1. The Structure and Dynamics of Solids
The Muppet’s Guide to:
The Structure and Dynamics of Solids
3. Ferroelectricity and Phase Transitions

2. Perovskites – ABO3
Classic example – BaTiO3 which exhibits ferroelectricity
BaTiO3
B (Ti) sits inside an octahedral cage of Oxygens
Figure adapted from Callister, Materials science and engineering, 7th Ed.

3. SrTiO3
Ti4+
Sr2+
O2- Sr O Ti
web.uniovi.es/qcg/vlc/luana.htm

4. Ideal Perovskite Structures
ABO3 O
SrTiO3
B sites are octahedrally bonded by oxygens B
For an undistorted cube: A a

5. Strain Energy vs. Bonding Energy
Thermodynamics
Strain Energy vs. Bonding Energy
Low Temp, TS < H Minimise enthalpy
High Temp, TS > H Maximise entropy
Low Temp Minimum G when H is at optimum value
U stabilised by bonding
Medium Temp Thermal motion of the atoms relaxes bonding requirements. Reducing strain in the underlying lattice becomes the dominant energy term.

6. Displacive Phase Transitions
Ionic radii never match ideal cubic requirements.
A site atoms smaller than hole:
Distortion of octahedra B
In displacive phase transitions the atoms only change position slightly. A

7. Structural changes can induce other phenomena
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
Structural changes can induce other phenomena
European Synchrotron Radiation Facility, Research Highlights, 2001

8. Antiferrodistortive transition – unit cell doubled
SrTiO3 - Tc=105K
Antiferrodistortive transition – unit cell doubled
Stabilises a phonon mode
web.uniovi.es/qcg/vlc/luana.html

9. Displacive Transitions
BaTiO3
Centrosymmetric
Non-centrosymmetric
Phonon mediated solid-solid phase transition

10. Ferroelectricity in Perovskites
CUBIC
TETRAGONAL
Classic example is Barium Titanate. Tc=393K, motion of atoms 0.1Å
Which breaks the local symmetry. Permanent structural change.

11. Ferroelectricity in Perovskites
TETRAGONAL
CUBIC

12. Tetragonally Distorted Perovskites

13. dijk is the piezoelectic constant (3rd rank tensor)
Piezoelectricity
Only possible in solids which lack a centre of inversion (20 of 32 point groups satisfy this)
dijk is the piezoelectic constant (3rd rank tensor)

14. Piezoelectric Effect in Perovskites
Movement of central atom breaks the point symmetry at the centre
– now has no centre of symmetry
Piezoelectric effect

15. Electrical analogue to Magnetism
Piezoelectric Effect
Long range order of electric dipoles
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

16. Piezo Actuators

17. Ferroelectric Transition
Disordered state where dipoles can only be aligned by application of stress due to an electric field
Ordered state where dipoles are aligned without the need for external stress of fields.

18. 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)

19. 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.

20. Phase Transition
ORDERED
DISORDERED
At the phase transition the Gibbs free energy of the two states is identical

21. Describing Phase Transitions
Ordering 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
Chemical potential
Applied Field

22. 1st Order Phase Transitions
Ehrenfest 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.

23. 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.

25. First Order h
Discontinuity
Transitions in liquid crystals

26. 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