Directly measured electrocaloric heat in multilayer capacitors of lead scandium tantalate

Electrocaloric (EC) effects are thermal changes that arise due to changes in the magnitude of a local polarization when there is a change in electric field, and useful EC effects are nominally reversible.¹ EC effects have been primarily studied in ceramics² and polymers,³ and also in liquid crystals,⁴ ammonium sulfate,⁵ and organic–inorganic hybrids.⁶ The perovskite ceramic PbSc_0.5Ta_0.5O₃ (PST) is attractive because it displays relatively large EC effects that can be tuned by doping^7,8 or by varying B-site cation order.⁹ B-site cation order is determined from x-ray diffraction data and parameterized via an order parameter of 0 ≤ S₁₁₁ ≤ 1, where S₁₁₁ = [(I₁₁₁/I₂₀₀)_measured/(I₁₁₁/I₂₀₀)_expected]^1/2 compares the measured and expected values of intensity I for the 111 and 200 reflections.¹⁰ 

In PST, low B-site cation order (S₁₁₁ ≤ 0.4) results in relaxor behavior,⁹ and reasonably large EC effects can be driven over a wide range of temperatures.⁷ Good B-site cation order (S₁₁₁ ≥ 0.8) results in a first-order ferroelectric phase transition near room temperature,^9,10 and using multilayer capacitors (MLCs) (Fig. 1) of PST (S₁₁₁ ∼ 0.9–0.96) that are similar to the MLC we study here, it was shown¹⁰ that large thermal changes arise when this transition is electrically driven, that additional thermal changes arise when the transformed phase is further electrically polarized, and that EC effects can thus be driven over a wide range of temperatures by applying supercritical driving fields. These EC effects represent an improvement over magnetocaloric working bodies of gadolinium spheres as exploited in prototype coolers and could, therefore, be important for applications.¹⁰ 

The earliest EC cooling devices^11–13 exploited thin bulk wafers of PST with good B-site order (S₁₁₁ ∼ 0.85–0.9). More recent EC cooling devices^14–16 have exploited the aforementioned MLCs of PST,¹⁰ which display a peak adiabatic temperature change of 5.5 K in response to field changes of 29.0 V μm⁻¹. For one such MLC, we present calorimetry data that were obtained during isofield thermal cycles and isothermal field cycles in which we drive the first-order ferroelectric phase transition with a Curie temperature of ∼290 K at zero field (the isothermal field cycles are in reality quasi-isothermal, but in this paper, we will refer to them as isothermal for simplicity). We avoid a breakdown during the long measurement times by using a maximum field (7.9 V μm⁻¹) that is relatively small but larger than the critical point field of 5 V μm⁻¹ (Ref. 10).

Our direct measurements of isothermal EC heat from the active PST (within the red dashed lines, Fig. 1) show that EC effects peak at temperatures between the ∼290 K Curie temperature and the 330 K critical point temperature.¹⁰ The transition becomes less first order with increasing proximity to the critical point, and the isothermal EC heat Q and isothermal entropy change ΔS = Q/T match well with complementary EC data for similar MLCs,¹⁰ i.e., indirectly measured EC effects and direct measurements of adiabatic EC temperature change.

Direct measurements of EC heat are less common than direct measurements of adiabatic EC temperature change and have not been reported for MLCs. Given that EC heat is important for applications, it should in the future be measured directly as a matter of routine.

We report data for two similar MLCs of PST that show negligible Joule heating. Figures 2–6 employ calorimetric data for MLC1 (S₁₁₁ ∼ 0.89), which was fabricated as explained in Ref. 10. Figures 4–6 employ a subset of previously published¹⁰ isothermal electrical polarization data for MLC2 (S₁₁₁ ∼ 0.96), measured on field removal while heating. Each of the two MLCs has 19 active layers of thickness d = 38 μm. Ignoring fringing fields, the active volume of PST is 35 mm³ (54% of MLC volume), the inactive volume of PST and Pt electrodes is 30 mm³ (46% of MLC volume), the active area per layer is 8.8 × 5.6 mm² = 49 mm², and external MLC dimensions of 10.45 × 7.43 × 0.84 mm³ are essentially invariant as piezoelectric effects in PST are small and the active volume is clamped by the inactive volume.

Calorimetry was performed using a bespoke differential scanning calorimeter.^17,18 The active area of the MLC and the copper reference were, respectively, attached via a thin layer of thermal paste (Prolimatech PK3) to relatively large sample and reference Peltier units (10 × 10 mm²) that were superglued to a relatively large copper block. The temperature of this block was set using a LAUDA Eco Gold 1050 temperature bath and measured using a Pt100 resistance thermometer. The MLC was electrically addressed via 0.2 mm-diameter coiled copper wires that were attached using silver paste, and the application of voltage V generated an electric field E = V/d in the active PST. Copper-block temperature and electric field were varied slowly, such that the MLC and the copper reference may be assumed to adopt the same temperature as the copper block despite the weak thermal link formed by the intervening Peltiers. MLC temperature T was thus identified from the temperature of the copper block, as measured by the Pt100 sensor.

While sweeping and recording temperature T(t) or voltage V(t) at time t, quasi-isothermal heat transfer through each Peltier generated a voltage. We recorded the voltage difference between Peltier units ΔV_Peltiers(t) and converted it to heat per unit time dQ(t)/dt via the calibration presented in Figs. S1 and S2 of the supplementary material. We then combined dQ(t)/dt with dT(t)/dt or dE(t)/dt to yield dQ/dT or dQ/dE, respectively. We present dQ/|dT| (Fig. 2) without volume normalization as the two peaks observed at finite field come from different regions of the MLC, namely, inactive and active PST. We present dQ/|dE| (Fig. 3) after normalization by active volume as the single peak comes from the active volume, there being no change in the inactive volume. Examples of raw data are shown in Figs. S3 and S4 of the supplementary material.

Slow isofield temperature sweeps at ±0.5 K min⁻¹ (260 K to temperatures as high as 340 K and back to 260 K) were performed while maintaining a constant voltage that was increased after each thermal cycle, and data were rejected from within 15 K of the two end temperatures to avoid the variations in ramp rate that follow the switch between heating and cooling. Slow isothermal field sweeps at ±6.3 mV μm⁻¹ s⁻¹ (0 to 7.9 V μm⁻¹, 10 min hold, back to 0) were performed after waiting 20 min for the system to thermalize at each measurement temperature, which was set every ∼5 K by heating from 288 to 346 K at 0.5 K min⁻¹. Note: 7.9 V μm⁻¹ corresponds to 300 V, and ±6.3 mV μm⁻¹ s⁻¹ corresponds to ±0.25 V s⁻¹.

We initially minimized exposure to large fields by performing thermal cycles at zero field and then in increasing fields (dQ/|dT|, Fig. 2). At zero field, each branch displays a single peak due to the thermally driven phase transition in all of the PST in the MLC. This single peak occurs at 292 K on heating and 288 K on cooling. At finite fields, the inactive PST displays the aforementioned zero-field transition that yields in each branch what is now a relatively small peak, while the active PST displays the intended finite-field transition that yields in each branch a peak that, for increasing values of the field, is up-shifted, shorter, broader, and, at least for low fields, nearer in temperature to its counterpart in the other branch (reduction of isofield thermal hysteresis). Therefore, the phase transition is seen to become less first order on moving along the phase boundary toward the critical point. The dQ/|dT| data were not subsequently used to identify EC effects via the quasi-direct method¹⁹ because of peak overlap at low field (red data, Fig. 2).

Isothermal unipolar field cycles at increasing values of temperature that lie above the first-order transition near 290 K modify only the active PST to produce in each branch a single peak due to the electrically driven phase transition in the active PST (dQ/|dE|, Fig. 3). For larger values of temperature, this peak is up-shifted, shorter, broader, and, at least for low temperatures, nearer in field to its counterpart in the other branch (reduction of isothermal field hysteresis). Thus we also see here that the transition becomes less first order on moving toward the critical point.

This reduction in first-order character at higher temperatures and fields is necessarily also seen in the net isothermal EC heat [Q(E), Fig. 4(a)] obtained by integrating dQ/|dE| for each unidirectional field sweep. Here, the field-up sweep from Q = 0 finishes at what we take for convenience to be the starting value of Q for the field-down sweep, such that positive field-down sweep values of Q appear negative, and the return to Q ∼ 0 implies that the hysteretic field cycle is repeatable and that the isothermal EC effects are nominally reversible.¹ The reduction in first-order character is necessarily also seen from the corresponding isothermal entropy change, which for the up-sweep is given with respect to the zero-field entropy [ΔS(E) = S(E) − S(0) = Q(E)/T, Fig. 4(b)]. Field-off polarization data obtained on heating [P(E), Fig. 4(c)] also evidence the reduction in first-order character.

For our maximum field of 7.9 V μm⁻¹, the magnitude of the field-on and field-off changes in heat and entropy [|Q_max| and |ΔS_max|, Figs. 5(a) and 5(b)] are identified from the plots of Q(E) and ΔS(E) [Figs. 4(a) and 4(b)]. Figures 5(a) and 5(b) also present 293 K values of |Q_max| and |ΔS_max| that we derive by integrating dQ/dt over time instead of converting to dQ/|dE| and integrating over the field:²⁰ because the 293 K peak occurs at low field and because heat transfer takes a finite time, a small quantity of heat is transferred just after the field has returned to zero (dQ/dt, Fig. S5 of the supplementary material), and this small quantity of heat is missed if one converts to dQ/|dE| (Fig. S6 of the supplementary material). Thus, for 293 K, we identify the maximum values of |Q| and |ΔS| but not their field dependences. Note that we are following the common practice of referring to heat transfer in order to describe the transfer of what is in reality thermal energy rather than heat.

For our maximum field of 7.9 V μm⁻¹, |Q_max| and |ΔS_max| peak near room temperature at |Q_max| ∼ 11 MJ m⁻³ and |ΔS_max| ∼ 36 kJ K⁻¹ m⁻³, and match well with indirectly measured EC data for MLC2, as shown in Figs. 5(a) and 5(b). At each measurement temperature, the field-on and field-off values of |Q_max| are essentially equivalent, as expected given the aforementioned nominal reversibility of our isothermal EC effects. Our peak values of |Q_max| and |ΔS_max| correspond to a peak adiabatic temperature change of |ΔT_max| ∼ 4 K. This temperature change was identified from indirectly measured data for MLC2 (Fig. 2d in Ref. 10) that are consistent with direct measurements of temperature change (Fig. 3b in Ref. 10), and this identification was made via an entropy map (Fig. 2c in Ref. 10) rather than the well-known relation −cΔT ∼ TΔS (Ref. 19) because c varies with both temperature and field (Fig. 3 in Ref. 21) (note that specific heat capacity c can be replaced with its volume normalized counterpart).

The fields and temperatures at which we resolve well the isofield calorimetry peaks (Fig. 2) and the isothermal calorimetry peaks (Fig. 3) are used to construct away from the critical point a hysteretic phase boundary that is plotted on (T,E) axes over a color map showing field-off isothermal polarization data obtained on heating (Fig. 6). We make two observations. First, the hysteretic phase boundary derived from calorimetry is similar to the corresponding section of the phase boundary derived from polarization data. Second, the use of (T,E) axes renders apparent the equivalence between field hysteresis and thermal hysteresis, both of which are reduced on moving toward the critical point and, thus, reducing the first-order character of the transition.

For MLCs based on PST with good B-site order, we deduce that the magnitude of directly measured isothermal EC heat is consistent with the magnitude of directly measured adiabatic EC temperature change, as each of these direct measurement types is consistent with indirectly measured EC effects based on polarization data, as discussed two paragraphs earlier.

The reduction in the first-order character of the phase transition on following the phase boundary in the direction of the critical point, which we see from both calorimetric data [e.g., Figs. 4(a) and 4(b)] and polarization data [e.g., Fig. 4(c)], is also seen for bulk PST (S₁₁₁ ∼ 0.80)^20,21 and MLCs of PST (S₁₁₁ ∼ 0.75),²² all with good B-site order. Electrically driving the phase transition at higher temperatures, therefore, yields smaller latent heats. These smaller latent heats are accompanied by larger EC effects in the untransformed phase [Fig. 4(a)], but overall, EC effects at our maximum field of 7.9 V μm⁻¹ are reduced on increasing temperature (Fig. 5). The observed reduction in first-order character is not often observed in EC materials, as the use of high fields is destructive. However, such a reduction has been observed in barocaloric²³ and magnetocaloric materials,²⁴ where large driving fields do not result in breakdown.

Quasi-direct¹⁹ evaluation of EC heat from our isofield thermal sweeps is not attempted due to the overlap between active and inactive peaks at low field (red data, Fig. 2); peak separation would require fitting, and this would compromise accuracy. By contrast, our directly measured EC heat [Fig. 4(a)] is derived from isothermal field sweeps in which the calorimetric peaks arise from active PST alone (Fig. 3). Directly measured EC heat therefore provides a good measure of EC effects in MLCs.

Although both indirect EC measurements and direct measurements of EC temperature change are currently employed by many laboratories, EC heat is rarely measured or deduced. Given that EC heat determines the heat pumped per cooling cycle, it is an important parameter for applications. We, therefore, suggest that calorimetry of the type performed here should in the future be widely employed to measure EC heat in MLCs and other EC samples.

Here, we present the data used to calibrate the calorimeter (Fig. S1), the resulting calibration curve (Fig. S2), examples of raw calorimetry data obtained while cycling temperature (Fig. S3) and field (Fig. S4), raw calorimetry data for the 293 K isothermal field cycle in which a small quantity of heat is transferred just after the field has returned to zero (Fig. S5), and a repeat of Fig. 3 (dQ/|dE| vs field E) with the addition of an incomplete field-off peak at 293 K (Fig. S6).

V.F. is grateful to St. John’s College, Cambridge, UK, for Ph.D. funding via the St. John’s College Benefactors’ Scholarships for Postgraduate Students. J.Z. is grateful for Ph.D. funding from the China Scholarship Council and the Cambridge Trust. X.M. acknowledges the support from UK EPSRC Grant No. EP/M003752/1, ERC Starting Grant No. 680032, and the Royal Society. We thank H. Kuramoto and K. Sasaki for their assistance in fabricating the new MLC for this study. M.G. was supported by a Newton International Fellowship from the Royal Society, UK.

The authors have no conflicts to disclose.

V. Farenkov: Data curation (lead); Formal analysis (lead); Methodology (equal); Software (lead); Writing – original draft (lead); Writing – review & editing (equal). J. Zhang: Writing – review & editing (supporting). B. Nair: Data curation (supporting); Methodology (equal). M. Guo: Data curation (equal); Formal analysis (supporting); Methodology (equal); Supervision (equal); Writing – review & editing (equal). X. Moya: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (equal); Project administration (supporting); Resources (equal); Supervision (equal); Writing – review & editing (equal). S. Hirose: Conceptualization (equal); Project administration (supporting); Resources (equal); Supervision (equal); Writing – review & editing (equal). N. D. Mathur: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (equal); Project administration (lead); Resources (equal); Supervision (lead); Writing – original draft (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.