Unveiling the key factor for the phase reconstruction and exsolved metallic particle distribution in perovskites

To significantly increase the amount of exsolved particles, the complete phase reconstruction from simple perovskite to Ruddlesden-Popper (R-P) perovskite is greatly desirable. However, a comprehensive understanding of key parameters affecting the phase reconstruction to R-P perovskite is still unexplored. Herein, we propose the Gibbs free energy for oxygen vacancy formation in Pr0.5(Ba/Sr)0.5TO3-δ (T = Mn, Fe, Co, and Ni) as the important factor in determining the type of phase reconstruction. Furthermore, using in-situ temperature & environment-controlled X-ray diffraction measurements, we report the phase diagram and optimum ‘x’ range required for the complete phase reconstruction to R-P perovskite in Pr0.5Ba0.5-xSrxFeO3-δ system. Among the Pr0.5Ba0.5-xSrxFeO3-δ, (Pr0.5Ba0.2Sr0.3)2FeO4+δ – Fe metal demonstrates the smallest size of exsolved Fe metal particles when the phase reconstruction occurs under reducing condition. The exsolved nano-Fe metal particles exhibit high particle density and are well-distributed on the perovskite surface, showing great catalytic activity in fuel cell and syngas production.

A comprehensive understanding of key parameters affecting the phase reconstruction from single perovskite to R-P perovskite is an interesting topic since most perovskite show phase reconstruction during reduction. But the main conclusion cannot be supported by the experimental results. This work is not suitable to be published in its present form in this journal. The questionable points are listed below.
This manuscript deals with studying the oxygen vacancy formation energies in perovskites as a potential descriptor for predicting the amount of exsolved metallic particles upon strong reduction of the material. To achieve as much exsolved metal particles as possible, the authors claim that complete phase reconstruction from simple to Ruddlesden-Popper perovskite is the most suitable pathway. Their approach is a combination of DFT calculations (to predict the most suitable composition for complete phase reconstruction) and in-situ X-ray diffraction (to map the phase diagram, where the observed phase evolution is plotted as a function of A-site doping). Furthermore, the material with the most promising exsolution behaviour is tested for its suitability as an SOFC electrode. The DFT and in-situ XRD part are sound and especially the obtained phase diagram is a strong result. However, what I completely missed is a discussion on why the oxygen vacancy formation enthalpy determines the phase transition behaviour. In this question, the reader is left entirely to his or her own thoughts, which should not be the case with a paper in Nature Communications. There definitely needs to be more detailed explanation and discussion before the paper can be recommended for publication. Moreover, I unfortunately have to say that the electrochemical part of the paper is rather poor and needs major revisions. I am sorry for this harsh judgement, since I principally like the approach of the authors, but there are yet too much flaws in the manuscript and I therefore recommend that it is reconsidered in a largely revised version. Detailed comments and criticism: • The definition of the enthalpy limits between the different phase regions given in Fig.1 is crucial for a correct prediction of exsolution behaviour, therefore it needs more discussion. Where do the values given as limits come from? This appears to be especially important, as three or four of the calculated values are quite close at these limits. Hence, slight shifts in the defined limits or small errors from the calculation may lead to wrong predictions. I suggest to compare the obtained oxygen vacancy formation enthalpies with several literature data. There is already quite some comparable data available -e.g. on (La,Sr)CoO3 or (La,Sr)MnO3 based materials. Moreover, quantitatively knowing the errors/uncertainties of the calculation results would be advantageous to being able judging the reliability of the calculated results. I am aware, that 2 commonly no errors are given for DFT results, since very often an accuracy of some 0.1eV is sufficient for supporting or disproving a hypothesis, which was gained by interpretation of experimental results. Here, however, the accuracy of the oxygen vacancy formation energies appears to be very important, since the DFT results are very close at the borderline that decides about which behaviour to expect. • Owing to my opinion several of the Figures from the supporting info should be moved to the main text. As far as I remember correctly, Nature Communications allows up to 7 display items. So there should be plenty of space available. • I do not agree with the fitting approach of the Fe XPS spectra. First of all, measuring only the Fe2p1/2 line provides not sufficient information for deciding the oxidation state of iron, since also the shake-up features between Fe2p1/2 and Fe2p3/2 peak need to be considered to draw such conclusions.
[1] Second, identification of Fe4+ only from XPS is daring -in perovskites for example, localisation of electron holes at the Fe-O molecular orbital is more likely as already confirmed by XAS experiments.
[2] • The electrical conductivity of an electrode material alone is not a suitable descriptor for predicting a good electrochemical behaviour. For a sufficiently thick 3D porous electrode with an electronic conductivity higher than the ionic conductivity -which appears to be the case for this material when looking at the relatively high values of total conductivity in Supp. Fig. 11 -the ionic conductivity and the surface reaction resistance are equally important, since the decay length of the electrochemical activity is √(Rreact/Rion). [3] • The chosen method is largely unsuitable for testing the electrochemical performance of the electrode material. The reason for this is that the performance of the electrolyte-supported SOFCs manufactured for this purpose is practically only limited by the ohmic resistance of the electrolyte in the investigated temperature range of 700-800°C. This can also be seen very clearly in the practically linear I-V characteristics (Figs. 4 and S14) at low to moderate current densities (the non-linearity at high current density points towards a concentration limitation). Especially at very low currents, the I-V-curves hardly show any discernible non-linearity, which could indicate an electrode polarisation limitation. This means that the high performance is mainly achieved either by a very good ion-conducting or comparatively thin LSGM electrolyte and therefore no quantitative statement about the electrode performance is permissible. Instead of cell measurements, a characterisation of the polarisation resistance of the electrodes would be much better suited to compare the investigated material with similar materials in the literature. However, it also needs to be noted that the polarisation resistance of porous electrodes strongly depends on their 3D structure (tortuosity, inner surface, etc.). This effect was also completely neglected in the comparison in Fig. 4. • Why did the authors decide not to use a Hubbard-U to properly consider effects of electron localisation? Especially for Fe-based perovskites this effect can be important (and at least in the XPS fits the authors do consider localised electrons). 3 References 1 M. Descostes, F. Mercier, N. Thromat, C. Beaucaire, M. Gautier-Soyer. Use of XPS in the determination of chemical environment and oxidation state of iron and sulfur samples: constitution of a data basis in binding energies for Fe and S reference compounds and applications to the evidence of surface species of an oxidized pyrite in a carbonate medium. Appl. Surf. Sci. 165 (2000), p.288-302 (http://dx.doi.org/10.1016/S0169-4332(00)00443-8). were relatively identified values that did not contain temperature and oxygen partial pressure factors. To contain the temperature and oxygen partial pressure terms in the E vf-O calculations, we additionally calculated the Gibbs free energy difference oxygen vacancy formation (G vf-O ) by using the Gibbs free energies of oxygen, hydrogen, and water molecules. For reference, the abbreviations for eight samples used for the G vf-O calculations are given in Table R1 to remove confusion concerning sample information. The re-calculated G vf-O for eight samples from the surface AO layer (green bar) and BO 2 layer (purple bar) are displayed in The detailed explanation for the G vf-O calculations from the surface AO and BO 2 layers in Pr 0.5 (Ba/Sr) 0.5 TO 3-δ (T = Mn, Fe, Co, and Ni) are as follows: (1) Phase decomposition at 750 o C and p(O 2 ) : 10 -9 atm (Surface AO layer) The phase for Pr 0.5 (Ba/Sr) 0.5 CoO 3-δ -based electrodes are reported to be decomposed at 700 o C under p(O 2 ) < 10 -6 atm (p(O 2 ) similar to argon gas) R1 . Considering this experimental data, we re-calculated the G vf-O values from the surface AO layer of Pr 0.5 (Ba/Sr) 0.5 TO 3-δ (T = Mn, Fe, Co, and Ni) at 750 o C and p(O 2 ) : 10 -9 atm (reducing condition) by using the following equations R2 (abbreviations given in Table R1):

Equation R1
and Equation R2: The and are the total energies of PrO-terminated (001) . 1a).
The phase reconstruction to Ruddlesden-Popper (R-P) perovskite or layered perovskite occurs by the reduction of BO 2 layers in the reduction atmosphere. Because the formation of oxygen vacancies at the BO 2 layer would include the hydrogen oxidation reaction (HOR, + ↔ ) at the surface and the oxygen vacancy diffusion toward the BO 2 layer, we also calculated the G vf-O from the BO 2 layer at the above specified condition (reducing condition) by using the following equations:

Equation R3, Equation R4
, and Equation R5: The In summary, we additionally calculated the G vf-O of eight samples (in Table R1) from the surface AO and BO 2 layers to include the main factors for the oxygen vacancy formation (in this case, temperature and oxygen partial pressure). In the presented calculations, the borderlines for two criteria (phase decomposition and phase reconstruction) were both set to the G vf-O of 0 eV for checking the spontaneity for two criteria 4 (Revised Fig. 1a). Furthermore, by calculation of spontaneous phase decomposition and/or reconstruction temperature where the G vf-O value from surface AO layer and BO 2 layer becomes zero (Fig. R1) 205-209 (2015).

[Original text]
Here, we systematically calculated the oxygen vacancy formation energies (E vf-O ) of perovskite oxides with various cations to investigate the unprecedented factor affecting the phase reconstruction. The type of phase 9 reconstruction could be predicted with the E vf-O value from PrO and TO 2 networks in Pr 0.5 (Ba/Sr) 0.5 TO 3-δ (T = Mn, Fe, Co, and Ni), in which the most appropriate cations for the complete reconstruction to R-P perovskite were determined.
[Revised text] Here, we systematically calculated the Gibbs free energy for oxygen vacancy formation (G vf-O ) of perovskite oxides with various cations to investigate the unprecedented factor affecting the phase reconstruction. The type of phase reconstruction could be predicted with the G vf-O value from PrO and TO 2 networks in Pr 0.5 (Ba/Sr) 0.5 TO 3-δ (T = Mn, Fe, Co, and Ni), in which the most appropriate cations for the complete reconstruction to R-P perovskite were determined.
[Revised text-(1)] To determine the unexplored factor for the phase reconstruction for the first time, the Gibbs free energy for oxygen vacancy formation (G vf-O ) and the oxygen vacancy formation energies (E vf-O ) from the surface AO (Asite) and BO 2 (B-site) networks were calculated for Pr 0.5 Ba 0.5 TO 3-δ and Pr 0.5 Sr 0.5 TO 3-δ (T = Mn, Fe, Co, and Ni) perovskite oxides ( Fig. 1 and Supplementary Fig. 1 should be in the range of about -1.2 to 0 eV (− 1.2 eV < B-site G vf-O < 0 eV) to demonstrate phase reconstruction to R-P perovskite in the reduction environment.

[Original text]
In summary, this study successfully calculated E vf-O value from PrO and TO 2 in Pr 0.5 (Ba/Sr) 0.5 TO 3-δ (T = Mn, Fe, Co, and Ni) as the key factor for identifying the type of the phase reconstruction.
[Revised text] In summary, this study successfully calculated G vf-O value from PrO and TO 2 in Pr 0.5 (Ba/Sr) 0.5 TO 3-δ (T = Mn, Fe, Co, and Ni) as the key factor for identifying the type of the phase reconstruction.
Comment 2. In Fig. 2b, the authors provided a comprehensive phase diagram based on in-situ XRD results. Take x = 0.5 as an example. Based on Fig. 1a, it should be a R-P perovskite phase. However, as shown in Fig. 2b, it is a simple perovskite (region I) after the reduction below 770 o C, simple perovskite + R-P perovskite + Fe metal (Region III) in 780-830 o C, and R-P perovskite + Fe metal (region IV) above 840 o C.
So I wonder if the points represent equilibrium and stable states (which should be a basic requirement for a phase diagram), or just transient states due to the short reduction time? If the Pr 0.5 Sr 0.5 FeO 3 is reduced at 830 o C for a much longer time, can it transform to R-P perovskite + Fe metal (region IV)? If it is reduced at 850 o C for a much longer time, will the R-P perovskite decompose further?

Response to Comment 2:
We appreciate the reviewer for suggesting us very interesting point. As we provided in Fig. 1 and "Response to Comment 1" part, we first predicted the possible perovskite oxide candidates that could demonstrate phase reconstruction to Ruddlesden-Popper (R-P) perovskite under particular temperature and atmosphere. Afterwards, we experimentally exemplified the phase reconstruction behavior of Pr 0.5 Ba 0.5-x Sr x FeO 3-δ material (x = 0, 0.1, 0.2, 0.3, 0.4, and 0.5) under reducing atmosphere via insitu temperature & environment-controlled X-ray diffraction (XRD) measurements and mapped out the phase diagram ( Fig. 2b). As listed in the "Methods: in-situ phase reconstruction tendency evaluation" part, the reduction temperatures were ranged from 700 o C to 870 o C and "two hours" were delayed at each temperature interval. To further confirm whether the plotted points in the phase diagram represent equilibrium and stable states (a basic requirement for a phase diagram) but not just a transient state due to short reduction time, we additionally conducted in-situ X-ray diffraction (XRD) measurements for Pr 0.5 Sr 0.5 FeO 3-δ (A-PBSF50) at 830 o C in the reduction environment with respect to time. The A-PBSF50 did not transform to R-P perovskite + Fe metal (region IV) but remained as simple perovskite + R-P perovskite + Fe metal (region III) at 830 o C even after 4 hours of reduction (enough reduction time for displaying phase transition behavior) R7-R9 (Fig. R2). This result implies that two hours of delay for each temperature interval (10 o C in this work) is sufficient for confirming the phase reconstruction behavior and the phase diagram represent equilibrium states for each temperature interval. Furthermore, we additionally reduced the A-PBSF50 material at 850 o C for 2 hours, 4 hours, and 100 hours under humidified H 2 atmosphere (3% H 2 O) to check whether the completely phase-transitioned R-P perovskite will decompose or not after a much longer reduction time. As shown in Fig. R3, the R-P perovskite is not decomposed and there was no secondary phases even after 100-hour H 2 -reduction process, implying that the R-P perovskite is structurally stable under reducing atmosphere. As a result, the phase diagram in Fig. 2b meets the basic requirements for the phase diagram and the temperature interval is much more important than the reduction time unless it is not just a 11 short-time reduction (e.g., 10 minutes).
[ [ Figure R2]  Fig. 2d-e, how to determine the concentration of oxygen vacancy in the material, which is remarkably influenced by the temperature and oxygen partial pressure, before DFT calculation?

Comment 3. In
Response to Comment 3: We think that there was a misunderstanding on Fig. 2d and 2e. In Fig. 2d and 2e, we did not determine the concentration of oxygen vacancies of four materials before the density functional theory (DFT) calculations. We think that there was a confusion on Fig. 2e (left y-axis on Fig. 2e is not the oxygen vacancy concentration term, but the oxygen vacancy formation energy term) since the oxygen vacancy formation energy (left y-axis) looks like the "3-δ" term in ABO 3-δ . Therefore, we feel sorry for giving confusion on this part, yet we did not determine the concentration of oxygen vacancies of four materials, but the oxygen vacancy formation energies of four materials (red color in 13 Revised text in the revised manuscript:
Therefore, the P max difference between A-PBSF30 symmetrical full-cell and A-PBSF50 symmetrical full-cell is affected by the electro-catalytic activity of both O 2 reduction and H 2 oxidation, but mostly derived from the 14 SOFC fuel electrode part (electrochemical H 2 oxidation) due to the difference in exsolved particle size and surface distribution of Fe metal particles. Furthermore, even though we compared the electrochemical performance of symmetrical full-cells with other reported papers, we also compared the electrochemical performance with well-known best anode and cathode material (Table R2). Despite the same electrolyte and similar electrolyte thickness, the A-PBSF30 symmetrical full-cell demonstrated higher electrochemical performance than the best-known SOFC cathodes and anodes.
[References for the revision- (1) [ Table R2] product. Thus, we performed the in-operando quantitative GC profiles of outlet gas during co-electrolysis of H 2 O and CO 2 at 800 o C and 1.5 V (Supplementary Fig. 19) R17 . The amount of produced H 2 and CO during co-electrolysis at 800 o C for the A-PBSF30 symmetrical cell were measured to be 0.18 ml min -1 (0.50 ml min -1 cm -2 ) and 3.89 ml min -1 (or 10.81 ml min -1 cm -2 ), respectively. These results indicate that the A-PBSF30 symmetrical cell could efficiently produce synthetic gas (H 2 & CO) during co-electrolysis.
[ Added text in the revised manuscript:

Results: Electrochemical performance
The in-operando quantitative analysis of the synthetic gas products (H 2 & CO) was further investigated via gas chromatography (GC) profiles for the A-PBSF30 symmetrical cell at 800 o C during co-electrolysis of H 2 O and CO 2 (Supplementary Fig. 19). The amount of generated H 2 and CO were measured to be 0.50 ml min -1 cm -2 and 10.81 ml min -1 cm -2 , respectively, implying that the A-PBSF30 symmetrical cell could efficiently produce synthetic gas during co-electrolysis.

Experimental: Electrochemical performance measurements
The Response to General Comments: We sincerely appreciate the reviewer for providing constructive comments to improve the quality of our manuscript. We endeavored to reflect the reviewer's comments as much as possible. The detailed point-by-point responses to the comments of the reviewer is provided below.  Fig. 2). Therefore, not only from reference, we also experimentally demonstrated that the Pr 0.5 Sr 0.5 MnO 3-δ material undergo phase reconstruction from simple perovskite to R-P perovskite under reducing condition. [Revised text] Considering the aforementioned results and the experimental data, only Pr 0.5 Sr 0.5 MnO 3-δ and Pr 0.5 Sr 0.5 FeO 3-δ (A-PBSF50) are the possible candidates for the phase reconstruction to R-P perovskite in this study (Supplementary Fig. 2).   Comment 2. The Sr doping can decrease the E recon , but the difference between x = 0 and x = 0.5 are only 0.3 eV, it is hard to understand that such a small difference can impose a big influence to phase reconstruction. The author should also calculate the formation energy of RP phase with different Sr contents.

Response to Comment 2:
We appreciate the reviewer for the helpful comment. The reviewer considered the phase reconstruction energy (E recon ) difference of 0.3 eV as somewhat low and was questionable that this small difference could induce a big influence in terms of phase reconstruction to R-P perovskite. This was a great chance to re-consider our mistake of energy unit in Fig. 2d since the actual unit was not eV but eV/unit cell. Hence, we are sorry for giving the reviewer a little confusion of the E recon value during the energy normalization by the unit cell. To eliminate the confusion of this data, we changed the unit from eV/unit cell to eV. Thus, the real difference between x = 0 sample (Pr 0.5 Ba 0.5 FeO 3-δ , A-PBSF00) and x = 0.5 sample (Pr 0.5 Sr 0.5 FeO 3-δ , A-PBSF50) is 3.94 eV or 380.04 kJ/mol (Revised Fig. 2d). This obvious E recon difference between A-PBSF00 and A-PBSF50 is meaningful since this much difference can impose a big influence on the phase reconstruction. Also, we agree with the reviewer's comment that it would be better to show more calculated E recon values with more different Sr 2+ contents. We additionally calculated the E recon values at x ≈ 0.06 and x ≈ 0.13, and then verified that E recon decreases as x increases (Supplementary Fig. 7).

Revised figure in the revised manuscript:
[

[Original text]
The E recon decreases with increasing Sr 2+ concentration in PBSF, indicating that the incorporation of Sr 2+ into Ba 2+ site promotes the phase reconstruction to R-P perovskite.
[Revised text] The E recon decreases with increasing Sr 2+ concentration in PBSF, indicating that the incorporation of Sr 2+ into Ba 2+ site promotes the phase reconstruction to R-P perovskite (Supplementary Fig. 7).

Methods: Computational methods [Original text]
The relative energies required for the phase reconstruction from simple perovskite to n = 1 R-P perovskite (E recon ) of four model structures with different Sr 2+ concentration were calculated using the total energy difference between simple perovskite and n = 1 R-P perovskite by the following equation: [Revised text] The relative energies required for the phase reconstruction from simple perovskite to n = 1 R-P perovskite (E recon ) of six model structures with different Sr 2+ concentration were calculated using the total energy difference between simple perovskite and n = 1 R-P perovskite by the following equation: Comment 3. The assignation of Fe in X-ray photoelectron spectra is questionable. The noted binding energy value of Fe is too high.

Response to Comment 3:
We thank the reviewer for the prudent comment. We stated in the caption of Supplementary Fig. 10 (before the revision) that the "binding energy peaks of 727.2, 725.6, 723.5, and 720.0 eV are corresponded to Fe 4+ , Fe 3+ , Fe 2+ , and Fe 0 2p 1/2 , respectively. There are two main binding energy regions for Fe spectra: Fe 2p 1/2 and Fe 2p 3/2 . To support our assignation of Fe 2p 1/2 in X-ray photoelectron spectra (XPS), we re-checked more references (For reference, the binding energy peaks of 710.8, 709.6, and 706.7 eV are corresponded to Fe 3+ , Fe 2+ , and Fe 0 2p 3/2 ) R20-R23 . Moreover, since the reviewer #3 gave us a valuable comment that the identification of Fe 4+ from only XPS fitting is daring, we also conducted X-ray absorption fine structure (XAFS) measurements (Figs. 4a, 4b, and 4c). Along with the identification of Fe 4+ from the XAFS measurements, the increase in Fe-Fe shell intensity after reduction process precisely proves the exsolution of Fe 0 metal. Comment 4. XRD refinement should give the phase ratios of RP to Fe metal to confirm the equation (2).

Response to Comment 4:
We thank the reviewer for the insightful comment. The equation (2)  exsolved Fe metal should be given from the X-ray diffraction (XRD) refinement profile to confirm equation (2). In general, the phase ratio of mixed phases is determined the fractional scale factor R24,R25 , in which the phase ratio is determined through the intensity ratio between two known phases (For reference, the sum of phase fraction for mixed phases is 100%). However, in our position, the intensity ratio between the R-P phase and the Fe metal phase after the exsolution phenomenon is hard to determine because it is hard to determine the fractional scale factor assuming 100% Fe metal exsolution. In addition, the amount of exsolved particles is hard to acquire from the intensity of XRD patterns, thus it is difficult to obtain the phase fraction of exsolved metal particles just from XRD spectra. As a result, since the phase ratio of R-P phase and exsolved Fe metal could not be determined from the XRD refinement data, we could only suggest equation (2)  [Equation (2) in the manuscript] Comment 5. In Supplementary Figure 2b, the XRD peak at 33 o of R-PBSF30 looks much higher than the standard peak, why? And it is also not well refined in the XRD refinement (Supplementary Figure 3).

Response to Comment 5:
We thank for the reviewer's prominent comment for improving the quality of this manuscript. Because the intensity ratio for Supplementary Fig. 2b and Supplementary Fig. 3 (used for X-ray diffraction (XRD) refinement) is different, we re-synthesized the same Pr 0.5 Ba 0.2 Sr 0.3 FeO 3-δ (A-PBSF30) sample via the Pechini method and then reduced the sample under humidified H 2 atmosphere (3% H 2 O) to check whether this phenomenon was originated from experimental error or preferred orientation effect (or preferential growth of certain crystal planes during the synthesis procedure) R26 . As shown in the XRD measurement in Supplementary Fig. 4b (was Supplementary Fig. 2b), the slight intensity difference between two main peaks for the Ruddlesden-Popper perovskite phase (2 theta ≈ 31.5 o and 33 o ) was displayed between (Pr 0.5 Ba 0.2 Sr 0.3 ) 2 FeO 4+δ -Fe metal (R-PBSF30) and (Pr 0.5 Sr 0.5 ) 2 FeO 4+δ -Fe metal (R-PBSF50) even after re-synthesis of samples. Accordingly, there is a slight preferential growth of certain crystal planes during the reduction procedure between R-PBSF30 and R-PBSF50 in the (110) plane (about 2 theta ≈ 33 o ). Furthermore, we also re-performed the XRD refinement for the re-synthesized R-PBSF30 using the GSAS II program along with using the crystallographic information file (CIF). The small difference in Supplementary Fig. 5 (was Supplementary Fig. 3) indicates that the R-PBSF30 is well-refined R27,R28 . This Comment 7. Some typos: in the part of Transmission electron microscopy analysis. "0.395 nm (Figure 3a) and 0.634 nm (Figure 3c)" and "the simple perovskite (Figure 3b) and R-P perovskite (Figure 3d)" should be changed to "0.395 nm (Figure 3a) and 0.634 nm (Figure 3d)" and "the simple perovskite (Figure 3b) and R-P perovskite (Figure 3e)".

Response to Comment 7:
We thank the reviewer for notifying the typos in our manuscript. We made corrections for the transmission electron microscopy (TEM) analysis part and colored as red color below.
Moreover, the authors also thoroughly checked whether there are more typos and/or mistakes in our manuscript and found some things that needs to be fixed (the caption for Supplementary Figure 4 (was Supplementary Figure 3)).

Revised text in the revised manuscript:
Results: Transmission electron microscopy analysis From the high-resolution TEM images and corresponding fast-Fourier transformed (FFT) patterns, the lattice spaces between planes of A-PBSF30 and R-PBSF30 are 0.395 nm (Fig. 3a) and 0.634 nm (Fig. 3d), The locations of cations are well-matched with the simple perovskite (Figure 3b) and R-P perovskite (Figure 3d) because the atomic column intensity is proportional to … [Revised text-(2)] The locations of cations are well-matched with the simple perovskite (Fig. 3b) and R-P perovskite (Fig.   3e) because the atomic column intensity is proportional to … [Revised text-(3)] Before examining the electro-catalytic effect of the in-situ exsolved Fe metal particles, an explicit comparison of exsolved particle and surface distribution for R-PBSF00, R-PBSF30, and R-PBSF50 samples were presented in scanning electron microscope (SEM) images ( Fig. 3c and 3f, Supplementary Figs. 9 and   10).

Answers to Reviewer #3 General Comments:
This manuscript deals with studying the oxygen vacancy formation energies in perovskites as a potential descriptor for predicting the amount of exsolved metallic particles upon strong reduction of the material. To achieve as much exsolved metal particles as possible, the authors claim that complete phase reconstruction from simple to Ruddlesden-Popper perovskite is the most suitable pathway. Their approach is a combination of DFT calculations (to predict the most suitable composition for complete phase reconstruction) and in-situ X-ray diffraction (to map the phase diagram, where the observed phase evolution is plotted as a function of A-site doping). Furthermore, the material with the most promising exsolution behaviour is tested for its suitability as an SOFC electrode. The DFT and in-situ XRD part are sound and especially the obtained phase diagram is a strong result. However, what I completely missed is a discussion on why the oxygen vacancy formation enthalpy determines the phase transition behaviour. In this question, the reader is left entirely to his or her own thoughts, which should not be the case with a paper in Nature communications. There definitely needs to be more detailed explanation and discussion before the paper can be recommended for publication.
Moreover, I unfortunately have to say that the electrochemical part of the paper is rather poor and needs major revisions. I am sorry for this harsh judgement, since I principally like the approach of the authors, but there are yet too much flaws in the manuscript and I therefore recommend that it is reconsidered in a largely revised version.

Response to General Comments:
First of all, we sincerely appreciate the reviewer for providing meaningful and thoughtful comments on our work. We are also thankful that the reviewer likes the approach of this work. The detailed comments were greatly helpful to further strengthen the quality of this work. We have revised the manuscript to address the reviewer's opinion as much as possible and the point-by-point response for each comment are listed as below: Detailed comments and criticism: Comment 1. The definition of the enthalpy limits between the different phase regions given in Fig.1 is crucial for a correct prediction of exsolution behaviour, therefore it needs more discussion. Where do the values given as limits come from? This appears to be especially important, as three or four of the calculated values are quite close at these limits. Hence, slight shifts in the defined limits or small errors from the calculation may lead to wrong predictions. I suggest to compare the obtained oxygen vacancy formation enthalpies with several literature data. There is already quite some comparable data available -e.g. on (La,Sr)CoO 3 or (La,Sr)MnO 3 based materials. Moreover, quantitatively knowing the errors/uncertainties of the calculation results would be advantageous to being able judging the reliability of the calculated results. I am aware that 2 commonly no errors are given for DFT results, since very often an accuracy of some 0.1 eV is sufficient for supporting or disproving a hypothesis, which was gained by interpretation of experimental results. Here, however, the accuracy of the oxygen vacancy formation energies appears to be very important, since the DFT results are very close at the borderline that decides about which behaviour to expect.
Response to Comment 1: We thank the reviewer for providing us insightful comment. We completely agree with the reviewer's comment that we need to clearly justify the physical meaning of two criteria (phase decomposition and phase reconstruction) with regards to the oxygen vacancy formation energy. Therefore, as the reviewer pointed out, we validated the physical meaning of both criteria by additional Gibbs free energy for oxygen vacancy formation energy (G vf-O ) calculations that contains real experimental conditions. Also, in addressing the reviewer's comment concerning density functional theory (DFT) errors in the borderline cases, we also checked that there was an internal error when using the generalized gradient approximation ( atm (reducing condition) by using the following equations R2 (abbreviations given in Table R1):
The phase reconstruction to Ruddlesden-Popper (R-P) perovskite or layered perovskite occurs by the reduction of BO 2 layers in the reduction atmosphere. Because the formation of oxygen vacancies at the BO 2 layer would include the hydrogen oxidation reaction (HOR, + ↔ ) at the surface and the oxygen vacancy diffusion toward the BO 2 layer, we also calculated the G vf-O from the BO 2 layer at the above specified condition (reducing condition) by using the following equations:

Equation R3, Equation R4
, and Equation R5: The zero-point energies were extracted from the previously calculated values R3 ). Thus, the G vf-O for eight samples from the BO 2 layer was recalculated at the above specified condition to find the appropriate samples that could demonstrate phase reconstruction to R-P perovskite.
In summary, we additionally calculated the G vf-O of eight samples (in Table R1) from the surface AO and BO 2 layers to include the main factors for the oxygen vacancy formation (in this case, temperature and oxygen partial pressure). In the presented calculations, the borderlines for two criteria (phase decomposition and phase reconstruction) were both set to the G vf-O of 0 eV for checking the spontaneity for two criteria (Revised Fig. 1a). Furthermore, by calculation of spontaneous phase decomposition and/or reconstruction temperature where the G vf-O value from surface AO layer and BO 2 layer becomes zero (Fig. R1) 205-209 (2015).
[ Table R1] Table R1. Chemical composition and abbreviation of specimens used for the density functional theory    Here, we systematically calculated the Gibbs free energy for oxygen vacancy formation (G vf-O ) of perovskite oxides with various cations to investigate the unprecedented factor affecting the phase reconstruction. The type of phase reconstruction could be predicted with the G vf-O value from PrO and TO 2 networks in Pr 0.5 (Ba/Sr) 0.5 TO 3-δ (T = Mn, Fe, Co, and Ni), in which the most appropriate cations for the complete reconstruction to R-P perovskite were determined.
[Original text-(2)] For the perovskite oxides to undergo phase reconstruction without phase decomposition under reducing condition, the A-site E vf-O value should be higher than 1.5 eV. Moreover, the B-site E vf-O value would be an important factor for determining the type of phase reconstruction. For instance, the B-site E vf-O should be in the range of about 1.6 to 2.8 eV to demonstrate phase reconstruction to R-P perovskite in the reduction environment.
[Revised text- (2) In summary, this study successfully calculated E vf-O value from PrO and TO 2 in Pr 0.5 (Ba/Sr) 0.5 TO 3-δ (T = Mn, Fe, Co, and Ni) as the key factor for identifying the type of the phase reconstruction.
[Revised text] In summary, this study successfully calculated G vf-O value from PrO and TO 2 in Pr 0.5 (Ba/Sr) 0.5 TO 3-δ (T = Mn, Fe, Co, and Ni) as the key factor for identifying the type of the phase reconstruction. Response to Comment 2: We thank the reviewer for the helpful comment. We checked the "manuscript checklist" for Nature Communications and found that Nature communication allows up to 10 display items (no more than 10 total). First, we moved the X-ray photoelectron spectra (XPS) data in Supplementary Fig.   10 to the main figure to support the X-ray absorption fine structure (XAFS) measurement data that we newly attached in Fig. 4. Furthermore, we added a schematic figure to help readers easily understand about this work (Fig. 6). From the addition of these two figures, the number of main figures is 6 total. This comment gave us a great chance to strengthen the quality of the figures explaining the main parts of this work.
Added figures in the revised manuscript: Figure 4. (a -e) Oxidation state characterization. (a -b) Fe K-edge X-ray absorption near-edge structure electrode material. The reason for this is that the performance of the electrolyte-supported SOFCs manufactured for this purpose is practically only limited by the ohmic resistance of the electrolyte in the investigated temperature range of 700-800°C. This can also be seen very clearly in the practically linear I-V characteristics (Figs. 4 and S14) at low to moderate current densities (the non-linearity at high current density points towards a concentration limitation). Especially at very low currents, the I-V curves hardly show any discernible non-linearity, which could indicate an electrode polarization limitation. This means that the high performance is mainly achieved either by a very good ion-conducting or comparatively thin LSGM electrolyte and therefore no quantitative statement about the electrode performance is permissible. Instead of cell measurements, a characterization of the polarization resistance of the electrodes would be much better suited to compare the investigated material with similar materials in the literature. However, it also needs to be noted that the polarization resistance of porous electrodes strongly depends on their 3D structure (tortuosity, inner surface, etc.). This effect was also completely neglected in the comparison in Fig. 4. included the electrochemical impedance spectroscopy (EIS) and the corresponding Nyquist plot of symmetrical full-cells that we did not attach in the initial submission (Supplementary Fig. 17). Moreover, to verify whether the P max difference is mostly originated from the SOFC fuel electrode (anode) part, we compared the polarization resistance between A-PBSF30 and Pr 0.5 Sr 0.5 FeO 3-δ (A-PBSF50, x = 0.5) symmetric half-cells (supplying air to both sides) and symmetrical full-cells. Since the polarization resistance difference between the symmetrical full-cells was much higher than those of symmetric half-cells supplying air to both sides at 800 o C, the P max difference between A-PBSF30 symmetrical full-cell and A-PBSF50 symmetrical fullcell is mostly derived from the SOFC fuel electrode part (electrochemical H 2 oxidation). The reviewer also mentioned that the polarization resistance of porous electrodes strongly depends on their 3D structure. In this work, since the 3D structure (surface morphology) of all PBSF series sintered at cell fabrication condition (950 o C for 4 hours in air atmosphere) are similar (Supplementary Fig. 15), the electrochemical performance and the polarization resistance would be influenced by the electro-catalytic activity of electrodes, not by the surface morphology of 3D-structured porous electrodes.
Added figure in the revised manuscript: [Supplementary Figure 17]