The Muppet’s Guide to:The Structure and Dynamics of Solids

3. Ferroelectricity and Phase Transitions

Perovskites – ABO3

Classic example – BaTiO3 which exhibits ferroelectricity

Figure adapted from Callister, Materials science and engineering, 7 th Ed.http://www.camsoft.co.kr

B (Ti) sits inside an octahedral cage of Oxygens

BaTiO3

web.uniovi.es/qcg/vlc/luana.htm

SrTiO3

Ti OSr

Sr2+ O2-Ti4+

Ideal Perovskite Structures

http://www.camsoft.co.kr

ABO3

a

A

B

O

B sites are octahedrally bonded by oxygens

For an undistorted cube:

2

2

2

A O

B O

O O

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SrTiO3

G H TS

Low Temp Minimum G when H is at optimum valueU stabilised by bonding

Low Temp, TS < H Minimise enthalpy

High Temp, TS > H Maximise entropy

G H

G S

ThermodynamicsStrain Energy vs. Bonding Energy

Medium Temp Thermal motion of the atoms relaxes bonding requirements. Reducing strain in the underlying lattice becomes the dominant energy term.

Displacive Phase Transitions

A

B

O

Ionic radii never match ideal cubic requirements.

A site atoms smaller than hole:

In displacive phase transitions the atoms only change position slightly.

Distortion of octahedra

LaMnO3

Most perovskite structures are distorted due to the ionic radii of

the cations and distortions caused by the local crystal fields

and electron interactions

- Temperature Dependent

European Synchrotron Radiation Facility, Research Highlights, 2001

Structural changes can induce other phenomena

web.uniovi.es/qcg/vlc/luana.html

SrTiO3 - Tc=105KAntiferrodistortive transition – unit cell doubled

Displacive TransitionsBaTiO3

Centrosymmetric

Non-centrosymmetric

Ferroelectricity in Perovskites

http://www.iue.tuwien.ac.at/phd/dragosits/node12.html

Classic example is Barium Titanate. Tc=393K, motion of atoms 0.1Å

Which breaks the local symmetry. Permanent structural change.

CUBIC TETRAGONAL

Ferroelectricity in Perovskites

CUBIC TETRAGONAL

Tetragonally Distorted Perovskites

PiezoelectricityOnly possible in solids which lack a centre of inversion (20 of 32 point groups satisfy this)

,ijk jk

j k

P d jk ijk ii

e d Edijk is the

piezoelectic constant (3rd rank tensor)

Piezoelectric Effect in Perovskites

Movement of central atom breaks the point

symmetry at the centre

– now has no centre of symmetry

Piezoelectric effect

Piezoelectric Effect

Electrical analogue to Magnetism

Spins or Dipoles

Ionic crystals can become polarised when subjected to an elastic strain

Electric field causes strain and hence a change in lattice parameter

Electrostriction – an analogue of magnetostriction

http://metwww.epfl.ch/Brillouin/images/Electrostriction.gif

Long range order of electric dipoles

Piezo Actuators

Ferroelectric Transition

Ordered state where dipoles are aligned without the need for external stress of fields.

Disordered state where dipoles can only be aligned by application of stress due to an electric field

Ferroelectric Hysteresis Loop

Ferroelectric materials can be reversed

from ±Ps using suitable applied electric fields.

If reversal field (Ec) is greater than the breakdown field of the material it is pyroelectric (LaNbO3 and LaTaO3 are examples)

-Ec

Phase Transitions

• The change from one state (or phase) or another is associated with a phase transition and a critical point.

• In this example it is a structural phase transition that occurs abruptly at a critical temperature, Tc.

Phase Transition

phase phase

Tc

Temperature

Fre

e E

ner

gy

At the phase transition the Gibbs free energy of the two states is identical

G H TS

ORDERED DISORDERED

Describing Phase TransitionsOrdering Parameter, h: This is the parameter which shows a change at the transition temperature or pressure.

Order parameter is a derivative of the Gibbs free energy with respect to a thermodynamic variable

G

densityChemical potential

G

magnetisation mH

Applied Field

1st Order Phase TransitionsEhrenfest classification:

Discontinuity in the 1st derivative of Gibbs free energy

Transitions that exhibit LATENT HEAT

– Energy must be supplied to change the local environment. This results in no temperature change.

Discontinuity in

Boiling Water

First-order transitions are associated with "mixed-phase regimes"

Some parts of the system have completed the transition whilst others have not.

Water does not instantly change from liquid to gas. Instead it forms a mixture of water and steam bubbles. Similarly it does not instantly freeze.

First Order

Transitions in liquid crystals

Discontinuity

h

Phase Transitions…

BaTiO3:

Volume change at Tc

Thus expect first order phase change with discontinuity in Ps at Tc

LaTaO3 shows second order phase transition