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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