Piezoelectric ceramics
Piezoelectricity
In a conventional solid, a mechanical stress X causes a proportional elastic strain x
X=Cx
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
D  0E  P
For FE materials D  P 
D: dielectric displacement; P: polarization;
Q: charge; A: area;
d: piezoelectric coefficient
P=dX
(polarization = d * stress)
Direct effect
F
F
Q
+
-
Q
+
P
F
Contraction
-
P
F
Expansion
Piezoelectricity
Converse piezoelectric effect:
x=dE
(strain = d * electric field)
An applied electric field E produces a proportional strain x (linear effect), expansion or
contraction, depending on polarity.
Converse effect
E
+
-
P
+
-
Contraction
Mechanical stress/pressure
Electric field
Mechanical energy
E
+
-
-
P
+
Expansion
Polarization/Charges/current
Strain
Transducers
Actuators
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.
Piezoelectricity
Equations for the piezoelectric effect are generally written in matrix form as they relate
properties along different directions of the crystal.
3 [001]C
6
Di   dij X j (i  1..3)
j 1
X4
Direction of
stress
6
d ij
Xj
stress components
Direction of
j = 1..3:
polarization
extensional/compressive stress
3x6=18 coefficients
j = 4, 5, 6: shear stress 15 independent (d =d ; I,j=1..3)
ij
xi   dij Ei
X2
4
( j  1..6)
j 1
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
2 [010]C
ji
di4, di5, di6: piezoelectric
shear coefficients
3
X2
X4
1 [100]C
Piezoelectricity
3 ≡ Polar axis
3 [001]C
4mm
d31: polarization generated in the 3 direction
P
(vertical direction) as a result of a stress
applied in a lateral direction (1 or 2)
(6)
(4)
d33: polarization generated in the 3 direction
(vertical direction) as a result of a stress
applied in vertical direction (3)
(5)
2 [010]C
1 [100]C
For a tetragonal crystal (4mm symmetry),
there are only 3 piezoelectric coefficients:
d31, d33, d15
d15 : polarization generate along axis 1 (or 2)
by a shear stress (d15 = d24)
D3  d31  X1  X 2   d33 X 3
3
3
P
P
D2  d15 X 5
(5)
1
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.
(5)
1
P
Poling direction
D1  d15 X 4 (d24  d15 )
3
1
2
Piezoelectricity
Sketch of the piezoelectric effect in a single domain PbTiO3 tetragonal crystal
3
X3
X1, X3, X5: stress
1
ΔP3, ΔP1: variation of polarization
(a)
X1
P3=d33X3
(b)
X5
P3=d31X1
(c)
P1=d15X5
(d)
(a) No field.
(b) Shift of the Ti ions further away from the
equilibrium position (ΔP1=ΔP2=0; ΔP3>0).
(c) Shift of the Ti ion back towards the cell
center (ΔP1=ΔP2=0; ΔP3<0)
(d) Tilting of the Ti position under a shear
stress (ΔP1>0; ΔP2=0; ΔP3<0).
Domain-wall contribution to the properties of ferroelectric materials
(5) POLARIZATION ROTATION
Piezoelectricity
The LGD (Landau-Ginsburg-Devonshire) theory for a tetragonal crystal predicts:
d33  2Q1133 Ps  2Q11  33 1Ps  2Q11 33 Ps
d31  2Q12 33 Ps  2Q12 33 Ps
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.
Piezoelectricity
Strength of the piezoelectric effect
Piezoelectric coupling factor , always <1.
 electricalenergyconvertedto m echanicalenergy

k p  
inputelectrical energy


1
2
 m echanicalenergyconvertedto electricalenergy

 
input
m
echanical
energy


1
2
Typical values of kp:
0.1 for quartz, 0.35 for BaTiO3, 0.5-0.7 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)
Properties of PZT and
piezoelectric ceramics
The morphotropic phase boundary in PZT
Polarization
TC
TC =370°C at MPB
Dielectric constant and
coupling coefficient
Morphotropic
phase
boundary
(MPB)
PbZrO3
PbTiO3
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.
The morphotropic phase transition is a key to
high piezolectric performance
Piezoelectric coefficients
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.
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.
C
T
O
G profiles along RC, MA and MB paths
The G profile is flatter along MA and MB
paths.
G profiles along MA and MB paths for two different PZT
compositions. The G profile is flatter for compositions
near MPB
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.
   r 1
Anisotropic softening of permittivity
vs. composition in PZT
1
4Q11  4Q12  Q44 11 P3
3
2
d 33  Q11  2Q12  Q44  33 P3
3
d15 
For the R phase
Enhanced by softening of ε11
Enhanced by softening of ε33
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.
   r 1
d33  2Q11 33 P3
The softening of ε11 near TO/T
determines the enhancement of d15. .
d31  2Q12 33 P3
Softening of ε11 prevails before TT/C.
d15  Q4411P3
Enhancement of piezoelectric properties near a polymorphic phase transition
MPB: enhanced properties observed over a
large T range
H, J : tetragonal
L: monoclinic
M: orthorhombic
MPB
PPT: enhanced properties observed only
in a narrow T range arout the transition
temperature.
PPT can be shifted to RT by doping.
TO/T
(AFE)
KNN
(FE)
Engineering piezoelectric properties by doping
Dopant
Site
Charge
compensation
Effect
Ca2+, Sr2+, Pb2+
Pb
-
Lower TC
Zr4+, Sn4+
Ti/Zr
-
Lower TC
Na+, K+
Pb
Oxygen vac.
Hard
Mg2+, Mn2+, Al3+, Fe3+,
Yb3+, Co3+, Mn3+, Cr3+
Ti/Zr
Oxygen vac.
Hard
La3+, Nd3+, Bi3+, Sb3+
Pb
Cation vac.
Soft
Nb5+, Sb5+, Ta5+
Ti/Zr
Cation vac.
Soft
Pb2+
Ti/Zr4+
O2-
Engineering piezoelectric properties by doping
Acceptor doping ( FeTi' ,
'
) Hard PZT
KPb
Hard and soft PZT
• Formation of oxygen vacancies and reorientable dipoles ( FeTi' VO ) 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.
Engineering piezoelectric properties by doping
Donor doping (NbTi ,
Hard and soft PZT

) Soft PZT
LaPb
• 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.
''
zero PZT

 VPb
 VO  2PbO

La2O3 PZT

 2LaPb
 VPb''  2PbO
Partial Schottky defects
PbO lost by evaporation
is replaced by “LaO”
without oxygen vacancy
formation
• 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
Isovalent modified
PZT
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
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
BS-PT
Drawbacks of PMN-PT based-materials:
•Low TC and TRT
•Low EC (need for a dc bias to avoid depoling)
PYN-PT
BS-PT
High performance PbTiO3 – relaxor materials
MPB
MPB
MPB
PIN-PMN-PT
PMN-xPT
[001] poled
PMN-xPT
MPB
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
Piezoceramics are a link between the mechanical and electronic world
Mechanical energy
into Electrical
energy
Electrical energy
into Mechanical
energy
Ultrasonic cleaning
Ignition units
Medical imaging
Nebulizers
Doppler systems
Actuators
Trasformers
Motors
NDT
Micro-pumps
Pressure sensors
Accelerometers
Push buttons
Airbag sensors
Ultrasonic machining
Direct effect
Converse effect
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?
BCT
BTZ
BTZ-BCT phase diagram (2009)
PZT
BZT-BCT
MPB effect or PPT to RT ?
d33  2Q11 33 Ps
Lead-free piezoelectric materials
Ba(Ti0.8Zr0.2)O3-(Ba0.7Ca0.3)TiO3 (BTZ-BCT)
C
T
R
BTZ
O
BCT
Modified BTZ-BCT phase diagram (2013)
Evolution of (220) reflection with temperature
(synchrotron radiation)
Lead-free piezoelectric materials
NaNbO3 - KNbO3 (KNN)
MPB
TO/T
Q, K and L : monoclinic;
M and G : orthorhombic ferroelectric;
F, H, and J : tetragonal ferroelectric;
P : orthorhombic antiferroelectric.
KNN
(AFE)
(FE)
TO/T
Dopants lower the
TOT around RT
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
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
Lead-free piezoelectric materials
Na1/2Bi1/2TiO3 - BaTiO3
MPB
Lead-free piezoelectric materials
Na1/2Bi1/2TiO3 - BaTiO3
MPB
PZT
BNT-BT
Medical ultrasonic transducers
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.
d332
k33 
 33 s33
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.
Piezoelectric materials:
• Soft PZT (PZT5H: k33 = 0.75)
• Relaxor-PT crystals (PMN-PT: k33 >0.90)
PMN-PT
PYN-PT
BS-PT
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.
Multilayer Piezoelectric Actuators
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
Multilayer Piezoelectric Actuators
Materials
TC > 350°C to reduce depoling (electromechanical losses)
(1)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 ( VO  ATi' ) 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 V   V '' pairs).
O
x3  d 0  E0 E 


E
2
2
0
 E2

Soft piezo
Pb
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 = 450-500 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
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.
Pb(Mg1/3Nb2/3)O3
Pb(Zn1/3Nb2/3)O3
d33 up to 2000 pC/N
TC <200°C
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).
Screen printing
Debinding and sintering.
Homogeneous shrinkage
required to avoid cracks,
pores and delamination.
Inner electrodes
are exposed.
Electrodes are
connected.
Multilayer Piezoelectric Actuators
Metallization processes
The cost of metallization can be as high as 80% of
the total material cost (market price of Pd)
Oxygen release
(1) Cofiring in air with Ag-Pd electrodes;
Sintering aid (excess PbO,
Bi2O3) needed to promote
liquid phase sintering
Chemical reactions
Alloy formation
PdO Bi2O3  PdBi2O4
Ag(Pd)
Ag(Pd)/PdO
Ag(Pd)
Delamination
Pd oxidation
Oxygen
release
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
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.
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.
(1) Ag oxidation in the presence of moisture
and high temperature.
1
1
H 2O  Ag2O  H   e'
2
2
1
1
Ag2O  H 2O  Ag  OH 
2
2
Ag 
(2) Migration of Ag+ under the DC bias.
(3) Reduction reaction at the cathode and
growth of metal dendrites
Ag  e'  Ag
The morphotropic phase boundary in PZT
What is the MPB ?
There are four different, even somewhat opposing, views of what an MPB is in
ferroelectrics, and in PZT in particular.
1. 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] 2059-61
(1999).).
2. 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] 184117 (2007).).
3. 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] 184123 (2004).).
4. 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).).