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

Abstract

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 å33PMN-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.