Scaling behavior for (Bi_0.5Na_0.5)TiO₃ based lead-free relaxor ferroelectric ceramics

The dynamic hysteresis and scaling behavior of unpoled 0.96(Bi_0.5Na_0.5)TiO₃-0.04BiAlO₃ lead-free relaxor ceramics were investigated through the evolution of the hysteresis loops at a wide frequency (f) and electric-field amplitude (E_o) range. The variation of the hysteresis area A and remanent polarization P_r clearly suggested three stages of polarization reversal with increasing external electric fields. It was found that the dynamic hysteresis area in the low-E_o and high-E_o regions followed the power law relationships: A f - 0.14 E o 3.30 (E_o ≤ 5.0 kV/mm) and A f 0.064 Eo - 0.6 Eo1.65(E_o ≥ 6.2 kV/mm), respectively. Those power-law functions did not fit in the second stage (5.0 kV/mm < E_o < 6.2 kV/mm), where different numbers of polar nanoregions or nanodomains can be activated and transformed into macrodomains. The polarization mechanisms of above mentioned three stages were ascribed to the domain wall motion, then the formation of microdomains within the disordered nanodomains or polar nanoregions, followed by the induced macrodomains aligning parallel to the applied electric field.