Piezoelectric Materials!Dr.  Tanmoy  Mai-    MSE  689  

Module-­‐Piezo-­‐II  

Certain  crystalline  ionic  materials  when  under  mechanical  stress    

leads  to  the  forma-on  of  dipoles  in  the  bulk  giving  rise  to    

polariza-on  charges  on  the  external  surface  of  this  crystal  (posi-ve  on    one  surface  and  nega-ve  on  opposite  surface)  .  This  charge  leads  to    

development  of  voltage  difference  across  the  two  surfaces.  

 The  reverse  is  also  true  for  these  crystals,  i.e.  if  external  bias  is    

applied  across  it’s  two  surfaces,  there  develops  strain  in  the  crystal,  

though  very  small.  

   These  two  effects  collec-vely  define  Piezoelectricity.  

Piezoelectricity  

•  Reason  for  Piezoelectric  effect:          The  origin  of  this  effect  lies  in  the  movement  of  ions  in  the  

crystal  due  to  the  mechanical  stress  or  external  electric-­‐filed.    

o    So  should  we  expect  all  ionic  solids  to  show  this  effect  ?       -­‐-­‐-­‐-­‐-­‐        No.  

   

    Only  those  ionic  solids  where  the  unit-­‐cell  does  Not  have  center  of  inversion  or  also  called  center  of  symmetry,  show  this  effect.  

   

No inversion center

SiO2 (Crystalline form)

NaCl

Trigonal crystal system

With inversion center

•  Piezoelectric  effect  in  ionic  solid  that  have  No  inversion  center  :  

   Quartz  (Crystalline  SiO2)  

•           A  field  of  1000V/cm  across  the  opposite  surface  of  a  cube  with  1  cm3  volume  causes    change  of  10  Angstrom  in  the  edge  length.  Of  course  it  is  negligible  and  may  not  look  very  interes-ng.    

•         However,  think  of  the  reverse  effect,  i.e.  a  mechanical  stress  causing  the  cube  edge  to  change  by  10Å  can  generate  voltage  difference  of  1000  V  !!!  

Principle of Electromechanical Coupling Enhancement

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P s

P s

E

E 2

E 1

E 1

Principle of Electromechanical Coupling Enhancement

d 33

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Ps

E 2

d 15

d15 >> d33 > d31 in Perovskites

Ps

E2

d31

Piezoelectric materials belong to the non-centrosymmetric point groups (with the exemption of 432) or non-centrosymmetric Curie groups.

Consider non-linear electric field strains:

Hooke’s Law Piezoelectric

Effect Electrostrictive Effect

Mijkl – electrostrictive coefficient

Electrostrictive coefficients are present in all non-metallic materials regardless of symmetry

Electrostriction can also be defined through the polarization:

x = QP2

In a ferroelectric: P = Pspontaneous + Pind; Pind ≈ ε0 εrE

x = Q (PS + Pind)2.

= Q (Ps + ε0εrE)2

= Q Ps2 + 2Qε0εrPsE + Q(ε0εr)2E2

Intrinsic Piezo term d= 2Qε0εrPs

M=Q(ε0εr)2

isotropic

Piezoelectric Materials

Application Examples • Piezoelectric Crystals– Quartz  Frequency Control Devics  e.g. Watches   SAW Devices - Filters

• Ferroelectric

– PZT

* Actuators

* Fuel Injectors (Automotive)

* Inkjet Printerheads

(Consumer Electronics)

* Ultrasound Probes

(Biomedical)

* Dynamic Pressure

Sensors

Development  of  PZT  

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 Lead zirconate titanate, Pb(ZrxTi1-x)O3 (PZT), belong to the family of A +2B+4O3 type perovskite structures. PZT is a solid solution of PbZrO3 and PbTiO3.

 The spontaneous polarization of PbTiO3 (≈81µC/ cm2) is also three times larger than that of BaTiO3 (≈25 µC/cm2)

  PbTiO3 has high tetragonality (c/a = 1.06) as compared to that of BaTiO3 (c/a = 1.008) which leads to the cracking of PbTiO3 on cooling through the Curie point (4900C) after sintering due to high transformation strains.

  In order to reduce the tetragonality of PbTiO3, several compositional modifications were performed and in this way PZT was discovered when Zr was substituted for Ti.

AXII BVI OVI

A O B

FE-Tetragonal FE-Rhombohedral

After Jaffe et. al., 1964.

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Doping of PZT

Typical Properties

“Hard” “Soft”

d33 150 pC/N 593 pC/N

d31 - 60 pC/N - 273 pC/N

Tc 300˚C 195˚C

r 7.7 g/cm3 7.8 g/cm3

e33 1,000 3,400

Loss 0.004 0.02

Ec 15 kV/cm 6 kV/cm

Q > 1,000 60–80

Hard PZT •Relatively low dielectric constant

~1000

•Low dielectric loss

tand0.005

•Moderately lowered electronic resistivity

•High mechanical Q

•More difficult to pole and depole

•Dark color

Soft PZT •Increased dielectric contant

~1800

•High dielectric loss

tan d 0.02

•Increased elastic compliance

•Low Qm

•High piezoelectric coupling

•Low coercive field

•Increased resistivity

•Small aging effects

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Softeners

  Widely used soft additives are La3+, Sb3+, Sb5+, Nb5+, Nd3+, Bi3+, V5+ cations. These softeners soften the properties of PZT.   They usually cause a decrease in the coercive field, electrical and mechanical quality factors and increase in the dielectric constant, electromechanical coupling coefficient, elastic compliance coefficient and resistivity.   The mechanism under which PZT ceramics exhibit enhanced piezoelectric response is mainly associated with the creation of Pb vacancies. The existence of Pb vacancies makes the domain wall motion easier during poling, which in turn enhances the dielectric and piezoelectric response of PZT.

Hardeners  Hardeners increase the coercive field and quality factors while they tend to decrease the dielectric constant, electromechanical coupling coefficient and resistivity.  Hard additives include K+, Na+, Fe 2+, Fe 3+, Co 2+, C03+, Ni 2+, Mg 2+, Al 3+, Cr 3+,Ga 3+, In 3+ Sc 3+ cations.

Hard PZT High power or hard PZT can withstand high levels of electrical

excitation and mechanical stress. Suited for high voltage, high power generators and transducers.

PZT-4 (DoD Type I)

PZT used for ultrasonic cleaning, sonar, high power acoustic radiation sources. Can be used under constant and repetitive conditions.

PZT-4D

Higher piezoelectric activity at the expense of slight increase in mechanical and dielectric loss. Used in motor-type applications.

PZT-8 (DoD Type III)

Slightly lower piezoelectric activity than PZT-4. Has extremely high mechanical quality and low tanfE losses. Modified MPB – Sr and Fe additions.

High Sensitivity “Soft” Materials -sensors, as under drive the higher loss can cause heating

PZT-5A (DoD Type II) High sensitivity and permittivity and time stability Pb (Zr0.52Ti0.48) O3+Nb2O5

PZT-5B Used in Bimorph-higher sensitivity and higher piezoelectric activities than PZT-5A. (lower TC than in PZT-5A.)

PZT-5J Used in fuses, hydrophones and other applications requiring a combination of high energy and high voltage output.

PZT-5H (DoD Type VI) The lowest Curie temperature of PZT-5 family. This limits the temperature stability. Wide range of uses from hydrophones to ink jet printers. High K, d33 and K33.

PZT-5R Applications as towed arrays – high accoustic sensitivity and high coupling with high permittivity

PZT-7A This material is used in ultrasonic delay lines and other high frequency shear resonance applications. High K15, low K and high temperature stability to provide low distortion in electric resonance circuits.

PZT-7D With lower dissipation than PZT-7A and used in applications requiring higher power handling. Higher K, higher d33 with a little reduction in K33. Low aging rates.

PMN-1 Used in accelometers, floor detection and thickness gauges. modified lead metaniobate – high Curie temperature.

PMN-2 Higher operating conditions than PZT but lower than PMN-1. Higher piezoelectric activity, low K.

Crystal Orientation Dependence of Piezoelectricity in PZT

Convential Orientation along Ps

Enhancement by 5 times

e 31 ef

f C/m 2

3.2

3.6

4

4.4

4.8

5.2

5.6

6

6.4

Zr/Ti content 40/60 50/50 60/40 70/30 80/20

PZT(100)

PZT(111)

Random Orientation

*Soft materials are sometimes developed from basic PZT by lower transition temperatures through isovalent substitutions such as Sr+2 and Ba+2

This raises both K and d33.

Other Piezoelectrics:

PNN (Relaxor)

PZ PT

xPbTiO3-(1-x) Pb (Mg1/3Nb2/3) O3

Electrostrictive→induced piezoelectric-piezoelectric

Modified Lead Titanate (PbSm) (Ti,Mn),(Pb,Ca) (Ti,Mn) O3

High Q – 1000

d33≃40 to 65 pC/N

Piezo multilayer actuators for Diesel Common Rail injection systems

Piezo actuator module Piezo Injector

Injector head

Injector body

Nozzle

K. Lubitz et. al [Siemens]

Search  for  New  Piezoelectrics  

€

P = dX

€

x = dE

Designing MPB from Tolerance Factor

Ref. Isupov et al. (1983)

AXII BVI OVI

Tolerance  Factor  –  TC  Rela-onship  

Look  to  lower  tolerance  factor  for  increased  TC  

Ref.: V.A. Isupov et al, Ferroelectrics 207 (3-4): 507–517 (1998):

‘t’ > 1 Tetragonal

‘t’<1 Rhombohedral

Electromechanical  Proper-es:    MPB  Behavior  

Properties Summary: • BiScO3-xPbTiO3 Analogous to PZT • Peak properties for 64mol% PT

• K33 = 2000 • kp = 0.56 • d33 = 460 pC/N (520pC/N-Berlincourt)

R. Eitel et al., Jap. J. Appl. Phys. 40, 5999 (2001).

Bi-­‐Perovskites—A  Wide  Composi-onal  Space  to  Explore  New  High  Tc,  Piezoelectric  Materials  

Binary Systems BiMe+3O3–PbTiO3

BiFe+3O3–PbTiO3

BiMn+3O3–PbTiO3

BiCuO3–PbTiO3

BiScO3–PbTiO3

BiInO3–PbTiO3

BiGaO3–PbTiO3

BiYbO3–PbTiO3

Bi(Me+21/2Me+4

1/2)O3–PbTiO3

Bi(Mg1/2Ti1/2)O3–PbTiO3

Bi(Ni1/2Ti1/2)O3–PbTiO3

Bi(Co1/2Ti1/2)O3–PbTiO3

Bi(Mg1/2Zr1/2)O3–PbTiO3

Bi(Zn1/2Zr1/2)O3–PbTiO3

Bi(Me+22/3Me+5

1/3)O3–PbTiO3 Bi(Mg2/3Nb1/3)O3–PbTiO3

Bi(Zn2/3Nb1/3)O3–PbTiO3

Bi(Mg2/3Ta1/3)O3–PbTiO3

Bi(Zn2/3Ta1/3)O3–PbTiO3

Bi(Co2/3Ta1/3)O3–PbTiO3

Bi(Co2/3Nb1/3)O3–PbTiO3

Bi(Me+23/4Me+6

1/4)O3–PbTiO3

Bi(Mg3/4W1/4)O3–PbTiO3

Bi(Co3/4W1/4)O3–PbTiO3

Bi(Me+zxMey

1-x)O3

For all zx+y(1-x)=3 and ionic radii compatible with perovskite stability