)
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Sources of Magnetic Fields
m = IAn
I
H = NIn
M = mB
(Bohr magneton)
A
•
Circulating current creates magnetic moment
–  For a closed current loop of area A:
•  Magnetic moment: m = IAn
–  For solenoid of N turns per meter:
•  Magnetic field:
•
MSE 200A
Fall, 2008
H = NIn
Spinning electron creates magnetic moment
–  m = mB (Bohr magneton)
J.W. Morris, Jr.
University of California, Berkeley
Basic Relations for the Magnetic Field
•  Magnetic field: H
•  Magnetic flux: B
B = µµ0 H
µ ≥ 0 (=1 in free space)
•  Magnetization in material: M
B = µ0 ( H + M )
•  Magnetic susceptibility: χ
Boundary conditions:
Normal: B = µ0(H+M) is continuous
B1
H1
B2
H2
M2
Transverse: H = (B/µ0)-M is continuous
H1
M = χH
µ = 1+ χ
MSE 200A
Fall, 2008
H2
M2
H1
J.W. Morris, Jr.
University of California, Berkeley
Magnetism in Valence Metals
F = -e(v x B)
m =IAn
diamagnetism
MSE 200A
Fall, 2008
E
A
I
B
E
N(E)
N(E)
band paramagnetism
•
Diamagnetism (Cu, Au, Zn, Hg)
•
Band paramagnetism (Al)
–  Magnetic (“Lorenz”) force ⇒ eddy currents
–  m of current loop opposes B (decreases H)
–  χ < 0 but small (except in superconductors)
–  Electron moment (mB) preferentially aligns with B
–  Increases electrons with parallel spins
–  χ > 0 but small
J.W. Morris, Jr.
University of California, Berkeley
Core Magnetism: Transition Metals
MSE 200A
Fall, 2008
Sc: 3d14s2
m = 1mB
Ti: 3d24s2
m = 2mB
V: 3d34s2
m = 3mB
Cr: 3d54s1
m = 5mB
Mn: 3d54s2
m = 5mB
Fe: 3d64s2
m = 4mB
Co: 3d74s2
m = 3mB
Ni: 3d84s2
m = 2mB
Cu: 3d104s1
m=0
J.W. Morris, Jr.
University of California, Berkeley
Core Magnetism
Ferromagnetism
antiferromagnetism
M = nm
•
High temperature:
•
Low Temperature (T < Tc)
M=0
ferrimagnetism
M = (n/2)(m1-m2)
–  Spins disordered ⇒ paramagnetism
–  Spins align = ferromagnetism
•
•
Elements: Fe, Ni, Co, Gd, Dy
Alloys and compounds: AlNiCo, FeCrCo, SmCo5, Fe14Nd2B
•
Compounds: Fe3O4 (lodestone, magnetite), CrO3, SrFe2O3
–  Like spins alternate = antiferromagnetism
–  Unlike spins alternate = ferrimagnetism
•
Ferromagnetic (and ferrimagnetic) materials have engineering applications
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Ferromagnetism is Uncommon
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Ferromagnetism
M
paramagnetic
ferromagnetic
T
Tc
•  Ferromagnetism occurs by mutation at Tc (Curie T)
•  Energy is minimized by ordering spins into “domains”
–  Net moment, M, would cause external field, increase energy
–  Magnetic domains cancel so that M = 0
–  Natural ferromagnetism does not produce net magnetic field
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Ferromagnetism
Hc
Ms
M
Mr
H
•
To magnetize a ferromagnet, impose H
•
Magnetic properties
–  Domains move to align M and H
–  Defects impede domain motion
–  Moment (Mr) retained when H removed
–  Ms = saturation magnetization
•  All spins aligned with field
–  Mr = remanent magnetization
•  Useful moment of permanent magnet
H
–  Hc = coercive force
•  Field required to “erase” moment
–  Area inside curve = magnetic hysteresis
•  Governs energy lost in magnetic cycle
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Hard Magnets: High Field
Mr
orientation
Ms
M
H=M
M
domain
motion
Hc
•
Strong natural magnet: maximize Ms
•
Microstructural obstacles: maximize Mr/Ms
–  AlNiCo –  Sm(Co,Fe,Cu,Zr)8
–  Fe14Nd2B
Ms ~ 1.0 T
Ms ~ 1.2 T
Ms ~ 1.3 T
–  Fine domain size
•  Grain size
•  Particle size (free particle or embedded precipitate)
–  Defects and non-magnetic inclusions
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Hard Magnets: Magnetic Memory
Mr
orientation
Ms
parallel recording
domain
motion
Hc
perpendicular recording
•
Magnetic elements on disc, tape or surface
–  Isolated, individual particles; field orientation records information
–  Magnetic clements:
•  Hard for good “memory”
•  Not too hard, for erasure and re-write
•
MSE 200A
Fall, 2008
Media characteristics
–  Generally magnetic oxides for shape and chemical stability
–  Size less than minimum domain size for “hardness”
–  Perpendicular recording difficult, but provides high density
J.W. Morris, Jr.
University of California, Berkeley
“Soft” Magnets
Mr
Hc
Ms
•
“Soft” magnetic materials
–  Small hysteresis loop
–  Low energy losses per cycle
–  Optimized for cyclic machinery
•
•
•
•
•
Generators, transformers
Motors
Read-write heads
Electromagnetic shielding
Materials requirements
–  Magnetic isotropy
•  Low energy required to rotate moment
–  Homogenous, “defect-free” microstructure
–  Large grain size
•  Large-grained Fe-Si “transformer” steel
•  Amorphous “metallic glasses”
–  Electrical insulation minimizes electrical losses
•  Ferrites (Fe2O3, LiFe2O3)
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Piezomagnetism (Magnetostriction)
•  Magnetic field ⇔ elastic strain
B
–  Magnetic ⇔ mechanical
–  Can reach very high frequency
–  Small energy requirements
•  Materials
–  Ni
–  Ni-Fe (invar)
–  TbDyFe (terfenol)
MSE 200A
Fall, 2008
36Ni-Fe
20
(dL/L)x106
•  Piezomagnetic transducers
–  High frequency oscillators
–  Sound recording
–  High quality speakers
30
10
0
0.2
0.4
B(tesla)
0.6
Fe
-10
-20
-30
Ni
J.W. Morris, Jr.
University of California, Berkeley
Superconductivity
•  Superconductivity = loss of electrical resistance
•  Superconductors are not just good conductors
–  Electrons are “fermions”, obey Pauli Exclusion
–  Because of exclusion, all metals have resistance
•  Electron is excited to conduct
•  Loses energy on collision, returns to paired state
–  For superconductivity, must turn electrons into “bosons”
•  Electrons are paired into carriers with integral spin
•  Integral spin ⇒ boson
•  All carriers may be in the same ground state
•  Applications
–  Conductors: high field magnets, storage devices, transmission
–  Junctions: Josephson junctions used in detectors (SQUIDS)
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Characteristics of Superconductivity
•
Zero resistance
•
Meissner Effect
•
Only certain materials exhibit this behavior
–  Material loses all resistance at a critical temperature, Tc
–  Material expels magnetic fields below a critical field, Hc
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Cooper Pairs
•
Electrons polarize the lattice in their immediate vicinity.
•
They may attract one another through the intermediary of polarizing phonons
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
The Superconducting Elements
H
He
Li
Be
Na
Mg
element
transition temperature (K)
critical field (gauss = 10-4T)
B
= superconducting at high P or in metastable state
= ferromagnetic
K
Ca
Sc
Rb
Sr
Y
Cs
Ba
La
6.0
0.11
Ac
Fr
Ra
Ti
V
Cr
Mn
0.39 5.38
100 1420
Zr
Nb Mo
Tc
0.55 9.5 0.92 7.77
47 1980 95 1410
W
Re
Hf
Ta
0.12 4.48 0.01 1.4
<10 830
1
198
Ce
Pr
Nd
Fe
Co
Ni
Cu
Ru
0.51
70
Os
Rh
Pd
Ag
Ir
0.14
19
Pt
Au
0.65
65
Pm
Sm
Eu
Gd
C
N
O
F
Ne
Si
P
S
Cl
Ar
Al
1.14
105
Zn
Ga
0.88 1.09
51
53
Cd
In
0.56 3.40
30 293
Hg
Tl
Ge
As
Se
Br
Kr
Sn
3.72
309
Pb
Sb
Te
I
Xe
Bi
Po
At
Ra
4.15
412
7.19
803
Tb
2.39
171
Dy
Ho
Er
Tm
Yb
Lu
0.1
Th
1.37
1.6
MSE 200A
Fall, 2008
Pa
1.4
U
Np
Pu
= superconductor
= superconducting under special conditions
J.W. Morris, Jr.
= ferromagnetic
University of California, Berkeley
Domain of Superconductivity
•  Superconducitvity appears
when
J
Jc
–  T < Tc
–  H < Hc
–  j < jc
•  Superconductors may be
–  Elements
–  Compounds
Tc
T
Hc
H
MSE 200A
Fall, 2008
•  Two basic types
–  Differ in their response to H
J.W. Morris, Jr.
University of California, Berkeley
Types of Superconductors
-M
-M
H
Hc
Hc1
Hc
H
Hc2
•  Type I superconductor
–  Magnetic field penetrates at Hc
–  Both Hc and jc small; little industrial interest
•  Type II superconductor
–  H penetrates gradually over a range from Hc1 to Hc2>>Hc1
–  With proper microstructure, can have high jc
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Conductivity in Type II Conductors
log(jc)[A/in2]
11
Nb3Sn
9
7
0
10
B(tesla)
20
•  In type II conductor, H penetrates in “flux vortices”
–  Quantized lines of magnetic flux
–  Density increases as H increases to Hc2
•  Current imposes “Lorenz force” on flux lines
–  Vortices will be swept out (jc small) unless microstructural pinning
–  Proper microstructural pinning can produce very high jc
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Properties of Type II Conductors
compound
NbTi
NbN
Nb3Sn
Nb3Ge
PbMo6S8
YBa2Cu3O7
Bi2Sr2CaCu2O8
Tc (K)
12
17.3
18.5
23.2
15.3
92
85
Hc2 (Tesla at 4K)
12
47
24
38
60
>100
>100
• jc controlled by microstructure
• Attainable jc increases with Hc2
• jc decreases with T (“flux creep”)
⇒ High-Tc conductors have low jc
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Microstructure: Nb3Sn
•  “Bronze process” multifilamentary conductor
–  Thousands of filaments in cross-section
•  Fine-grained filaments pin flux
–  Create high Tc
MSE 200A
Fall, 2007
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley