2014 Physics 403 Summer

PMN-PT(40%) 7/9/2014 Physics 403 Summer 2014 1 Ferroelectricity. outline •Ferroelectricity. Definition •Discovery •Main properties •Phenomenologi...
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PMN-PT(40%)

7/9/2014

Physics 403 Summer 2014

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Ferroelectricity. outline •Ferroelectricity. Definition •Discovery •Main properties •Phenomenological theory • Some materials

•Relaxors •Applications

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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 7/9/2014

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Ferroelectricity: Discovery Rochelle Salt KNaC4H4O6*4H2O

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Ferroelectricity: Discovery Rochelle Salt KNaC4H4O6*4H2O

Fig3. Piezoelectric response as a function of temperature [2]

Fig.1. The first published hysteresis loop [1]

1920

1969

Joseph Valasek (1897-1993) University of Minnesota 1. J. Valasek, Phys. Rev. 17, 475 (1921) 2. J. Valasek, Phys. Rev. 19, 478 (1922)

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Ferroelectricity: Two classes of ferroelectrics

Order-Disorder Displacement type

disorder O P

Ba Ti

O

N O order

BaTiO3

P

NaNO2 7/9/2014

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Ferroelectricity: Polarization reversible (P-E hysteresis) PLZST ceramics 40

Sn:Ti = 0.24:0.11

30

2

P (C/cm )

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

-30

-20

-10

0

10

20

30

40

EDC(kV/cm)

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Ferroelectricity: Domains

Single domain state

+ Multi domain state

90o domains

Pnet~0

Courtesy of Igor Lukyanchuk http://www.lukyanc.net/stories/nano-worldofdomains

180o domain pattern Y Lu et al. Science 1997;276:2004-2006

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Ferroelectricity: Domains PMN-PT40%

BaTiO3 Courtesy of Benjamin Vega-Westhoff and Scott Scharfenberg, P403, Fall2009

KH2PO4 Courtesy of Allison Pohl, P403, Fall2009

PMN-PT30%

BaTiO3

191K

KD2PO4

Crystal from Forschungsinstitut für mineralische und metallische Werkstoffe -Edelsteine/Edelmetalle

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Ferroelectricity: Landau-Ginzburg phenomenological theory Order parameter (polarization)

Free energy

Electric field

1 2 1 4 1 6 aP  bP  cP  ...  EP 2 4 6 F To find the equilibrium solution we need to 0 find the minima of FP by solving the equation: P FP 

Ignoring higher terms we can get the linear solution:

F  aP  E  0 P



P 1  E a

Assuming linear dependence of a on temperature we will have:

1   (T  Tc ) C 7/9/2014

and finally we will have Curie-Weiss law

Physics 403 Summer 2014



C (T  Tc ) 10

Ferroelectricity: Landau-Ginzburg phenomenological theory

80 70

In case of b>) (C>0 also) We will 60

phase

transition

with

two

equilibrium points –p0 and p0. Both these states are equivalent

F (a.u.)

have the solution for second order

50

T>Tc

E=0

40

T=Tc

30

T>1 and  ≈ 

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Curie-Weiss law:

C=1.9*105;

'/1000

TCW=385.2K



6

C   00 (T  TCW )

3

0 400

450

500

T (K) 7/9/2014

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Ferroelectricity: Typical ferroelectric materials KH2PO4

EDC=1.2kV/cm

Courtesy Max Candocia, P403 Spring 2011

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Ferroelectricity: Typical ferroelectric materials BaTiO3

cubic

rhombohedral

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orthorhombic

tetragonal

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Ferroelectricity: Typical ferroelectric materials

KDP type

Perovskites

TC(K)

Ps (C/cm2)

KH2PO4

123

4.75

KD2PO4

213

4.83

RbH2PO4

147

5.6

BaTiO3

408

26

KNbO3

708

30

PbTiO3

765

>50

LiTiO3

938

50

LiNbO3

1480

71

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

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Antiferroelectrics

~0 PNZST (film)

PLZST (ceramic)

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Courtesy of E. Colla and City University of Hong Kong

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Antiferroelectricity in BaTiO3

Courtesy of Alan Selewa and Nathaniel Scheidler (2014, unpublished)

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Ferroelectricity: Relaxors - PMN Pb(Mg1/3 Nb2/3)O3 35 0.35 28

0.30

0.20 14

0.15

1000/'

21

0.10 7 0.05

22 20 18

200

250

300

350

T (K) Temperature dependencies of the real part of the dielectric constant measured in a broad frequency range: 3*10-3 -106 Hz [1,2]

400

0.00 16 450 3

0 150

'/10

'/10

3

0.25

250

K

14 12

240

10

230K

8

K

220K

6 4

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)

10

1

10

2

10

3

4

5

10 10 10 f (Hz) Frequency dispersion of e’

6

at different temperatures

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Ferroelectricity: Solid solution relaxor-regular ferroelectric. (PMN)0.7(PT)0.3

Tc (K)

500

Paraelectric (cubic)

PT: PbTiO3, ferroelectric with Curie temperature 763K

(PMN)(1-x)(PT)(x) phase diagram Literature data single crystals ceramics

Regular ferroelectric (tetragonal) (PMN)0.6(PT)0.4

400

300

0.0

0.1

0.2

0.3

0.4

0.5

x

(PMN)0.9(PT)0.1

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“Relaxor”state (pseudocubic)

(PMN)0.7(PT)0.3

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Ferroelectricity: Relaxors - some aplications

Actuators Transducers Adaptive optics Capacitors Line motors for SFM Material

Dielectric constant

Piezoelectric coefficient, (pC/n)

Electromechanical coupling factor

Quartz Rochelle salt (30C) Barium titanate ceramic Lead zirconate titanate PZT 45/55 PMN-PT (sc) PZN-PT (sc)

4.5 9.2 1700

2.3 27 190

0.1 0.3 0.52

450

140

060

4200 2500

2200 2400

0.92-0.94 0.91-0.93

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Transducer stack for ultrasonic sonar application (TRS Ceramics)

Piezoelectric properties of different materials

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