netserver.aip.orgnetserver.aip.org/.../E-APPLAB-109-058640/supplementary.docx · Web viewIn the second experimental case, we placed a second sample under the active sample and again

Supplementary material to manuscript »Coupling of the electrocaloric and electromechanical effects for solid-state refrigeration« by

A. Bradeško,1,2 Đ. Juričić,1,2 M. Santo Zarnik,1 B. Malič,1,2 Z. Kutnjak1,2 and T. Rojac1,2

1Jožef Stefan Institute, Jamova cesta 39, 1000, Ljubljana, Slovenia2Jozef Stefan International Postgraduate School, Jamova cesta 39, 1000, Ljubljana, Slovenia

In the supplementary material we justify the calculated heat-exchange times between the cantilever elements by experiment verification.

For the experiment, we used two ~100-m thick, 7 x 20 mm2 0.9Pb(Mg1/3, Nb2/3)O3-0.1PbTiO3 (PMN-10PT) ceramic plates. The samples were prepared by thinning bulk ceramics, which were prepared as described by Vrabelj et al., JECERS, 36, 75-80 (2016).

We built a set-up for measuring the temperature on these plates (Figure S1). First, through electrical wires (Au wires with diameter of ~100 m), one of the plates was electrically connected to a voltage source (Wavetek 395 connected to a TREK 610E voltage amplifier). A small bead thermistor (GR500KM4261J15, Measurement Specialties) was glued approximately in the middle of this plate (referred to as the “active” plate) as shown in Figure S1. For monitoring and recording the temperature, we used a multimeter Keithley 7510 connected to a computer. A custom Labview application was made to acquire the thermistor data.

Figure S1: The set-up built for characterization of heat transfer between PMN-10PT plates.

By applying a step-like voltage, we first measured the electrocaloric (EC) temperature response of a single (active) plate. In a second stage, we placed another plate (further referred to as the “non-active”) under the active one so the plates were in contact and re-measured the EC response. The two EC cycles, i.e., those of the single sample and sample in contact, are shown in Figure S2. A clear difference is observed between the two measurements, confirming the notable effect of the sample contact on the EC temperature change.

Figure S2: Temperature response of the EC PMN-10PT samples at 10 kV/cm.

The adiabatic polarization of the first EC cycle for the two cases is shown in more detail in Figure S3. The measurements show that the single sample (black curve) heats up to 0.275 K in ~700 ms (dark blue region udner the blue curve) and then dissipates the generated heat to the air (large cyan region). Since the adiabatic EC polarization should be in principle several magnitudes faster (in dipole switching range, ~s) than the measured value, we may safely assume that the longer experimentally determined time (~700 ms) is related to the internal thermalization of the thermistor and also probably to the heat transfer to the non-electroded parts of the sample (the samples’ surfaces were not covered entirely with the electrode, see Fig. S1).

In the second experimental case, we placed a second sample under the active sample and again re-measured the temperature evolution (this is shown with a red curve in Figure S3). We observed that the magnitude of the EC effect was lower (0.17 K) relative to the single element (0.275 K), however, the time to reach the maximum temperature was comparable to that of the single sample (dark blue region under the red curve).

The reduced magnitude of the EC heating of the two samples in contact relative to the single sample can be attributed to the heat transfer from the active to the non-active sample and is thus a signature of the realized heat transfer between the two samples in thermal contact. The rate of heating of the sample is similar in the two cases, therefore, the heat between the two samples in contact was transferred with a much faster rate than the thermalization time of the thermistor.

Figure S3: Measured temperature during adiabatic polarization of the EC elements on the single sample (black) and two samples in contact (red).

In the next stage, we deconvoluted the measured temperature for the case of the two samples in contact to cancel the effect of the thermistor thermalization (see Figure S4). From the deconvoluted signal we estimated that the heat transfer time between the 100-m samples is ~170 ms.

Considering that the heat diffusion distance is nonlinear, proportional to the square root of time (Incropera et al., Fundamentals of heat and mass transfer. John Wiley & Sons, p. 258 (2007)), we can estimate that if the same samples as used in our experiment would be thinned to 60 m, the thermalization time would be around ~60 ms. The obtained time of 60 ms is longer than the one used to illustrate the best-case performance of our device (10 ms), due to the non-ideal contacts between the cantilevers. However, according to our simulations, such value of the heat exchange time would make our device feasible (see Fig. 5 in manuscript; for 60 ms, the regeneration factor is around 2.8).

Figure S4: Raw signal (red) and deconvoluted raw signal from the thermalization time of the thermistor (green). The data are shown for the case of two samples in contact.