Post on 14-Apr-2018
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Piezoelectric Materials
Background
Certain materials generate an electric charge
(or voltage) when they are under mechanical
s ress. s s nown as e rec e ec o
piezoelectricity.
The same materials would be able to produce amechanical deformation (or force) when an
electric field is a lied to them. This is called
the inverse effect of piezoelectricity (or the
converse effect of piezoelectricity).
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Background In 1880, Pierre and Jacques Curie experimentally
discovered the direct piezoelectric effect in various
naturally occurring substances including Rochelle salt
andquartz.
In 1881, Hermann Hankel suggested using the term
piezoelectricity, which is derived from the Greek
piezen meaning to press.
It was mathematically hypothesized and then
experimentally proven that a material exhibiting thedirect effect of piezoelectricity would also exhibit the
inverse effect.
Background In 1921, Walter Cady invented the quartz crystal-
controlled oscillator and the narrow-band quartz
crystal filterused in communication.
Two important artificial piezoelectic crystals,barium
titanate and lead zirconate titanate were invented in
the early 1950s. They are synthesized materials andmust be electrically poled in order to exhibit
significant significant piezoelectric effects.
In 1958, synthetic quartz material became available.
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Application Historically
Phonograph pickups, microphones, acoustic modems,
acoustic imaging for underwater, underground objects, and
medical observation.
Today
MEMS sensors and actuators, on-chip acoustic
transducers, pumps and valves for liquid and
particles, accelerometers, speakers and
microphones, mirrors, and chemical sensors, etc.
Advantages Unlimited resolution: subnanometer range
Large force generation: a force of several 10,000 N
No magnetic fields
Low power consumption No wear and tear
Vacuum and clean room compatible
Operation at cryogenic temperature
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Types of Piezoelectric materials
zSingle crystals)(quartz)(Rochelle salt)
z
(ZnO)PLZTPZT(sputtering)z (Polymer)
z (Ceramics)
(PZT, lead zirconate titanate, )33 PbTiOPbZrTiO (barium titanate, )
z
3BaTiO
Material Aspects Piezoelectric crystals can be considered to be a mass
of minute crystallites (domains). The macroscopic
behavior of the crystal differs from that of individual
, .
The direction of polarization between neighboring
crystal domains can differ by 90 or 180 degrees.
Owing to the random distribution of domains
throughout the material, no overall polarization or
iezoelectric effect is exhibited.
A crystal can be made piezoelectric in any chosen
direction bypoling, which involves exposing it to a
strong electric field at an elevated temperature.
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Material Aspects
Under the action of this field, domains most nearlyaligned with the field will grow. The material will
also lengthen in the direction of the field. When the
,
approximate alignment.
A crystal may be depolarized mechanically,
electrically, orthermally.
Exposure to a strong electric field of opposite polarity
element. The threshold is typically between 200-500
V/mm.
Material Aspects Mechanical depolarization occurs when mechanical
stress on a piezoelectric element becomes high
enough to disturb the orientation of the domains and
.
If a piezoelectric element is heated to a certain
threshold temperature, the crystal vibration may be sostrong that domains become disordered and the
element becomes completely depolarized. This
the Curie point.
A safe operating temperature would normally be
halfway between 0 and the Curie temperature.
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Material Aspects
The properties of piezoelectric elements are timedependent.
Many piezoelectric materials do not provide long-
erm s a c o ng power w en use n ac ua ors.
The design of piezoelectric actuators operating in DC
conditions must consider electric leakage.
Material Aspects Piezoelectric materials are crystals, naturally
occurring or synthesized.
The microscopic origin of piezoelectricity is the
sp acemen o on c c arges w n a crys a ,
leading to the polarization and electric field.
A stress (tensile or compressive) applied to apiezoelectric crystal will alter the spacing between
centers of positive and negative charge sites in each
.
manifested as open circuit voltages measurable at the
crystal surface. Compressive and tensile stresses will
generate electric fields and hence voltages of opposite
polarity.
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Material Aspects
An external electric field will exert a force betweenthe centers of positive and negative charges, leading
to an elastic strain and changes of dimensions
.
Hysteresis All piezoelectric ceramics exhibit hysteresis.
This is the difference in the strain that occurs when a particular
voltage is approached from lower voltage and from higher
voltage.
The magnitude of the hysteresis is specified as the maximum
difference in extension at any point on the extension versus
voltage curve expressed as a percentage of the maximumextension.
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butterfly diagram The normal hysteresis curve ABwhen the applied voltage is positive
Reverse bias produces negative
extension along curve C until at the
depoling voltage the extension per
vo su en y urns pos ve
following the curve D.
The process is repeated along
curves EFG when the voltage is
made positive again.
The butterfly diagram provides acomplete characterization of the
depoling and repoling process.
Manufacturing Process for Piezoelectric
Ceramics
The manufacturing process starts with mixing and
ball millin of the raw materials.
Next, the mixture is heated to 75% of the sintering
temperature to accelerate reaction of the components.
The polycrystalline, calcinated powder is ball milled
again to increase its reactivity.
processing properties.
After shaping andpressing the (green) ceramics is
heatedto 750 to burn out the binder.
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Manufacturing Process for Piezoelectric
Ceramics
The next phase is sintering at temperature between
1250 and 1350 .
The ceramic block is cut, ground,polished, lapped,
etc., to the desired shape and tolerance.
Electrodes are applied by sputtering or screen
printing processes.
The last ste is the olin rocess which takes lace
in a heated oil bath at electrical fields up to several
kV/mm.
Manufacturing Process for Piezoelectric Thin
Film
Thickness below 100 micrometers.
S utter De osition or radio fre uenc ma netron
sputter deposition method () Metal organic chemical vapor deposition method(
) Sol-gel method()
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Piezoelectric Equations
The direction of positive polarization is customarily
-
system.
Piezoelectric Equations- Direct effect
The constitutive equation that relates electrical
polarization (D) and appliedmechanical stress (T) is
EdTD +=
where dis thepiezoelectric coefficient matrix, theelectric permittivity matrix, andEthe electrical field.
1T
+
=
3
2
1
333231
232221
131211
6
5
4
3
2
363534333231
262524232221
161514131211
3
2
1
E
E
E
T
T
T
T
T
dddddd
dddddd
dddddd
D
D
D
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Piezoelectric Equations- Inverse effect
The constitutive equation that relates the total strain S
and the applied electrical field (E)
where s is the compliance matrix.
s +=
1232221
131211
2
1
262524232221
161514131211
2
1
Eddd
ddd
T
T
ssssss
ssssss
S
S
+
=
3
2
636261
535251
434241
333231
6
5
4
3
666564636261
565554535251
464544434241
363534333231
6
5
4
3
E
E
ddd
ddd
ddd
T
T
T
ssssss
ssssss
ssssssssssss
S
S
S
The unit ofelectric field
The unit ofstress iT
m
V
thickness
VoltageEi ==
2mN
CVFe un o e ec r c sp acemen i
The unit ofpermittivity mF/i
2mmm
===
The unit ofpiezoelectric constantN
Columb
m
NmV
mF
T
E
T
Ddij ====
2
The unit ofcompliance m
There is no unit forstrain.
ij
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Another form of equation
{ } [ ] { } [ ] { } 1336166616 = EeScTE
1333166313 += ESeD
[ ] [ ] 1= sc [ ] [ ] [ ] [ ] [ ] 66631
666363
==EE
cdsde
Stiffness matrix Piezoelectric coefficient matrix 2m
C
[ ]
=
000
00000
00000
333231
24
15
2
eee
e
e
e mm [ ]
=
000
00000
00000
333131
15
15
6
eee
e
e
e mm
Electromechanical coupling coefficient
A measure of how much energy is transferred from
electrical to mechanical energy, or vice versa, during the
actuation process.
energyinput
convertedenergyk
_
_2 =
The magnitude ofkis a function of not only the material,
but also the geometries of the sample and its oscillation
mo e.
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Quartz
[ ]N
ms
212
10
904.200000
0004.2005.45.4
0006.922.122.1
005.422.177.1279.1
005.422.179.177.12
=
[ ] )(10000000
6.467.00000
0067.003.23.212
N
Cor
V
md
=
[ ]
=
52.400
052.40
0052.4
10854.8 12T
1.2990000
Youngs modulus 107 GPa, density 2650 kg/m3, coupling
factork=0.09.
PZT-4
= 11
11
33 00
00
T
[ ]N
ms
212
100039000
0005.1531.531.5
00031.53.1205.4
00031.505.43.12
=
[ ]
=
66
44
44
331313
131112
131211
00000
00000
00000
000
000
000
s
s
s
sss
sss
sss
s
[ ]
=
130000
014750001475
10854.8 12T
04960000
3300
[ ]
=000
00000
00000
333131
15
15
6
ddd
d
d
d mm
7.3200000
0390000
[ ] )(10000289123123
0049600012
Nor
V
md
=
Youngs modulus 48-135 GPa, density 7500 kg/m3, coupling
factork=0.6, Curie temperature 365 C.
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PZT-5A
11 00
T
[ ]N
ms
21210
005.47000
0008.1822.722.7
00022.74.1674.5
00022.774.54.16
=
[ ]
=
66
44
44
331313
131112
131211
00000
0000000000
000
000
000
s
ss
sss
sss
sss
s
[ ]
=
170000
017300
001730
10854.8 12T
=
33
1133
00
[ ]
=
000
00000
00000
333131
15
15
6
ddd
d
d
d mm
3.4400000
05.470000
[ ] )(10000374171171
00584000 12
N
Cor
V
md
=
Youngs modulus 48-135 GPa, density 7750 kg/m3, coupling
factork=0.66, Curie temperature 365 C.
PZT-5H
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Ys 111 = Ys =12 ( ) Ys += 1244
9100.2 =Y 33.0=
2PVF
[ ]
=
44
44
111212
121112
121211
00000
00000
000
000
000
s
s
sss
sss
sss
s
[ ]
= p
pT
00
00
00
331110854.8
12 = p
[ ]V
md PVF
122 10
00033323
000000
000000
= 3231 dd 015 =d 024 =d
44s
PVDF (polyvinylidenfluoride) is a synthetic
fluoropolymer with monomer chains of (-CH2-CF2-)n
[ ] )(1000030220
001000
01000012
N
Cor
V
md