Piezoelectric ceramics. Piezoelectricity In a conventional solid, a mechanical stress X causes a proportional elastic strain x X = C x C: elastic modulus

Piezoelectric ceramics

Piezoelectricity

In a conventional solid, a mechanical stress X causes a proportional elastic strain xX = 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

Direct effect

Contraction

P+

-

F

F

Q

Expansion

P+

-

F

F

Q

PED 0D: dielectric displacement; P: polarization; Q: charge; A: area; d: piezoelectric coefficient

(polarization = d * stress)

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.

Piezoelectricity

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.

Piezoelectricity

Equations for the piezoelectric effect are generally written in matrix form as they relate properties along different directions of the crystal.

)3..1(6

1

iXdDj

jiji

)6..1(3

1

jEdxj

iiji

3x6=18 coefficients15 independent (dij=dji; I,j=1..3)

di4, di5, di6: piezoelectric shear coefficients

Xj stress components

j = 1..3: extensional/compressive stress

j = 4, 5, 6: shear stress

xj strain components

j = 1..3: elongation/contractionj = 4, 5, 6: shear strain: variation of the angles between the two axis in the plane perpendicular to axis 1, 2, 3.

d i j

Direction of stress

Direction of polarization

X4

3 [001]C

2 [010]C

1 [100]C

X2X2

X4

4

6

5

3 [001]C

2 [010]C

1 [100]C

P

(4) (5)

(6)

4mm

Piezoelectricity For a tetragonal crystal (4mm symmetry), there are only 3 piezoelectric coefficients: d31, d33, d15

33321313 XdXXdD

5152 XdD

)( 15244151 ddXdD

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

3

1(5)(5)

PP

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.

3

21P

oli

ng

dir

ec

tio

n

P

3 ≡ Polar axis

Piezoelectricity

Sketch of the piezoelectric effect in a single domain PbTiO3 tetragonal crystal

X1, X3, X5: stress

ΔP3, ΔP1: variation of polarization

(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).

(a) (b)

(c) (d)

3

1

X3

X1

X5

P3=d33X3

P3=d31X1 P1=d15X5

Domain-wall contribution to the properties of ferroelectric materials

(5) POLARIZATION ROTATION

Piezoelectricity

The LGD (Landau-Ginsburg-Devonshire) theory for a tetragonal crystal predicts:

sss PQPQPQd 33113311331133 2122 dij: piezoelectric coefficients;

Qij: electrostrictive coefficients;

Ps: spontaneous polarization (P3)ε33: permittivity along polar axis

ss PQPQd 3312331231 22

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.

2

1

energyelectricalinput

energymechanicaltoconvertedenergyelectricalk p

2

1

energymechanicalinput

energyelectricaltoconvertedenergymechanical

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

Property BaTiO3 PZT-1

(hard PZT)

PZT-2

(soft PZT)

Na1/2K1/2NbO3

TC130 315 220 420

331900 1200 2800 400

tan 0.007 0.003 0.016 0.01

kp0.38 0.56 0.66 0.45

d31-79 -119 -234 -50

d33190 268 480 160

Qm500 1000 50 240

Properties of commercial piezoelectric ceramics

Qm: mechanical quality factor = f / f0 (inverse of mechanical loss)

Properties of PZT and piezoelectric ceramics

The morphotropic phase boundary in PZT

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

Dielectric constant and coupling coefficient

The morphotropic phase transition is a key to high piezolectric performance

PolarizationTC

Morphotropic phase

boundary (MPB)

PbZrO3 PbTiO3

TC =370°C at MPB

Enhancement of electromechanical properties near the MPB: polarization rotation.

PZT 60/40

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).

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.


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 pathsThe 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


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.

33344121133 23

2PQQQd

31144121115 443

1PQQQd

For the R phase

Enhanced by softening of ε11

Enhanced by softening of ε33

1 r

Anisotropic softening of permittivity vs. composition in PZT

Enhancement of piezoelectric properties near a polymorphic phase transition

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.

1 r

3331133 2 PQd

3331231 2 PQd

3114415 PQd

The softening of ε11 near TO/T determines the enhancement of d15. .

Softening of ε11 prevails before TT/C.

Example: tetragonal BaTiO3

MPB

(AFE) (FE)KNN

TO/T

H, J : tetragonalL: monoclinicM: orthorhombic

Enhancement of piezoelectric properties near a polymorphic phase transition

MPB: enhanced properties observed over a large T range

PPT: enhanced properties observed only in a narrow T range arout the transition temperature. PPT can be shifted to RT by doping.

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-

Hard and soft PZT

Acceptor doping ( ) Hard PZT'' , PbTi KFe• 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.

OTi VFe '


Hard and soft PZT

Donor doping ( ) Soft PZTPbTi LaNb ,

• 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

PbOVLaOLa PbPbPZT 22 ''

32

PbOVVzero OPbPZT 2'' Partial Schottky defects

PbO lost by evaporation is replaced by “LaO” without oxygen vacancy formation


Isovalent modifiedPZT

Hard and soft PZTEngineering piezoelectric properties by doping

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

BS-PT

PYN-PT

Drawbacks of PMN-PT based-materials:•Low TC and TRT

•Low EC (need for a dc bias to avoid depoling)

PMN-PT BS-PTPYN-PT

High performance PbTiO3 – relaxor materials MPB MPB

PIN-PMN-PT

MPB MPB

PMN-xPT

[001] poled

PMN-xPT

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;

=1: normal ferroelectric= 2: relaxor

PMN-xPT

Piezoceramics are a link between the mechanical and electronic world

Ignition units

Pressure sensors

Accelerometers

Push buttons

Airbag sensors

Ultrasonic cleaning

Nebulizers

Actuators

Motors

Micro-pumps

Ultrasonic machining

Medical imaging

Doppler systems

Trasformers

NDT

Mechanical energy into Electrical

energy

Electrical energy into Mechanical

energy

Direct effect Direct effect Converse effectConverse effect

PZT BZT-BCT

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?

BTZBCT

BTZ-BCT phase diagram (2009)

sPQd 331133 2

Lead-free piezoelectric materials

Evolution of (220) reflection with temperature(synchrotron radiation)

C

T

R O

BCTBTZ

Modified BTZ-BCT phase diagram (2013)

Ba(Ti0.8Zr0.2)O3-(Ba0.7Ca0.3)TiO3 (BTZ-BCT)

NaNbO3 - KNbO3 (KNN)

Q, K and L : monoclinic; M and G : orthorhombic ferroelectric; F, H, and J : tetragonal ferroelectric; P : orthorhombic antiferroelectric.

Dopants lower the TOT around RT

MPB

(AFE) (FE)KNN

TO/T

TO/T


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

LF1, LF2, LF3: (K,Na)NbO3 + LiTaO3

LF4: (K,Na)NbO3 + LiSbO3

LF3T: textured LF3LF4T: textured LF4

d33 = 416 pC/NTC = 253°C

Textured KNN ceramics

textured conventional


Na1/2Bi1/2TiO3 - BaTiO3

MPB


Na1/2Bi1/2TiO3 - BaTiO3

MPB

PZT BNT-BT


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.

3333

233

33 s

dk

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 BS-PTPYN-PT


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

Advantages:Very quick response (< 10-4 s) high speed operations, good control of the injection processHigher efficiency of the combustion processLower CO2 emissions

Material requirements:High strain materials (converse piezoelectric effect: x3 = d33E3): d33 = 550 pC/NOperating temperature: -50 to 150 °C


Application in injection systems for diesel engines

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 ( ) 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).

'TiO AV

''PbO VV

Soft piezo


220003 2EEEEdx


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

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(Ni1/3Nb2/3)O3

Pb(Mg1/3Nb2/3)O3

Pb(Zn1/3Nb2/3)O3

d33 up to 2000 pC/N

TC <200°C


The multilayer cofire process

Multilayer devices reduce the driving voltage required to attain the desired strainFabrication technology: multilayer cofire process (same as multilayer ceramic capacitors)

Optimized binder systemsHigh green densityAbsence 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

Ag(Pd) Ag(Pd)/PdO Ag(Pd)

Oxygen release

Sintering aid (excess PbO, Bi2O3) needed to promote liquid phase sintering

Pd oxidation


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;

Chemical reactions

4232 OPdBiOBiPdO

Alloy formation

Oxygen release

Delamination

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


Effect of sintering aids

Produce good densification with controlled grain growth (optimal size for maximum d33: 2m. 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.


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.

(2)Migration of Ag+ under the DC bias.

(3)Reduction reaction at the cathode and growth of metal dendrites

OHAgOHOAg

eHOAgOHAg

22

22

2

1

2

1

'2

1

2

1

AgeAg '

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).).


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Piezoelectric ceramics. Piezoelectricity In a conventional solid, a mechanical stress X causes a proportional elastic strain x X = C x C: elastic modulus