Piezoelectric ceramics 1

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

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.

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.

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.

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

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

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.

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, 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) 9

Properties of PZT and piezoelectric ceramics 10

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

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

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

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

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.

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.

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+

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

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

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

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)

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

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

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)

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

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 30

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

Medical ultrasonic transducers 32 32

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)

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 35

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

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

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 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

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

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

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

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

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

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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] 2059-61 (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] 184117 (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] 184123 (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