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Smart Mater. Struct. 21 (2012) 025021 F Y Lee et al electric displacement to reach steady state (∂D/∂t = 0) during processes 2–3 and 4–1 before varying the electric field and then moving the sample from one bath to the other. This ensures that the cycle was performed under quasiequilibrium conditions to achieve the maximum energy density. Note that the thermal characteristic time constant can be estimated as τ = ρcp/hb [53], where h is the heat transfer coefficient and b is the sample thickness, while ρ and cp are the sample density and specific heat, respectively. For example, the thermal characteristic time constant was estimated to be 2.5 s for a 290 μm thick 8/65/35 PLZT sample with ρ = 7900 kg m−3 [54], cp =329 J kg−1 K−1 [55] and h= 300 W m−2 K−1, corresponding to convective quenching in an oil bath [56]. The electrical subsystem used to perform the Olsen cycle consisted of a modified Sawyer–Tower circuit [31] to apply the required electric field across the pyroelectric material and to measure the charge Q collected at the electrode surfaces. Details of the circuit used in the present study were provided in [19] and need not be repeated. This circuit was also used to measure the unipolar and bipolar D–E loops at various temperatures. 3.3. Experimental procedure 3.3.1. Isothermal D–E loops. Figure 2. Bipolar isothermal electric displacement versus electric field (D–E) hysteresis curves at various temperatures (colored figure). The D–E paths travel in a counter-clockwise direction. The electric field was cycled between −2.5 and 2.5 MV m−1 at 0.33 Hz. The D–E loops at 45 and 65 ◦ C correspond to the ferroelectric phase while those at 100, 110, 120, 130 and 160 ◦ C indicate that the material was in the ergodic relaxor phase. 4. Experimental results and discussion 4.1. D–E loops Figure 2 plots the bipolar D–E loops at 45, 65, 100, 110, 120, 130 and 160 ◦ C measured at 0.33 Hz with sample 4. The electric field was isothermally cycled between −2.5 and 2.5 MV m−1. The isothermal D–E loops corresponding to 45 and 65◦C featured square loops typical of a ferroelectric state. On the other hand, the D–E loops corresponding to 100, 110, 120, 130 and 160 ◦C exhibited slim linear hysteresis with small remnant polarization (Pr ≤ 0.02 C m−2), indicating that the material was in the ergodic relaxor phase. Note that the unipolar D–E loops (not shown) were very narrow with little hysteresis and nearly identical to the upper curve of the bipolar D–E loops between 0 and 2.5 MV m−1 for the temperatures investigated in this study. Thus, analysis of the upper curves of unipolar or bipolar D–E loops resulted in nearly identical values of saturation and remnant polarizations Ps(T) and Pr(T) and relative permittivity εr(T). Moreover, the isothermal bipolar D–E loops correspond- ing to the ferroelectric phase plotted in figure 2 show the nonlinear behavior of the electric displacement D with respect to the electric field E. The electric displacement decreased sharply for a decreasing applied electric field around the critical electric field Ecr (T ). This nonlinearity was also observed for [110]-oriented PZN-4.5PT by Zhu et al [18] and was attributed to electric-field-induced phase transitions. The sudden decrease in electric displacement D around Ecr (T ) could also be explained by the 180◦ polarization switching in which the polarization of each crystal’s unit cell reversed direction from +P to −P when the polarization vector aligned with the applied electric field vector [34, 37, 57]. Thus, Isothermal unipolar and bipolar D–E loops were collected at 45, 65, 100, 110, 120, 130 and 160◦C for samples 4–6 and at 25 and 160 ◦C for sample 7 using the electrical circuit previously discussed. The measurements were taken while the sample was immersed in a silicone oil bath maintained at the desired temperature. For bipolar loop measurements, a continuous triangular voltage signal was applied across the sample at 0.33 Hz, corresponding to the frequency at which the electric field was changed during isothermal processes 1–2 and 3–4 in the Olsen cycle. The amplitude of the applied voltage corresponded to an electric field cycled between −2.5 and 2.5 MV m−1. Similarly, the applied voltage for unipolar D–E loop measurements corresponded to an electric field varying from 0.0 to 2.5 MV m−1. These measurements were taken at 0.66 Hz, corresponding to the same rate of change in electric field as that imposed to collect the 0.33 Hz bipolar D–E loops. Moreover, the saturation polarization Ps (T ), the remnant polarization Pr (T ) and the relative permittivity εr (T ) of 8/65/35 PLZT samples were evaluated by linearly fitting the upper curve of isothermal bipolar D–E loops corresponding to a decrease in electric field from EH to EL as shown in figure 1. 3.3.2. Olsen cycle. The Olsen cycle was performed on 8/65/35 PLZT at various electric fields and temperatures to investigate their respective effects on the energy harvested. For example, the low electric field EL was varied between 0.0 and 0.4 MV m−1 and the high electric field EH from 0.4 to 7.5 MV m−1. The cold source temperature Tcold was either 25, 45 or 65 ◦C, while the hot source temperature was varied from 100 to 160 ◦ C. The Olsen cycles were recorded in the D–E diagram and the energy density ND, defined in equation (2), was estimated by applying the trapezoidal rule. 4PDF Image | Pyroelectric waste heat harvesting using relaxor ferroelectric
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