Piezoelectricity: Basics and applications Friday Morning Meeting, 30.07.2010 Technical Talk Petar Jurcevic 1
Overview -A simple molecular model -Mathematical modelling -Some general notes -Overview Motors -Slip-stick motion -Few calculation regarding Slip-stick motion motors 2
Definition: Piezoelectricity Piezoelectricity is the ability of some materials to generate an electric charge in response to applied mechanical stress The piezoelectric effect is revesible: direct piezoelectric effect: charge separation due to stress converse piezoelectric effect: occurens of stress and strain when electric field is applied 3
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 4
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 5
A simple molecular model Applied external stress: -Internal structure is deformed separation of charge centers dipols are generated Lecture Notes, Tomasz G. Zielinski, Warsaw, Poland 6
A simple molecular model Poles inside material are mutually cancelled Charge occurs on surface polarization of material Lecture Notes, Tomasz G. Zielinski, Warsaw, Poland 7
Mathematical modeling Piezoelectricity is the combination of: The materials electrical behavior: And Hook s law: S = st D = ²E D: electric displacement, ε: permittivity, E: electric field strength S: strain, s: compliance, T: stress The coupled strain-voltage equation: S = s E T + d t E D=² T E + dt converse piezoelectric effect direct piezoelectric effect d ij,k = S ij E k piezoelectric coefficient 8
Mathematical Modeling S αβ T γχ S S S T T T 11 12 13 11 12 13 S21 S22 S 23????? s T21 T22 T E αβγχ 23 S31 S32 S 33 T31 T32 T 33 3 3 S s T E 1 1 : strain of the β-normal in α-direction : stress action in γ-direction on plane with χ-normal D 1 D 2 D 3 = ² 11 0 0 0 ² 22 0 0 0 ² 33 E 1 E 2 E 3 9
Mathematical Modeling Polarization direction Piezoelectric body Stress & strain are symmetric tensors: Voigt Notation 11 1; 22 2; 33 3; 23 4; 13 5; 12 6 10
An example A 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: d 31 =4pm/V, d 33 =12pm/V, d 15 =0pm/V What is the strain? = S1 S2 S3 S4 S5 S6 0 0 d31 0 d31 0 0 d33 0 d15 0 d15 0 0 0 0 0 E 1 E2 E3 = 0 0 4E 12m/V 0 0 4E 12m/V 0 0 12E 12m/V 0 0 0 0 0 0 0 0 0 4 3 = 23 8E 12 8E 12 24E 12 0 0 0 And L? L = 8E 15m 8E 15m 120E 15m 11
Real behavior Piezoelectric ceramics show hysteresis in polarization And they show hysteresis in strain http://www.americanpiezo.com/piezo_theory/, 07.28.2010 12
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: ρ σ = ( ρ ρ ) S ρ σ : 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 13
Electrostriction -Change in shape by applying electrical field - Proportional to the square of the field S ij = γ ijkl E k E l γ ikjl = 1 2 2 S ij E k E l -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 14
Some piezoelectric materials Naturally 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) 15
Applications Sensor -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 16
Piezoelectric motors -Traveling wave motor -Inchworm motor -Piezo ratchet motor -Stepping sotor using slip-stick motion 17
Traveling wave motor 1996 Smart Mater. Struct. 5 361 18 http://www.technohands.co.jp/en/, 07.28.2010
Inchworm Motor 19 http://en.wikipedia.org/wiki/piezoelectric_motor, 07.28.2010
Piezo ratchet stepping motor 20 http://en.wikipedia.org/wiki/piezoelectric_motor, 07.28.2010
ANRv51/RES 21
Slip-Stick Inertial Motion 1 2: Slow rising flank of voltage, Rod and table move simutaneously 2 3: Fast decreasing voltage flank, piezo contracts 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 22
Currents at 1000Hz slow rising flank or loading voltage: fast falling flank of discharge voltage: τ rise 1ms τ fall 10μs C P,RT =2.8μF du RT =30V I rise,rt =84mA I fall,rt =8.4A I = CU τ C P,LT =0.2μF du LT =70V I rise,lt =14mA I fall,lt =1.4A Ī average,rt =167mA Ī average,lt =28mA 23
Effects of resistive wiring 70V sawtooth signal 1µF capacitance RC time constant τ = RC Cabling capacitance of up to 10nF has barely no effect Attocube systems AG, Technical note: Effects of resistive wiring 24
Heat dissipation Assumption: F friction =5N, Step size: 100nm 500nJ At 1000Hz 500µW Electrical loss: P = CU 2 ftan(δ), δ 1 P =17mW Rotator has 2 piezos U 1.1J 2P, t 90 30s 25
Absolut position encoder Position is read out with a potentiometer R AW depends on T R AB depends on T http://www.markallen.com/teaching/ucsd/147a/lectures /lecture3/1.php, 07.29.2010 But, R AW /R AB is T independent in equilibrium Absolut position Encoder has a blind spot of about 40 26
Did you really pay attention? 15 27