Anisotropy free energy contribution of the ferroelectric domain dynamics in PMN-PT and PIN-PMN-PT relaxor ferroelectrics

A direct correlation between the materials property behavior with its associated ferroelectric domain mechanisms and the anisotropic component of the Landau free energy is established for binary PMN-PT (generation I) and ternary PIN-PMN-PT (generation II) relaxor ferroelectric single crystal material systems. In addition to their trade-off in material properties, the observed ferroelectric domain dynamic and the determined free energy anisotropies, especially as approaching phase transition, provide direct insights into the materials field-dependent behavior between the binary and ternary ferroelectric systems. Domain configuration features such as lamellar structures in binary PMN-PT and concentric oval-like structures in ternary PIN-PMN-PT result in different material responses to external stimuli. Compared to binary PMN-PT, the concentric oval-like domain structures of ternary PIN-PMN-PT result in a 20°C higher temperature range of field-dependent linear behavior, 40% increase in coercive electric field $E_C,$ higher elastic stiffness during ferroelectric domain switching, and lower electromechanical energy losses. Separation of the isotropic and anisotropic components in the Landau free energy reveals a higher anisotropic free energy contribution from the ternary system, especially at temperature for practical applications. The high anisotropic free energy found in the ternary PIN-PMN-PT system implies that the concentric oval-like domain structure contributes to reduced electromechanical energy losses and enhanced stability under external applied fields.