Scaling behavior of different shapes of hysteresis loops and recoverable energy storage density in Na_0.5Bi_0.5TiO₃, K_0.5Bi_0.5TiO₃, and Na_0.25K_0.25Bi_0.5TiO₃ ferroelectrics

In this work, the dependency of the polarization (P) - electric field (E) loop area of lead free ferroelectrics Na_0.5Bi_0.5TiO₃ (NBT), K_0.5Bi_0.5TiO₃ (KBT), and Na_0.25K_0.25Bi_0.5TiO₃ (NKBT) on the amplitude (E₀) of the electric field is studied. Based on the nature of the hysteresis loop with increasing E₀, the lnA versus lnE₀ graph is divided into three stages and the scaling exponents of each stage are estimated. In the third stage, NBT, KBT, and NKBT show different shapes of P-E loops (square, slanted and pinched, respectively). Although, almost similar slopes in the third stage are obtained from the lnA versus lnE₀ graphs of KBT and NKBT, the formation of pinched P-E loop of NKBT is discussed based on the current-time curve under a complete cycle of the applied electric field. The shape of the P-E loop also affects the recoverable energy storage density (W_rec) of the material. Similar to the scaling of A, the variation of lnW_rec with lnE₀ of NBT, KBT and NKBT are examined. Interestingly, three stages are only noticed in the lnW_rec-lnE₀ curve of pinched P-E loop (NKBT), whereas lnW_rec linearly increases with lnE₀ for square and slanted P-E loop. Such type of behavior of W_rec of NKBT is explained based on the reversible domain switching mechanism of the pinched P-E loop.