Fourth and sixth order nonlinear permittivity and thermodynamics of tunability in 0.9Pb(Mg1/3,Nb2/3)O3?0.1PbTiO3 and Ba(Ti0.85,Sn0.05)O3 paraelectric ceramics

The nonlinear dielectric properties of 0.9Pb[Mg1/3,Nb2/3]O3?0.1PbTiO3 (PMN-PT) and Ba[Ti0.85,Sn0.15]O3 (BTS) paraelectrics were studied experimentally and theoretically. The nonlinear dielectric response was measured in the parallel plate capacitor configuration, whereby the low frequency linear permittivity ( ?33 ), and the higher order permittivities ( ?3333, ?333333 ) at 298 K were obtained as ?33PMN-PT = 2.1x10?7 and ?33BTS = 4.1x10?8 (F/m), ?3333PMN-PT= ?4.9x10?20 and ?333333BTS = 9.85x10?34 (F3m/C2), and ?333333PMT-PT = 7.6x10?33 and ?3333BTS = ?7.3x10?21 (F5m3/C4). By using a self-consistent thermodynamic theory in conjunction with the experimental data, we compute the E3 dependence of electrostatic energy ?G , the field-induced polarization response P3 , the thermodynamic tunability ?2P3/?E32 , and prove that electrostatic free energy has to be expanded at least up to the sixth order in electric field define the critical field |E3*| at which maximum tunability is attained. We also show that |E3*| is a function on |?3333|/?333333 only. Consequently, we find |E3*|PMT-PT = 8.6x105 V/m and |E3*|BTS =8.0x105 V/m. We compute the engineering tunabilities as ?PMN-PT =65% and ?BTS =55%, and then define a normalized tunability ? to take into account the |E3*| parameter. Thereof, we determine |?|PMT-PT = 8.1x10?5 and |?|BTS =6.4x10?5 %/Vm?1. Our results reveal that |E3*|BTS >|E3*|PMNPT although ?BTS < ?PMNPT, unequivocally showing the need for defining a critical field parameter in evaluating the nonlinear dielectric response and tunability in particular, and in nonlinear dielectrics in general. The results also indicate that the nonlinear dielectric properties of PMN-PT are an order of magnitude higher than that of BTS, which we discuss in the context of structure-property relations of relaxors.