Question

a) Define the following terms: (i) ferroelectric (ii) piezoelectric

b)Draw perspective and plan views of the unit cell of cubic barium titanate. Label the fractional co-ordinates of the non-equivalent ions and state the co-ordination number of the ions. [6 marks] (ii) Describe, with the aid of appropriate diagrams, the various structural changes which occur as a barium titanate crystal cools from 200°C to -100°C. Specify the temperatures of the relevant phase transitions.

Answer 1

• BaTiO₃ is ABO₃ type compound.
• In ABO₃ structured compounds, Ba ion is twelve fold coordinated by oxygen (like a dodecahedra) and Ti ion is octahedrally coordinated by oxygen ions.
• Bond strength check:
  Cation: Ba: ^2/₁₂ = ^1/₆  and Ti: ^4/₆ = ^2/₃
  Oxygen valence = ^1/₆ x Coordination number by Ba + ^2/₃ x coordination number by Ti .

Barium titanate and phase changes

The temperature at which the spontaneous polarisation disappears is called the Curie temperature, T_C.

Above 120°C, barium titanate has a cubic structure. This means it is centro-symmetric and possesses no spontaneous dipole. With no dipole the material behaves like a simple dielectric, giving a linear polarisation. T_C for barium titanate is 120°C.

Below 120°C, it changes to a tetragonal phase, with an accompanying movement of the atoms. The movement of Ti atoms inside the O₆ octahedra may be considered to be significantly responsible for the dipole moment:

Cooling through 120°C causes the cubic phase of barium titanate to transform to a tetragonal phase with the lengthening of the c lattice parameter (and a corresponding reduction in a and b). The dipole moment may be considered to arise primarily due to the movement of Ti atoms with respect to the O atoms in the same plane, but the movement of the other O atoms (i.e. those O atoms above and below Ti atoms) and the Ba atoms is also relevant.

This shows the BaTiO3 structure with an O6 octahedron surrounding the important Ti atom.

The switching to a cubic structure is the reason for the polarisation spontaneously disappearing above 120°C. Barium titanate has two other phase transitions on cooling further, each of which enhances the dipole moment:

The phase which is reached after cooling to ~ 0°C from tetragonal is orthorhombic.

And then rhombohedral below -90°C:

All of these ferroelectric phases have a spontaneous polarisation based to a significant extent on movement of the Ti atom in the O6 octahedra in the following way (using pseudo-cubic notation):