Optimized electrocaloric effect by field reversal: Analytical model

Abstract

Application of a negative field on a positively poled ferroelectric sample can enhance the electrocaloric cooling and appears as a promising method to optimize the electrocaloric cycle. Experimental measurements show that the maximal cooling does not appear at the zero-polarization point, but around the shoulder of the P-E loop. This phenomenon cannot be explained by the theory based on the constant total entropy assumption under adiabatic condition. In fact, adiabatic condition does not imply constant total entropy when irreversibility is involved. A direct entropy analysis approach based on work loss is proposed in this work, which takes the entropy contribution of the irreversible process into account. The optimal reversed field determined by this approach agrees with the experimental observations. This study signifies the importance of considering the irreversible process in the electrocaloric cycles.The electrocaloric (EC) effect shows great application potential in the technology of solid state refrigeration. 1-3Even though much effort has been made to explore material candidates with large EC effect and device concepts, there are few work concerning the optimization of electrocaloric cycle. In a conventional EC cycle of a solid refrigerant, the cooling effect is obtained simply by removing the previously applied electric field. Using direct heat flux calorimetry on poly(vinylidene fuoridetride-trifuoroethylene) films, Basso et al. 4 demonstrated that the electrocaloric cooling can be doubled if a negative electric field to a positively poled sample is applied. The EC hysteresis of ferroelectric ceramics measured by Thacher et al.5 indicated also that a reversed electric field can increase the cooling effect of ferroelectric ceramics. In the authors' previous work, 6 experimental and numerical studies were carried in PMN-29PT and BaTiO 3 , which demonstrated that there exists an optimal reversed electric field, corresponding to a position around the shoulder of the dielectric hysteresis. At this point, the EC cooling effect reaches its maximum (also see Fig. 1). This phenomenon was also observed in Ref. 4. It is of scientific and engineering importance to deter- mine and understand this optimal reversed electric field. In the literature, as reviewed in Ref. 7, the EC cycle is considered to be reversible, with constant total entropy under the adiabatic condition. This assumption leads to the conclusion that the maximal cooling takes place at the zero polarization point, since at this point the dipolar entropy takes maximum (see Model I). This conclusion deviates obviously from the experimental observations. In fact, the total entropy S total should satisfy:where S dip and S vib are the dipolar and the vibrational entropy, respectively. In the case of applying a reversed electric field, the irreversible contribution becomes considerable. In other words, to correctly determine the optimal reversed electric field, the change of the total entropy induced by the work loss W loss due to the irreversible process s...

Impact of Polarization Dynamics and Charged Defects on the Electrocaloric Response of Ferroelectric Pb(Zr,Ti)O3 Ceramics

“…To reveal the underlying mechanism, we utilized an analytical model to calculate Δ T EC for soft and hard doped material, as displayed in Figures and , respectively. By separation of the total polarization change into reversible and irreversible components, reversible work (green area) and total work (grey area) can be evaluated .…”

“…To reveal the underlying mechanism, we utilized an analytical model to calculate Δ T EC for soft and hard doped material, as displayed in Figures and , respectively. By separation of the total polarization change into reversible and irreversible components, reversible work (green area) and total work (grey area) can be evaluated . In this way, Δ T EC can be calculated, considering the total entropy change caused by work losses W loss (see difference of the grey and green areas), which significantly influences the ECE when the polarization switches direction.…”

“…The analytical model was developed to evaluate the electrocaloric effect for the defect doped system with internal bias field E int , and more details can be found elsewhere . Here, for completeness only the key points are summarized.…”

Origins of the Inverse Electrocaloric Effect

“…For an intuitive interpretation of the ECE in a simple ferroelectric (or paraelectric) phase under a collinear field, one can also use Landau theory and expand the (dipolar) free energy density with respect to P : …”

“…Similarly, an electric field favors the FE phase with homogeneous polarization and can eventually reduce the ordering in AFE phases resulting in an inverse EC response . Several suggestions have been made to utilize a combination of the conventional and inverse ECE to achieve a larger overall temperature change (Δ T ) and thus enable optimized EC cooling cycles . On the other hand, an unintentional combination of inverse and conventional effects can also reduce the overall EC response of a system, for example, in polycrystals or in inhomogeneous materials.…”