Giant adiabatic temperature change and its direct measurement of a barocaloric effect in a charge-transfer solid

Solid refrigerants exhibiting a caloric effect upon applying external stimuli are receiving attention as one of the next-generation refrigeration technologies. Herein, we report a new inorganic refrigerant, rubidium cyano-bridged manganese–iron–cobalt ternary metal assembly (cyano-RbMnFeCo). Cyano-RbMnFeCo shows a reversible barocaloric effect with large reversible adiabatic temperature changes of 74 K (from 57 °C to −17 °C) at 340 MPa, and 85 K (from 88 °C to 3 °C) at 560 MPa. Such large reversible adiabatic temperature changes have yet to be reported among caloric effects in solid–solid phase transition refrigerants. The reversible refrigerant capacity is 26000 J kg−1 and the temperature window is 142 K. Additionally, cyano-RbMnFeCo shows barocaloric effects even at low pressures, e.g., reversible adiabatic temperature change is 21 K at 90 MPa. Furthermore, direct measurement of the temperature change using a thermocouple shows +44 K by applying pressure. The temperature increase and decrease upon pressure application and release are repeated over 100 cycles without any degradation of the performance. This material series also possesses a high thermal conductivity value of 20.4 W m−1 K−1. The present barocaloric material may realize a high-efficiency solid refrigerant.

1.In the abstract, as well as on pages 9, 11, and 12, the authors assert that the adiabatic temperature change and the refrigerant capacity in cyano-RbMnFeCo are the largest among all caloric effects (or a word record).This claim does not hold true.For cyano-RbMnFeCo, an adiabatic temperature change of 44 K can be induced by a pressure of 440 MPa.In reference 26, a temperature change of 57 K is achieved with only 400 MPa for n-alkanes.Furthermore, in terms of refrigerant capacity, cyano-RbMnFeCo is not superior to n-alkanes.For instance, for cyano-RbMnFeCo, the refrigerant capacity is 26000 Jkg<sup>-1</sup> at 560 MPa.But for n-alkane (C18H38), due to the high reversible entropy change (about 700 Jkg<sup>K-1</sup>), only 232 MPa can lead to such a refrigerant capacity.So, the related sentences should be rewritten.Besides, the size of the applied pressure should be mentioned along with the values of directly measured adiabatic temperature and the refrigerant capacity.
2. On page 3, references 42-44 are cited to support the notion that metal-insulator transition (MIT) materials may exhibit a significant reversible barocaloric effect.However, these references do not pertain to the barocaloric effect specifically.Instead, Hexagonal nickel-iron sulfide, a typical MIT compound, that has been reported to show giant barocaloric effect (Mater. Horiz., 2020，7，2690-2695).
3. Cyano-RbMnFeCo displays large thermal hysteresis which increases at higher pressures, which was reproduced by SD calculations on page 7. But, the underlying reason behind such remarkable changes in thermal hysteresis with pressure remains unclear.Therefore, further discussions are desired.
4. On page 10, a uniaxial pressure was utilized to measure the adiabatic temperature changes.However, the use of uniaxial pressure differs significantly from hydraulic pressure particularly when applied to inorganic compounds.The possible effects of these different pressure loadings on the adiabatic temperature should be discussed.
5. On page 11 and in Fig. S11, it is observed that as the starting temperature approaches -15℃, the application of pressure results in a significantly larger increase in temperature compared to the decrease in temperature upon releasing the same pressure.However, this asymmetric behavior is not evident when the starting temperature approaches 77℃.How to understand this? 6.On page 13, the comparison of thermal conductivity between cyano-RbMnFeCo and Al2O3 is not so meaningful because Al2O3 is not typically considered a high-thermalconductivity material.7. Page 13, it is claimed that the refrigerant volume of solid cyano-RbMnFeCo may be reduced to 1-2% compared with current gaseous refrigerants.Additional discussion and supporting data are necessary to substantiate this claim.
8. what does the asterisk in the XRD pattern (Fig. 1b and 1e) represent for?

Reviewer #3 (Remarks to the Author):
The authors present a study on the barocaloric effect in the Prussian blue analogue ((cyano-RbMnFeCo) showing the charge transfer process.The applications of molecular magnets in magnetic refrigeration were considered for many years, mainly in the sub-Kelvin temperatures range.The presented paper shows, that molecular magnetic materials can be also considered as a room-temperature coolers and can open a new perspective on molecular magnet applications.In general, the presented paper shows excellent results, supported by the deep data analysis and what is most important, the direct measurements of the temperature change using a self-constructed system based on thermocouples.The work is clear and the outcome could be interesting for the community.In my opinion, this paper is suitable for publication in the Journal of Nature Communications.A few minor comments should be addressed: -The reason for choosing RbMn{[Fe(CN)6]0.92[Co(CN)6]0.08}ꞏ0.3H2Oinstead of pure RbMnFe network is unclear.What is the advantage of Co ions in this system?-The "Methods" section is incomplete-some of the techniques are not described while the paragraph materials cost is not necessary and should be sifted to SI or Introduction.
-The paper will be even better if include the study of pressure-dependent PXRD studies

Response to Reviewer 1
We greatly appreciate your constructive comments.Below is our response to each of your comments.
Comment 1.In abstract "gaseous refrigerants negatively impact the environment and contribute to global warming" is not rigorous, the absolute certain tone used here is not appropriate.
Answer 1.This sentence was written in the Introduction section.As per the reviewer's comment, this sentence was removed.
Comment 2. There's redundancy in the abstract.
Answer 2. The abstract is revised as follows: Revised Abstract: Solid refrigerants exhibiting a caloric effect upon applying external stimuli are receiving attention as one of the next-generation refrigeration technologies.Herein, we report a new inorganic refrigerant, rubidium cyano-bridged manganese-iron-cobalt ternary metal assembly (cyano-RbMnFeCo).Cyano-RbMnFeCo shows a reversible barocaloric effect with large reversible adiabatic temperature changes (|∆Tad,rev|) of 74 K (from 57 ℃ to −17 ℃) at 340 MPa, and 85 K (from 88 ℃ to 3 ℃) at 560 MPa.Such large |∆Tad,rev| values have yet to be reported among caloric effects in solid-solid phase transition refrigerants.The reversible refrigerant capacity (RCrev) is 26000 J kg −1 and the temperature window (Tspan,rev) is 142 K. Additionally, cyano-RbMnFeCo shows barocaloric effects even at low pressures, e.g., |∆Tad,rev| = 21 K at 90 MPa.Furthermore, direct measurement of the temperature change (∆Tobs) using a thermocouple shows ∆Tobs = +44 K by applying pressure.The temperature increase and decrease upon pressure application and release are repeated over 100 cycles without any degradation of the ∆Tobs performance.This material series also possesses a high thermal conductivity value of 20.4 W m −1 K −1 .The present barocaloric material may realize a high-efficiency solid refrigerant.Answer 4. Thank you for this insightful comment.We thoroughly checked the conditions of the variable-temperature PXRD (VT-PXRD) measurement and found a discrepancy between the sample temperature and the temperature of the thermometer at the sample holder, which is attributed to an insufficient vacuum level inside the cryostat.In the revised manuscript, we remeasured the VT-PXRD data under a high vacuum level of 2.4×10 −4 Pa (Fig. A1).The transition temperatures agreed well with those obtained from the magnetic measurements.In the revised manuscript, Fig. S3 in the Supplementary Information is updated with the remeasured data.Comment 5. Explain the lab made heater and time it takes to transfer the pressure cell.
Answer 5. Detailed explanation of the procedure for sample heating above 400 K is as follows.The pressure cell with cyano-RbMnFeCo (Fig. A2a) was put in a glass tube along with a thermometer.Then the cell was heated in an oil bath (Fig. A2b).Once the desired temperature was reached, the pressure cell was transferred from the lab-made heater to the SQUID device in 20 s (Fig. A2c). Figure A2d shows the decay of the temperature versus time plot during this transfer, which is expressed as T = 433 + 39 exp(−t/30).Here, t is time in seconds.For example, when the sample was heated to 473 K in the labmade heater, the sample temperature after 20 s of transfer from the lab-made heater to the SQUID magnetometer was 453 K. Then the measurement started after the sample was cooled in the SQUID device to 400 K, which is the upper temperature limit of SQUID.Cooling took about 10 min.A detailed explanation is added to the revised Supplementary Information.Obs.

HT phase LT phase
Far-IR spectrum Symmetric bending and asymmetric bending modes of Fe-C≡N-Mn Comment 7. The thermocouple measurement is interesting but could be problematic due to unknown/unexpected signals could come from uniaxial pressure.In order to prove its feasibility calibration experiment needs to be carried out to the thermocouple.Answer 7. Thank you for the insightful comment.The calibration temperature in response to pressure is 0.101 ± 0.003 K per 100 MPa.In the revised manuscript, the ΔTobs values from the direct measurement experiment were calibrated.This is mentioned in the revised Supplementary Information.

Supplementary Information, Page S8, Right column:
Calibration for the temperature deviation by pressure: 0.101±0.003K per 100 MPa

Response to Reviewer 2
We greatly appreciate your constructive comments and suggestions to improve our manuscript.Below are our responses to each of your comments and an outline of the revisions to our manuscript.

Comment 0.
The barocaloric effect has the potential to be utilized for environmentally friendly refrigeration.In this study, the authors present a novel inorganic barocaloric refrigerant, cyano-RbMnFeCo.Comprehensive experimental and theoretical investigations were conducted to assess the barocaloric performance of cyano-RbMnFeCo and elucidate its underlying mechanism.Notably, this compound exhibits several advantages compared to previously reported barocaloric materials, including a wide operating temperature range, relatively high thermal conductivity, and large barocaloric coefficient.Therefore, I recommend its publication in Nature Communications.However, certain aspects need to be addressed.Answer 0. We appreciate the reviewer's high evaluation of our work.Below are the answers to each of your comments.
Comment 1.In the abstract, as well as on pages 9, 11, and 12, the authors assert that the adiabatic temperature change and the refrigerant capacity in cyano-RbMnFeCo are the largest among all caloric effects (or a world record).This claim does not hold true.For cyano-RbMnFeCo, an adiabatic temperature change of 44 K can be induced by a pressure of 440 MPa.In reference 26, a temperature change of 57 K is achieved with only 400 MPa for n-alkanes.Furthermore, in terms of refrigerant capacity, cyano-RbMnFeCo is not superior to n-alkanes.For instance, for cyano-RbMnFeCo, the refrigerant capacity is 26000 J kg −1 at 560 MPa.But for n-alkane (C18H38), due to the high reversible entropy change (about 700 J kg K −1 ), only 232 MPa can lead to such a refrigerant capacity.So, the related sentences should be rewritten.Besides, the size of the applied pressure should be mentioned along with the values of directly measured adiabatic temperature and the refrigerant capacity.
Answer 1.As the reviewer has pointed out, n-alkane, which exhibits a solid-liquid phase transition, shows a good barocaloric performance.On the other hand, since the present study focuses on "solid refrigerants due to solid-solid phase transition", which does not accompany pressure-induced melting, we have revised the manuscript to make this point clear to the readers.As for the reviewer's additional comment on the applied pressure in the direct measurement on the temperature change, we added the information in Figure 5  Comment 2. On page 3, references 42-44 are cited to support the notion that metal-insulator transition (MIT) materials may exhibit a significant reversible barocaloric effect.However, these references do not pertain to the barocaloric effect specifically.Instead, Hexagonal nickel-iron sulfide, a typical MIT compound, that has been reported to show giant barocaloric effect (Mater. Horiz., 2020, 7, 2690-2695).
Answer 2. Thank you for your suggestion.The revised manuscript cites the literature on hexagonal nickel-iron sulfide as a typical MIT compound displaying a barocaloric effect.
Comment 3. Cyano-RbMnFeCo displays large thermal hysteresis which increases at higher pressures, which was reproduced by SD calculations on page 7. But, the underlying reason behind such remarkable changes in thermal hysteresis with pressure remains unclear.Therefore, further discussions are desired.
Answer 3. To understand the influence of the applied pressure on the changes in the thermal hysteresis, we discuss using the interaction parameter γ in the Slichter-Drickamer (SD) model.The γ parameter is interpreted as the interface stress between the HT and LT domains inside the crystal (Fig. A4).One of the reasons for the changes of the thermal hysteresis is considered as follows.The transition temperature shifts to higher temperatures upon applying external pressure, increasing the volume difference between the HT and LT phases.The increase in the volume difference induces a larger mismatch between the HT and LT phase domains, which is expected to enhance the surface stress at the domain interface.When 560 MPa pressure is applied, the volume difference should increase by 1.5% compared to that under atmospheric pressure due to the increased transition temperature.
The γ value plot and the explanation are added to the Supplementary Information as Figure S8.
Comment 4. On page 10, a uniaxial pressure was utilized to measure the adiabatic temperature changes.
However, the use of uniaxial pressure differs significantly from hydraulic pressure particularly when applied to inorganic compounds.The possible effects of these different pressure loadings on the adiabatic temperature should be discussed.
Answer 4. Because the current measurement is performed using randomly oriented powder samples, and the pressure is applied to the crystal from all directions, the present experiment is considered to be applying a pseudo-hydrostatic pressure.In the case of cyano-RbMnFeCo with a cubic crystal structure, an anisotropic barocaloric effect is expected to occur between the [100], [110], and [111] directions.For example, in the field of superconducting materials, superconducting properties are tuned by changing the direction of the uniaxial pressure.If a large single crystal of the present material can be prepared, then the barocaloric effect may be activated at lower pressures by selecting a specific crystallographic direction for the uniaxial pressure.This information is added to the main text in the revised manuscript.
Page 13, Line 16: Furthermore, if a large single crystal is realized in the future, the barocaloric effect may be activated at lower pressures by selecting a specific crystallographic direction for the pressure application.

Response to Reviewer 3
We greatly appreciate your constructive comments and suggestions to improve our manuscript.Below are our responses to each of your comments and an outline of the revisions to our manuscript.Comment 2. The "Methods" section is incomplete-some of the techniques are not described while the paragraph materials cost is not necessary and should be shifted to SI or Introduction.
Answer 2. Thank you for this insightful comment.We revised the Methods section to include the technical details.The explanation of the material cost was moved from the Methods section to the Supplementary Information.
Methods, Page 14, Line 10: Elemental analyses were performed using a standard microanalytical method and an inductively coupled plasma mass spectrometer (ICP-MS, Agilent 7700x).
We greatly appreciate your constructive comments.Below is our response to your comment.
Comment 1.Most of my concerns in previous review are addressed, my only comment would be checking some of the results using synchrotron and neutrons, the long waiting time is not a very good excuse for such studies, but overall this manuscript worths be published on nature comm.
Answer 1.We greatly appreciate your comments and your evaluation.We are now making a plan for synchrotron and neutron measurements in the future.

Response to Reviewer 2
We greatly appreciate your constructive comments.Below is our response to your comment.
Comment 1.The authors have addressed most of my concerns.However, one more modification is needed.In the response to my comment 4, the authors added a sentence in the revised manuscript about the barocaloric effect of single crystal sample.This is misleading because hydraulic pressure means pressing the sample from all directions.So, none direction can be selected to apply hydraulic pressure even if a single crystal is available.It is better to remove that sentence.
Answer 1.We agree that hydraulic pressure is different from applying uniaxial pressure to randomly oriented powder sample.According to the reviewer's suggestion, we removed the corresponding sentence (Page 13, Line 16 in the previous manuscript).

Response to Reviewer 3
We greatly appreciate your constructive comments.Below is our response to your comment.
Comment 1.The manuscript's authors have revised their contribution and replied to the reviewers' comments.Now, in my opinion, the manuscript is suitable for publication in Nature Communications.
Answer 1.We greatly appreciate your comments and your evaluation.

Comment 3 .
No photos showing sample size of 3.6 ± 1.9 microns.Answer 3. We added the SEM image and particle size distribution as Fig.S1in the Supplementary Information.

Figure A1 .
Figure A1.Temperature dependence of the HT phase fraction obtained from the VT-PXRD measurement.

Figure A2 .
Figure A2.Details of the sample transfer from the lab-made heater to the SQUID magnetometer.a, Photograph and schematic illustration of the pressure cell containing the cyano-RbMnFeCo sample.b, Photograph of the lab-made heater.c, Photograph of placing the pressure cell into the SQUID magnetometer.d, Temperature versus time plot during the transfer of the pressure cell from the labmade heater to the SQUID device.Plot is fitted with an exponential decay.

Figure A3 .
Figure A3.Raman and Far-IR spectra of cyano-RbMnFe.a, Observed Raman spectrum of the LT phase.Pink shading indicates the peak attributed to the residual HT phase.b, Observed Raman spectrum of the HT phase.c, Calculated Raman spectrum of the LT phase.d, Calculated Raman spectrum of the HT phase.e, Observed far-IR spectrum of the LT phase at 100 K. f, Observed far-IR spectrum of the HT phase at 300 K. g, Calculated IR spectrum of the LT phase.h, Calculated IR spectrum of the HT phase.
Figure A3 of the revised manuscript.The corrections in the revised manuscript are as follows: Abstract, Page 2, Line 6: Such large |∆Tad,rev| values have yet to be reported among caloric effects in solid-solid phase transition refrigerants.Page 4, Line 4: These |∆Tad,rev| values are the largest reversible adiabatic temperature changes among caloric effects in solid-solid phase transition materials reported to date.Page 9, Line 3: The |∆Tad,rev| values of 59-85 K are the largest ones among the caloric effects in solidsolid phase transition refrigerants.Page 12, Line 5: The |∆Tad,rev|, Tspan,rev, and RCrev values are much larger than those previously reported for caloric effects in solid-solid phase transition refrigerants (Tables S3, S5, and S6).Page 12, Line 11: To date, such large ΔTobs values have yet to be directly measured in solid-solid phase transition materials, although pressure-induced solid-liquid transitions in n-alkanes (n = 16 and 18) have been reported to show a large temperature change of +57 K at 400 MPa 26 .

Figure A4 .
Figure A4.Schematic illustration of the phase transition process with internal stress within the crystal.

Figure A5 .Answer 6 .
Figure A5.Direct measurement of the temperature change using a thermocouple.Mapping of ∆Tobs on the entropy versus temperature curves.Black and orange shaded areas indicate the thermal hysteresis loops at 0.1 MPa and 490 MPa, respectively.Red and blue arrows indicate ∆Tobs upon applying and releasing pressure, respectively, for each starting temperature.

Figure 1b ,
Figure 1b, 1e legend: Asterisk indicates the peak from the silicon standard.

Comment 0 .
The authors present a study on the barocaloric effect in the Prussian blue analogue (cyano-RbMnFeCo) showing the charge transfer process.The applications of molecular magnets in magnetic refrigeration were considered for many years, mainly in the sub-Kelvin temperatures range.The presented paper shows, that molecular magnetic materials can be also considered as a room-temperature coolers and can open a new perspective on molecular magnet applications.In general, the presented paper shows excellent results, supported by the deep data analysis and what is most important, the direct measurements of the temperature change using a self-constructed system based on thermocouples.The work is clear and the outcome could be interesting for the community.In my opinion, this paper is suitable for publication in the Journal of Nature Communications.A few minor comments should be addressed: Answer 0. We appreciate the reviewer's high evaluation of our work.Below are the answers to each of your comments.Comment 1.The reason for choosing RbMn{[Fe(CN)6]0.92[Co(CN)6]0.08}•0.3H2Oinstead of pure RbMnFe network is unclear.What is the advantage of Co ions in this system?Answer 1.The T↑ value of the phase transition from the LT phase to the HT phase in pure RbMnFe network is 304 K (31 °C), which is above room temperature.Unfortunately, a system using a pure RbMnFe system network cannot be cooled below room temperature.To realize a barocaloric effect over a wide temperature range around room temperature, materials with lower phase transition temperatures are necessary.In the present work, we found that partially replacing [Fe(CN)6] with [Co(CN)6] can lower the phase transition temperature.Therefore, we used the Co-substituted sample in the present work.The revised manuscript contains this explanation.Page 11, Line 17: In cyano-RbMnFeCo, such a barocaloric effect is realized over a wide temperature range above and below room temperature because the phase transition temperature between the HT and LT phases are strategically adjusted by introducing Co ions.