Piezoelectricity and ferroelectricity Piezoelectric materials Property measurement. Prof.Mgr.Jiří Erhart, Ph.D. Department of Physics FP TUL

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1 Piezoelectricity and ferroelectricity Piezoelectric materials Property measurement Prof.Mgr.Jiří Erhart, Ph.D. Department of Physics FP TUL

2 Piezoelectric materials Single crystals Polycrystals (ceramics) Polymers Composites Thin films FPM Piezoelectricity 2 2

3 Single crystals α-quartz (SiO 2 ),α-berlinite (AlPO 4 ),Galium Orthophosphate (GaPO 4 ), Langasite (La 3 Ga 5 SiO 14 ), Langatite (La 3 Ga 5.5 Ta.5 O 14 ), Langanite (La 3 Ga 5.5 Nb.5 O 14 ) Lithium Tetraborate (Li 2 B 4 O 7 ) Lithium Niobate (LiNbO 3 ), Lithium Tantalate (LiTaO 3 ) Perovskites - Lead Titanate (PbTiO 3 ), Barium Titanate (BaTiO 3 ), Potassium Niobate (KNbO 3 ) Solid solutions - (1-x)Pb(Mg 1/3 Nb 2/3 )O 3 xpbtio 3 (PMN-PT), (1-x) Pb(Zn 1/3 Nb 2/3 )O 3 xpbtio 3 (PZN-PT) Rochelle Salt, KDP, ADP, KTP, FPM Piezoelectricity 2 3

4 Crystals homeomorphic to quartz Symmetry 32 GaPO 4 AlPO 4 (berlinite) Langasite La 3 Ga 5 SiO 14, langanite La 3 Ga 5.5 Nb.5 O 14, langatite La 3 Ga 5.5 Ta.5 O 14 GaPO 4 crystal FPM Piezoelectricity 2 4

5 LiNbO 3 and LiTaO 3 Discovered in 6 s, synthetic crystals Very high Curie temperature 1195 o C and 61 o C Applications in optics and for resonators BAW and SAW LiNbO 3 LiTaO 3 FPM Piezoelectricity 2 5

6 Solid solutions - perovskites (1-x)Pb(Mg 1/3 Nb 2/3 )O 3 xpbtio 3 (PMN-PT) (1-x)Pb(Zn 1/3 Nb 2/3 )O 3 xpbtio 3 (PZN-PT) 3 2 Cubic PMN-PT Transition Temperature (ºC) 1-1 Tetragonal Rhombohedral.1.2 Curie Temperature (ºC) Poled Unpoled Tm Td Cubic Pseudo-cubic Region I Electrostrictive Region III Relaxor Piezo MOLE (x) PT Tetragonal Normal Piezo. PZN x PT FPM Piezoelectricity 2 6

7 Domain engineering Piezoelectric coefficient is elevated due to proper polarization direction E E Crystal Cut d 33 [pc/n] k 33 [%] PZN (111) (1)eng PZN-8%PT (111) (1)eng PMN-33%PT (1)eng J.Kuwata, K.Uchino, S.Nomura: Dielectric and Piezoelectric Properties of.91pb(zn1/3nb2/3)o3-.9pbtio3 Single Crystals, Jpn.J.Appl.Phys. 21,9 (1982), FPM Piezoelectricity 2 7

8 Polycrystals (ceramics) Small grains (grain size 1-1µm) Polarization by electric field ferroelectric materials ( ) mm E P S Before poling Textured ceramics after poling FPM Piezoelectricity 2 8

9 Piezoelectric ceramics PZT PZT ceramics Pb(Zr x Ti 1-x )O 3 6 DS 8 DS FPM Piezoelectricity 2 9

10 Textured ceramics Texture of grains and their arrangement G.L.Messing et al: Templated Grain Growth of Piezoelectric ceramics, Critical Reviews in Solid State and Material Sciences 29 (24) FPM Piezoelectricity 2 1

11 Textured grains Textured ceramics G.L.Messing et al: Templated Grain Growth of Piezoelectric ceramics, Critical Reviews in Solid State and Material Sciences 29 (24) FPM Piezoelectricity 2 11

12 Piezoelectric polymers PVDF (- CH 2 CF 2 -, β-phase), F C F F C F F C F dipole moment C C C H H H H H H H.Kawai: The Piezoelectricity of Poly(Vinylidene Fluoride), Jpn.J.Appl.Phys. 8 (1969) Heiji Kawai (191-?) Eiichi Fukada (1922) Copolymer P(VDF-TrFE), electrically poled - m, and stretched - 2 Bone, colagen, DNA, FPM Piezoelectricity 2 12

13 Bubble polypropylen - ferroelectret Bubbles inside charged dipole moments Very high piezoelectric properties, low acoustic impedance, soft and flexible FPM Piezoelectricity 2 13

14 Piezoelectric composites Two and more phases Parallel (a) and series (b) connection of phases Series connection d eff 33 = v (1) d v (1) 33 (1) (2) 33 (2) 33 + v + v (2) (2) (2) 33 (1) 33 Parallel connection ε ε (1) (1) (2) v d33 s33 d eff + 33 = (1) (2) v s33 + v v (2) (2) d ε d s (2) 33 (1) 33 s ε (1) 33 (1) 33 a) b) FPM Piezoelectricity 2 14

15 Piezoelectric composites Effective combination of electromechanical properties Properties: Enhanced Possibly new FPM Piezoelectricity 2 15

16 Polymer + ceramics Effective hydrostatic coefficient FPM Piezoelectricity 2 16

17 Piezoelectric properties d 33 [pc/n] cymbal composite PMN-PT PZN-PT soft PZT hard PZT BaTiO 3 PbTiO 3 KNbO 3 PVDF polymer LiNbO 3 FPM Piezoelectricity LiTaO3 2 α-sio 2

18 Structure, phase diagram Chemical composition Ferroelectric properties Material properties Applicability limits Piezoelectric ceramics FPM Piezoelectricity 2 18

19 Piezoelectric ceramics PZT ceramics Pb(Zr x Ti 1-x )O 3 6 DS 8 DS FPM Piezoelectricity 2 19

20 Solid solutions Solution of phases at the basic unit level Co-existence of both phases at the morphotropic phase boundary (MPB) Both phases exhibit ferroelectric properties Doping by isovalent or heterovalent ion FPM Piezoelectricity 2 2

21 Modification of PZT ceramics A-position or B-position A 2+ B 4+ O 2- isovalent Ca 2+, Sr 2+, Ba % Sn 4+ G.Helke, K.Lubitz: Piezoelectric PZT ceramics, in Piezoelectricity, Springer Verlag 28 FPM Piezoelectricity 2 21

22 Modification of PZT ceramics Heterovalent doping generation of oxygen or lead vacancies G.Helke, K.Lubitz: Piezoelectric PZT ceramics, in Piezoelectricity, Springer Verlag 28 FPM Piezoelectricity 2 22

23 Hard and soft PZT Doping by heterovalent ions changes material properties G.Helke, K.Lubitz: Piezoelectric PZT ceramics, in Piezoelectricity, Springer Verlag 28 FPM Piezoelectricity 2 23

24 Complex solid solutions Three and more component systems FPM Piezoelectricity 2 24

25 Other ceramics systems BaTiO 3 (BT) Lead metaniobate - PbNb 2 O 6 Bi 4 Ti 3 O 12 Aurivillius structure (Na 1/2 Bi 1/2 )TiO 3 NBT (K 1/2 Bi 1/2 )TiO 3 KBT NBT-BT, KBT-BT Solid solutions with MPB are the best piezoelectric ceramic materials FPM Piezoelectricity 2 25

26 Spontaneous polarization orientation averaging Spontaneous polarization inside grains arbitrary orientation, switching in external field Average dipole moment FPM Piezoelectricity 2 26

27 Ceramic materials Any ferroelectric material might be used for the ceramics Perovskite structure is the most successful Perovskite mineral - CaTiO 3, species Perovskite ceramics solid solutions - Morphotropic phase boundary (MPB) m3m 4mm m3m 3m m3m mm2 m3m 4mm FPM Piezoelectricity 2 27

28 Piezoelectric ceramics Electromechanical tensors symmetry class mm, poling direction = 3 d ε ε 11 d 31 ε 33 d 33 d 15 d 15 ( p ) 3 s11 s12 s13 s = 66 s s s ( s 11 s s s s 12 s 44 ) s 44 s 66 FPM Piezoelectricity 2 28

29 Material properties of PZT ceramics Extremaly high material properties MPB composition, the best polarizability FPM Piezoelectricity 2 29

30 Properties of soft and hard PZT J.Tichý, J.Erhart, E.Kittinger, J.Přívratská: Fundamentals of Piezoelectric Sensorics, Springer Verlag 21 FPM Piezoelectricity 2 3

31 Properties of other piezoelectric ceramics J.Tichý, J.Erhart, E.Kittinger, J.Přívratská: Fundamentals of Piezoelectric Sensorics, Springer Verlag 21 FPM Piezoelectricity 2 31

32 Morgan Electroceramics, UK Temperature dependence of material properties FPM Piezoelectricity 2 32

33 Applicability limits Temperature (T<T C ) depoling by the pyroelectric charges Mechanical pressure Electric field (E<E C ) - Parallel - Antiparallel - Perpendicular to the poling direction FPM Piezoelectricity 2 33

34 Driving conditions for ceramics Electric field - Unipolar Electric field time - Bipolar Electric field time FPM Piezoelectricity 2 34

35 Driving conditions for ceramics Mechanical pressure pre-stress - Without pre-stress Mechanical Stress stress amplitude{ time - With pre-stress (only compression stress) Mechanical Stress pre-stress{ time FPM Piezoelectricity 2 35

36 Property measurement techniques Measurement of material properties Poling of ceramics and crystals Hysteresis loop Material property tensors (resonance, interferometric, hydrostatic, ultrasound etc.) Temperature dependences of material properties FPM Piezoelectricity 2 36

37 Poling Strong DC field HV power source Spellman 3kV/1mA Sample holder AC voltage and pulses HV amplifier Matsusada AMT-5B2 (±5kV, 2mA, <2kHz) Magnetic stirrer and heater Heidolph MR 31K (8W) Silicon oil (Lukosiol M5, non-flammable up to 2 o C) electrical isolation and heat transfer FPM Piezoelectricity 2 37

38 Pulse poling Pulse application and switching current analysis Merz s circuit FPM Piezoelectricity 2 38

39 PZT ceramics poling Electric field 2-4kV/mm, temperatures o C FPM Piezoelectricity 2 39

40 FPM Piezoelectricity 2 4

41 Sawyer - Tower circuit Hysteresis loops HV amplifier Matsusada AMT-5B2 (±5kV, 2mA, <2kHz) Capacitive decade Cosinus C-25 (.1nF-11µF) Magnetic stirrer and heater Heidolph MR 31K (8W) Silicon oil (Lukosiol M5, non-flammable up to 2 o C) reasonable electrical breakdown strength up to 4-5kV/mm FPM Piezoelectricity 2 41

42 Typical result - loops Hysteresis loops measured at room temperature (23 o C) frequency 1Hz PZT ceramics.5.4 soft.3 APC84 APC841 APC856, 85 Hard APC84, 841, 88 D [C/m2] APC85 APC856 APC E [kv/mm] P.Půlpán, L.Rusin, J.Erhart, Japanese Journal of Applied Physics 47, 1 (28) FPM Piezoelectricity 2 42

43 Piezoelectric property measurement Measurements techniques use direct or converse effect Resonance method Hydrostatic chamber Laser interferometry Ultrasound (e.g. pulse-echo) d 33 -meter (uniaxial pressure) Quasistatic method (lock-in) FPM Piezoelectricity 2 43

44 FPM Piezoelectricity 2 44 Resonance method Mechanical resonance generated piezoelectrically Example: ceramic disc, radial mode admittance resonance Y antiresonance Y p r r r J J σ = η η η 1 ) ( ) ( 1 P r r c r f 11 2 ρ π = η η η η σ η ω = 1 ) ( ) ( ) (1 ) ( ) 2( J J J k C j Y P P

45 Resonator in the vicinity of resonance C R h C h L h FPM Piezoelectricity 2 45

46 Disc, PZT APC841, D=4mm, t=2,2mm Z[Ohm] impedance phase phase[rad] f[khz] FPM Piezoelectricity 2 46

47 Hydrostatic chamber Direct piezoelectric effect sample is in the chamber under isotropic hydrostatic pressure, pressure and charge response is measured Hydrostatic pressure p p Hydrostatic piezoelectric coefficient D d 31 p 3 = d h ( p) h = d + d 32 + d 33 FPM Piezoelectricity 2 47

48 Charge density dependence on the pressure, P(VDF-TrFE): 1 - pressure increase, 1 - pressure decrease. Burianová, L., Hána, P., Tyagur Y. I. and Kulek, J.: Piezoelectric hydrostatic coefficients of PVDF and P(VDF,TrFE) copolymer foils at high hydrostatic pressures. Ferroelectrics 224 (1999), FPM Piezoelectricity 2 48

49 Laser interferometry Converse effect, displacement is measured by interferometry Displacements 1-12 m up to 1-5 m Quasistatic method, lock-in Single- or double-beam (micro)interferometer Piezoelectric, electrostrictive or electrooptic material coefficients FPM Piezoelectricity 2 49

50 Laser interferometry Interference of two coherent laser beams (point) Intensity I = I + I + 2 I I cos(4π d / λ) p r It is for small displacements and π/2 phase shift in LI branches 1 1 I = ( I max + I min ) + ( I max I min )4π d / λ 2 2 Small AC signal interference pattern response is measured by photodiode, phase lock-in amplification (lock-in amplifier) L.Burianová, M.Šulc, M.Prokopová: J.Europ.Ceram.Soc. 21 (21) p r FPM Piezoelectricity 2 5

51 Single-beam LI (Michelson) L.Burianová, M.Šulc, M.Prokopová: J.Europ.Ceram.Soc. 21 (21) FPM Piezoelectricity 2 51

52 Double-beam LI (Mach Zehnder) L.Burianová, M.Šulc, M.Prokopová: J.Europ.Ceram.Soc. 21 (21) FPM Piezoelectricity 2 52

53 FPM Piezoelectricity 2 53 Interferometric d 15 measurement d d d d d Rotation by 45 o around axis ' E d S = P E S Measurement S 11, calculation d 15

54 FEM simulation of sample clamping in interferometer holder d 33 1 NODAL SOLUTION STEP=1 SUB =1 TIME=1 UZ (AVG) RSYS= DMX =.573E-8 SMN =-.554E-8 MX JUL :55:25 MN Y Z X -.554E E E E E E E E E-8 PZT square plate in interferometer - face glued to the holder - d33 measurement FPM Piezoelectricity 2 54

55 FEM simulation of sample clamping in interferometer holder d 31 1 NODAL SOLUTION STEP=1 SUB =1 TIME=1 UX (AVG) RSYS= DMX =.157E-8 SMN =-.17E-9 SMX =.765E-9 MN JUL :16:49 Y Z X MX -.17E-9.866E-1.28E-9.474E-9.668E E-1.184E-9.377E-9.571E-9.765E-9 PZT square plate in interferometer - face glued to the holder - d31 measurement FPM Piezoelectricity 2 55

56 FEM simulation of sample clamping in interferometer holder d 15 1 NODAL SOLUTION STEP=1 SUB =1 TIME=1 USUM (AVG) RSYS= DMX =.16E-8 SMX =.16E-8 MN MX JUL :9:59 Y Z X.355E-9.79E-9.177E-9.532E-9.886E-9 PZT square plate in interferometer - d15 measurement.16e-8.124e-8.142e-8.16e-8 FPM Piezoelectricity 2 56

57 Ultrasound measurement Ultrasound velocity is a function of elastic constants, piezoelectric coefficients and permittivity Pulse-echo method (measurement time-of-flight ) sample sample US transducers US polarization longitudinal or transversal wave FPM Piezoelectricity 2 57

58 Christoffel s tensor Γ ik = c E ijkl Ultrasound wave velocity ν ν + j l e kij ν k S ik ε ν j ν e k ikl ν i ν Propagation direction ( ν ν ) Wave velocity condition 1 2 ν 3 l ν i det( Γ ik 2 ρv δ ik ) = FPM Piezoelectricity 2 58

59 FPM Piezoelectricity 2 59 Example for symmetry d d ) ( c c c c c c c c c c c c c ε ε ε Material tensors

60 Wave propagation in [1] - direction Γ Γ 11 Γ 22 Γ 33 Γ Γ = c = Γ E 11 13, Γ 22 = Γ = 23 c = E 66, Γ 33 = c E 44 ρv ρv ρv = Γ = Γ = Γ longitudinal wave 2 transversal waves Piezoelectrically free waves c 11 E c 44 E 1 c 66 E 3 (press) 2 FPM Piezoelectricity 2 6

61 Wave propagation in [1]-direction Γ Γ 11 Γ 22 Γ 33 Γ Γ = Γ = Γ = c = Γ E 44 23, Γ = 33 = c E 33 ρv 2 = Γ 11 2 transversal waves ρv 2 = Γ 33 1 longitudinal wave Piezoelectrically free waves FPM Piezoelectricity 2 61

62 Wave propagation in [11]-direction Γ Γ Γ Γ 22 Γ Γ Γ Γ Γ = = ( c ( c =, Γ E 11 E c + c = 1 2 E 44 E 44 ( c ), Γ ), E c = E ( c ), Γ E = ε S 11 e ε S 33 ), ρv 2 = Γ 22 Transversal wave (piezoelectrically clamped) ) + 4Γ 13 ρv = { Γ11 + Γ33 ± ( Γ11 Γ 2 Piezoelectrically free waves } 1 longitudinal 1 transversal wave FPM Piezoelectricity 2 62

63 Typical result P.Hána et al.: Ferroelectrics 319 (25) FPM Piezoelectricity 2 63

64 d 33 - meter Quasistatic measurement, uniaxial pressure is applied to the sample, charge response is analyzed and compared with the response of the known sample d 33 -measurement mechanical pressure perpendicular to the electrodes d 31 -measurement mechanical pressure parallel to the electrodes FPM Piezoelectricity 2 64

65 Temperature dependences of material properties analyzer Tesla BM57 (5Hz-5kHz) + counter HP5326B LCR meter HP4261A (12Hz or 1kHz, series or parallel circuit) Ultrathermostat U-1 (± several o C, room temperature up to 8 o C) Resonance measurement furnace Classic (room temperature up to 12 o C) measurement of Curie temperature from the temperature dependence of permittivity, Curie-Weiss law FPM Piezoelectricity 2 65

66 Temperature dependence of elastic compliance s 11 Elastic constant s11e for APC s11e [1^-12 m2/n] y = -.42x R 2 = temperature [ C] FPM Piezoelectricity 2 66

67 Typical result Curie temperature T C =319 o C Temperature dependence for APC85 1/C linear fit [1/C] y =.71x R 2 = T C 1/C [nf-1] T[oC] FPM Piezoelectricity 2 67

68 Examples: Measurement of parameters for the piezoelectric elements Bimorphs and unimorphs deflection, blocking force Piezoelectric transformers transformation ratio and efficiency FPM Piezoelectricity 2 68

69 Piezoelectric ceramic bimorph PZT Metallic plate FPM Piezoelectricity 2 69

70 Laser beam u << x, x >> x, ls >> light beam bimorph Bimorph deflection visualization screen L u,δ [mm] V [V] u ( x + x ) 2 ( L + ) L l s x 2x 2 + ( L + l ) + ( ) s 2x x x u [mm] f [Hz] FPM Piezoelectricity 2 7

71 P.Půlpán f=117hz FPM Piezoelectricity 2 71

72 P.Půlpán f=735hz FPM Piezoelectricity 2 72

73 MTI21 Fotonic sensor Reflected light intensity analysis Probes MT262R (1-15µm) MT2125R (1-4µm) FPM Piezoelectricity 2 73

74 Piezoelectric ceramic unimorphs Brass membrane Ag electrode PZT ceramics Buzzers, with Helmholtz s resonator FPM Piezoelectricity 2 74

75 Typical results Scan of unimorph s surface (resonance frequency, peak-to-peak measurement) 5 4 upp [µm] x / d PL Deflection in x-axis for unimorph 2-123, FT 41T, U = 5 V, f = 927 Hz; fit by parabolic curve u PP = (x / d PL.512) FPM Piezoelectricity 2 75

76 Typical results Circumference mechanical clamping deflection in the unimorph s center u pp [ m] f [Hz] Peak-to-peak deflection in unimorph s center 2-123, FT 41T. Voltage amplitude 5V. FPM Piezoelectricity 2 76

77 P.Půlpán FPM Piezoelectricity 2 77

78 P.Půlpán FPM Piezoelectricity 2 78

79 Piezoelectric transformer Transformation ratio P.Půlpán Resistive load decade Cosinus R1-1 (1Ω-11MΩ) VOLTAGE GAIN ~ V V Z L Function generator HP 3325A Multimeter Agilent 3441A Multimeter Agilent 3441A Resistive load FPM Piezoelectricity 2 79

80 Efficiency P.Půlpán Piezoelectric transformer Resistive load decade Cosinus R1-1 (1Ω-11MΩ) EFFICIENCY V Differential probe N2772A 5R62 ~ V V Z L Function generator HP 3325A Oscilloscope DSO322 Oscilloscope DSO312 Resistive load FPM Piezoelectricity 2 8

81 Transformation ratio frequency dependence Ring-dot disc PT, r 1 = 3.4 mm, r 2 =12.5mm, t=2mm 35 3 Gain [-] Ω 1kΩ 1kΩ 1kΩ no-load f [khz] FPM Piezoelectricity 2 81

82 Efficiency frequency dependence Ring-dot disc PT, r 1 = 3.4 mm, r 2 =12.5mm, t=2mm Load 5kΩ 1 2 Efficiency [%] efficiency Voltage gian [-] 6 gain frequency [khz] FPM Piezoelectricity 2 82

83 Load dependence of transformer efficiency Ring-dot disc PT, r 1 = 3.4 mm, r 2 =12.5mm, t=2mm 1 8 Efficiency [%] Load [Ω] FPM Piezoelectricity 2 83

84 Output power Ring-dot PT, r 1 =3.4mm, r 2 =12.5mm, t=2mm P.Půlpán, J.Erhart: Transformation ratio of ring-dot planar piezoelectric transformer, Sensors and Actuators A14 (27) FPM Piezoelectricity 2 84

85 Planar vibration mode Piezoelectric transformers IN OUT IN OUT IN OUT FPM Piezoelectricity 2 85

86 Typical results FPM Piezoelectricity 2 86

87 Typical results FPM Piezoelectricity 2 87

88 Thank you for your attention! FPM Piezoelectricity 2 88