6 Special Methods

6.1 Microwave Techniques

6.2 Dielectric Measurements

6.3 Thermoelectric Measurements

6.1 Microwave Techniques

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

6.2 Dielectric Measurements

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

6.3 Thermoelectric Measurements

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