Advanced Solid State Physics

In fig. 134 we can see the spontaneous polarization of barium titanate as a function of temperature.
The phase transition from tetragonal to cubic is not in the plot, but that will happen at about 120 ◦
C. In this case the spontaneous polarization will go to zero. In the specific heat-over-temperature
diagram this transition again has the form of aλ.

Figure 133: The structure of a perovskit with the example BaTiO 3

Figure 134: Spontaneous polarization of BaTiO 3 as a function of temperature

If we compare the dielectric constant of barium titanate (fig. 127) to the spontaneous polarization
(fig. 134), we can see that the peaks are at the same temperatures. If the material is at a temperature
near a phase transition (for example− 80 ◦) the energies of the two states are almost the same. So it
easy for an electric field to switch between these two states, because of the nearly same free energies.
That makes a high susceptibility and explains the peaks in the dielectric diagram. Above 120 ◦C the
material becomes paraelectric, which means that there is only polarization if an electric field is applied.
This transition is similar to the ferromagnetic to paramagnetic transition. The susceptibility diverges