Large electrocaloric effects in single-crystal ammonium sulfate

Abstract

Electrocaloric (EC) effects are typically studied near phase transitions in ceramic and polymer materials. Here, we investigate EC effects in an inorganic salt, namely ammonium sulfate (NH₄)₂SO₄, with an order–disorder transition whose onset occurs at 223 K on cooling. For a single crystal thinned to 50 μm, we use a Maxwell relation to find a large isothermal entropy change of 30 J K⁻¹ kg⁻¹ in response to a field change of 400 kV cm⁻¹. The Clausius–Clapeyron equation implies a corresponding adiabatic temperature change of 4.5 K.

This article is part of the themed issue ‘Taking the temperature of phase transitions in cool materials’.

1. Introduction

Reversible electric-field-driven thermal changes are known as electrocaloric (EC) effects and have been proposed for solid-state cooling applications. They peak at finite temperatures near ferroelectric and ferrielectric phase transitions and are typically parametrized in terms of isothermal entropy change ΔS and the corresponding adiabatic temperature change ΔT. Ceramic oxides such as PbSc_0.5Ta_0.5O₃ [1–3] show first-order ferroelectric phase transitions that are traditionally considered to be displacive, implying relatively small entropic changes when applying tens of kilovolts per centimetre. In sub-micrometre-thick films of these materials, EC effects are enhanced because one may apply hundreds of kilovolts per centimetre without breakdown [4]. Somewhat larger EC effects are seen near order–disorder phase transitions in few-micrometre-thick polymer films, but these require larger fields of a few thousand kilovolts per centimetre [5,6]. EC effects in both ceramic and polymer films could be exploited in multilayer capacitors to enhance active thermal mass [7–9], with active layer thicknesses of several micrometres [10–12] or tens of micrometres [13]. Here, we report large EC effects in a 50 μm-thick single crystal of the inorganic salt ammonium sulfate (AS) [(NH₄)₂SO₄], using a moderate field of 400 kV cm⁻¹.

AS displays a predominantly order–disorder ferrielectric phase transition and thus a large thermally driven zero-field entropy change |ΔS|∼133 J K⁻¹ kg⁻¹ for the full transition that spans a wide range of temperatures [14,15]. Among known ferroelectrics, this value is exceeded only by certain halides [16]. More generally, most inorganic ferroelectric/ferrielectric salts show predominantly order–disorder transitions, such that the ordered state is destroyed above the Curie temperature T_C by the thermally activated randomization of ionic positions. Each randomization contributes an entropy of of ionic groups (R=8.314 J K⁻¹ mol⁻¹), which corresponds to tens of J K⁻¹ kg⁻¹ for typical salts [15]. Despite these large entropy changes, the study of EC effects in inorganic salts is rare [17,18]. That said, large entropy changes of |ΔS|=60 J K⁻¹ kg⁻¹ were recently achieved near the ferrielectric transition in powdered AS using relatively small changes of pressure |Δp|=0.1 GPa, i.e. barocaloric effects of giant strength [19].

The ferrielectric phase transition in AS involves the ordering of all three ionic groups [14]. On cooling, partial order results in a first-order ferrielectric transition at T_C∼223 K, followed by a continuous increase of order down to approximately 160 K [14,18–20]. Here, for a bulk sample thinned to 50 μm, we achieve relatively large electrically driven changes of entropy |ΔS|∼30 J K⁻¹ kg⁻¹ with |ΔE|=400 kV cm⁻¹, as deduced from measurements of electrical polarization P(E) that were dense in temperature, using the well-known indirect method [21] with Maxwell relation (∂S/∂E)_T=(∂P/∂T)_E. Adiabatic temperature changes of up to |ΔT|∼4.5 K are inferred from the Clausius–Clapeyron equation.

2. Experimental methods

Samples were prepared by mixing one equivalent of sulfuric acid (more than aq. 95%) and two equivalents of ammonium hydroxide (aq. 35%) in water. The resultant white precipitate was dissolved in excess water and kept at room temperature over a few days to yield transparent crystals of mixed morphologies. Small crystals (less than 1 mm³) were used for X-ray diffraction and larger crystals (several cubic millimetres) were used for calorimetry and electrical measurements.

Temperature-dependent X-ray diffraction (performed using an Oxford Diffraction Gemini E Ultra, with Oxford Instruments Cryojet) confirmed the presence of a single phase with the expected lattice parameters [22] and revealed the presence of twins in the low-temperature phase.

Calorimetry was performed on an unelectroded crystal of mass 9.429 mg, using a TA Instruments Q2000 differential scanning calorimeter to measure heat flow while ramping temperature T at . As shown in [23], the resulting plots of c(T) on cooling and heating were shifted to remove the offset in c away from T_C. The zero-field entropy change with respect to the absolute entropy at 230 K was evaluated from c(T) using .

For dielectric and electrical polarization measurements, a single sample was prepared from a large crystal, as described in [23] and summarized here. The polar c-axis was identified by room-temperature X-ray diffraction using a Bruker D8 Advance. A surface lying normal to this direction was polished flat, covered with a bottom electrode of sputter-deposited Pt and glued with conducting silver epoxy to insulating Kapton tape on a Cu substrate. The free surface was then polished flat, resulting in an AS thickness of approximately 50 μm, as measured in an optical microscope by focusing on the lower and upper surfaces of the transparent crystal and assuming a refractive index of 1.53 [24]. A smaller top electrode of Pt was sputter-deposited through a bespoke lift-off mask and its approximately 0.5 mm² area was assumed to represent the electrically active area, ignoring fringing fields. Wiring was attached using epoxy glue, and vacuum grease (Apiezon ‘n’) was liberally smeared over the samples to discourage electrical arcing.

Dielectric measurements were performed using an Agilent 4294A Impedance Analyzer, with excitation amplitude 0.5 V and frequency 1 kHz. Temperature was ramped slowly at −0.2 K min⁻¹ using an evacuated probe in liquid nitrogen, with a Cu heat reservoir and PID temperature control [23]. At all measurement temperatures, a constant parasitic parallel capacitance of 1.8 pF was subtracted from the measured capacitance, yielding a sample capacitance of 0.4 pF at 298 K. Subsequent temperature sweeps yielded a stable dielectric response, which was smaller than the response obtained during the initial sweep, due to some degree of cracking and degradation associated with the large and abrupt volume change at T_C ([19] and references therein).

Electrical polarization measurements of the same sample were obtained with a Radiant Precision Premier II and an external Trek amplifier, using a triangular wave excitation with period 0.1 s and amplitude 2 kV. The aforementioned probe was used to ramp temperature slowly at −0.1 K min⁻¹, in order to collect a dense set of polarization loops every approximately 0.07 K. Polarization data were noisy after correcting for a relatively large parasitic capacitance. An additional correction for temperature-independent high-field resistive losses (electronic supplementary material, figure S1) had no influence on (∂P/∂T)_E and the resulting values of ΔS(E,T). A second sample measured with coaxial cable showed no such losses [23], which implies negligible Joule heating in direct measurements and any practical applications.

3. Results

For our unclamped sample, the first-order structural transition near T_C (figure 1a) is accompanied by a large peak in c(T) and thus a large zero-field entropy change of |ΔS₀|∼50 J K⁻¹ kg⁻¹ (figure 1b), with start and finish temperatures that from c(T) we identify to be T_C1=221.9 K and T_C2=221.1 K. The other notable feature in c(T) is that the background value of 1.5 kJ K⁻¹ kg⁻¹ near and below T_C is enhanced with respect to the background value of 0.9 kJ K⁻¹ kg⁻¹ near and above T_C, as a consequence of the transition extending below T_C [19]. The ferrielectric transition is also seen in dielectric data obtained for the virgin sample (figure 1c), where the ε∼80 peak in relative permittivity corresponds to the first-order transition. Further order on further cooling increases the very small high-temperature loss to a large value at 200 K, where tan δ∼0.2.

Figure 1.

Zero-field 223 K phase transition in AS observed on reducing temperature. (a) Lattice parameters a,b,c. (b) Specific heat capacity c and hence entropy change ΔS₂₃₀ with respect to absolute entropy at 230 K. (c) Relative dielectric constant ε and tan δ.

Electrical polarization loops for our clamped sample were noisy (figure 2), but below T_C it is possible to discern that the low-field rise in P is followed by a further step near E∼200 kV cm⁻¹, perhaps seen better in plots of |P(T)| (figure 3a) that were obtained every E∼5 kV cm⁻¹ by spline fitting to data from all 276 P(E) loops (selected spline fits appear in figure 4). This further step in P(E) is associated with ferrielectric sublattice switching, yielding triple loops that were clearly resolved in fig. 1b of [18]. Above T_C, the high-field step can also be detected, but it is not preceded by the low-field rise in P, implying the double loop associated with driving a transition above T_C [23,25,26].

Figure 2.

Electrical polarization P versus electric field E for AS, on cooling.

Figure 3.

EC properties of AS. (a) |P(E,T)| obtained from upper (E>0) and lower (E<0) branches of approximately 350 P(E) loops, some of which are shown in figure 2. (b) The resulting plot of |(∂P/∂T)|_E. (c) Isothermal entropy change |ΔS(E,T)| deduced from (b) using Maxwell relation (∂S/∂E)_T=(∂P/∂T)_E.

Figure 4.

EC properties of AS plotted in the traditional manner. The information presented in figure 3 is replotted here, for selected values of field E. In (a), we show data (black curves) along with the corresponding spline fits.

In order to quantify EC effects in our clamped sample of AS, we first used our smoothed |P(T,E)| dataset (figure 3a) to obtain |(∂P/∂T)_E| in (E,T) space (figure 3b). From these data, we obtained the isothermal entropy change (figure 3c) due to the application or removal of field E, using Maxwell relation (∂S/∂E)_T=(∂P/∂T)_E and density 1.770 g cm⁻³ [27]. We see that large EC effects with a peak value of |ΔS|∼30 J K⁻¹ kg⁻¹ may be driven by |ΔE|=400 kV cm⁻¹ in an approximately 5 K temperature range.

4. Discussion

The EC effects that we have observed near the first-order transition in ferrielectric AS were conventional, but inverse EC effects are expected at lower temperatures, given that further cooling implies further ferrielectric ordering [19] and thus a fall of spontaneous polarization [20], not seen in our narrow temperature range of measurement. The maximum applied field of 400 kV cm⁻¹ is large for a sample thickness of 50 μm: it is far larger than all fields previously applied to AS [14,18,28], larger than the 105 kV cm⁻¹ that could be applied across a 38 μm-thick ceramic film [29], and comparable with the fields used to achieve large EC effects in sub-micrometre-thick ceramic films.

The mass-normalized EC effects of |ΔS|∼30 J K⁻¹ kg⁻¹ in our 50 μm-thick sample are only by a small factor smaller than those seen in much thinner micrometre-thick polymer films of similar density [5,6], where |ΔS|∼60–130 J K⁻¹ kg⁻¹ [21]. This implies an order-of-magnitude improvement in the entropy change for a given sample. Moreover, our mass-normalized EC effects are somewhat larger than the typical range of values obtained for bulk and thin-film ceramics, where |ΔS|∼1–10 J K⁻¹ kg⁻¹ [21]. Alternatively, we may note that the corresponding volume-normalized entropy change of 53 kJ K⁻¹ m⁻³ exceeds the typical values for bulk ceramics by a small factor and is comparable with the values obtained for thin ceramic films [21].

In order to convert our maximum isothermal entropy change |ΔS| into an adiabatic temperature change |ΔT| for our clamped sample of AS, we cannot use the heat capacity c(T) data for unclamped AS (figure 1b) to construct adiabats [23,26]. However, AS powder possesses a 7 K transition width that is similar to the 5 K transition width for our clamped crystal and therefore we may use the powder value of c=1.2 kJ K⁻¹ kg⁻¹ at 223 K to deduce |ΔT|=5.6 K for our clamped crystal.

A better estimate of |ΔT| may be obtained via the Clausius–Clapeyron equation for the gradient dE/dT₀=−ρΔS₀/ΔP₀ of the first-order phase boundary in (E,T) space, where the small value of |ΔP₀|∼1 μC cm⁻² (figure 3a) and the large value of |ΔS₀|∼50 J K⁻¹ kg⁻¹ (figure 1b) represent the changes of polarization and entropy across the full transition. The large resulting value of vastly exceeds the 1 kV cm⁻¹ K⁻¹ obtained for PbSc_0.5Ta_0.5O₃ with larger |ΔP₀|∼25 μC cm⁻² and smaller [23]; it is slightly larger than the 38 kV cm⁻¹ K⁻¹ that we tentatively read from the short phase boundary that changes by approximately 150 kV cm⁻¹ in approximately 4 K (figure 3a) and implies that our 400 kV cm⁻¹ field change should shift transition temperature T₀ by 4.5 K. This shift corresponds directly to an adiabatic temperature change |ΔT|=4.5 K of the same order of magnitude as the 5.6 K deduced in the previous paragraph.

5. Summary

We have reported large EC effects of |ΔS|=30 J K⁻¹ kg⁻¹ and |ΔT|=4.5 K when applying 400 kV cm⁻¹ to a 50 μm-thick single crystal of AS, whose transition width was smeared by clamping from approximately 2 K (figure 1b) to approximately 5 K (figure 3). As discussed above, the mass-normalized entropy change reported here is only a small factor less than the values reported for much thinner polymer films and it is larger than the values reported for bulk and thin-film ceramics.

In future, one might hope to achieve even larger EC effects in AS, given a value of for the first-order component of the transition in an unclamped sample (figure 1b). Alternatively, large entropy changes of |ΔS|=60 J K⁻¹ kg⁻¹ can be achieved at T=219 K by subjecting AS powder to changes of hydrostatic pressure [19]. Using the value of c=1.7 kJ K⁻¹ kg⁻¹ for the powder at this temperature implies a correspondingly large value of |ΔT|=(T/c)|ΔS|=8 K.

Overall, we have seen that the order–disorder nature of the ferrielectric transition in AS yields a large entropy change per sample. However, the large entropy change combined with the small ferrielectric polarization implies that large fields are required to achieve the large EC effects, as also seen for polymer films [5,6] by considering the field required to shift T₀ in the Clausius–Clapeyron equation dT₀/dE=−ΔP₀/ρΔS₀. In future, we hope that our findings will inspire EC studies in other order–disorder crystals, with enhanced values of |ΔP₀| and perhaps a value of |ΔS₀| that represents a compromise between EC effects ΔS and their strength ΔS/ΔE. It would also be attractive to develop cryogenic micro-thermometry and perform direct EC measurements.

Authors' contributions

The people we thank below in the Acknowledgements section fabricated the sample and performed the calorimetry. W.L. performed the X-ray diffraction. S.C. performed the electrical measurements, analysed the data and prepared the figures. S.C., X.M. and N.D.M. identified the context and significance of the work, and wrote the manuscript. All authors approved publication.

Competing interests

We declare we have no competing interests.

Funding

X.M. is grateful for support from the Royal Society. W.L. acknowledges financial support from NSFC (grant no. 21571072 and 61138006).