Scaling behavior of different shapes of hysteresis loops and recoverable energy storage density in Na_(0.5)Bi_(0.5)TiO_(3), K_(0.5)Bi_(0.5)TiO_(3), and Na_(0.25)K_(0.25)Bi_(0.5)TiO_(3) ferroelectrics

In this work,the dependency of the polarization(P)-electric field(E)loop area A of lead free ferro-electrics Na_(0.5)Bi_(0.5)TiO_(3)(NBT), K_(0.5)Bi_(0.5)TiO_(3)(KBT),and Na_(0.25)K_(0.25)Bi_(0.5)TiO_(3)(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(Wrec)of the material.Similar to the scaling of A,the variation of lnWrec with lnE0 of NBT,KBT and NKBT are examined.Interestingly,three stages are only noticed in the lnWrec-lnE0 curve of pinched P-E loop(NKBT),whereas lnWrec linearly increases with lnE0 for square and slanted P-E loop.Such type of behavior of Wrec of NKBT is explained based on the reversible domain switching mechanism of the pinched P-E loop.