Ferroelectricity

ABX3

Ferroelectricity

Perovskites

Spontaneous polarizationAnalogous to ferromagnetismStructural phase transitionTc is transition temperature

Electric field inside the material,is not conducting

Ferroelectric domains

Increasing the electric field polarizes the material.

BaTiO3

cubic (contains i = > no spontaneous P)

Can be used to make nonvolatile memory

BaTiO3

Can be used to make ultracapacitors

1r

+++ +++

- - - - - -

Ferroelectric

Paraelectric state

Above Tc, BaTiO3 is paraelectric. The susceptibility (and dielectric constant) diverge like a Curie-Weiss law.

1

cT T

This causes a big peak in the dielectric constant at Tc.

01

Paraelectric

PbTiO3

Pyroelectric constant

Dielectric constant

Specific heat

1

cT T

Polarization

Antiferroelectricity

Polarization aligns antiparallel.

Associated with a structural phase transition.

Large susceptibility and dielectric constant near the transition.

Phase transition is observed in the specific heat, x-ray diffraction.

PbZrO3

T > Tc T < Tc

Applied fieldT < Tc

Piezoelectricity

lead zirconate titanate (Pb[ZrxTi1−x]O3 0<x<1)—more commonly known as PZT

barium titanate (BaTiO3) Tc = 408 Klead titanate (PbTiO3) Tc = 765 Kpotassium niobate (KNbO3) Tc = 708 Klithium niobate (LiNbO3) Tc = 1480 Klithium tantalate (LiTaO3) Tc = 938 K

quartz (SiO2), GaAs, GaNGallium Orthophosphate (GaPO4) Tc = 970 K

Piezoelectric crystal classes: 1, 2, m, 222, mm2, 4, -4, 422, 4mm, -42m, 3, 32, 3m, 6, -6, 622, 6mm, -62m, 23, -43m

Third rank tensor, No inversion symmetry

Many ferroelectrics are piezoelectric.

Electric field couples to polarization, polarization couples to structure.

Piezoelectricity

When you apply a voltage across certain crystals, they get longer.

AFM's, STM'sQuartz crystal oscillatorsSurface acoustic wave generatorsPressure sensors - EpcosFuel injectors - BoschInkjet printers

PZT (Pb[ZrxTi1−x]O3 0<x<1)A

ntife

rroe

lect

ric

Large piezoelectric response near the rhombohedral-tetragonal transition.Electric field induces a structural phase transition.

Nitinol

Ni Ti alloy

Shape memory: If it is bent below a certain transition temperature and then heated above that temperature,

it returns to its original shape.

Superelasticity: Just above the transition temperature, the material exhibits elasticity 10-30 times that of an

ordinary metal.

Martisite - Austinite

Phase change memory

Phase-change memory (PRAM) uses chalcogenide materials. These can be switched between a low resistance crystalline state and a high resistance amorphous state.

GeSbTe is melted by a laser in rewritable DVDs and by a current in PRAM.

nonvolatile

Institute of Solid State PhysicsTechnische Universität Graz

Landau Theory of Phase Transitions

Landau theory of phase transitions

A phase transition is associated with a broken symmetry.

magnetism direction of magnetizationcubic - tetragonal different point groupwater - ice translational symmetryferroelectric direction of polarizationsuperconductivity gauge symmetry Lev Landau

Temperature dependence of the order parameter

At T=Tc = 0

2 410 0 2cf f T T m m

The temperature dependence of the magnetization is

0 cc

T Tm T T

Expand interms of T - Tc. Keep only the linear term. m and T - Tc are both small near Tc.

minimize m

Landau theory of phase transitions

0 cc

T Tm T T

Free energy

2 410 0 2cf f T T m m

0 cc

T Tm T T

220

0cT T

f f

Entropy

220

0 ( ) cT Tf f T

20

0

2( ) cT Tfs s T

T

0c A BL T S S

This is a second order phase transition

Kink in the entropy

1st order 2nd order

Specific heat

20

0

2 cT Tfs s TT

Entropy

Specific heat 20

02 v c

Tsc T c T T TT

There is a jump in the specific heat at the phase transition and then a linear dependence after the jump.

202 c

vTc

Introduction to Superconductivity, Tinkham

Specific heat

normal

superconducting

Specific heat

Fe

Specific heat

HePbTiO3

CuZn alloy -brassorder - disorder

Landau theory, susceptibility

2 410 0 2cf f T T m m mB

Add a magnetic field

0

2 c

c

Bm T TT T

302 2 0c

df T T m m Bdm

Above Tc, m is finite for finite B. For small m,

0

1 2 cT T

Curie-Weiss

Landau theory of phase transitions

LiTaO3

Curie-Weiss law

1r 0

1 2 cT T

Fitting the and parameters

0

1 2 cT T

202 c

vTc

Landau theory of phase transitions

0 cc

T Tm T T

0

can be determined from the temperature dependence of the order parameter

First order transitions

There is a jump in the order parameter at the phase transition.

2 4 61 10 0 02 3 0, 0, 0cf f T T m m m

First order transitions

BaTiO3

Tc?

Tc T1Tc

First order transitions

There will be a minimum at finite m as long as m2 is real

2 4 61 10 0 2 3 0 0cf f T T m m m

3 502 2 2 0c

df T T m m mdm

202 4

0,2

cT Tm

2

104 cT T

2 40 0cT T m m

One solution for m = 0.

Jump in the order parameter

At Tc

202 4

2cT T

m

m

At T1

2m

First order transitions, entropy, cv

2004 ( )

2 cfs T TT

2 4 61 10 0 2 3 0cf f T T m m m

204

0,2

cT Tm

20

204 ( )

v

c

Tsc TT T T

branch where the order parameter is nonzero

First order transitions, susceptibility

At the minima

2 4 61 10 0 2 3 0cf f T T m m m mB

3 502 2 2 0c

df T T m m m Bdm

3 502 2 2cB T T m m m

0 0

12m c

dmdB T T

Curie - Weiss

0 12

12m

dmdB T T

For small m,