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6 Special Methods
6.1 Microwave Techniques
6.2 Dielectric Measurements
6.3 Thermoelectric Measurements
Electromagnetic Spectrum
34 19, 6.63 10 Js, 1.6 10 CE h eV h e
microwave
IR light
cosmic rays
X-rays
rays
UV light
visiblelight
radio frequency
Frequency [Hz]
10 1081064 10 1014101210 10 1020101816 1022 1024
Energy [eV]
10 10-610-8-10 10 10010-2-4 10 1061042 108 1010
Wavelength [m]
10 1001024 10 10-610-4-2 10 10-1210-10-8 10-14 10-16
typical lattice constant
Electromagnetic WavesPlane waves:
in dielectrics:
( )0
i t k xy y yE E e E e e ( )
0i t k x
z z zH H e H e e
0
0
E i
H i
( )k i i
in conductors:
/ ( / )0
x i t xyE e e E e
/ ( / )0
x i t xzH e e H e
1 ik
1i i
1
f
00
0377
0 0
0 r n
( / )0
i t x cyE e E e
( / )0
i t x czH e H e
kc
0
0 0
1
r
cc
n
8
00 0
13 10 m/sc
Reflection/Transmission between Dielectrics
x
y
incident
reflected transmitted
I dielectric II dielectric
0 0I II
I II,
n n
strong penetration
perceivable reflection
I II
I II
n nR
n n
Reflection from Conductors
x
y
incident
reflected transmitted“diffuse” wave
I dielectric II conductor
10
f
0II I
i
n
II I
II I1R
negligible penetration
almost perfect reflection with phase reversal
Far-Field Measurement Configurations
detectorisolatoroscillatorcirculator
hornantenna
specimen
reflection (monostatic radar, pulse-echo)
detector
isolatoroscillator
hornantenna
specimen
transmission (bistatic radar, pitch-catch)
scattering (bistatic radar, pitch-catch)
isolatoroscillator
hornantenna
specimen
detector
detec
tor
Near-Field Inspection
detectorisolatoroscillatorcirculator
open-endedwaveguidespecimen stand-off
distance
air backing
foam coreadhesive
substrate
skin laminatecorrosion damage
coating
(Qaddoumi et al., 1997)
Microwave Image of Rust Under Paint
40 mm 40 mm area of rust on a steel plate
24 GHz, 12.5 mm standoff distance, 0.267 mm of paint
60
40
20
06040200 [mm]
[mm]
Lock-in Thermographyglass fiber-reinforced polymer plates (50 75 mm2)
(Diener, 1995)
detectorisolatoroscillatorcirculator
open-endedwaveguidespecimen stand-off
distance
infraredcamera
lock-inamplifier
modulator
microwave raster scan
lock-in thermography(phase image)
150-µm-thickdelamination
bondingdefects
Fundamentals
t
D
H J
t
B
E
Maxwell's Equations:
Harmonic solution:
i i
t
E
H E
t
H
E
i H E
i E H
i
J E
D E
B H
E electric field
H magnetic field
D electric flux density
B magnetic flux density
J electric current density
σ electric conductivity
ε electric permittivity
µ magnetic permeability
complex electric permittivity
ω angular frequency
t time
Electric Polarizatione dQ Qd p d e
+Q -Q +Q -Q
E
FeFe
e e T p Ee tQF E
E
0 D E P
ee 0V
p
P E
P electric polarization
pe electric dipole moment
V volume
χe electric susceptibility
ε0 permittivity of free
space
dipole formation dipole rotation
0 r D E
r e1
Capacitance
QD
AA
CDE
V E
Q CV dQ dVI C
dt dt
1V I dt
C
0 r
Y i C G
1Z
i C
Y i C
AG
Y i C
( ) '( ) ''( )i
E
Q
A
I
ideal dielectric lossy dielectric
( ) i
conducting dielectric
Y i C
AC
''( )tan
'( )D
Complex Electric Permittivity( ) '( ) ''( )i
frequency [Hz]
Ele
ctri
c P
erm
itti
vity
[a.
u.]
+
_
ε’
ε’’
_
+
dipolar
+
_
+
atomicresonance electronic
resonance
ionic
103 106 109 1012 1015 1018
_
's s0 0
lim ( ) lim i
Capacitive Probesparallel plate electrodes
sensor with guard electrodes
Vg
basic sensor
Rg
Vm
Im
stray field electrodes
Vg
Rg
Vm
Vm
Im
1
buffer
Auto-Balancing Bridge
Vg
Rg
Im
H
device under
test L
+
_
RrefIm
high-gainoperationalamplifier
2 m refV I R
1 m dutV I Z
1dut ref
2
VZ R
V
1V 2V
dutZ
vectorvoltmeter
vectorvoltmeter
“virtual”ground
Woven Composite
0
10
20
30
40
0.1 1 10 100Frequency [kHz]
Cap
acit
ance
[pF
] .
coated
uncoated
0.001
0.01
0.1
1
10
0.1 1 10 100Frequency [kHz]
Con
duct
ance
[μS
] .
coated
uncoated
conductive cloth for electric shielding
Adhesively Bonded CompositePethrick et al., 2002
0 0.5 1.0 1.5 2.0 2.5
Water Uptake [%]
Thi
ckne
ss V
aria
tion
[%
]
2.5
2.0
1.5
1.0
0.5
0.00 10 20 30 40 50 60 70 80
Time1/2 [hr1/2]
Wat
er U
ptak
e [%
]
2.5
2.0
1.5
1.0
0.5
0.0
intact122 hr580 hr
1,007 hr1,590 hr5,350 hr
Frequency [Hz]
Rel
ativ
e P
erm
itti
vity
50
40
30
20
10
010-1 100 101 102 103 104 105 106 107 108 109
Frequency [Hz]
Die
lect
ric
Los
s
103
102
101
100
10-1
10-2
10-1 100 101 102 103 104 105 106 107 108 109
intact122 hr580 hr
1,007 hr1,590 hr5,350 hr
Thermoelectric EffectSeebeck, Peltier, and Thomson effect: coupled electric and thermal flux
J electric current density
h thermal flux density
σ electric conductivity (T = 0)
κ thermal conductivity (V = 0)
V voltage
T temperature
S thermoelectric power
closed-circuit Seebeck effect:
hA
T1 T2
A
B hB
JA
JB
I
open-circuit Seebeck effect:
T1 T2
A
B
hA
hB
JA = 0
JB = 0
VS
T0 T0V+ _
S V
S T T
J
h
V J
T h
( )V S T J 0 V S T
01 2
0 1 2
S B A B
TT T
T T TV S dT S dT S dT
2 2
1 1
S A B AB( )T T
T TV S S dT S dT
Absolute Thermoelectric Power
Temperature [K]0 500 1000 1500
-40
-30
-20
-10
0
10
20
30T
herm
oele
ctri
c P
ower
[µ
V/K
]
W (tungsten)
Mo (molybdenum)
Ag (silver)
Cu (copper)
Au (gold)
Pt (platinum)
Pd (palladium)
2 2
1 1
S A B AB( )T T
T TV S S dT S dT
S AB 2 1( )V S T T
Contact Thermoelectric Tester
Primary Effect:
chemical composition
Secondary Effects:
anisotropy, texture
fatigue, cold work, plasticity, residual stress, etc.
open-circuit Seebeck effect
specimen (A)
electrical heating
“cold” junction “hot” junction
referenceelectrodes
(B)
~~
V+ _
TEP versus Chemical Composition
Ag Content [%]
20
0
-20
-40
-60
The
rmoe
lect
ric
Pow
er [
µV
/K]
0 20 40 60 80 100
273 K
83 K
Ag Content [%]
50
40
30
20
10
0
Ele
ctri
c R
esis
tivi
ty [
µΩ
cm
]
0 20 40 60 80 100
293 K
4.2 K
palladium-silver binary alloy
(Rudnitskii, 1956)
TEP Anisotropy
hexagonal single crystal
Zinc, relative to basal plane
(Rowe and Schroeder, 1970)
Temperature [K]
-3
-2
-1
0
1
2
3
0 50 100 150 200 250 300
perpendicular
parallel
The
rmoe
lect
ric
Pow
er [
µV
/K]
TEP versus Texturecold-worked polycrystalline material
Ti-6Al-4V, relative to cold work direction
(Carreon and Medina, 2006)
50 µm
before annealing after annealing
0 30 60 90 120 150 180Azimuthal Angle [deg]
-5.1
-5.0
-4.9
-4.8
The
rmoe
lect
ric
Pow
er [
µV
/°C
]
0
5
10
15
20
80 60 40 80 60 40Cold-rolling reduction [%]
Dif
fere
nce
in T
EP
[%
] gold tip referencecopper tip reference
before annealing
after annealing
Noncontacting Thermoelectric Testerclosed-circuit Seebeck effect
relative to surrounding intact material
no artificial interface
penetrating (with substantial depth)
noncontact (with substantial lift-off)
specimen
heat
thermoelectric current
magnetometer
Material Effects versus GeometryTEP is independent of size and shape
C11000 copper
diameter 0.375”
T 0.5 C/cm
2 mm lift-off distance
3” 3” scanning dimension
18 nT peak magnetic flux
before annealing
after annealing
plastic zonemilled
T
pressed
T
Residual Stress Characterizationshot-peened C11000 copper
0
5
10
15
20
25
0 2A 4A 6A 8A 10A 12A 14A 16A
Almen Peening Intensity
Mag
neti
c S
igna
ture
[nT
]
before relaxation
relaxation at 235 ºC
relaxation at 275 ºC
relaxation at 315 °C
2nd relaxation at 315 °C
3rd relaxation at 460 °C
recrystallization at 600 °C
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