Inverse barocaloric effects in ferroelectric BaTiO₃ ceramics Open Access

The discovery one decade ago of giant electrocaloric (EC) effects near ferroelectric phase transitions in ceramic thin films,¹ and then in thicker films of polymers,² triggered intense research into ferroelectric materials for environmentally friendly EC cooling.^3–6 Although there have been significant advances in materials developments,^7–9 measuring techniques,^10–16 and heat-pump prototypes,^17–21 the commercial application of EC materials remains elusive. The main obstacle is that EC performance is limited by breakdown field, while another major obstacle is that electric-field-induced strain produces mechanical fatigue and ultimately failure. This second obstacle arises because the ferroelectric phase transitions exploited in EC effects are typically accompanied by significant changes in volume.^22–24 It therefore follows that EC materials are good candidates for solid-state barocaloric (BC) cooling.^5,6,25

BC effects are reversible thermal changes driven by changes of hydrostatic pressure and have long been exploited in fluids to achieve continuous cooling in the well known vapour-compression systems employed in refrigerators and air conditioners. Given that these BC fluids are harmful for the environment, it would be attractive to replace them with non-volatile materials that show large BC effects. Large BC effects have recently been predicted in two ferroelectric materials [PbTiO₃ and BaTiO₃ (BTO)^26,27] and experimentally demonstrated in ferrielectric ammonium sulphate.²⁸ Moreover, it is easier to exploit ferroelectric materials for BC cooling than EC cooling, as there is no need to fabricate multilayer capacitor devices for electrical access to films; there is no mechanical fatigue/failure during operation; and the range of operating temperatures is not compromised by the need to avoid breakdown.^5,6,28

Here we use temperature-dependent x-ray diffraction, and pressure-dependent calorimetry, to experimentally demonstrate BC effects in ceramics of the prototypical ferroelectric BTO. The combination of these two techniques is essential for evaluating contributions to the BC response that arise from the non-isochoric phase transitions and the volumetric thermal expansion on either side of each transition.²⁸ At high temperatures, BTO displays a centrosymmetric cubic ABO₃ perovskite structure, with A cations at the corners, B cations at the centres, and oxygen anions at the face-centred positions. Near the transition between cubic (C) and tetragonal (T) phases^22,23 at Curie temperature T_C ∼ 400 K, we find inverse isothermal entropy changes of magnitude |ΔS| ∼ 1.6 J K⁻¹ kg⁻¹ due to small changes of applied pressure |Δp| ∼ 1 kbar (assuming ambient pressure to be zero, such that |Δp| ∼ p). At lower temperatures, near the ∼280 K transition between T and orthorhombic (O) phases, we find inverse isothermal entropy changes of magnitude |ΔS| ∼ 1.3 J K⁻¹ kg⁻¹, also with |Δp| ∼ 1 kbar. We did not explore the ∼200 K transition between O and rhombohedral (R) phases, as the change in unit-cell volume is small [Figure S1 of the supplementary material].

Powdered BTO (≥99.99%) from Sigma-Aldrich had a typical grain size of <1 μm. The powder was first cold-pressed isostatically in air at 10 kbar and then sintered in air at 1673 K for 48 h. The sintered ceramic (2.3 cm in diameter, 0.2 cm in thickness) was cooled down to room temperature at −3 K min⁻¹. A small piece (∼0.005 cm³) was cut in order to perform temperature-dependent calorimetry and x-ray diffraction at ambient pressure. The larger remaining piece was used for pressure-dependent calorimetry.

Measurements of dQ/dT at atmospheric pressure were performed using a commercial TA Q2000 differential scanning calorimeter at ±2 K min⁻¹ (Q is heat, T is temperature). Heat $Q 0 = ∫ T 1 T 2 ( d Q / d T ′ ) d T ′$ and entropy change $Δ S 0 = ∫ T 1 T 2 ( d Q / d T ′ ) / T ′ d T ′$ across the first-order transitions were obtained after subtracting baseline backgrounds,²⁹ with T₁ chosen above (below) each transition on cooling (heating), and T₂ chosen below (above) each transition on cooling (heating). The entropy change on partially driving each transition by heating to temperature T, with respect to each low-temperature phase, is $ΔS ( T ) = ∫ T 1 T ( d Q / d T ′ ) / T ′ d T ′$⁠. The entropy change on partially driving each transition by cooling to temperature T, with respect to each low-temperature phase, is $ΔS ( T ) = Δ S 0 − ∫ T 1 T ( d Q / d T ′ ) / T ′ d T ′$⁠.

High-resolution x-ray diffraction was performed in transmission-mode using Cu Kα₁ = 1.5406 Å radiation in an INEL diffractometer, with a curved position-sensitive detector (CPS120), and Debye-Scherrer geometry. The sample was introduced into a 0.3-mm diameter Lindemann capillary to minimise absorption, and temperature was varied using a liquid-nitrogen 700 series Oxford Cryostream Cooler. Lattice parameters were determined by pattern matching using FullProf software.³⁰ 

Measurements of dQ/dT under hydrostatic pressure were performed at approximately ±2 K min⁻¹, using a differential thermal analyser constructed in-house. At high temperatures, we used an Irimo Bridgman pressure cell that operates at up to 3 kbar and a resistive heater (room temperature-473 K). At low temperatures, we used a Cu-Be Bridgman pressure cell that operates at up to 3 kbar and a circulating thermal bath (Lauda Proline RP 1290, 183-473 K). In order to guarantee optimal thermal contact between the heat sensor and the sample, a chromel-alumel thermocouple was inserted inside a hole that was drilled in the centre of the large BTO ceramic sample. The ceramic sample and thermocouple were then immersed in the pressure-transmitting medium (Caldic silicon oil for high-temperature measurements; DW-Therm, Huber Kältemaschinenbau GmbH for low-temperature measurements).

The first-order structural phase transitions are seen in calorimetry [Figure 1(a)] to be sharp, with a small thermal hysteresis of ∼4 K (C-T) and ∼7 K (T-O). Integration of (dQ/dT)/T yields the thermally driven entropy change ΔS(T) [Figure 1(b)], with |ΔS₀| = 2.4 ± 0.2 J K⁻¹ kg⁻¹ for the full C-T transition and |ΔS₀| = 2.0 ± 0.2 J K⁻¹ kg⁻¹ for the full T-O transition. Integration of dQ/dT across the full transition yields heats of |Q₀| = 960 ± 90 J kg⁻¹ (C-T) and |Q₀| = 560 ± 60 J kg⁻¹ (T-O). These values are in good agreement with previous experimental values^12,31 of |ΔS₀| ∼ 2.4 J K⁻¹ kg⁻¹ and |Q₀| ∼ 900 J kg⁻¹ for the C-T transition and are similar to previous values^31,32 of |ΔS₀| ∼ 1.6-2.3 J K⁻¹ kg⁻¹ and |Q₀| ∼ 450-640 J kg⁻¹ for the T-O transition.

On heating through the two transitions, x-ray diffraction data [Figure 1(c)] confirm the expected changes in crystal structure.^22,23 The unit-cell volume V decreases sharply by ∼0.03% (O-T transition, ΔV₀ = − 0.02 ± 0.01 ų) and ∼0.11% (T-C, ΔV₀ = − 0.07 ± 0.02 ų). On either side of each transition, the volume thermal expansion is large [Figure S1 of the supplementary material], implying large additional BC effects.²⁸ By writing isothermal BC entropy change per unit mass m due to pressure change Δp = p₂ − p₁ as^5,28 $ΔS p 1 → p 2 =− m − 1 ∫ p 1 p 2 ∂ V / ∂ T p ′ d p ′$ (using the Maxwell relation m⁻¹(∂V/∂T)_p = − (∂S/∂p)_T), we therefore anticipate inverse BC effects in the transition regimes where (∂V/∂T)_p=0 < 0, and conventional BC effects outside the transition regimes where (∂V/∂T)_p=0 > 0.

dQ/dT measurements through the two transitions under various applied pressures are shown in Figure 2. For the C-T transition, there is a strong pressure-induced shift of transition temperature T₀, with dT₀/dp = − 5.8 ± 0.1 K kbar⁻¹ on heating and dT₀/dp = − 5.4 ± 0.2 K kbar⁻¹ on cooling [Figures 2(a) and 2(c)]. A larger shift of −7.9 ± 2.0 K kbar⁻¹ on heating is obtained via the Clausius-Clapeyron equation dT₀/dp = Δv₀/ΔS₀, using ΔS₀ = 2.4 ± 0.2 J K⁻¹ kg⁻¹ [Figure 1(b)] and specific volume change Δv₀ = − (0.19 ± 0.03) × 10⁻⁶ m³ kg⁻¹ [from Figure 1(c)]. These values of dT₀/dp are similar to those reported for BTO in the form of single crystals (∼ −4-6 K kbar⁻¹, Refs. 33–40) and ceramics (∼ −4-5 K kbar⁻¹, Refs. 36, 40, and 41), and they imply that the narrow first-order transition of width ∼4 K may be fully driven using low values of |Δp| ∼ 1 kbar.

For the T-O transition, the pressure-induced shift in T₀ is weaker, with dT₀/dp = − 3.5 ± 0.1 K kbar⁻¹ on heating and dT₀/dp = − 2.6 ± 0.1 K kbar⁻¹ on cooling [Figures 2(b) and 2(c)]. A similar shift of dT₀/dp = − 2.8 ± 1.3 K kbar⁻¹ on heating is obtained via the Clausius-Clapeyron equation, using ΔS₀ = 2.0 ± 0.2 J K⁻¹ kg⁻¹ [Figure 1(b)] and specific volume change Δv₀ = − (0.06 ± 0.03) × 10⁻⁶ m³ kg⁻¹ [from Figure 1(c)]. These values of dT₀/dp are similar to those reported for single-crystal BTO (∼ −3 K kbar⁻¹, Refs. 35, 37, 40, and 42) and indicate that the wider first-order transition of width ∼7 K may be fully driven using |Δp| ∼ 2 kbar.

For each of the two transitions, integration of (dQ/dT)/T at finite pressure reveals that the entropy change |ΔS₀| decreases with increasing pressure [Figure 2(d)]. This fall in |ΔS₀| arises because of additional²⁸ changes in isothermal entropy ΔS₊(p) that are conventional, reversible, and opposite in sign with respect to the pressure-driven isothermal entropy changes associated with each transition. These additional changes in entropy are challenging to detect via the calorimetry used for Figure 2 but may be expressed away from the first-order transitions via ΔS₊(p) = − [m⁻¹(∂V/∂T)_p=0]p, where we have used the aforementioned Maxwell relation with S₊ replacing S, and with (∂V/∂T)_p assumed independent of pressure.^5,28

In order to plot ΔS(T, p) with respect to the zero-pressure entropy at a temperature T₊ above the C-T transition [Figures 3(a) and 3(b)] and the T-O transition [Figures 4(a) and 4(b)], we obtained finite-pressure plots of ΔS(T) [from the integration of data in Figures 2(a) and 2(b)] that we displaced²⁸ at T₊ by evaluating ΔS₊(p) at this temperature. Note that ΔS₊(p) was evaluated at T₊ > T₀(p) to avoid the forbidden possibility of T₀(p) falling to T₊ at high pressure.

For the C-T transition, our plots in Figure 3(a) of ΔS(T, p) for dQ/dT data obtained on heating permit us to establish isothermal BC effects on applying pressure [Figure 3(c)], as heating and high pressure both favour the high-temperature cubic phase with smaller volume. Similarly, our plots in Figure 3(b) of ΔS(T, p) for dQ/dT data obtained on cooling permit us to establish isothermal BC effects on decreasing pressure [Figure 3(d)], as cooling and low pressure both tend to favour the low-temperature tetragonal phase with larger volume. Values of |ΔS(T, p)| on applying and removing pressure are similar at all temperatures studied. The BC response near the C-T transition is therefore highly reversible, consistent with the low thermal hysteresis of the transition [Figures 1(a) and 1(b)]. The peak isothermal entropy change |ΔS| ∼ 1.6 ± 0.2 J K⁻¹ kg⁻¹ near ∼400 K is achieved with a low value of |Δp| = 1 kbar [Figures 3(c) and 3(d)], yielding large BC strengths,⁵ |ΔS|/|Δp| and |Q|/|Δp| (Table I). Larger pressures extend inverse reversible BC effects to lower temperatures, causing an increase of refrigerant capacity RC [Figure 5(b)], despite the reduction in |ΔS₀(p)| [Figure 2(d)] and thus the peak value of |ΔS(p)| [Figure 5(a)]. Note that recently predicted BC effects (|ΔS| ∼ 3.9 J K⁻¹ kg⁻¹ with 10 kbar at 353 K) are larger because additional entropy changes were neglected.²⁷ 

For the T-O transition, our plots in Figures 4(a) and 4(b) of ΔS(T, p) for dQ/dT data obtained on heating and cooling permit us to establish isothermal BC effects on increasing pressure [Figure 4(c)] and decreasing pressure [Figure 4(d)]. Although the peak entropy change of |ΔS| ∼ 1.3 ± 0.2 J K⁻¹ kg⁻¹ appears to be similar for Δp = ± 1 kbar, the peak occurs at different temperatures, evidencing inverse irreversible BC effects. This irreversibility, which is also seen for conventional EC effects near the T-O transition,⁴³ arises because of the relatively large thermal hysteresis. Therefore caloric effects near the T-O transition are unsuitable for continuous cooling, and so we do not present RC values.

In summary, we have combined temperature-dependent x-ray diffraction data with pressure-dependent calorimetry to demonstrate BC effects in BTO ceramic samples. For the T-O phase transition at ∼280 K, we found small inverse BC effects that are irreversible, whereas for the C-T phase transition at Curie temperature T_C ∼ 400 K, we found larger inverse BC effects that are reversible. Our observation of reversible BC effects near the Curie temperature of BTO should inspire studies of BC effects in a wide range of ferroelectric materials. This should expand the range of BC materials beyond ammonium sulphate²⁸ and a small number of magnetic materials,^44–48 allowing caloric properties to be exploited in cooling devices without the electrical breakdown that limits EC effects.

See supplementary material for Figures S1, S2, and S3. All relevant data are presented via this publication and supplementary material.

This work was supported by the ERC Starting Grant No. 680032, the UK EPSRC Grant No. EP/M003752/1, by CICyT (Spain), Project Nos. MAT2013-40590-P and FIS2014-54734-P, and by DGU (Catalonia), Project No. 2014SGR00581. P.Ll. acknowledges support from SUR (DEC, Catalonia). E.S.T. acknowledges support from AGAUR. E.D. acknowledges support from FNR Luxembourg through COFERMAT project. X.M. is grateful for support from the Royal Society.