1FFM, 30.07.2010

Piezoelectricity: Basics and applications

Friday Morning Meeting, 30.07.2010Technical TalkPetar Jurcevic

2FFM, 30.07.2010

Overview-A simple molecular model

-Mathematical modelling

-Some general notes

-Overview Motors

-Slip-stick motion

-Few calculation regarding Slip-stick motion motors

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Definition: Piezoelectricity

Piezoelectricity is the ability of some materials to generatean electric charge in response to applied mechanicalstress

The piezoelectric effect is revesible:

direct piezoelectric effect: charge separation dueto stress converse piezoelectric effect: occurens of stress and strain when electric field is applied

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A simple molecular model

- Only insulating materials- Insulating Ferroelectrica and materials with a permanent

dipol- In crystals: only crystals without symmetry centre

20 point groups

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A simple molecular model

Without any external stress:

-Centers of charges coincide-charges are reciprocally cancelled-electrical neutral unit cell

Lecture Notes, Tomasz G. Zielinski, Warsaw, Poland

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A simple molecular model

Applied external stress:

-Internal structure is deformedseparation of charge centersdipols are generated

Lecture Notes, Tomasz G. Zielinski, Warsaw, Poland

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A simple molecular model

Poles inside material are mutually cancelled

Charge occurs on surfacepolarization of material

Lecture Notes, Tomasz G. Zielinski, Warsaw, Poland

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Mathematical modelingPiezoelectricity is the combination of:

The materials electrical behavior:

And Hook’s law:

D = ²E

S = sT

D: electric displacement, ε: permittivity, E: electric field strengthS: strain, s: compliance, T: stress

converse piezoelectric effect

D=²TE + dT direct piezoelectric effect

piezoelectric coefficient dij,k =∂Sij∂Ek

The coupled strain-voltage equation:

S = sET + dtE

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Mathematical Modeling11 12 13 11 12 13

21 22 23 21 22 23

31 32 33 31 32 33

?????S S S T T TS S S T T TS S S T T T

sEαβγχ

3 3

1 1ES s T

: strain of the β-normal in α-direction

: stress action in γ-direction on plane with χ-normal

Sαβ

Tγχ ⎡⎣ ²11 0 00 ²22 00 0 ²33

⎤⎦⎡⎣ E1E2E3

⎤⎦⎡⎣ D1D2D3

⎤⎦=

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Mathematical ModelingPiezoelectric body

Pol

ariz

atio

n di

rect

ion

Stress & strain are symmetric tensors:

Voigt Notation

11 → 1; 22 → 2; 33 → 3; 23 → 4; 13 → 5; 12 → 6

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An exampleA proper voltage is applied over a free standing piezoelectric element to create a electrical field of E=(4, 3, 2) V/m. The dimensions of the element are L=(1, 1, 5)mm. The constants are: d31=4pm/V, d33=12pm/V, d15=0pm/V

What is the strain?

And ∆L?

⎡⎢⎢⎢⎢⎢⎢⎣S1S2S3S4S5S6

⎤⎥⎥⎥⎥⎥⎥⎦=⎡⎢⎢⎢⎢⎢⎢⎣0 0 d310 d310 0 d330 d15 0d15 0 00 0 0

⎤⎥⎥⎥⎥⎥⎥⎦⎡⎣ E1E2E3

⎤⎦ ⎡⎣ 4323

⎤⎦=

⎡⎢⎢⎢⎢⎢⎢⎣0 0 4E−12m/V0 0 4E−12m/V0 0 12E−12m/V0 0 00 0 00 0 0

⎤⎥⎥⎥⎥⎥⎥⎦ =

⎡⎢⎢⎢⎢⎢⎢⎣8E − 128E − 1224E − 12

000

⎤⎥⎥⎥⎥⎥⎥⎦

∆L =

⎡⎣ 8E − 15m8E − 15m120E − 15m

⎤⎦

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Real behaviorPiezoelectric ceramics show hysteresis in polarization

And they show hysteresis in strain

http://www.americanpiezo.com/piezo_theory/, 07.28.2010

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Piezoresistive effect- Change in resistivity due to applied mechanical stress.

- But differs from Piezoelectric effect: It changes only resistivity and does not create an electric potential.

- Effect is mainly seen in semiconductors:

ρσ =( ∂ρρ )S ρσ: Piezoresistivity, ρ: origninal resistivity, S: strain

Mechanism:

- Change in inter-atomic spacing affects bandgaps- Bandgaps might be shifted- Shape might be affected -> change in effective mass

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Electrostriction-Change in shape by applying electrical field

- Proportional to the square of the field

γikjl =12

∂2Sij∂Ek∂El

Sij = γijkl ×Ek × El

-Is not reversible

-Occurs in all dielectric materials and in all 32 point groups

-Caused by randomly aligned electrical domains-applied field aligns electrical domains-opposite charges of domains attract each other-material thickness is reduced along applied field

Eswar Prasad, Lecture Notes

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Some piezoelectric materialsNaturally occuring:

-Quarz -Cane sugar -Collagen-Topaz -DNA-Rochelle salt -Wood-many many others -Tendon

Man-made crystals-Gallium orthophosphate (GaPO4), a quartz analogic crystal -Langasite (La3Ga5SiO14), a quartz analogic crystal

Man-made ceramics-Barium titanate(BaTiO3)-Barium titanate was the first petzoelectric ceramic discovered-Lead zirconate titanate (Pb[ZrxTi1−x]O3 0<x<1)—more commonly known as PZT, lead zirconate titanate is the most common piezoelectric ceramic in use today-Lithium niobate (LiNbO3)

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ApplicationsSensor

-Microphones, Pick-ups-Pressure sensor-Force sensor-Strain gauge

Actuators-Loudspeaker-Piezoelectric motors-Nanopositioning in AFM, STM-Acuosto-optic modulators-Valves

High voltage and powersource-Cigarette lighter-Energy harvesting-AC voltage multiplier

Frequency standart

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Piezoelectric motors

-Traveling wave motor

-Inchworm motor

-Piezo ratchet motor

-Stepping sotor using slip-stick motion

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Traveling wave motor

1996 Smart Mater. Struct. 5 361

http://www.technohands.co.jp/en/, 07.28.2010

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Inchworm Motor

http://en.wikipedia.org/wiki/Piezoelectric_motor, 07.28.2010

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Piezo ratchet stepping motor

http://en.wikipedia.org/wiki/Piezoelectric_motor, 07.28.2010

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ANRv51/RES

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Slip-Stick Inertial Motion1 2: Slow rising flank of voltage, Rod and table move simutaneously

2 3: Fast decreasing voltage flank, piezocontracts fast and rod slips through table, inertia is overcome

Conversion of motion:Signal is inverted in time, not in voltage

Attocube systems AG, Technical note

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Currents

CP,LT = 0.2μF

dULT = 70V

at 1000Hz slow rising flank or loading voltage:fast falling flank of discharge voltage:

τrise ≈ 1ms

τfall ≈ 10μs

I = CUτ

CP,RT = 2.8μF

dURT = 30V

Ifall,RT = 8.4A

Irise,RT = 84mA

| I |average,RT=167mA

Ifall,LT = 1.4A

Irise,LT = 14mA

| I |average,LT=28mA

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Effects of resistive wiring

Attocube systems AG, Technical note: Effects of resistive wiring

70V sawtooth signal1µF capacitance

RC time constantτ = RC

Cabling capacitance of up to 10nF has barely no effect

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Heat dissipationAssumption: Ffriction=5N, Step size: 100nm

At 1000Hz 500µW

500nJ

Electrical loss: P = CU2ftan(δ), δ ≈ 1◦

P = 17mW

Rotator has 2 piezos 2P, t90° ≈ 30s

U ≈ 1.1J

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Absolut position encoderPosition is read out with a potentiometer

RAW depends on TRAB depends on T

But, RAW/RAB is T independent in equilibrium

Absolut position

Encoder has a “blind spot” of about 40°

http://www.markallen.com/teaching/ucsd/147a/lectures/lecture3/1.php, 07.29.2010

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