Characterization of Polar Dielectrics

Electromechanical properties of dielectrics –

piezo-, pyro- and ferroelectricity

Jiří ErhartDepartment of Physics and

International Center for Piezoelectric Research, Technical University of Liberec, Liberec, Czech Republic

5th Socrates-Erasmus Intensive Programme on Advanced Materials for Optical, Electronic and Biomedical Applications(ADMAT), University of Limerick, Materials and Surface Science Institute (MSSI), May 10-12, 2006

2

Outline

• Electromechanical properties–Piezoelectricity–Pyroelectricity–Ferroelectricity–Electrostriction

• Materials• Property measurement

–Resonant, interferometric, hydrostatic, ultrasound etc.• Conclusion

3

History1880, 1881 - Pierre a Jacques Curie, piezoelectricity on tourmaline and quartz1917 – A.Langevin – ultrasound generation in sonar1921 – ferroelectricity - J.Valasek: Piezoelectricity and allied phenomena in

Rochelle Salt, Phys.Rev. 17 (1921) 4751926 – W.Cady –oscillator circuit frequency stabilization by quartz crystal1944-1946 – USA, USSR, Japan – ferroelectric ceramics BaTiO3

1954 – B.Jaffe et al – PZT ceramics60’s – LiNbO3 and LiTaO3

70’s – ferroelectric polymer PVDF80’s – piezoelectric composites90’s – domain engineering in PZN-PT, PMN-PT

4

Electromechanical properties

Direct relationship between electrical and mechanical properties

• Piezoelectricity• Pyroelectricity• Ferroelectricity• Electrostriction

Analogy in magnetic materials• Piezomagnetic property, magnetostriction, magnetoelectricity, etc.

5

Piezoelectricity

Direct effectmechanical stress → electric charge

Converse effectelectric field → mechanical strain

Anisotropy

Example: Quartz SiO2, symmetry 32

6

Crystallographic constraints for piezoelectricity

Noncentrosymmetrical classes (except of 432)20 piezoelectric classes

• Polar classes (10) – singular polar axis1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm• Polar-neutral classes (10) – multiple polar axes222, , 422, , 32, , 622, , , 234 2m4 6 m26 3m4

7

Pyroelectricity

Direct effectTemperature change → electric chargeConverse effect (electrocaloric effect)Electric field → heat generatedAnisotropyExample: Lithium tetraborate Li2B4O7, symmetry 4mm

8

Crystallographic constraints for pyroelectricity

Polar classes (10) – singular polar axis1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm

Pyroelectric polarization (dipole moment) –direction of polar axis

9

Ferroelectricity

Spontaneous dipole moments exist = pyroelectrics with switchable polarization

Electrical analogy of permanent magnets

Characteristic features• Ferroelectric domains and domain walls• Hysteresis curve D-E (S-E)

10

BaTiO3 – paraelectric phase

Perovskite structure

A2+

B4+

O2-

11

BaTiO3 – ferroelectric phase

Different dipole moment directions

PS

PS PS

mm4mm3

m32mm

12

D-E hysteresis curve

13

Domains, domain walls

Domains – continuous space region with the same spontaneous dipole moment (polarization)

Domain walls – interfaces between domains• Charged wall• Neutral wall

Ferroelectric domains exist in ferroelectric phasePhase transition – Curie temperature

14

BaTiO3 ceramics domains mmmm 43 →

Detwinning process observed during heating of the BaTiO3specimen. Note that the heating direction is (a) parallel and (b) perpendicular to the band walls.

Sang-Beom Kim, Doh-Yeon Kim:J. Am. Ceram. Soc., 83 [6] 1495–98 (2000)

15

Electrostriction

• Nonlinear effectStrain is proportional to the square of electric

field

• No symmetry restriction• 4th rank tensor coefficients

lkklijij EEQS =

16

Piezo-, pyro- and ferroelectricity

Piezo-

Pyro-

Ferro-

SiO2, GaPO4, AlPO4, ...

Li2B4O7, ...

BaTiO3, PbTiO3, PZT, KNbO3, TGS, KDP, ...

17

Piezoelectric materials

• Single-crystals• Polycrystals (ceramics)• Polymers• Composites

18

Single-crystals• α-Quartz (SiO2),α-Berlinite (AlPO4),Galium Orthophosphate

(GaPO4), Langasite (La3Ga5SiO14), Langatite (La3Ga5.5Ta0.5O14),Langanite (La3Ga5.5Nb0.5O14)

• Lithium Tetraborate (Li2B4O7)

• Lithium Niobate (LiNbO3), Lithium Tantalate (LiTaO3)• Perovskites - Lead Titanate (PbTiO3), Barium Titanate (BaTiO3),

Potassium Niobate (KNbO3) • Solid solutions - (1-x)Pb(Mg1/3Nb2/3)O3 – xPbTiO3 (PMN-PT), (1-x)

Pb(Zn1/3Nb2/3)O3 – xPbTiO3 (PZN-PT)• Rochelle Salt, KDP, ADP, KTP, …

19

Polycrystals (ceramics)

• Grained polycrystals (grain 1-10µm)• Electric field poling – ferroelectric materials (∞mm)

Before poling after poling• Textured ceramics

E PS

20

Polymers

• PVDF (- CH2 – CF2 -, β-phase)• Electrically poled - ∞m, and stretched - ∞2• Copolymer with TrFE

C

C

H H

F F

C

C

H H

F F

C

C

H H

F Fdipolemoment

21

Piezoelectric composites

• Two or more phases• Parallel (a) or series (b) connectivity of

phasesSeries

Parallel

a) b)

)1(33

)2()2(33

)1(

)1(33

)2(33

)2()2(33

)1(33

)1(

33 ε+ε

ε+ε=

vvdvdv

d eff

)1(33

)2()2(33

)1(

)1(33

)2(33

)2()2(33

)1(33

)1(

33 svsvsdvsdv

d eff

+

+=

22

Piezoelectric composites

• Effective combination of electromechanical properties

Properties:• Sum• Combination• Product

2-2 1-3

0-3

23

Piezoelectric propertiesd33[pC/N]

α-SiO2

28

LiT

aO3

16

LiN

bO3

PVD

Fpolym

er

35

KN

bO3

31

PbTiO

3

84 86

BaT

iO3

hard PZT

200

soft PZT

PMN

-PTPZ

N-PT

„cymbal“

composite

600 2000 15000

24

Linear equations of state

Coupled variables – mechanical (stress/strain), thermal (entropy/temperature) and electrical (field/displacement)

∆ΘΘ

++α=σ∆

∆Θ+ε+=

∆Θα++=

CEpT

pETdD

EdTsS

kTkkl

Ekl

Tik

Tikklikli

Eijkkijkl

Eijklij

25

Symmetry of the tensor components

• Elastic• Electrostriction • Piezoelectric• Dielectric (thermal expansion, refraction index,

etc.)• Pyroelectric

Compare: symmetry of optical activity (axial 2nd rank tensor)

]]][[[ 22 VVssss klijijlkjiklijkl ===

][ 2VVdd ikjijk =

][ 2Vjiij ε=εVp j

][)(det 2Vgag jiij ε=

]][[ 22 VVQQQ kljilkijklij ==

26

Tensor vs. matrix notation

• Elastic

• Piezoelectric

=βα=β=α

=βα=αβ

6,5,4,46,5,4;3,2,12

3,2,1,

ijkl

ijkl

ijkl

ss

ss

6,...,2,1, =βα=αβ ijklcc

=α=α

=α 6,5,423,2,1

ijk

ijki d

dd

6,...,2,1=α=α ijki ee

654321matrix12,2113,3123,32332211tensor

27

Different choice of state variables

Example: piezoelectric effect

kTikii

kkE

ETdD

EdTsS

ε+=

+=

νν

µνµνµ

kTikii

kkD

DTgE

DgTsS

β+−=

+=

νν

µνµνµ

kSikii

kkE

ESeD

EeScT

ε+=

−=

νν

µνµνµ

kSikii

kkD

DShE

DhScT

β+−=

−=

νν

µνµνµ

28

Material property tensorial coefficients

• Elastic moduli/compliances (21)• Piezoelectric coefficients (18)• Dielectric permittivity or thermal expansion (6)• Pyroelectric coefficient (3)

665646362616

565545352515

464544342414

363534332313

262524232212

161514131211

ssssssssssssssssssssssssssssssssssss

363534333231

262524232221

161514131211

dddddddddddddddddd

εεεεεεεεε

332313

232212

131211

( )321 ppp

29

Anisotropy in material properties d33-surface

BaTiO3 – 4mm

d33l33+(d31+d15)l3(l1

2+l22)

l1=sin(θ)cos(φ), l2=sin(θ)sin(φ), l3=cos(θ)d33= 90, d31= -33.4, d15= 564 [pC/N]

PS[001]T

Maximum 224pC/N at θ = 51o

90pC/N at [001]C221pC/N at [111]C

30

Piezoelectric ceramics

Electromechanical tensors – symmetry class ∞mm, poling direction 3

)(200000

0000000000000000000

121166

66

44

44

331313

131112

131211

ssss

ss

sssssssss

−=

0000000000000

333131

15

15

dddd

d

εε

ε

33

11

11

000000

( )300 p

31

Primary and secondary pyroelectricity

• Primary – constant mechanical strain• Secondary – constant mechanical stress

Example: non-pyroelectric quartz SiO2 – symmetry 32νµνµα+= k

EESk

Tk dcpp

)(21

00000000

0000000000

121166

6614

1444

441414

331313

14131112

14131211

ccc

cccc

cccccc

cccccccc

−=

−

−

−−

−

00000020000000

1114

141111

ddddd

αα

α

3

1

1

000000

0== Sk

Tk pp

32

Measurement of piezoelectric properties

Direct or converse piezoelectric effect• Resonant technique• Hydrostatic chamber• Laser interferometry• Ultrasound (pulse-echo technique)• d33-meter (uni-axial mechanical stress)

33

Resonant technique

Mechanical resonance piezoelectrically generatedExample: ceramic disc in radial vibrations

admittance

resonance Y→∞antiresonance Y→0

p

r

rr

JJ

σ−=ηηη

1)(

)(

1

0

Prr crf

11

2 ρπ=η

−

ηη−ησ−η

ω= 1)()()1(

)()(2

01

120 JJ

JkCjY P

P

34

Dis c , PZT APC841, D=40mm, t=2,2mm

0.1

1

10

100

1000

10000

100000

10 100 1000

f[kHz]

Z[O

hm]

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

phas

e[ra

d]

impe dancephas e

35

Hydrostatic chamber

Direct piezoelectric effect – sample mechanically stressed in chamber, charge is measured

Hydrostatic pressure

Hydrostatic piezoelectric coefficient

−−

−

pp

p

000000

333231

3 )(dddd

pdD

h

h

++=−=

36

Pressure dependence of the charge density for P(VDF-TrFE): 1 - increase, 1´ - decrease of pressure.Burianová, L., Hána, P., Tyagur Y. I. and Kulek, J.: Piezoelectric hydrostatic coefficients of PVDF andP(VDF,TrFE) copolymer foils at high hydrostatic pressures. Ferroelectrics 224 (1999), 29-38.

37

Laser interferometry

• Displacement measured by laser interferometry

Displacements of 10-12 m to 10-5 m• Subresonant frequency range• Single- or double-beam

(micro)interferometer• Piezoelectric, electrostrictive and electro-

optic material coefficients measurement

38

Laser interferometry

Interference of two coherent light beamsIntensity

For small sample surface displacement and π/2 phase shift in LI branches

Application of small AC signal – response from photodiode amplified by lock-in

)/4cos(2 λ∆π++= dIIIII rprp

λ∆π−++= /4)(21)(

21

minmaxminmax dIIIII

39

Single-beam LI(Michelson)

L.Burianová, M.Šulc, M.Prokopová: J.Europ.Ceram.Soc. 21 (2001) 1387-1390

40

Double-beam LI (Mach – Zehnder)

L.Burianová, M.Šulc, M.Prokopová: J.Europ.Ceram.Soc. 21 (2001) 1387-1390

41

Ultrasound measurements

Ultrasound velocity is a function of elastic constants, piezoelectric moduli and permittivity

Pulse-echo technique (time-of-flight)

US polarization - longitudinal or transverse wave

sample sample

US transducers

42

US velocity measurementChristoffel’s tensor

ikSik

ilikljkkijlj

Eijklik

eec

ννε

νννννν +=Γ

( )321 νννPropagation direction

Calculation of the ultrasound velocity

0)det( 2 =−Γ ikik v δρ

43

Example of US velocity calculation - symmetry class •2

Electromechanical material tensors

−

0000000000000000

14

14d

d

− )(2100000

0000000000000000000

1211

44

44

331313

131112

131211

cc

cc

ccccccccc

33

11

11

000000

εε

ε

44

Propagation direction [100]

0,,

231312

443366221111=Γ=Γ=Γ

=Γ=Γ=Γ EEE ccc

ΓΓ

ΓΓ

33

22

11

000000

332

222

112

Γ=

Γ=

Γ=

v

v

v

ρ

ρ

ρ

2 transversal modes

1 longitudinal mode

1

3

2

c11E

c44E

c66E

Piezoelectrically free – not dependent on piezocoefficients

US

45

P.Hána et al.: Ferroelectrics 319 (2005) 145-154

46

d33- meter

• Quasistatic mechanical pressure applied to the sample, electric charge analyzed

d33-measurement – mechanical stress perpendicular to electrodes

d31-measurement - mechanical stress parallel to electrodes

47

Conclusions

• Electromechanical properties are important properties of solid state materials

• Anisotropy and microstructure is key issue• Applicable in many today’s commercial

devices

48

Ferroelectric domains and walls

Ferroelectric/ferroelastic domainsDomain walls

Domain-average and domain-geometry engineering

Principles, results and materials

49

Ferroic phaseStructural phase transition

Parent (e.g. paraelectric) →ferroic phaseFerroelectrics

LiNbO3

KNbO3

BaTiO3

Pb5Ge3O11

KIO3

mm 33 →

23 mmmm →

mmmm 43 →

36 →

mm →3

FerroelasticsAgNbO3NaNbO3Pb3(PO4)2

mmmmm →3

mm /23 →

50

Bi4Ti3O12

xymmmm →/4

ctetr

atetr

btetr

bmon

cmon

amon8 ferroelectric DS4 ferroelastic DS

Pa>>Pc

51

Bi4Ti3O12

Spontaneous strains/polarizations (parent phase coordinates)

),,(),,(

),,(),,(

),,(),,(

),,(),,(

)(

)(

)(

)(

caaVIII

caaVII

caaVI

caaV

caaIV

caaIII

caaII

caaI

PPPPPPPPSSSSSSSSS

S

PPPPPPPPSSSSSSSSS

S

PPPPPPPPSSSSSSSSS

S

PPPPPPPPSSSSSS

SSSS

−=−−=

−−−−−−

=

−−=−=

−

−=

−−−==

−

−=

−−=−=

−−=

21

21

21

21

21

21

21

21

21

21

21

21

21

21

21

21

331313

131112

1312114

331313

131112

1312113

331313

131112

1312112

331313

131112

1312111

52

Domain wall orientation

0122122 =−=− jiijij dsdsSSdsds )()()( )()()()(

Example for Bi4Ti3O12domain pair S(1) (P(1), P(2)) and S(2) (P(3),P(4))

Two perpendicular domain wallsCharged wall (010) W-wallNeutral wall (10K) S-wall

02312

131 =− dsds

SSds )(

12

13

SSK −=

53

Domain wall orientations in Bi4Ti3O12

N/AS(4)

P(7),P(8)

(010)(10K)

N/AS(3)

P(5),P(6)

(110)(001)

(100)(01-K)

N/AS(2)

P(3),P(4)

(100)(01K)

(1-10)(001)

(010)(10-K)

N/AS(1)

P(1),P(2)

S(4)

P(7),P(8)

S(3)

P(5),P(6)

S(2)

P(3),P(4)

S(1)

P(1),P(2)

54

Types of domain wallsW-walls

W∞ - arbitrary orientation of wall

Wf – fixed crystallographic plane wall

S-walls (“strange” walls, also W’-walls)

S1 – direction of PS

S2 – bijk and/or Qijkl

S3 – direction of PS, bijk and/or Qijkl

S4 – direction and magnitude of PS, bijk and/or Qijkl

S5 – magnitude of PS, bijk and/or Qijkl

55

Permissible domain wall pairs

W∞ - arbitrary orientation of wall

WfWf – fixed crystallographic plane walls

WfS – fixed and strange wall

SS – pair of strange walls

R – no permissible walls between two domains

J.Fousek, V.Janovec: J.Appl.Phys. 40 (1969) 135

J.Sapriel: Phys.Rev. B12 (1975) 5128

J.Erhart: Phase Transitions 77 (2004) 989-1074

56

Species without any allowed DW’s – R case

13→13→13→

mmmm →3

zymxmm 23→2223→m

22223→

Species with all allowed DW twin types – W-W, S-S, W-S, R

zmm 23 →

zmmm →3zmzmm /23 → zm 234 →

z2432→Species with only allowed strange DW twins – S-S case

zm 2/4 →

zmm→/4zmzm /2/4 →

z24→z24→

zm 2/6 →

zmm→/6zmzm /2/6 →

zm→6z26→

57

Spontaneous strain experimentally

Lattice parameters measured by X-ray

• in parent phase (extrapolated to the ferroic phase)

• in ferroic phaseLB Tables III/16a

General formula for strain tensor componentsJ.L.Schlenker, G.V.Gibbs, M.B.Boisen, Jr.: Acta Cryst. A34 (1978) 52-54

58

Spontaneous strain is related to spontaneous polarization

In general (for proper ferroelectrics)

Example for speciesxymmmm →/4iikljiijklkl PbPPQS +=

=

21

31

31

23

21

21

66

44

44

333131

131112

131211

6

5

4

3

2

1

000000000000000000000000

PPPPP

PPP

QQ

QQQQQQQQQQ

SSSSSS

),,( 311 PPPPS =

59

mmmm 43 →

PI

PIV

PII

PIII

PV

PVI)(),(),(

),(),(),(100010001

001010100

SVI

SV

SIV

SIII

SII

SI

PPPPPPPPPPPP===

===

P P P P P P

PIN/A (110)

(1-10)(101)(10-1)

any (110)(1-10)

(101)(10-1)

PIIN/A (011)

(01-1)(110)(1-10)

any (011)(01-1)

PIIIN/A (101)

(10-1)(011)(01-1)

any

PIVN/A (110)

(1-10)(101)(10-1)

PVN/A (011)

(01-1)

PVIN/A

Domain walls180o, 90o

{110}

I II III IV V VI

60

PI

PIV

PII

PIII

PVIIPVIII

PV PVI

)(),(),(),(

),(),(),(),(

1113

11113

11113

11113

1

1113

11113

11113

11113

1

SVIII

SVII

SVI

SV

SIV

SIII

SII

SI

PPPPPPPP

PPPPPPPP

====

====

PI PII PIII PIV PV PVI PVII PVIII

PIN/A (010)

(101)(001)(110)

(100)(011)

any (010)(101)

(001)(110)

(100)(011)

PIIN/A (100)

(0-11)(001)(-110)

(010)(101)

any (100)(0-11)

(001)(-110)

PIIIN/A (010)

(-101)(001)(110)

(100)(0-11)

any (010)(-101)

PIVN/A (100)

(011)(001)(-110)

(010)(-101)

any

PVN/A (010)

(101)(001)(110)

(100)(011)

PVIN/A (100)

(0-11)(001)(-110)

PVIIN/A (010)

(-101)

PVIIIN/A

mmm 33 →

Domain walls180o, 109o, 71o

{100}, {110}

61

23 mmmm →PI

PIVPII

PIII

PVII PVIII

PV

PVI

PIXPX

PXI PXII

)(),(),(),( 1102

10112

10112

11012

1S

IVS

IIIS

IIS

I PPPPPPPP ====

)(),(),(),( 1012

11102

11102

11012

1S

VIIIS

VIIS

VIS

V PPPPPPPP ====

)(),(),(),( 1012

10112

10112

11102

1S

XIIS

XIS

XS

IX PPPPPPPP ====

1211

44

QQQK−

=

Domain walls180o, 120o, 90o, 60o

{100}, {110}, {11K}

K=0.38 for BaTiO3, K=0.33 for KNbO3

62

PbTiO3 crystal domains mmmm 43 →

PbTiO3 under a polarized optical microscope. The regions with different color represent ferroelectric domains, and the size of the crystal is about 1.5 mm. Contributed by Sang-Wook Cheong. http://www.physics.rutgers.edu/cmx/gifs/pbti.html

63

BaTiO3 ceramics domains mmmm 43 →

Photographs of etched surface of BaTiO3 ceramicsa) Herringbone and square-net patternb) Banded structure over many grains

G.Arlt, P.Sasko: J.Appl.Phys. 51 (1980) 4956-4960

64

BaTiO3 crystal domains mmmm 43 →

Piezoresponse SFMa) Topographyb) Out-of-plane component of piezoelectric response (c-domains)c) In-plane component of piezoelectric response (a-domains)

L.M.Eng, M.Abplanalp, P.Günter: Appl.Phys. A66 (1998) S679-683

65

BaTiO3 crystal domains mmmm 43 →

P.W.Forsbergh, Jr.: Phys.Rev.76 (1949) 1187-1201

66

Orthorhombic BaTiO3 multi-domain crystal

23 mmmm →

Three directions of polarization in orthorhombic BaTiO3 as revealed by the etching technique at 0oC. In the smoothest areas, the negative ends of the dipoles are at the surface; in the roughest areas, the positive ends of the dipoles are at the surface. In the areas of intermediate roughness, the dipoles are parallel to the surface.

F.Jona, G.Shirane: Ferroelectric Crystals, Dover Publications 1993, page 169 Figure IV-42(reproduced from D.P.Cameron: IBM J.Res.Development 1 (1957) 2-7)

67

KNbO3 crystal domains 23 mmmm →

[011][01-1]

[101]

[10-1](100)

(010)

(110)

Effective symmetry -Triclinic 1

Optical micrograph of 90° and 60° domain walls in KNbO3

Li Lian et al: J. Appl. Phys. 80 (1996) 376-381

68

S-walls in KNbO3

[100][001]

[010]

[011]

[01-1]

[-110]

[110]

(1/0.3/1)

(1/-0.3/1)

(010)

as-grown crystal

E.Wiesendanger: Czech.J.Phys. B23 (1973) 91-99

69

S-wall in KNbO3 artificially created

[110]C

[011]C

E[10-1]

“Differential vector poling”

J.Hirohashi et al.: J.Korean Phys.Soc. 42 (2003) S1248-S1251

70

Ferroelastic S-wall temperature rotation NaNbO3 crystal mmmmm →3

S.Miga, J.Dec, M.Pawelczyk: J. Phys.: Condens. Matter 8 (1996) 8413–8420 (in NaNbO3)S.Miga, J.Dec: J.Appl.Phys. 85 (1999) 1756-1759 (in AgNbO3)

71

Domain engineering

Domain-geometry engineeringExact space distribution of domains – optical superlattices,

suppressed mode resonators

Domain-average engineeringSubstantial increase of piezoelectric coefficients in multi-

domain ferroelectric system - strongly piezoelectric single crystals PZN-PT, PMN-PT

J.Fousek, D.B.Litvin, L.E.Cross: J.Phys.: Condens.Matter 13 (2001) L33-L38

72

Domain-geometry engineering

LiNbO3Crystal plateresonator

Thickness mode

V.D.Kugel, G.Rosenman, D. Shur: J. Appl. Phys. 78 (1995) 5592-5596

73

Domain-average engineeringJ. Kuwata, K. Uchino, S. Nomura: Jpn.J.Appl.Phys. 21 (1982) 1298

PZN-PT (3m)S.-E. Park,T. R. Shrout:J.Appl.Phys.82 (1997) 1804-1811

KNbO3(mm2)S. Wada, A. Seike, T.Tsurumi: Jpn.J.Appl. Phys. 40 (2001) 5690–5697

74

85500(001)eng at 0oC

k31=29d31=18(110)KNbO3

k31=31d31=52(001)eng

200-300(111)eng

79400(001)eng at –90oC

53100(001)BaTiO3

942800(001)engPMN-33%PT

942500(001)eng

3984(111)PZN-8%PT

851100(001)eng

3883(111)PZN

k33[%]d33[pC/N]cutCrystal