Piezoelectric Materials 1

7/29/2019 Piezoelectric Materials 1

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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

Piezoelectric Materials 1

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