piezoelectricity: basics and ... - · pdf file-slip-stick motion -few calculation ... and...
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1FFM, 30.07.2010
Piezoelectricity: Basics and applications
Friday Morning Meeting, 30.07.2010Technical TalkPetar Jurcevic
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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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3FFM, 30.07.2010
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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4FFM, 30.07.2010
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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5FFM, 30.07.2010
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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6FFM, 30.07.2010
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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7FFM, 30.07.2010
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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8FFM, 30.07.2010
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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9FFM, 30.07.2010
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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10FFM, 30.07.2010
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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11FFM, 30.07.2010
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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12FFM, 30.07.2010
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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13FFM, 30.07.2010
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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14FFM, 30.07.2010
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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15FFM, 30.07.2010
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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16FFM, 30.07.2010
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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17FFM, 30.07.2010
Piezoelectric motors
-Traveling wave motor
-Inchworm motor
-Piezo ratchet motor
-Stepping sotor using slip-stick motion
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18FFM, 30.07.2010
Traveling wave motor
1996 Smart Mater. Struct. 5 361
http://www.technohands.co.jp/en/, 07.28.2010
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19FFM, 30.07.2010
Inchworm Motor
http://en.wikipedia.org/wiki/Piezoelectric_motor, 07.28.2010
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20FFM, 30.07.2010
Piezo ratchet stepping motor
http://en.wikipedia.org/wiki/Piezoelectric_motor, 07.28.2010
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21FFM, 30.07.2010
ANRv51/RES
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22FFM, 30.07.2010
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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23FFM, 30.07.2010
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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24FFM, 30.07.2010
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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25FFM, 30.07.2010
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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26FFM, 30.07.2010
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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27FFM, 30.07.2010 15
Did you really pay attention?