Temperature/electric field scaling in Ferroelectrics

The effects of the field amplitude (E) and temperature on the polarization and their scaling relations were investigated on rhombohedral PMN-xPT ceramics. The scaling law was based on the physical symmetries of the problem and rendered it possible to express the temperature variation (Δθ) as an electric field equivalent ΔE_eq=(α2β×P(E, θ₀))×Δθ. Consequently, this was also the case for the relationship between the entropy (Γ) and polarization (P). Rhombohedral Pb(Mg_1/3Nb_2/3)_0.75Ti _0.25O₃ ceramics were used for the verification. It was found that such an approach permitted the prediction of the maximal working temperature, using only purely electrical measurements. It indicates that the working temperature should not exceed 333 K. This value corresponds to the temperature maximum before the dramatic decrease of piezoelectric properties. Reciprocally, the polarization behavior under electrical field can be predicted, using only purely thermal measurements. The scaling law enabled a prediction of the piezoelectric properties (for example, d₃₁) under an electrical field replacing the temperature variation (Δθ) by ΔE/(α2β×p(E,θ₀)). Inversely, predictions of the piezoelectric properties (d₃₁) as a function of temperature were permitted using purely only electrical measurements.