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

E K Akdogan,A Safari

doi:10.1109/isaf.2008.4693770

Abstract

The nonlinear dielectric properties of 0.9Pb[Mg 1/3 ,Nb 2/3 ]O 3 ·0.1PbTiO 3 (PMN-PT) and Ba[Ti 0.85 ,Sn0.15]O 3 (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 ( ε 33 ), and the higher order permittivities ( ε 3333 , ε 333333 ) at 298 K were obtained as å 33 PMN-PT = 2.1x10 -7 and ε 33 BTS = 4.1x10 -8 (F/m), ε 3333 PMN-PT = -4.9x10 -20 and ε 333333 BTS = 9.85x10 -34 (F 3 m/C 2 ), and ε 333333 PMT-PT = 7.6x10 -33 and ε 3333 BTS = -7.3x10 -21 (F 5 m 3 /C 4 ). By using a self-consistent thermodynamic theory in conjunction with the experimental data, we compute the E 3 dependence of electrostatic energy ΔG , the field-induced polarization response P 3 , the thermodynamic tunability ∂ 2 P 3 /∂E 3 2 , 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 |E 3 *| is a function on |㎵ 3333 |/ε 333333 only. Consequently, we find |E 3 *| PMT-PT = 8.6x10 5 V/m and |E 3 *| BTS =8.0x10 5 V/m. We compute the engineering tunabilities as Γ PMN-PT =65% and Γ BTS =55%, and then define a normalized tunability ξ to take into account the |E 3 *| parameter. Thereof, we determine |ξ| PMT-PT = 8.1x10 -5 and |ξ| BTS =6.4x10 -5 %/Vm -1 . Our results reveal that |E 3 *| BTS >|E 3 *| PMNPT although Γ BTS < Γ 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.

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