Giant barocaloric effects in sodium hexafluorophosphate and hexafluoroarsenate

Around 25% of global electricity consumption is already devoted to refrigeration technologies, both at the domestic and industrial levels.^1,2 Unfortunately, use of refrigeration is also responsible for around 7.8% of global greenhouse gas emissions and destruction of the ozone layer, which affects the environment.³ The search for environmentally friendly refrigeration technologies to replace traditional vapor-compression refrigeration is an inevitable trend in today's sustainable development requirements. Solid-state refrigeration technology based on caloric effects, which has no carbon emissions and high energy efficiency, has attracted extensive attention in recent years.^4,5 Solid-state phase transition caloric effects mainly include MagnetoCaloric Effects (MCEs),^6,7 ElectroCaloric Effects (ECEs),^8,9 elastoCaloric Effects (eCEs),^10,11 and BaroCaloric Effects (BCEs).^12–16 The first three originate from the modulation of the magnetic moment, the ferroelectric polarization, or the ordering of the crystal structure domains in ferroics by the corresponding external fields, while the latter often involves the pressure-induced phase transitions in the crystal structure.

BCEs have been found in a wide variety of systems including plastic crystals,^12,13 hybrid organic–inorganic compounds,^17–19 inorganic plastic crystals,^14,15,20 thermoelectrics,²¹ ferroelectrics,²² ferroelastics,²³ frustrated antiferromagnet,²⁴ charge-transfer oxide,²⁵ spin-crossover complexes,^26,27 materials with metal-to-insulator transitions,²⁸ liquid–solid-transition n-alkanes,²⁹ and so forth. The discovery of colossal BCEs in plastic crystals paves a new route to barocaloric refrigeration.^12–15 They usually possess small driving pressures as well as large entropy changes due to giant compressibility, extensive molecular orientational disorder, and highly anharmonic lattice dynamics of these materials.¹² However, limitations for the applicability of these plastic crystals are low density, relatively large hysteresis, and low thermal conductivities caused by the strong disorder in plastic crystals.³⁰ The phase transition temperature varying with pressure (dT_t/dP) is about 100 K GPa⁻¹ for plastic crystals.³⁰ Currently, as barocaloric refrigeration is still under development, it is important to find more barocaloric materials with excellent properties.³¹ 

In the present study, we report two inorganic plastic crystals NaPF₆ and NaAsF₆ with giant BCEs. We have determined the low-temperature phase structure of NaPF₆ is a rhombohedral structure with space group $R 3 ¯$ by neutron powder diffraction (NPD). The phase transition temperature varies with pressure at a rate of dT_t/dP 250 and 310 K GPa⁻¹ for NaPF₆ and NaAsF₆. For the cubic-to-rhombohedral phase transition, NaAsF₆ is more sensitive to pressure than NaPF₆. The pressure-induced entropy changes of NaPF₆ and NaAsF₆ are approximately 45.2 and 35.6 J kg⁻¹ K⁻¹, respectively. The saturation drive pressure is 40 MPa. We further study the relationship between the structural and thermal properties, which will contribute to the discovery of higher-performing barocaloric materials in the future.

Polycrystalline NaPF₆ (purity of 98%) samples were purchased from Sigma Aldrich. Polycrystalline NaAsF₆ (purity of 98%) samples were purchased from Macklin.

The sample was pelletized and put into high-pressure Hastelloy cells. The heat flow data were collected using a differential scanning calorimeter (DSC) (μDSC 7 evo, Setaram) under 0.1, 20, 40, 60, 80, and 100 MPa. The rate of temperature change is 1 K min⁻¹. Details have been published elsewhere.¹² 

NPD experiments were performed on the polycrystalline NaPF₆ powder using the general purpose powder diffractometer (GPPD) of China Spallation Neutron Source (CSNS) in Dongguan, China.³² The best resolution Δd/d will be better than 0.2% at a high angle detector bank. The sample was loaded into a vanadium can, and the NPD pattern was collected with a wavelength range from 0.1 to 4.9 Å under vacuum conditions at temperatures of 240 and 300 K. Pressure-dependent NPD experiments were performed on the polycrystalline NaPF₆ powder using the powder diffractometer, which specializes in high-pressure experiments, BL11 PLANET of J-PARC in Japan.³³ The resolution Δd/d is approximately 0.5%. In the experiments, we used a piston cylinder cell made of CuBe. Two plates of Pb are placed at the bottom of the cell as a pressure marker.³⁴ We chose a combination of pressure conditions (∼0.1 and 400 MPa) and temperature conditions (250 and 297 K). Rietveld refinement was used to analyze crystal structures by GSAS.^35,36

Temperature-variable x-ray diffraction (XRD) patterns of NaPF₆ were collected by using an x-ray diffractometer (D8 Advance, Bruker) with Cu-Kα₁ radiation (λ = 1.5406 Å). The accuracy in peak positions (2 Theta) is about 0.01°. The measurements were performed at 230, 240, 250, 260, 270, 280, 290, 300, 310, and 320 K after keeping for 10 min. All patterns were analyzed with Le Bail refinement using the program Fullprof_Suite.³⁷ Temperature-variable XRD patterns of NaAsF₆ were collected by using an x-ray diffractometer (Smartlab, Rigaku) with Cu-Kα₁ radiation (λ = 1.5406 Å). The accuracy in peak positions (2 Theta) is approximately 0.01°. The measurements were performed at 300, 310, 320, 330, 340, 360, and 380 K after keeping for 10 min. All patterns were analyzed with Rietveld refinement method using the program Fullprof_Suite.³⁷ 

The Raman spectra at various temperatures were acquired on the Raman spectrometer (LabRAM HR Evolution, HORIBA Jobin Yvon) with a wavelength of 532 nm. The spectral resolution is about 0.6 cm⁻¹. We pressed the sample into the block. Raman spectra were collected at a constant temperature on heating from 240 to 330 K with 10 K as the step, and NaAsF₆ samples were collected at a constant temperature on heating from 290 to 360 K with 10 K as the step. Every constant-temperature scan was carried out for 10 min under ambient pressure.

The experimental pressure-induced temperature changes were measured on the VX3 Paris–Edinburgh press with a K-typed thermocouple at room temperature.^13,15,42 A few drops of silicon oil were added to the sample to make the pressure received by the sample more uniform. Practical temperature as a function of time (T–t) is recorded in the cycle of pre-pressurization (from 0.1 to 15 MPa), pressurization (from 15 to 300 MPa), and de-pressurization (from 300 to 0.1 MPa).

It is known that NaPF₆ crystallizes in a cubic structure, space group $Fm 3 ¯m$ with an eightfold disorder of the anions at room temperature.^43,44 Shown in Fig. 1(a) is the NPD patterns for the cubic phase. Refined parameters of the cubic cell are a = 7.603 553(35) Å at 300 K. As we can see from Fig. 1(b), each F-atom has eight possible placeholders in the cubic phase by the VESTA program.⁴⁵ The crystal structure of NaPF₆ at low temperatures has not been determined, but it was assumed that the unit cell is a trigonally distorted body-centered cube.⁴⁶ However, we first obtained its crystal structure and space group at low temperatures by refining the NPD pattern. NaPF₆ at low temperatures crystallizes in a rhombohedral structure with space group $R 3 ¯$⁠. Refined parameters of the rhombohedral cell are a = 5.165 74(4) Å, c = 13.531 62(18) Å, and γ = 120°. Figure 1(c) is the NPD patterns for the rhombohedral phase at 240 K. Figure 1(d) is the NaPF₆ crystal structure at 240 K and there is not a disorder. Figure 1(e) is the contour plot of the temperature-dependent x-ray powder diffraction (XRPD) patterns from 230 to 320 K with 10 K as the step. The temperature-dependent XRPD measurements are consistent with the previous thermal test that there is a first-order phase transition at about 280 K.⁴⁴ The XRPD patterns at each temperature were refined by Le Bail refinement using the FullProf_Suite program to obtain the cell parameters.³⁷  Figure 1(f) is the variation of the unit cell volume per formula (V) as the temperature increases. There is a zone of coexistence of the cubic and rhombohedral phases at 280 K, and $ΔV/V$ is 2.8%.

After determining the temperature-induced structural phase transition, we study lattice dynamics as a function of temperature. Figure 2(a) is the temperature-dependent Raman scattering spectra which exhibit a significant phase transition with increasing temperature. The cubic and rhombohedral phases of NaPF₆ are the same as those of NaSbF₆ and CaZrF₆, so the Raman spectra that it produces are similar.^47,48 There are also three Raman active vibration modes in NaPF₆, which are named F_2g, E_g, and A_1g modes corresponding to three peaks located near 470, 580, and 760 cm⁻¹, respectively.^44,47,48 The biggest difference is that the rhombohedral phase has two peaks located near 470 cm⁻¹, while the cubic phase has one. The Raman spectrum of polycrystalline NaPF₆ at room temperature displays the A_1g mode (symmetric stretching) as the most intense vibration located at 760 cm⁻¹, the E_g mode (asymmetric stretching) as the weakest vibration located at 580 cm⁻¹, and the F_2g mode (bending) as the medium intensity vibration located at 470 cm⁻¹. The F_2g mode is the bending vibrations of fluorine atoms perpendicular to the linear Na−F−P bonds resulting in the twisting of the PF₆⁻ octahedra. As shown in Fig. 2(b), the very small splitting of F_2g implies that there are two kinds of different bending vibrations of fluorine atoms at the rhombohedral phase in NaPF₆. Figure 2(c) is the temperature-dependent vibrational frequency of the A_1g mode. The vibrations within the cubic phase are redshifted as the temperature increases. In the rhombohedral phase with increasing temperature, however, there is a blueshift. Note that there is a marked blueshift for the A_1g mode at the rhombohedral-to-cubic phase transition. Figure 2(d) is the PDOS up to 150 meV at 240 and 300 K under ambient pressure. There are many smaller peaks on the larger main peak (∼20 meV) at 240 K. Still, they gradually disappear at 300 K. The peak around 30 meV is also much wider at 300 K. As the temperature increases, the phonons are very noticeably redshifted. There is a broadening of the peaks. This indicates the presence of strong lattice anharmonicity in NaPF₆.

Here, the isothermal entropy change $| Δ S rev|$ is about 45.2 J kg⁻¹ K⁻¹ under 100 MPa and the specific heat capacity C_p is about 930 J kg⁻¹ K⁻¹,⁵¹ so the adiabatic temperature change ΔT_ad is approximately 14 K. Due to the poor thermal insulation performance of the experimental equipment, the value of the practical ΔT_ad (9 K) is smaller than the calculated one (14 K). For adiabatic temperature change testing, this is a situation that seems to be very normal and common.^13,15,52

To verify the pressure-induced phase transition, we conducted the pressure-dependent NPD measurements (Fig. 4). When the applied pressure is about 400 MPa, the crystal structure is the rhombohedral phase, which is the same as at low temperatures. We are, therefore, confident that pressure can induce the onset of phase transition.

It is known that there are plenty of compounds undergoing a variety of phase transitions around room temperature in the A^IM^VF₆ family.^53,54 As one more example, we also found the giant barocaloric effect in its sister system NaAsF₆. Figure 5(a) is the contour plot of the temperature-dependent XRPD patterns of NaAsF₆ from 300 to 380 K. There is a first-order phase transition at about 327 K, which is consistent with the previous calorimetry data.⁵⁵ The XRPD patterns at each temperature were refined by Rietveld refinement to obtain the cell parameters.³⁷  Figure 5(b) is the variation of the unit cell volume per formula (V) as the temperature increases for NaAsF₆. There is also a zone of coexistence of the cubic and rhombohedral phases at 330 K, and $ΔV/V$ is 3.5%. Figure 5(c) is the temperature-dependent Raman scattering spectra for NaAsF₆. There are also three Raman active vibration modes (F_2g, E_g, and A_1g) in NaAsF₆, which correspond to three peaks located near 370, 585, and 700 cm⁻¹, respectively. Although the splitting of its F_2g mode is not obvious in the rhombohedral phase, we can see that the peak is not very symmetrical. This means that there are at least two peaks here, which is just like NaPF₆. Figure 5(d) is the temperature-dependent vibrational frequency of the A_1g mode for NaAsF₆. We also found that there is a marked blueshift for the A_1g mode when the rhombohedral phase transforms into the cubic phase in NaAsF₆. Figure 5(e) is the phase diagram for NaAsF₆, which is constructed based on the pressure dependence of T_t. The dT_t/dP slope is 313 K GPa⁻¹ on heating (pink) and 324.07 K GPa⁻¹ on cooling (blue) for NaPF₆, respectively. For the cubic-to-rhombohedral phase transition, NaAsF₆ is more sensitive to pressure than NaPF₆. The diameter of the As⁵⁺ cation is larger than that of the P⁵⁺ cation, which leads to a large cell parameter in NaAsF₆ and, thus, twisting of the anionic octahedron during the phase transition is easier.⁵¹ Due to the volume change $Δ V t$ (1.16 × 10⁻⁵ m³ kg⁻¹) at the phase transition, the calculated entropy change $Δ S t$ is about 37 J kg⁻¹ K⁻¹ for the rhombohedral-to-cubic phase transition for NaAsF₆. Figure 5(f) shows the pressure-induced entropy changes at different pressures. As we can see from this figure, $Δ S P 0 → P max$ is 35.6 J kg⁻¹ K⁻¹. When the pressure reaches 40 MPa, the pressure-induced entropy changes have reached its maximum value. The calculated 37 J kg⁻¹ K⁻¹ (ΔS_t) is highly consistent with the value of 35.6 J kg⁻¹ K⁻¹ $( Δ S P 0 → P max)$⁠. For NaAsF₆, $δ T FWHM$ is 31.0 K and $Δ S P 0 → P max$ is 35.6 J kg⁻¹ K⁻¹ at 100 MPa, so the RCP is about 1104 J kg⁻¹. As the M^V atomic number increases, the compounds may have an increasing rate of change in volume and become more sensitive to pressure.

To summarize, we have determined the low-temperature phase structure of NaPF₆ is a rhombohedral structure with space group $R 3 ¯$ by NPD. There are three Raman active vibration modes in NaPF₆ and NaAsF₆, which are named F_2g, E_g, and A_1g modes. There is a marked blueshift for the A_1g mode at the rhombohedral-to-cubic phase transition. The phase transition temperature varies with pressure at a rate of dT_t/dP 250 and 310 K GPa⁻¹ for NaPF₆ and NaAsF₆. For the cubic-to-rhombohedral phase transition, NaAsF₆ is more sensitive to pressure than NaPF₆. The diameter of the As⁵⁺ cation is larger than that of the P⁵⁺ cation, which leads to a large cell parameter in NaAsF₆ and, thus, the twisting of the anionic octahedron during the phase transition is easier. The pressure-induced entropy changes of NaPF₆ and NaAsF₆ are around 45.2 and 35.6 J kg⁻¹ K⁻¹, respectively. The saturation drive pressure is 40 MPa. The experimental adiabatic temperature change is 9 K for NaPF₆. The pressure-dependent NPD establishes a pressure that can induce the phase transition to take place. We further study the relationship between the structural and thermal properties, which will contribute to the discovery of higher-performing barocaloric materials in the future.

The supplementary material contains figures of NaPF6 and NaAsF6 XRPD refinement data; figures of NaAsF6 heat flow Q(P,T) under different pressures; table of NaPF6 lattice parameters at different temperatures and pressures; and table of structural information of phase transition on AIMVF6.

This work was supported by the Ministry of Science and Technology of China (Grant Nos. 2022YFE0109900 and 2021YFB3501201), the Key Research Program of Frontier Sciences of Chinese Academy of Sciences (Grant No. ZDBS-LY-JSC002), the International Partner Program of Chinese Academy of Sciences (Grant No. 174321KYSB20200008), the IMR Innovation Fund, the CSNS Consortium on High-performance Materials of Chinese Academy of Sciences, the Young Innovation Talent Program of Shenyang (Grant No. RC210435), and the National Natural Science Foundation of China (NNSFC) (Grant Nos. 11934007 and 11804346). We also acknowledge the beam time provided by ANSTO (Proposal Nos. 7867 and IC8021), GPPD (Proposal No. P1820033000002), and J-PARC (No. 2018I0011).

The authors have no conflicts to disclose.

Zhao Zhang: Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Takanori Hattori: Data curation (equal); Formal analysis (equal). Ruiqi Song: Formal analysis (equal); Investigation (equal); Methodology (equal). Dehong Yu: Formal analysis (equal); Investigation (equal). Richard Mole: Formal analysis (equal); Investigation (equal). Jie Chen: Investigation (equal); Methodology (equal). Lunhua He: Investigation (equal); Methodology (equal). Zhidong Zhang: Supervision (equal). Bing Li: Conceptualization (lead); Supervision (equal); Writing – review & editing (equal).

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