Thermal expansion studies on ferroelectric materials

Thermal expansion data is reported over a wide temperature range (80-800 K) for $BaTiO_3 (BT)$ and $Pb(Fe_{1/2}Nb_{1/2})O_3 (PFN)$, belonging to different classes of ferroelectric materials. The sharp structural phase transitions of BT result in lowering of the thermal expansion coefficient (α) at the transitions which is proportional to the change in polarization at the transitions. In PFN, a relaxor ferroelectric, lowering of α is spread over a wider temperature range across the dielectric maxima