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Smart Mater. Struct. 21 (2012) 025021 F Y Lee et al where εo is the vacuum permittivity (=8.854×1012 F m−1) and εr(T) is the relative permittivity of the material at electric field E and temperature T. The saturation polarization denoted by Ps(T) is estimated as the displacement in the linear fit of D versus E extrapolated at zero electric field. The slope of this linear fit corresponds to the product ε0εr(T) as illustrated in figure 1. 2.2. Olsen cycle The Olsen cycle consists of two isothermal and two isoelectric processes in the electric displacement versus electric field (D–E) diagram [7] as illustrated in figure 1. Process 1–2 consists of charging the pyroelectric element (PE) at Tcold by increasing the applied electric field from EL to EH. Process 2–3 corresponds to discharging the PE by heating it from Tcold to Thot under constant electric field EH. Process 3–4 consists of reducing the electric field from EH to EL under isothermal conditions at Thot. Finally, process 4–1 closes the cycle by cooling the PE from Thot to Tcold under constant electric field EL. Note that the Olsen cycle, in the D–E diagram, is analogous to the Ericsson cycle defined in the pressure versus specific volume diagram. The area enclosed by the clockwise 1–2–3–4 loop in the D–E curve represents the electric energy produced per unit volume of material per cycle denoted by ND (in J l−1/cycle) and defined as [7] ND = The corresponding power density PD (in W l−1) produced by the pyroelectric element is expressed as PD = NDf (3) where f is the cycle frequency. Note that ND is also dependent on the cycle frequency [18, 20]. 2.3. Materials Relaxor ferroelectrics are a promising class of materials which feature exceptional electro-optical, dielectric and piezoelectric properties [32]. These materials can be used in devices such as piezoelectric actuators, pyroelectric sensors, multilayer capacitors and optical shutters [33]. The material investigated in this study is a relaxor ferroelectric composed of 8 mol% lanthanum doped into a 65 mol% lead zirconate and 35 mol% lead titanate solid solution (Pb0.92La0.08(Zr0.65Ti0.35)0.98O3), also denoted as 8/65/35 PLZT [34]. The lanthanum doping increases the resistivity of the material and contributes to the strong electromechanical coupling [34–36]. At room temperature, the 8/65/35 PLZT crystal structure has rhombohedral symmetry [37]. The material undergoes complex phase transitions which are very sensitive to temperature and applied electric field [35]. It is paraelectric beyond the Burns temperature TB ≃ 350 ◦C [38]. Upon cooling below TB, the material transforms from the paraelectric phase to the ergodic relaxor phase. In the latter phase, nanoscale polar regions with randomly distributed Figure 1. Isothermal unipolar electric displacement versus electric field (D–E) hysteresis loops for a typical pyroelectric material at temperatures Thot and Tcold along with the Olsen cycle. The electrical energy generated per cycle is represented by the area enclosed between 1–2–3–4. This paper reports, for the first time, experimental measurements of the energy harvested by commercially available lead lanthanum zirconate titanate (PLZT) subjected to the Olsen cycle. The effects of low electric field EL, cold source temperature Tcold, hot source temperature Thot and high electric field EH on the energy harvested were systematically investigated. Then, experimental data were compared with predictions made by a recently developed physical model [19]. 2. Background 2.1. Pyroelectricity/ferroelectricity Pyroelectric materials possess a spontaneous polarization defined as the average electric dipole moment per unit volume in the absence of an applied electric field [29]. A subclass of pyroelectric materials known as ferroelectric materials have the ability to switch the direction and magnitude of the spontaneous polarization by reversing the applied coercive electric field [30]. Figure 1 shows the isothermal unipolar hysteresis curves between electric displacement D and electric field E exhibited by a pyroelectric material at two different temperatures Tcold and Thot. These so-called D–E loops are traveled in a counter-clockwise direction. The D–E loops corresponding to Tcold and Thot are characteristic of a typical ferroelectric and paraelectric material, respectively. In fact, a ferroelectric material undergoes a phase transition from ferroelectric to paraelectric when it is heated above its Curie temperature, de- noted by TCurie. Then, the spontaneous polarization vanishes. The electric displacement D of an isotropic material at electric field E and temperature T can be expressed as [30, 31] D(E, T) = ε0εr(T)E + Ps(T) (1) EdD. (2) 2PDF Image | Pyroelectric waste heat harvesting using relaxor ferroelectric
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