1. Piezoelectric ceramics1

2. X = C x C: elastic modulus
Piezoelectricity
In a conventional solid, a mechanical stress X causes a proportional elastic strain x
X = C x C: elastic modulus
Piezoelectricity (“piezo”: Greek word meaning “to press”) is the additional creation of electric charges by the applied stress. The charge is proportional to the force (linear effect) and has opposite sign for compression and tension.
Direct piezoelectric effect: D = Q/A = d X
For FE materials D  P  P = d X
D: dielectric displacement; P: polarization;
Q: charge; A: area;
d: piezoelectric coefficient
(polarization = d * stress)
Direct effect
Contraction P + - F Q
Expansion

3. Piezoelectricity Converse effect + - + - Transducers Actuators
Converse piezoelectric effect: x = d E (strain = d * electric field)
An applied electric field E produces a proportional strain x (linear effect), expansion or contraction, depending on polarity.
Converse effect
Contraction P + - E P + -
Expansion E
Mechanical stress/pressure Polarization/Charges/current
Electric field Strain
Transducers
Actuators
Mechanical energy
Electrical energy
Piezoelectric crystals: quartz, ZnO, tourmaline (also pyroelectric), polyvinylidene fluoride (PVDF), PZT and all ferroelectric crystals. In the following only piezoelectric ferroelectric materials (single crystals, ceramics and films) will be discussed.

4. d i j Piezoelectricity X2 X4
Equations for the piezoelectric effect are generally written in matrix form as they relate properties along different directions of the crystal. X4
3 [001]C
2 [010]C
1 [100]C X2
d i j
Direction of
stress
polarization 6 Xj
stress components
j = 1..3: extensional/compressive stress
j = 4, 5, 6: shear stress 4 5
3x6=18 coefficients
15 independent (dij=dji; I,j=1..3)
di4, di5, di6: piezoelectric
shear coefficients xj
strain components
j = 1..3: elongation/contraction
j = 4, 5, 6: shear strain: variation of the angles between the two axis in the plane perpendicular to axis 1, 2, 3.

5. Piezoelectricity 4mm P P P
For a tetragonal crystal (4mm symmetry), there are only 3 piezoelectric coefficients: d31, d33, d15
3 [001]C
2 [010]C
1 [100]C P
(4)
(5)
(6)
4mm
3 ≡ Polar axis
d31: polarization generated in the 3 direction (vertical direction) as a result of a stress applied in a lateral direction (1 or 2)
d33: polarization generated in the 3 direction (vertical direction) as a result of a stress applied in vertical direction (3)
d15 : polarization generate along axis 1 (or 2) by a shear stress (d15 = d24) 3 1
(5) P 3 2 1
Poling direction P
Ceramics. Poling is needed for the alignment of the electrical dipoles inside each grain or domain. A piezoelectric ceramic is a poled ferroelectric ceramic material.
For a poled ceramic (mm symmetry ) sample there are only 3 piezoelectric coefficients d31, d33, d15 as in tetragonal 4mm crystals.

6. Piezoelectricity
Sketch of the piezoelectric effect in a single domain PbTiO3 tetragonal crystal
(a)
(b)
(c)
(d) 3 1 X3 X1 X5
P3=d33X3
P3=d31X1
P1=d15X5
X1, X3, X5: stress
ΔP3, ΔP1: variation of polarization
No field.
Shift of the Ti ions further away from the equilibrium position (ΔP1=ΔP2=0; ΔP3>0).
Shift of the Ti ion back towards the cell center (ΔP1=ΔP2=0; ΔP3<0)
Tilting of the Ti position under a shear stress (ΔP1>0; ΔP2=0; ΔP3<0). 6

7. Domain-wall contribution to the properties of ferroelectric materials
(5) POLARIZATION ROTATION 7

8. dij: piezoelectric coefficients; Qij: electrostrictive coefficients;
Piezoelectricity
The LGD (Landau-Ginsburg-Devonshire) theory for a tetragonal crystal predicts:
dij: piezoelectric coefficients;
Qij: electrostrictive coefficients;
Ps: spontaneous polarization (P3)
ε33: permittivity along polar axis
A large dielectric constant and a high spontaneous polarization are required to attain high values of the piezoelectric coefficients. The coefficients Qij are nearly independent of temperature.

9. Strength of the piezoelectric effect
Piezoelectricity
Strength of the piezoelectric effect
Piezoelectric coupling factor , always <1.
Typical values of kp:
0.1 for quartz, 0.35 for BaTiO3, for PZT, 0.9 for Rochelle salt. 0-9 for PMN-PT
Properties of commercial piezoelectric ceramics
Property
BaTiO3
PZT-1
(hard PZT)
PZT-2
(soft PZT)
Na1/2K1/2NbO3 TC
130
315
220
420
33
1900
1200
2800
400
tan 
0.007
0.003
0.016
0.01 kp
0.38
0.56
0.66
0.45
d31
-79
-119
-234
-50
d33
190
268
480
160 Qm
500
1000 50
240
Qm: mechanical quality factor = f / f0 (inverse of mechanical loss) 9

10. Properties of PZT and piezoelectric ceramics10

11. Morphotropic phase boundary (MPB)
The morphotropic phase boundary in PZT
Polarization TC
Morphotropic phase boundary (MPB)
PbZrO3
PbTiO3
TC =370°C at MPB
Dielectric constant and coupling coefficient
Morphotropic phase boundary (MPB): abrupt structural change with composition at constant temperature. R-T transition mediated by the M phase.
Phase coexistence occurs around the MPB.
Coupling coefficients, piezoelectric coefficients and dielectric constant peak at the MPB.
Piezoelectric coefficients
The morphotropic phase transition is a key to high piezolectric performance 11

12. The morphotropic phase boundary in PZT
Enhancement of electromechanical properties near the MPB: polarization rotation.
High piezoelectric properties determined by flat free energy surface (structural instability)
Gibbs free energy diagram for PZT 60/40.
R: rhombohedral (stable, P1 = P2 = P3),
T: tetragonal (P3 >0, P1 = P2 = 0),
O: orthorhombic (P1, P2 >0, P3 = 0)
C: cubic (P1 = P2 = P3 = 0).
PZT 60/40
R-C path: variation of PS along the [111] direction (GR)
MA ([111]c-[001]c) monoclinic distortion path: R  T:
field applied along [001]C (up, P3 > P1, P2)
MB ([111]c-[110]c) monoclinic distortion path: R  O:
field applied along [001]C (down, P3 < P1, P2)
The G profile is flatter along MA and MB paths. 12

13. The morphotropic phase boundary in PZT
A flatter G profile is the manifestation of the higher susceptibility of the system to atom displacements, leading to an enhancement of the dielectric permittivity and piezoelectric coefficients.
G [RC] > G[MA] > G [MB] : the crystal is most susceptible to polarization rotation along the [MB] path. Facilitated polarization rotation indicates large permittivity perpendicular to polarization, the large shear piezoelectric coefficient, and therefore the large and maximimum d33 along nonpolar axes.
G profiles along RC, MA and MB paths
The G profile is flatter along MA and MB paths. C T O
G profiles along MA and MB paths for two different PZT compositions. The G profile is flatter for compositions near MPB 13

14. The morphotropic phase boundary in PZT
The profile becomes flatter when moving from Ti –rich compositions to compositions closer to the MPB. This is consistent with the increase of the electromechanical properties as the MPB is approached.
Anisotropic softening of permittivity vs. composition in PZT
For the R phase
Enhanced by softening of ε11
Enhanced by softening of ε33

15. Enhancement of piezoelectric properties near a polymorphic phase transition
Example: tetragonal BaTiO3
Gibbs’ free energy for the tetragonal phase of BaTiO3 along the MC path. Polarization rotation occurs close to the TO/T. TT/C: 125°C; TO/T: 5°C.
The softening of ε11 near TO/T determines the enhancement of d15. .
Softening of ε11 prevails before TT/C.

16. Enhancement of piezoelectric properties near a polymorphic phase transition
MPB: enhanced properties observed over a large T range
MPB
(AFE)
(FE)
KNN
TO/T
H, J : tetragonal
L: monoclinic
M: orthorhombic
PPT: enhanced properties observed only in a narrow T range arout the transition temperature.
PPT can be shifted to RT by doping.

17. Engineering piezoelectric properties by doping
Pb2+
Ti/Zr4+
O2-
Dopant
Site
Charge compensation
Effect
Ca2+, Sr2+, Pb2+ Pb -
Lower TC
Zr4+, Sn4+
Ti/Zr
Na+, K+
Oxygen vac.
Hard
Mg2+, Mn2+, Al3+, Fe3+, Yb3+, Co3+, Mn3+, Cr3+
La3+, Nd3+, Bi3+, Sb3+
Cation vac.
Soft
Nb5+, Sb5+, Ta5+

18. Engineering piezoelectric properties by doping Hard and soft PZT
Acceptor doping ( ) Hard PZT
Formation of oxygen vacancies and reorientable dipoles ( ) resulting in domain wall pinning and internal bias field. Lower domain wall mobility and stable domain configuration.
Increase of Qm, Ec and .
Decrease of  and dij .
More linear strain-field behaviour.
More difficult poling and depoling .
High power, high voltage applications. 18

19. Engineering piezoelectric properties by doping Hard and soft PZT
Donor doping ( ) Soft PZT
Formation of cation vacancies. Donor-cation vacancy pairs are hardly reorientable because of the low hopping rate of cation vacancies. Lack of pinning and higher mobility of domain walls.
Decrease of oxygen vacancy concentration and hole conductivity related to PbO loss during sintering.
Increase of , dij, kp, tanδ.
Decrease of Qm, Ec and .
Easier poling and depoling.
More hysteretic behaviour
Applications in medical transducers, pressure sensors
and actuators
Partial Schottky defects
PbO lost by evaporation is replaced by “LaO” without oxygen vacancy formation
Isovalent modified
PZT 19

20. Engineering piezoelectric properties by doping Hard and soft PZT
Hysteretic behaviour
Enhanced domain wall mobility (extrinsic effect: nonlinear & hysteretic)
Easier poling
Reduced domain wall mobility (pinning by dipolar defects and internal bias field)
More difficult poling 20

21. High performance PbTiO3 – relaxor materials
1954: PZT as piezoelectric material;
1961: PMN [(PbMg1/3Nb2/3)O3 ] as relaxor ferroeloectric;
Late 1970s: PMN-PT solid solutions as electrostrictive actuators;
1987: MPB in PMN-PT ceramics with d33 up to 700 pC/N;
1997: PMN-PT and PZN-PT [(PbZn1/3Nb2/3)O3 -PT] single crystals with d33 up to 2500 pC/N;
PMN-PT
PYN-PT
PMN-PT
PYN-PT
BS-PT
BS-PT
Drawbacks of PMN-PT based-materials:
Low TC and TRT
Low EC (need for a dc bias to avoid depoling)

22. High performance PbTiO3 – relaxor materials
MPB
PMN-xPT
[001] poled
MPB
PIN-PMN-PT
PMN-xPT

23. High performance PbTiO3 – relaxor materials
Critical factors for high piezoelectricity:
Flattened free energy surface (induced by structural instability: MPB, PTT, polarization rotation);
Monoclinic phase as a bridge facilitating polarization rotation and phase transition;
Phase instability induced by the relaxor end member;
PMN-xPT
=1: normal ferroelectric
= 2: relaxor

24. Piezoceramics are a link between the mechanical and electronic world
Mechanical energy into Electrical energy
Electrical energy into Mechanical energy
Ultrasonic cleaning
Nebulizers
Actuators
Motors
Micro-pumps
Ultrasonic machining
Ignition units
Pressure sensors
Accelerometers
Push buttons
Airbag sensors
Medical imaging
Doppler systems
Trasformers
NDT
Direct effect
Converse effect 24

25. Lead-free piezoelectric materials
Investigation of new systems with MPB mainly driven by the need to avoid lead
Ba(Ti0.8Zr0.2)O3-(Ba0.7Ca0.3)TiO3 (BTZ-BCT)
MPB effect or PPT to RT ?
MPB?
BTZ
BCT
BTZ-BCT phase diagram (2009)
PZT
BZT-BCT 25

26. Lead-free piezoelectric materials
Ba(Ti0.8Zr0.2)O3-(Ba0.7Ca0.3)TiO3 (BTZ-BCT) C T R O
BCT
BTZ
Evolution of (220) reflection with temperature
(synchrotron radiation)
Modified BTZ-BCT phase diagram (2013)

27. Lead-free piezoelectric materials
NaNbO3 - KNbO3 (KNN)
MPB
(AFE)
(FE)
KNN
TO/T
Q, K and L : monoclinic;
M and G : orthorhombic ferroelectric;
F, H, and J : tetragonal ferroelectric;
P : orthorhombic antiferroelectric.
TO/T
Dopants lower the TOT around RT 27

28. Lead-free piezoelectric materials
NaNbO3 - KNbO3 (KNN)
Doping with LiTaO3, LiSbO3 and SrTiO3 lowers the TOT from 200°C to RT. The T/O transition strongly enhances the piezoelectric properties.
LT: LiTaO3; LS: LiSbO3

29. Lead-free piezoelectric materials
Textured KNN ceramics
d33 = 416 pC/N
TC = 253°C
LF1, LF2, LF3: (K,Na)NbO3 + LiTaO3
LF4: (K,Na)NbO3 + LiSbO3
LF3T: textured LF3
LF4T: textured LF4
textured
conventional

30. Lead-free piezoelectric materials
Na1/2Bi1/2TiO3 - BaTiO3
MPB 30

31. Lead-free piezoelectric materials
Na1/2Bi1/2TiO3 - BaTiO3
MPB
PZT
BNT-BT

32. Medical ultrasonic transducers32 32

33. Medical ultrasonic transducers
Ultrasonic imaging: 1.5 – 60 MHz depending on the organ to me imaged.
Requirements for piezoelectric materials: high electromechanical coupling constant (k33), low acoustic impedance and broad bandwidth.
State of the art materials:
Piezoelectric/polymer composites with 1-3 or 2-2 connectivity (k33 highest in 3-3 composites).
Epoxy resin has low density and decreases the acoustic impedance. Properties can be tuned by varying the volume fraction and composition of each constituent.
PMN-PT
BS-PT
PYN-PT
Piezoelectric materials:
Soft PZT (PZT5H: k33 = 0.75)
Relaxor-PT crystals (PMN-PT: k33 >0.90)

34. Medical ultrasonic transducers
Fabrication: dice- and fill- process.
For frequency above 20 MHz, the lateral size of the pillars need to be <50 m to keep a longitudinal aspect ratio. Photolithography needed.
Degradation of preperties at high frequency.

35. Multilayer Piezoelectric Actuators35

36. Multilayer Piezoelectric Actuators
Application in injection systems for diesel engines
Advantages:
Very quick response (< 10-4 s)  high speed operations, good control of the injection process
Higher efficiency of the combustion process
Lower CO2 emissions
Material requirements:
High strain materials (converse piezoelectric effect: x3 = d33E3): d33 = 550 pC/N
Operating temperature: -50 to 150 °C 36

37. Multilayer Piezoelectric Actuators
Materials
TC > 350°C to reduce depoling (electromechanical losses)
Donor-doped (La on the Pb site, Nb on the Ti site) PZT with MPB composition
> Donors decrease TC (20 °C/at.%) and increase hysteretic behaviour.
> Donors reduce the oxygen vacancy concentration and enhances the non-180° domain wall mobility leading to an additional extrinsic piezoelectric effect in addition to the intrinsic lattice contribution (higher strain). (soft piezoelectric)
> Donors increase hysteretic behaviour and nonlinearity.
> Acceptors increase the oxygen vacancy and defect pairs ( ) concentration decreasing the mobility of non-180° domain walls and the maximum strain. (hard piezoelectric)
> Processing has to carefully optimized to limit PbO volatilization (formation of pairs).
Soft piezo 37

38. Multilayer Piezoelectric Actuators
Materials
(2) Binary and ternary solid solutions PbTiO3 – M1M2O3 and PbTiO3-PbZrO3-Pb(B1B2)O3 with MPB
- (1-x)BiScO3 – xPbTiO3: MPB at x = 0.64 with TC = 450°C and d33 = pC/N;
- (1-x)Bi(Mg0.5Ti0.5)O3 – xPbTiO3: MPB at x = 0.38 with TC = 470°C and d33 = 240 pC/N
Pb(Ni1/3Nb2/3)O3
Pb(Mg1/3Nb2/3)O3
Pb(Zn1/3Nb2/3)O3
d33 up to 2000 pC/N
TC <200°C
The main goal is to increase TC retaining good piezoelectric properties.
A piezoelectric material can be used in applications without significant performance degradation up to T = 0.5 TC. 38

39. Multilayer Piezoelectric Actuators
The multilayer cofire process
Multilayer devices reduce the driving voltage required to attain the desired strain
Fabrication technology: multilayer cofire process (same as multilayer ceramic capacitors)
Optimized binder systems
High green density
Absence of defects (large pores & aggregates)
Metal ink formulation: binders, solvents, oxide additives, optimization of metal particulate. The selected metal or alloy determine the max. firing temperature (900°C for Ag).
Debinding and sintering. Homogeneous shrinkage required to avoid cracks, pores and delamination.
Inner electrodes are exposed.
Electrodes are connected.
Screen printing 39

40. Multilayer Piezoelectric Actuators
Metallization processes
The cost of metallization can be as high as 80% of the total material cost (market price of Pd)
(1) Cofiring in air with Ag-Pd electrodes;
Oxygen release
Chemical reactions
Sintering aid (excess PbO, Bi2O3) needed to promote liquid phase sintering
Pd oxidation
Alloy formation
Ag(Pd)
Ag(Pd)/PdO
Oxygen release
Delamination 40

41. Multilayer Piezoelectric Actuators
Metallization processes
(2) Base-metal electrode process: cofiring in reducing atmosphere with Cu electrodes (Ni can not be used as it rapidly reacts with PZT). Max firing T: 1000°C (m.p. Cu : 1040°C). Sintering aids required.
Firining atmosphere: N2-H2-H2O. Optimization of binder removal to avoid formation of graphitic carbon which can oxididie to CO2 and CO leading to variations of p(O2).
Two-step process: (i) debinding in air and (ii) firing at low p(O2). Possible using silica coated copper particles to avoid copper oxidation.
d33 = 390 pC/N 41

42. Multilayer Piezoelectric Actuators
Effect of sintering aids
Produce good densification with controlled grain growth (optimal size for maximum d33: 2m. Smaller size determine a decrease d33 because of reduced dw mobility and smaller number of dw configurations.
Residual intergranular phase can determine:
> Poorer mechanical properties.
> Lower dielectric constant.
> Issues with reliability and lifetime. The grain boundary phase is a fast pathway for Ag electromigration under a DC bias. 42

43. Multilayer Piezoelectric Actuators
Degradation of multilayer actuators
Failure of multilayer actuators unde DC bias or quasi rectangular voltage pulses is determined by electromigration of Ag+ ions.
Ag oxidation in the presence of moisture and high temperature.
Migration of Ag+ under the DC bias.
Reduction reaction at the cathode and growth of metal dendrites 43

44. 44

45. What is the MPB ? The morphotropic phase boundary in PZT
There are four different, even somewhat opposing, views of what an MPB is in ferroelectrics, and in PZT in particular.
The MPB region in PZT consists of a monoclinic phase, which bridges Zr-rich rhombohedral and Ti-rich tetragonal phases. (B. Noheda, Appl. Phys. Lett., 74 [14] (1999).).
The Monoclinic distortion observed in X-ray diffraction experiments is only apparent and due to the coexistence of tetragonal microdomains and rhombohedral nanodomains. (K. A. Schonau, Phys. Rev. B, 75 [18] (2007).).
There is no sharp boundary across the MPB in the PZT phase diagram. All three phases (tetragonal, monoclinic, and rhombohedral) can be considered as monoclinically distorted, with progression from short-range to long-range order across the MPB region. (A. M. Glazer, Phys. Rev. B, 70 [18] (2004).).
PbTiO3 is crucial for appearance of an MPB in all lead-based systems. Lead titanate exhibits a pressure-induced transition from tetragonal to monoclinic to rhombohedral phases at 0 K. The other end member (e.g., PbZrO3) simply tunes this phase transition to room temperature (M. Ahart, Nature, 451 [7178] 545–8 (2008).). 45 45