7/21/2015 Physics 403 Summer 2015 1

Ferroelectricity. Phase transition.

Material properties

DKDPBaTiO3

PMN-PT(30%)PZN-PT(9%) PMN-PT(40%)

KDP

7/21/2015 Physics 403 Summer 2015 2

Ferroelectricity.

outline

•Ferroelectricity. Definition

•Discovery

•Main properties

•Phenomenological theory

• Some materials

•Relaxors

•Applications

7/21/2015 Physics 403 Summer 2015 3

Ferroelectricity. Definitions.

Ferroelectric Materials. A ferroelectric material is

a material that exhibits, over some range of

temperature, a spontaneous electric polarization

that can be reversed or reoriented by application

of an electric field.

An American National Standard

IEEE Standard Definitions of

Primary Ferroelectric Terms

7/21/2015 Physics 403 Summer 2015 4

Rochelle Salt KNaC4H4O6*4H2O

Ferroelectricity: Discovery

7/21/2015 Physics 403 Summer 2015 5

Rochelle Salt KNaC4H4O6*4H2O

Joseph Valasek (1897-1993)

University of Minnesota

1. J. Valasek, Phys. Rev. 17, 475 (1921)

2. J. Valasek, Phys. Rev. 19, 478 (1922)

Fig.1. The first published

hysteresis loop [1]Fig3. Piezoelectric

response as a function

of temperature [2]

Ferroelectricity: Discovery

1920 1969

7/21/2015 Physics 403 Summer 2015 6

Ferroelectricity: Two classes of ferroelectrics

Displacement type

N

O

O

Order-Disorder

disorder

order

NaNO2

Ba

Ti O

P

PBaTiO3

-40 -30 -20 -10 0 10 20 30 40

-40

-30

-20

-10

0

10

20

30

40 Sn:Ti = 0.24:0.11

PLZST ceramics

P (C

/cm

2)

EDC

(kV/cm)

7/21/2015 Physics 403 Summer 2015 7

Ferroelectricity: Polarization reversible

(P-E hysteresis)

7/21/2015 Physics 403 Summer 2015 8

Ferroelectricity: Domains

+

-

Pnet~0

Single domain state

Multi domain state

180o domain pattern

90o domains

Y Lu et al. Science 1997;276:2004-2006

Courtesy of Igor Lukyanchuk

http://www.lukyanc.net/stories/nano-worldofdomains

7/21/2015 Physics 403 Summer 2015 9

Ferroelectricity: Domains

Courtesy of Benjamin Vega-Westhoff

and Scott Scharfenberg, P403, Fall2009

BaTiO3

BaTiO3

Crystal from Forschungsinstitutfür mineralische und metallische

Werkstoffe -Edelsteine/Edelmetalle

KH2PO4

Courtesy of Allison Pohl, P403,

Fall2009

KD2PO4191K

PMN-PT40%

PMN-PT30%

7/21/2015 Physics 403 Summer 2015 10

Ferroelectricity: Landau-Ginzburg

phenomenological theory

EPcPbPaPFP ...6

1

4

1

2

1 642

Free energy Order parameter (polarization)Electric field

To find the equilibrium solution we need to

find the minima of FP by solving the equation:0

P

F

Ignoring higher terms we can get the linear solution:

0F

aP EP

aE

P 1

Assuming linear dependence of a on temperature we will have:

1( )

cT T

C and finally we will have Curie-Weiss law

( )c

C

T T

-7 0 7

0

10

20

30

40

50

60

70

80

F (

a.u

.)

P (a.u.)

7/21/2015 Physics 403 Summer 2015 11

Ferroelectricity: Landau-Ginzburg

phenomenological theory

In case of b>) (C>0 also) We will

have the solution for second order

phase transition with two

equilibrium points –p0 and p0. Both

these states are equivalent

T>Tc

T=Tc

T<Tc

E=0

p0

-p0

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-20

-10

0

10

20

30

40

F (

a.u

.)

P (a.u.)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-20

-10

0

10

20

30

40

F (

a.u

.)

P (a.u.)

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-20

-10

0

10

20

30

40

F (

a.u

.)

P (a.u.)

-40 -30 -20 -10 0 10 20 30 40

-40

-30

-20

-10

0

10

20

30

40 Sn:Ti = 0.24:0.11

PLZST ceramics

P (C

/cm

2)

EDC

(kV/cm)

7/21/2015 Physics 403 Summer 2015 12

Ferroelectricity: Landau-Ginzburg

phenomenological theory

EPcPbPaPFP ...6

1

4

1

2

1 642

Including EP term can illustrate

the P-E hysteretic behavior

-PsPs

Pr

Pr

Ps

400 450 5000

3

6

9

T (K)

'/1

00

0

7/21/2015 Physics 403 Summer 2015 13

Ferroelectricity: Susceptibility

0P E

0 0 0 0 0(1 )D E P E E E E

For ferroelectrics >>1 and ≈

Curie-Weiss law:

00)(

CWTT

C

C=1.9*105;

TCW=385.2K

7/21/2015 Physics 403 Summer 2015 14

Ferroelectricity: Typical ferroelectric materials

KH2PO4

Courtesy Max Candocia, P403 Spring 2011

EDC=1.2kV/cm

7/21/2015 Physics 403 Summer 2015 15

Ferroelectricity: Typical ferroelectric materials

BaTiO3

cubic

tetragonalorthorhombicrhombohedral

7/21/2015 Physics 403 Summer 2015 16

Ferroelectricity: Typical ferroelectric materials

Number of publications concerning ferroelectricity.

From Jan Fousek “Joseph Valasek and the Discovery of

Ferroelectricity”

Number of ferroelectric substances discovered in each year.

Springer Handbook of Condensed Matter and Materials Data

TC(K) Ps (C/cm2)

KDP

typeKH2PO4 123 4.75

KD2PO4 213 4.83

RbH2PO4 147 5.6

Perovskites BaTiO3 408 26

KNbO3 708 30

PbTiO3 765 >50

LiTiO3 938 50

LiNbO3 1480 71

7/21/2015 Physics 403 Summer 2015 17

Antiferroelectrics

<P> ~0

PNZST (film)

PLZST (ceramic)

Courtesy of E. Colla and

City University of Hong Kong

7/21/2015 Physics 403 Summer 2015 18

Antiferroelectricity in BaTiO3

Courtesy of Alan Selewa and

Nathaniel Scheidler

(Physics403 class, 2014,

unpublished)

7/21/2015 Physics 403 Summer 2015 19

Ferroelectricity: Relaxors - PMN Pb(Mg1/3 Nb2/3)O3

Frequency dispersion of e’

at different temperatures

Temperature dependencies of the

real part of the dielectric constant

measured in a broad frequency

range: 3*10-3 -106 Hz [1,2]

1. E.V. Colla et all., J. Phys.: Cond. Matter, 4,3671, (1992)

2. E.V. Colla et all. J. Appl. Phys., 83, 3298, (1998)

150 200 250 300 350 400 4500

7

14

21

28

35

T (K)

'/1

03

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

10

00

/'

101

102

103

104

105

106

4

6

8

10

12

14

16

18

20

22

220K

230K

240K

250K

'/1

03

f (Hz)

0.0 0.1 0.2 0.3 0.4 0.5

300

400

500 Literature data

single crystals

ceramics

Tc

(K)

x

7/21/2015 Physics 403 Summer 2015 20

(PMN)(1-x)(PT)(x)

phase diagram

“Relaxor”state

(pseudocubic)

Regular ferroelectric

(tetragonal)

Paraelectric

(cubic)

(PMN)0.9(PT)0.1(PMN)0.7(PT)0.3

(PMN)0.6(PT)0.4

(PMN)0.7(PT)0.3PT: PbTiO3, ferroelectric with

Curie temperature 763K

Ferroelectricity: Solid solution relaxor-regular

ferroelectric.

7/21/2015 Physics 403 Summer 2015 21

Material Dielectric

constant

Piezoelectric

coefficient, (pC/n)

Electromechanical

coupling factorQuartz 4.5 2.3 0.1

Rochelle salt (30C) 9.2 27 0.3

Barium titanate

ceramic

1700 190 0.52

Lead zirconate

titanate PZT 45/55

450 140 060

PMN-PT (sc) 4200 2200 0.92-0.94

PZN-PT (sc) 2500 2400 0.91-0.93

Actuators

Transducers

Adaptive optics

Capacitors

Line motors for SFMTransducer stack for

ultrasonic sonar application

(TRS Ceramics)

Piezoelectric

properties of different

materials

Ferroelectricity: Relaxors - some aplications