Ferro and anti-ferro materials

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Dr. Tanmoy MaitiDr. Tanmoy Maiti

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Definition:

A ferroelectric material is a polar dielectric for which a spontaneous dipole polarization can be switched between two or more equilibrium symmetry equivalent states by the application of an appropriate electric field.

PSaturation Polarization, (PS)

Remanent Polarization, (Pr)

In nearly every case, the crystallographic symmetry of the ferroelectric phase is related to the symmetry of the high temperature paraelectric phase.

E

Coercive Field, Ec


Curie-Weiss Law: 1

!=

T " T0

C

where T0 is the Curie temperature and C is the Curie-Weiss constantTC is the curie point ! phase transition temperature.The fitting parameters (C and T0) calculated only in the high temperature linear part using Curie-Weiss law (equation).

T0


Order parameter for the ferroelectric phase transition is Ps spontaneous polarization.

Ps!0

Ferroelectric

T>TC

PS=0

Paraelectric T

PS

-PS

Continuous – 2nd Order Phase Transition, TC = T0

TC

Temp

"!# =

"!

C

T TC

Tc

P

E

EC

TC

Ferroelectric Paraelectric

E

P

"Ferroelectric effect was first observed in Rochelle salt (KNaC4H4O6·4H2O) by Czech scientist Roger Valasek in 1921. Dr. Tanmoy MaitiDr. Tanmoy Maiti

"In BaTiO3, high temperature phase is Centro-symmetric and nonpolar.

"In general we expect a phase change on heating to a nonpolar paraelectric phase, but not mandatory, an exception for this general case is, e.g., GASH or Guanidinium Aluminum Sulfate Hexahydrate. In GASH, no ferroelectric phase transition occurs because the crystal melts before this temperature is reached.

"In general it is unusual to find other high temperature ferroelectric to low temperature paraelectric phase transitions.

"Where we do have a phase change to high temperature nonpolar phase, we find that on cooling, the loss in symmetry must be such that there is more than one orientation for the polar axes to occur in low temp form, e.g. BaTiO3 m3m # 4mm Any one of 3 equal 4-fold axes can become polar direction! 6 possible orientationsTGS (CH2NH2COOH)3H2SO42/m # 2 loss of the mirror2-fold axis polar ! P ! only 2 possible orientations.


Domain Walls and Orientations

A domain is a nearly uniform region of polarization in aferroelectric crystal. Domain walls separate each domain.

Domain configurations are such that both strain and electrostatic energy is minimized.

180" domains –present in all FE materialsmaterials

(inversion symmetry operation linking the two states

zyxxyz i$%$


Non 180" (Ferroelastic-ferroelectric) walls–depends on symmetryeg: BaTiO3

domain wall ~ 90"domain wall ~ 90"


3Domains in Tetragonal BaTiO3

Domains are observed in a variety of microscopy techniques:

optical AFMTEM FESEM

Domain walls are transition regions from one domain variant (or orientation) to another.

x

&

xh tanPP 0Z ±=

&~1.0 nm (180")~ 10 to 15 nm (non 180")

0P

x

&


Symmetry Relations (Domain Structures)

Example: BaTiO3 m3m (cubic)$4mm (tetragonal)

order m3m = 48order 4mm = 8

From Group Theory:

00]1[ [100], 0],1[0 [010], ],1[00 [001],

symmetry F/E of order

symmetry prototype of order6

8

48 States Domain of Number ===


Ferroic Symmetry Species

The complete series of prototype-ferroic (FE, ferroelastic and ferromagnetic) have been determined by Aizu and Shuvalov.

Shuvalov Notation:

m3m(3) D4 F 4mm

high temperature prototype

F = ferroelectric

prototype

there are three equivalent 4-fold axes

indicates polarization, has definite orientation along 4-fold symmetry axis

Ref: K. Aizu Phys. Rev B2, 754 (1970)Dr. Tanmoy MaitiDr. Tanmoy Maiti

Example: Sr0.5Ba0.5Nb2O6

Tetragonal Tungsten Bronze

tric)(Ferroelecric)(Paraelect

4mmmmm

4 %

%

% %%

%

%

% %

order = 16 order=8

]1[00

and [001] 28

16 States Domain # ==


920'"#"0(0*:$$7920'"#"0(0*:$$7Initial polarization P increases linearly with the increasing electric field and the crystal behaves like a dielectric because the applied E-field is not large enough to switch any of the domains oriented opposite to its direction. Further increase in the field strength forces nucleation and growth of favorably oriented domains at the expense of oppositely oriented domains and polarization starts increasing rapidly until all the domains are aligned in the direction of the electric field i.e. reach a single domain state when polarization saturates to a value called saturation polarization (PS). The domains reversal actually takes place by formation of new favorably oriented domains at the expense of unfavorable domains. Now, when the field is decreased, the polarization generally does not domains. Now, when the field is decreased, the polarization generally does not return to zero and at zero field some of the domains still remain aligned in the positive direction and the crystal exhibits a remnant polarization (PR). To bring the crystal back to zero polarization state, a negative electric field is required which is also called the coercive field (EC). Further increase of electric field in the opposite direction will cause complete reversal of orientation of all domains in the direction of field and the loop can be completed. This relation between P and E is called a ferroelectric hysteresis loop which is an important characteristic of a ferroelectric crystal. The principle feature of a ferroelectric crystal is not only the presence of spontaneous polarization but also the fact that this polarization can be reversed by application of an electric field.

Domains tend towards single domain if orientation is correct and low concentration of defects.

E

PNucleation of reverse polarization domain

Domain wall movement

Extrapolation back to zero field will give saturation polarization.

Back-switching of domains gives a

Saturation Polarization (PS)

movementReverse polarization nucleation

Back-switching of domains gives a remnant polarization.

Coercive field magnitudes depend on Frequency and sample size-linked to nucleationor domain wall movement!

D,k are constants-Dr. Tanmoy MaitiDr. Tanmoy Maiti

Domain Switching an Application of an External Electric Field in a Ferroelectric (Classical View)

Two Major Processes- domain nucleation- domain wall motion

Total switching time:<'s> = <'u> + <'d> average switching time

average nucleation time

average domain wall motion switching


Total switching time:<'s> = <'u> + <'d>average switching time

average nucleation time

average domain wall motion switching

<'S> is determined by the slower of the two mechanisms, and there is a distribution of them about each average switching in a real crystal.crystal.

low field

high field-linear Dependence Switching dominated by domain walls

µ – domain walls mobility

-exponiental fielddependence


Low Field:

dn

s Eexp

11

''

''

>>

"

><(

a

n

<'>n

High Field:Domain wall motion

)( c

d

E'Eds

"=><

(><

µ

''

11

Ed

Velocity µ'

=><

=d Forward growth

Side wall movement-2-D

d

1-D


So What is Spontaneous Polarization (PS)??

P

E

EC

Pr

" For high drive levels, PR (shown equals to PS) is usually reproduciblebut EC depends completely on conditions. This is general to allferroelectrics known till today."Polarization hysteresis is an essential reflection of the spontaneouslypolarized domain structure in the crystal. If E is large enough to orient alldomains, then PR will be a measure of the spontaneous polarization of asingle domain. The fact that EC is variable is an indication of the timedependence of the reorientation processes.


Antiferroelectric Materials

These have some characteristics that are similar to F/E.

!#(T), Curie Constants ~ 10 5 "C

Changes to a lower Symmetry at the phase transition

Domains below the phase transition.

But Antiferroelectrics have:

No net spontaneous polarization – there are two sets of antiparallel polarizations in a unit cell.

!! =ii ba PP Pa = -Pb


Example:PbZrO3

4x4 primitive prototype lattice

“Superlattice structure”

Defining Characteristics:

i) Double hysteresis loopii) Superlattice structure in the

antiferroelectriciii) Unit cell volumeAFE < Unit Cell PEiv) Hydrostatic pressure raises TC

(opposite to FE’s)TC

Hydrostatic Pressure

Pressure stablises the AFE over the PE and raises TC


Phase transitions that drive the Paraelectric# Ferroelectric Phasein Crystallographic lattice.

a) Order-disorder Phase transition

b) Displacive Phase transitionCooperative phenomenaonset of Polarization is overlarger volumes than a single unit cell.

Order-Disorder Ferroelectrics have isolated dipoles that are thermally disordered at T>Tc. As T approaches Tc cooperative dipole ordering occurs and dipoles align over significant volumes of the lattice.

KDP : KH2PO4

Potassium-dihydrogen phosphate

Other examples:Rochelle SaltNaNO2


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Uniaxial FE-polarization along C-axis

Curie Constant ~10 3 K


Displacive Phase TransitionsDisplacive Phase Transitions

Consider a simple diatomic lattice:

A displacive phase transition is one in which the atoms in the low temperature phase are a small departures from their position in the high temperature phase. These transitions are driven through a specific phonon known as the soft mode.

In ionic crystals the vibrational spectra can be represented in a phonon dispersion spectra relating the phonon frequency and wave vector K.

M m M Mmk k

a

k – Spring Constant M masses of two a – lattice parameter m atomic species


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Both tetragonal and first order.Ferroelectrics.Pb displacements but notBa ?Volume increase at Tc


Role of Domain Wall Motion in Piezoelectrics (Ferroelectrics)

180" domain wall motion:

PS PS

c

a a

c

PS PS

c

a a

c

No dimensional change, no contribution to piezoelectricity

under E field

a a a a

90" domain wall motion:

PSc

a

c

a

c

a

PS

PSc

c

a

c

a

PS

under E field

dimensional change, significant contribution to piezoelectricity

c>a


Ferro and anti-ferro materials

Engineering

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