PST-MLC Manufacturing
In this study, we worked on MLCs in PST. These devices consist of a succession of Pt and PST electrodes so as to obtain several capacitors all connected in parallel. PST was chosen because it is an excellent EC material and therefore potentially an excellent NLP material. It exhibits a sharp ferroelectric-paraelectric first-order phase transition around 20°C, which infers that its entropy varies similarly to what is shown in Figure 1. Similar MLCs have already been described in detail in purposes of EC devices13.14. In this study, we used 10.4 × 7.2 × 1 mm³ and 10.4 × 7.2 × 0.5 mm³ MLCs. The 1 mm and 0.5 mm thick MLCs consist of 19 and 9 inner layers of 38.6 µm thick PST, respectively. In both cases, the inner PST layers are sandwiched between 2.05 µm thick Pt electrodes. The design of these MLCs implies that 55% of the PST is active, which corresponds to the part between the electrodes (Supplementary Note 1). Active electrode area is 48.7mm2 (Supplementary Table 5). PST MLCs were prepared by solid state reaction and tape molding methods. Details of the preparation processes have been reported in a previous article14. One of the differences between the MLC PSTs and this previous article14 is the B-site order, which strongly influences EC performance in PST. The B-site order of PST MLCs is 0.75 (Supplementary Note 2), obtained by sintering at 1400°C followed by a long annealing period of several hundred hours at 1000°C. Details on MLC PSTs are given in Supplementary Notes 1 through 3 and Supplementary Table 5.
Experimental set-up of Olsen cycles
The main concept of this study is based on Olsen cycles (Fig. 1). For such cycles we need a cold and hot heat sink and a power supply capable of controlling and monitoring the voltage and current in the various MLC modules. Two different configurations were used for these direct cycles, namely (1) a Linkam module heating and cooling a single MLC associated with a Keithley 2410 power supply and (2) three prototypes (HARV1, HARV2 and HARV3) based on multiple MLC PSTs connected in parallel to the same power supply. In the latter case, a dielectric fluid (silicone oil with a viscosity of 5 cP at 25°C, purchased from Sigma Aldrich) was used to exchange heat between the two reservoirs (hot and cold) and the MLCs. The hot reservoir consisted of a glass container which contained the dielectric fluid and was placed above a heating plate. The cold reservoir consisted of a heat bath of the fluid tube containing the dielectric fluid in a large plastic container filled with water and ice. Two three-way pinch valves (purchased from Bio-Chem Fluidics) were placed at each end of the harvester to properly switch fluid flow from one reservoir to the other (Fig. 2a). To ensure thermal balance between the PST-MLC stack and the heat transfer fluid, the cycle period was extended until the inlet and outlet thermocouples (placed as close to the PST-MLC stack as possible) read the same temperature. A Python script governed and synchronized all the instrumentation (source meter, pump, valves and thermocouples) so that the proper Olsen cycles were run i.e. the hot fluid loop started flowing through the PST stack after the sourcemeter has charged them so that they are heated to the desired applied voltage of a given Olsen cycle.
Alternatively, we confirmed these direct measurements of harvested energy with an indirect method. These indirect methods are based on the electric displacement field (D)– electric field (E) loops collected at different temperatures and allowing an accurate estimation of the amount of energy that can be harvested by calculating the area between the two OF loops, as shown in Fig. 1b. These OF loops were also collected with the Keithley sourcemeter.
Description of the harvester
HARV1
Twenty-eight 1 mm thick MLC PSTs were assembled in a 4 row × 7 column parallel plate structure following the design described in ref. 14. The fluid gap between the rows of PST-MLC was 0.75 mm. This was achieved by adding strips of double sided tape acting as fluid spacers to the edges of the MLC PSTs. The PST MLCs were electrically connected in parallel with silver epoxy bridges that contacted the electrode terminals. After that a wire was glued with silver epoxy on each side of the electrode terminal so that it could be connected to the power supply. Finally, the entire structure was inserted into a polyolefin pipe. The latter was glued to the fluid tubes to ensure a good seal. Finally, 0.25 mm thick K-type thermocouples were integrated at each end of the PST-MLC structure to monitor the fluid inlet and outlet temperature. To do this, the pipe first had to be perforated. Once the thermocouple was integrated, the same glue as before was applied between the pipe and the thermocouple wire to restore the seal.
HARV2
Eight individual prototypes were built, four of them with 40 MLC PSTs of 0.5 mm thickness each, distributed in 5-column × 8-row parallel plate structures, and the other four with 15 MLC PSTs of 1 mm thick each, divided into 3 columns × 5 rows parallel plate structures. The total number of MLC PSTs used was 220 (160 MLC PSTs of 0.5 mm thickness and 60 MLCs of 1 mm thickness). We call these two subunits HARV2_160 and HARV2_60. The fluid slot in the HARV2_160 prototypes consisted of two strips of 0.25mm thick double-sided tape and a 0.25mm thick wire between them. For the HARV2_60 prototypes, we repeated the same procedure but with 0.38mm thick wires instead. For symmetry, HARV2_160 and HARV2_60 had their own fluid circuit, pump, valve and cold side (Supplementary Note 8). The hot reservoir, a three liter (30 cm × 20 cm × 5 cm) container above two hot plates with rotating magnets, was shared by the two HARV2 subunits. The eight individual prototypes were electrically connected in parallel. In the Olsen cycle which led to 11.2 J of recovered energy, the HARV2_160 and HARV2_60 subunits operated simultaneously.
HARV3
A single 0.5 mm thick MLC PST was placed in a polyolefin pipe, with strips of double-sided tape and wires on the sides to create spaces for the fluid to flow. Due to its small size, the prototype was placed next to the valve that feeds fluid from either the hot fluid reservoir or the cold fluid reservoir, minimizing cycle time.
Olsen cycles
A constant electric field was imposed in the MLC PSTs by applying a constant voltage along the heating leg. As a result, a negative pyroelectric current was generated and energy was harvested. After the MLC PSTs warmed up, the field was removed (V = 0), and the energy that was stored there was brought back to the source meter, which corresponds to another contribution of the recovered energy. Finally, at the applied voltage V= 0, the MLC PSTs have been cooled to their initial temperature so that a cycle can start again. In this step, no energy was recovered. We ran Olsen cycles with a Keithley 2410 source meter charging the PST MLCs to the voltage source and setting the current compliance to the appropriate value so that enough points in the charging step were gathered to allow a reliable calculation of energy.
Stirling Cycles
In Stirling cycles, PST MLCs were charged in voltage source mode to an initial electric field value (initial voltage VI> 0), a desired compliance current so that the charging step lasts about 1 s (and enough points are gathered for a reliable energy calculation), and a cold temperature. Before the MLC PST was heated, the electrical circuit was opened by imposing current compliance I= 0 mA (the lowest current compliance value our source meter could take was 10 nA). As a result, the charges were retained in the MLC PSTs and the voltage increased as the sample was heated. In segment BC, no energy was recovered because I= 0mA. After reaching the hot temperature and the voltage in the MLC PSTs having been amplified (in some cases it was more than 30 times, see Supplementary Fig. 7.2), the MLC PSTs were discharged (V= 0), and the electrical energy stored there is brought back to the meter-source with the same current compliance with which they were initially charged. Due to the voltage amplification, the energy stored when hot was greater than the energy supplied at the start of the cycle. Thus, energy was recovered by converting heat into electrical energy.
Calculation of recovered energy and power
We monitored the voltage and current applied to the MLC PSTs with a Keithley 2410 source meter. The corresponding energy was calculated by integrating the product of the voltage and current read by the Keithley source meter over time, (E={int }_{0}^{tau }{I}_{{rm{meas}}}left(tright){V}_{{rm{meas}}}