Effects of Long- and Short-Range Ferroelectric Order on the Electrocaloric Effect in Relaxor Ferroelectric Ceramics

We study the electrocaloric effect (ECE) in a typical relaxor ferroelectric ceramic of ${\mathrm{Pb}}_{0.91}{\mathrm{La}}_{0.06}{\mathrm{Zr}}_{0.8}{\mathrm{Ti}}_{0.2}{\mathrm{O}}_3$ by analyzing the respective contributions of long-range-ordered ferroelectric macrodomains and short-range-ordered polar nanoregions (PNRs) by both direct and indirect characterization. The ECE exhibits two peaks in its dependence on temperature, the former responds to the transition from long-range ferroelectric order to short-range-ordered PNRs and the latter likely to the transition between two kinds of PNRs with different phase structures or motion states. The contributions of different mechanisms are clarified by resolving the overlapping peaks in direct heat flow experimental results. The first peak has a $\mathrm{\Delta }{T}_{\max }=0.7\mathrm{K}$ at 80 °C (approximately $T_d$) and the second a $\mathrm{\Delta }{T}_{\max }=0.98\mathrm{K}$ at 140 °C (approximately $T_m$) under 40 kV/cm. We conclude that the thermodynamic method based on the Maxwell relation is not applicable if PNRs are involved as their signatures are only picked up by direct measurements, but is valid for the case of ferroelectric domain rotation or phase transition where it provides a reasonably accurate ECE result. Besides the impact on aspects related to metrology, our work suggests that the region between the peaks in ΔT-T curves may be used to produce a large electrocaloric ΔT over a broad temperature range, which is highly desirable in cooling applications.

Figure 1

(a) Temperature dependence of reversible specific heat curve. (b) Temperature-dependent relative permittivity ($\epsilon$) and loss tangent for ceramic during heating process under different frequencies. (c) The reciprocal of dielectric permittivity ($1/\epsilon$) as a function of temperature at 100 kHz. The green symbols represent experimental data, whereas the red solid line is the fitting curve by Eq. (1). (d) The plot (green symbols) and linear fitting curve (red solid line) of ln(1/$\epsilon$-1/${\epsilon }_m$) as a function of ln(T-T_m).

Figure 2

(a) Raman spectra of unpoled and poled ceramics. (b) Temperature-dependent relative permittivity and loss tangent for unpoled and poled ceramics. Frequency-dependent relative permittivity under different temperatures for (c) unpoled and (b) poled ceramics.

Figure 3

(a)-(e) Ferroelectric hysteresis loops and corresponding current changes at different temperatures from 30^oC to 150 °C under E = 40 kV/cm and 1 Hz frequency. (f) Polarization intensity as a function of temperature for different electric fields.

Figure 4

(a) Typical isothermal heat flow changes with electric field of 40 kV/cm applied and removed at 140 °C. (b) Isothermal heat flow curves at 140 °C under different electric fields from 5 to 40 kV/cm. Temperature dependence of ΔT under different electric fields (E₁ = 0) by (c) direct isothermal heat flow measurement and (d) indirect Maxwell calculations.

Figure 5

Comparison of the direct and indirect ΔT under different electric fields for (a) Peak 1 and (b) Peak 2. (c) The difference in values between indirect and direct ΔT for Peak1 and Peak 2. (d) The temperatures associated with peak positions for direct and indirect ECE for Peak 1 and Peak 2.

Figure 6

(a) Contour plots of the I-E loops from Fig. 3 as a function of temperature. (b) Schematic illustration of the domain evolution processes for PLZT relaxor ceramics under coupling of electric field and temperature. (c) A comparison of the actual situation near T_d in which PNRs contribute to the dipole order entropy with the Maxwell relation, which assumes a paraelectric phase. Thus, the electric field-induced actual entropy change near T_d is smaller than predicted using the Maxwell calculation. (d) Temperature dependence of ΔT (E₁ = 20 kV/cm, E₂ = 30 kV/cm, and 40 kV/cm) by direct isothermal heat flow measurement and indirect Maxwell calculation.