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

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. http://www.camsoft.co.kr

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

Ideal Perovskite Structures ABO3 O SrTiO3 B sites are octahedrally bonded by oxygens B For an undistorted cube: A a http://www.camsoft.co.kr

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.

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

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

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

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

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

Ferroelectricity in Perovskites TETRAGONAL CUBIC

Tetragonally Distorted Perovskites

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)

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

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

Piezo Actuators

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.

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)

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

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

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.

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 h Discontinuity Transitions in liquid crystals

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