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Article
Peer-Review Record

Ytterbium Disilicate/Monosilicate Multilayer Environmental Barrier Coatings: Influence of Atmospheric Plasma Spray Parameters on Composition and Microstructure

Coatings 2023, 13(9), 1602; https://doi.org/10.3390/coatings13091602
by Giulia Di Iorio, Laura Paglia *, Giulia Pedrizzetti, Virgilio Genova, Francesco Marra, Cecilia Bartuli and Giovanni Pulci
Reviewer 1: Anonymous
Reviewer 2:
Reviewer 3: Anonymous
Coatings 2023, 13(9), 1602; https://doi.org/10.3390/coatings13091602
Submission received: 10 August 2023 / Revised: 31 August 2023 / Accepted: 11 September 2023 / Published: 13 September 2023

Round 1

Reviewer 1 Report

1. Fig. 3, each diffraction peak should be labeled with crystal face index rather a symbol.

2. The as-sprayed coating is composed of Yb2Si2O7 and Yb2SiO5 phases, so what are their contents? How the spraying parameters affect the phase compositions of the coatings?

3. For the same spraying parameters, do Yb2Si2O7 and Yb2SiO5 phases have the same relative content in YbDS and YbMS coatings? Why?

4. Fig. 10 left, the as-sprayed YbDS coating is found to have no Yb2SiO5 phase, which might not agree with the phase diagram in Fig. 1 and the SEM results.

5. There is many research investigating the preparation of YbDS and YbMS coatings, including the effects of spraying power, so what are the special features of this study?

6. Recently, the journal of <coatings> has published many papers on TBCs and EBCs, which are suggested to be add in the reference.

Needs some improvements

Author Response

  1. 3, each diffraction peak should be labeled with crystal face index rather a symbol.

Thank you very much for this request: we worked again on the XRD spectra of the powders and we labeled the XRD spectra as requested.  Morover we modified some comments related  to the XRD spectra.

 

  1. The as-sprayed coating is composed of Yb2Si2O7 and Yb2SiO5phases, so what are their contents? How the spraying parameters affect the phase compositions of the coatings?

This request is very important and the authors considered several possibilities for quantifying the monosilicate and disilicate content, for example the image analysis and the XRD Rietveld analysis. Anyway, in the first case it is impossible because the monosilicate and dilisilicate phases are not so distinguishable at the BSE micrographs: the two phases are often very finely dispersed one in each other resulting in an intermediate gray shadow at the BSE micrographs. On the other hand, the Rietveld analysis is not suitable for these particular compounds because of the presence of the amorphous phases and because of the superimposition of numerous peaks in the monosilicate and disilicate pattern.

Obviously there are other suitable analysis for obtaining these important  information, for example the Raman spectroscopy, but it is impossible in this moment to obtain that analysis within the deadline for the paper resubmission. That kind of analysis will be definitely considered in future works.

Nevertheless the authors, in section 3.1, figure 6, proposed an analysis of the Si content: even if it is not a direct measurement of the quantity of monosilicate and disilicate, it can give an important clue about the relative presence of these two phases in the as-sprayed coatings.

  1. For the same spraying parameters, do Yb2Si2O7 and Yb2SiO5phases have the same relative content in YbDS and YbMS coatings? Why?

The variation of the spraying parameters affect the content of Si present in the final coatings (section 3.1, figure 6) and, as a consequence, the relative content of ytterbium disilicate and monosilicate. In particular it is possible to notice that for the YbDS layer the Si content is higher for the lower torch power while for the YbMS the Si content is lower for the higher torch power. A statement for explain the connection between the Si content and the relative content of the different phases is added in section 3.1 as follow.

“This means that, for YbDS, the SiO2 volatilization is more relevant for higher torch power and this phenomenon promotes the formation of phases with a lower Si content, like ytterbium monosilicate and ytterbium oxide. On the other hand, for YbMS the behavior is in countertrend, so the higher the torch power and the higher the Si content.”

Furthermore the possible reason of the Si content trend in the two as-sprayed layers were discussed in section 4.

  1. 10 left, the as-sprayed YbDS coating is found to have no Yb2SiO5phase, which might not agree with the phase diagram in Fig. 1 and the SEM results.

The observation is interesting: in fact the XRD spectrum of sample DS-25 shows only relevant peaks of Yb2Si2O7, but also Yb2SiO5 is expected. The main Yb2SiO5 peaks are 30,65° and 31,02° which were identified in DS-20 and DS-16 coatings. Observing the three DS spectra it is evident that the hump due to the amorphous phase is more relevant for sample DS-25 so that it can hide the presence of those two main peaks. Thus, the presence of the  Yb2SiO5 cannot be excluded although no evident peak can be detected. Nevertheless the SEM micrographs analysis and the information given by the phase diagram let understand that Yb2SiO5 is present in the coating.

This consideration is very important because allows to add an important detail and it will be add to the paper.

“Nevertheless, the wider humps corresponding to the amorphous phase in the sample DS-25 can hide the effective presence of the Yb2SiO5 which shows its main characteristic peaks at 30,65° and 31,05°. This hypothesis is supported by the BSE SEM micrographs (Figure 4 e,f) which shows brighter areas corresponding to Yb2SiO5. ”

  1. There is many research investigating the preparation of YbDS and YbMS coatings, including the effects of spraying power, so what are the special features of this study?

Similar multilayer EBC were previously deposited by other authors, for example Richards et al [a] and Gracia et al [b] studied the monosilicate and disilicate deposited via APS and discussed the effect of the deposition parameters, but the two ytterbium silicate are not used as interlayer and top coat in the same system, like in our case, but as a composite system.

Some studies presented the possibility to obtain a tri-layer coating with Yb2Si2O7/Yb2SiO5/Si [A7, A8, A9] but deposited with other techniques such as direct vapor deposition [c] and reactive sputter [d] and a study was about the FEM  modelling  of a multilayer  made by ytterbium disilicate and monosilicate and a mix of these two phases [e].  Only Zhong et al. [f] presented a work in which a similar tri-layer coating is deposited via APS. In the present research the multilayer coating Yb2Si2O7/Yb2SiO5/Si was deposited via APS and for the first time three different torch powers were used and the influence of the deposition parameters on the tri-layer coating properties was deeply analyzed.

 [a] B. T. Richards, H. Zhao, H. N. G. Wadley. Structure, composition, and defect control during plasma spray

deposition of ytterbium silicate coatings. J Mater Sci (2015) 50:7939–7957. https://doi.org/10.1007/s10853-015-9358-5

[b] E. Garcia, O. Sotelo-Mazon , C.A. Poblano-Salas, G. Trapaga, S. Sampath. Characterization of Yb2Si2O7–Yb2SiO5 composite environmental barrier coatings resultant from in situ plasma spray processing. Ceramics International 46 (2020) 21328–2133. https://doi.org/10.1016/j.ceramint.2020.05.228

[c] Poerschke L.; Hass D. D.; Eustis S.; Seward G.G.E.; Van Sluytman J. S.; Levi C. G. Stability and CMAS Resistance of Ytterbium-Silicate/Hafnate EBCs/TBC for SiC Composites. J. Am. Ceram. Soc., 98 [1] 278–286 (2015) https://doi.org/10.1111/jace.13262.

[d] Anton R.; Leisner V.; Laska N.; Schulz U. Reactive Sputtered Ytterbium Silicate Environmental Barrier Coatings for Protection of Mo-Si-Based Alloys. Coatings 2022, 12, 1086. https://doi.org/10.3390/coatings12081086.

[e] Kawai E.; Kakisawa H.; Kubo A.; Yamaguchi N.; Yokoi T.; Akatsu T.; Kitaoka S.; Umeno Y. Crack Initiation Criteria in EBC under Thermal Stress. Coatings 2019, 9, 697; https://doi.org/10.3390/coatings9110697

[f] Zhong X.; Niu Y.; Li H.; Zhou H.; Dong S.; Zheng X.; Ding C.; Sun J. Thermal shock resistance of tri-layer Yb2SiO5/Yb2Si2O7/Si coating for SiC and SiC-matrix composites. J Am Ceram Soc. 2018;101:4743–4752. https://doi.org/10.1111/jace.15713

  1. Recently, the journal of <coatings> has published many papers on TBCs and EBCs, which are suggested to be add in the reference.

The following papers published in Coatings were added to the bibliography:

Fang, G.; Gao, X.; Song, Y. A Review on Ceramic Matrix Composites and Environmental Barrier Coatings for Aero-Engine: Material Development and Failure Analysis. Coatings 2023, 13, 357. https://doi.org/10.3390/coatings13020357

 

 

Mehta, A.; Vasudev, H.; Singh, S.; Prakash, C.; Saxena, K.K.; Linul, E.; Buddhi, D.; Xu, J. Processing and Advancements in the Development of Thermal Barrier Coatings: A Review. Coatings 2022, 12, 1318. https://doi.org/10.3390/coatings12091318

 

Vaßen, R.; Bakan E.; Gatzen C.; Kim S.;Mack D. E.; Guillon O. Environmental Barrier Coatings Made by Different Thermal Spray Technologies. Coatings 2019, 9, 784. https://doi.org/10.3390/coatings9120784.

 

 

Gatzen C.; Mack D. E.; Guillon O.;  Vaßen R. YAlO3—A Novel Environmental Barrier Coating for Al2O3/Al2O3–Ceramic Matrix Composites. Coatings 2019, 9, 609; https://doi.org/10.3390/coatings9100609.

 

Kawai E.; Kakisawa H.; Kubo A.; Yamaguchi N.; Yokoi T.; Akatsu T.; Kitaoka S.; Umeno Y. Crack Initiation Criteria in EBC under Thermal Stress. Coatings 2019, 9, 697; https://doi.org/10.3390/coatings9110697

 

Anton R.; Leisner V.; Laska N.; Schulz U. Reactive Sputtered Ytterbium Silicate Environmental Barrier

Coatings for Protection of Mo-Si-Based Alloys. Coatings 2022, 12, 1086. https://doi.org/10.3390/coatings12081086.

 

The manuscript was double checked in order to improve the English and remove some errors.

Author Response File: Author Response.pdf

Reviewer 2 Report

In this work, the authors deposited Yb2SiO5 Yb2Si2O7 double-layer coatings using different torch power.  The microstructure of the resultant coatings has been analysed and compared.  The following issues need to be addressed:

1.       The torch power has been controlled by adjusting the voltage while keeping the current constant.  What about changing the current while keeping the voltage constant?  Will the same trend for the coating microstructure and phase be expected?

2.       The caption for Figure 2 doesn’t match the figures.  It looks like (b) is the binarized image and (c) is the one after removing the porosity. 

3.       Page 8, line 290-293.  The authors have claimed that the impurities have not been detected by XRD.  However, there are some un-identified peaks in Figure 3 (c) and (d).  What phases do these peaks represent?

4.       Page 8 Line 304.  What does the ‘cracks are deeper’ mean?  More widely open or running through a larger distance across the coating’s thickness direction?

5.       In Figure 4, the samples only have one layer.  It is advised that these are clearly stated in the main test.  Please also include a clear statement for the aim of investigating these single-layer coating. 

6.       Page 9, line 321. Please specify how the EDS quantitative analysis has been done.  Is this from a point analysis or a map? If a map has been used, how big is the are analysed? 

7.       Page 11, line 358.  What samples are used to generate the histogram for YbDS in Figure 9?  Figure 4 and Figure 7 show two different types of samples, both of which have a YbDs layer.

8.       SiC bulk ceramic has been used as the substrate in this work.  For real applications, EBCs will be used on SiC CMCs. How would the different substrate material affect the conclusions in this work?

The language is in general good and easy to follow.  Some typos need to be fixed.  

Author Response

In this work, the authors deposited Yb2SiO5 Yb2Si2O7 double-layer coatings using different torch power.  The microstructure of the resultant coatings has been analysed and compared.  The following issues need to be addressed:

  1. The torch power has been controlled by adjusting the voltage while keeping the current constant.  What about changing the current while keeping the voltage constant?  Will the same trend for the coating microstructure and phase be expected?

The thermal spray processes are very complex: the modification of a single parameter can have several effects on the quality of the deposited coatings. In particular, it can affect both the temperature and the velocity experienced by the particles. Furthermore the particles trajectory and distribution in the torch plume can be modified, with a consequent variation of the percentage of particles that go through the hottest area of the torch plume and that one’s which run in the cooler flux. Further experimentations can be conducted for understand the influence of the variation of the current, but for this study we choose only one parameter in order to have a more systematic study with useful results which can give an idea of the consequence of the torch power variation through the variation of the secondary gas. Moreover, in plasma spraying the voltage is not an independent and free-settable parameter, but it depends on the others deposition settings (e.g. secondary plasma gas flow).

  1. The caption for Figure 2 doesn’t match the figures.  It looks like (b) is the binarized image and (c) is the one after removing the porosity. 

The comment is correct: there was a mistake in the caption and it was fixed.

  1. Page 8, line 290-293.  The authors have claimed that the impurities have not been detected by XRD.  However, there are some un-identified peaks in Figure 3 (c) and (d).  What phases do these peaks represent?

All the peaks in the XRD spectra of Figure 3 belong to the ytterbium disilicate (c) and ytterbium monosilicate (d). We just chose to avoid labels for the minor peaks. Now the XRD spectra were modified and each peak was labeled with the Miller indexes.

  1. Page 8 Line 304.  What does the ‘cracks are deeper’ mean?  More widely open or running through a larger distance across the coating’s thickness direction?

The comment is correct: we chose the adjective “deeper” inappropriately, so we substitute it with “wider”. In fact the goal is to compare the cracks and the wider the crack, the higher the possibility that it can propagate.

  1. In Figure 4, the samples only have one layer.  It is advised that these are clearly stated in the main test.  Please also include a clear statement for the aim of investigating these single-layer coating. 

The single layers were analyzed for two reasons: before obtaining the multi-layer it was necessary to understand the right number of pass with the torch in order to obtain comparable thickness of the coatings. Furthermore the coating with only the YbDS were used for the XRD measurements which, according to the XRD facility requirements, have to be carried out on the top of the coatings. The following statement is added to the text:

“First of all only the YbDS coatings were deposited in order to understand the deposition efficiency for each program and adjust the number of passes for obtaining comparable thickness. These coatings were also used for the XRD analysis. Then the multi-layer coatings (YbDS and YbMS) were deposited.”

  1. Page 9, line 321. Please specify how the EDS quantitative analysis has been done.  Is this from a point analysis or a map? If a map has been used, how big is the are analysed? 

There isn’t the required information in the paper, thus a statement was added: “The EDS analyses were carried out on areas of about 100 x 400 μm: for each coating 10 areas were taken along all the sample and then the average values and the standard deviation were calculated.”

  1. Page 11, line 358.  What samples are used to generate the histogram for YbDS in Figure 9?  Figure 4 and Figure 7 show two different types of samples, both of which have a YbDs layer.

The analysis of crack density and porosity were carried out on multilayer samples (Yb2Si2O7 as intermediate layer and Yb2SiO5 as top layer): this choice is important because the formation of a multilayer can influence the presence of defects. For example, we found some cracks that originated in the YbMS and propagate inside the YbDS. Since we want to analyze the performance of the multilayer system, we believe that this is the right choice.

This observation is very important, so we add a sentence to clarify the adopted strategy: “All these measurements were performed on the multilayer coatings in which the YbDS is the intermediate layer and YbMS is the top layer: this strategy is fundamental to consider the interaction between the two layers.”

  1. SiC bulk ceramic has been used as the substrate in this work.  For real applications, EBCs will be used on SiC CMCs. How would the different substrate material affect the conclusions in this work?

In the presented research we explore APS deposition parameters for the proposed EBC coatings and we studied the microstructure of three different set of deposition parameters. Thus, it is important to have a substrate with a chemical compatibility comparable with a SiC/SiC CMC and, because of the thermal expansion during the heating due to the APS process, a comparable CTE. These two requirements are guaranteed by the SiC substrates. Obviously, if the mechanical properties have to be studied, the SiC substrate is not more adequate.

 

Since this observation is relevant, a statement was added in section 2.1

“SiC substrates are considered adequate for this study because they guarantee the same chemical compatibility and a similar CTE of a SiC/SiC CMC substrate”

 

Comments on the Quality of English Language

The language is in general good and easy to follow.  Some typos need to be fixed.  

A double check of the paper was carried out and some typos were identified and fixed.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

In this work the authors study the effect of the spray parameters on the compositions and microstructure of Ytterbium disilicate/monosilicate multilayer coatings deposited on a Si bondcoat/ SiC substrate with APS.

 

1) Please add a scale bar at figure 2.

2) Materials and methods need to describe the experimental procedure. It is suggested to remove multiple references and relevant discussion that belongs to the introduction.

3) While the introduction and the materials and methods sections are analytical it feels like the results and discussion sections are brief. Expansion of the discussion would help improve the paper.

4) Authors need to add a section for conclusions.

5) While the authors study the effect of the APS power on the Si content/porosity/crack density for YbDS/YbMS, they don`t comment how these features affect the protective properties of the coatings.

6) Why did the authors decide to study the specific power range? How does this compare to literature? Is it possible to improve the Si bond coat layer properties by tuning the spray power?

7) The sequence of the figures is confusing. Start from the XRD of the coatings, then low mag SEM images, then the higher mag SEM images with EDS and then the diagrams on the microstructural features.

8) Since misrostructural analysis is the focus of this work, high magnification SEM BSE images and EDX are required for MS20-MS25 and DS20-DS16. This will help expand the discussion on the effect of the the power on the microstructure.

9) Try to be more consistent with abbreviations. In some cases it`s YbDS/YbMS and on other cases it`s DS/MS. Use the same in the manuscript.

 

Author Response

In this work the authors study the effect of the spray parameters on the compositions and microstructure of Ytterbium disilicate/monosilicate multilayer coatings deposited on a Si bondcoat/ SiC substrate with APS.

  • Please add a scale bar at figure 2.

Done

2) Materials and methods need to describe the experimental procedure. It is suggested to remove multiple references and relevant discussion that belongs to the introduction.

The “Materials and Methods” section was modified according to the request.

3) While the introduction and the materials and methods sections are analytical it feels like the results and discussion sections are brief. Expansion of the discussion would help improve the paper.

The section 4. Discussion was modified and some comments were added in order to give a more complete overview of the obtained results

4) Authors need to add a section for conclusions.

A section dedicated to the Conclusions was added in order to reassume the most relevant conclusions obtained with the presented research activity.

5) While the authors study the effect of the APS power on the Si content/porosity/crack density for YbDS/YbMS, they don`t comment how these features affect the protective properties of the coatings.

The aim of this research activity is to give an idea of how the torch parameters can influence the main features (Si content/porosity/crack density) of the proposed multilayer YbDS/YbMS deposited via APS on a Si bond coat. Each of this selected quantity have a great influence on the final coating which has the main purpose to protect the SiC/SiC component from water vapor corrosion.

In particular:

- The evaluation of the Si content in the final coating allows for understanding how the thermal spray process can modify the chemical composition of the as-sprayed coating with respect to the initial powder.  This information is important because the presence of a layer composed by a single phase or multiple phases can behave differently. For example when we have mixed layers with ytterbium monosilicate and dilisicate, the different CTE of the two phases has to be considered because it can promote the formation of micro-cracks (which can act as stress releasing mechanism) or cracks (which invalidate the required protection). Nevertheless we propose the upper layer of ytterbium monosilicate because it can guarantee a superior protection to water vapor compared to disilicate, thus in this layer the presence of a certain percentage of disilicate is not desired;

- The evaluation of the porosity is required because if the level of the porosity is too high, the presence of porosities can facilitate the propagation of cracks. Furthermore the porosities themselves can increase the water vapor permeability.

- The crack density is a direct measure of the cracks in the coating after the APS deposition process. Micro-cracking can have also a good effect for the stress releasing, but larger cracks are not desired because they can coalesce and connect the surface of the coating to the substrate and let the water vapor to penetrate.

Since in the introduction the crack density importance was emphasized while the study of the porosity and chemical composition was not mentioned, some comments were added at the end of the introduction:

“Furthermore also the porosity and the chemical composition of the coatings were studied. In fact the presence of porosity can facilitate the coalescence of cracks and the failure of the coating. The APS process produced thermal-sprayed coatings with a chemical composition different compared with the initial powders and it is important to understand the evolution of the compounds in the final coatings.”

 

6) Why did the authors decide to study the specific power range? How does this compare to literature? Is it possible to improve the Si bond coat layer properties by tuning the spray power?

The power range was selected considering the deposition parameters which are described in other works in literature and which were cited in section 2.1

  • Bakan, D. Marcano, D. Zhou, and Y. Jung, “Yb2Si2O7 Environmental Barrier Coatings Deposited by Various Thermal Spray Techniques : A Preliminary Comparative Study,” J. Therm. Spray Technol., vol. 26, pp. 1011–1024, 2017.
  • T. Richards and H. N. G. Wadley, “Plasma spray deposition of tri-layer environmental barrier coatings,” J. Eur. Ceram. Soc., vol. 34, pp. 3069–3083, 2014.
  • T. Richards, S. Sehr, F. De Franqueville, M. R. Begley, and H. N. G. Wadley, “Fracture mechanisms of ytterbium monosilicate environmental barrier coatings during cyclic thermal exposure,” Acta Mater., vol. 103, pp. 448–460, 2016.
  • Jian, Y. Wang, R. Liu, F. Wan, and J. Zhang, “Property evolutions of Si / mixed Yb 2 Si 2 O 7 and Yb 2 SiO 5 environmental barrier coatings completely wrapping up SiC f / SiC composites under 1300 ◦ C water vapor corrosion,” Ceram. Int., vol. 47, pp. 22373–22381, 2021.
  • Xiao, Q. Liu, J. Li, H. Guo, and H. Xu, “Microstructure and high-temperature oxidation behavior of plasma-sprayed Si / Yb 2 SiO 5 environmental barrier coatings,” Chinese J. Aeronaut., vol. 32, no. 8, pp. 1994–1999, 2019.
  • T. Richards, H. Zhao, and H. N. G. Wadley, “Structure, composition, and defect control during plasma spray deposition of ytterbium silicate coatings,” J. Mater. Sci., vol. 50, pp. 7939–7957, 2015.
  • Wang, J. Zhang, L. Sun, and J. Wang, “Microstructure and phase composition evolution of dual-phase ytterbium silicate coatings plasma sprayed from stoichiometric Yb 2 Si 2 O 7 feedstock powder,” Surf. Coat. Technol., vol. 437, p. 128373, 2022.
  • Han, Y. Wang, R. Liu, and Y. Cao, “Thermal shock behavior of mixed ytterbium disilicates and ytterbium monosilicates composite environmental barrier coatings,” Surf. Coat. Technol., vol. 352, pp. 348–353, 2018.

The Si bond coat was deposited via APS and considering APS parameters available in literature. Some attempts were carried out, but this deposition is quite easy and we obtained a satisfying result without numerous attempt. Thus we decided to not added the optimization of this layer in the paper. Obviously it can be of interest to modify the torch power also for the Si bond coat and understand the consequent modifications.  

7) The sequence of the figures is confusing. Start from the XRD of the coatings, then low mag SEM images, then the higher mag SEM images with EDS and then the diagrams on the microstructural features.

The suggestion is totally understandable, anyway the sequence of the figures follows the presentation of the results. Since the Si content is obtained with the EDS analysis which is conducted with the SEM micrographs, the results were put together in the section 3.1. Furthermore the Si content diagram cannot be put at the end because it is mentioned after the discussion on the YbDS. The XRD analysis were presented at the end, after the EDS analysis which is very important for the interpretation of the XRD spectra.

8) Since microstructural analysis is the focus of this work, high magnification SEM BSE images and EDX are required for MS20-MS25 and DS20-DS16. This will help expand the discussion on the effect of the the power on the microstructure.

The reason of this request is perfectly reasonable and it is adequate. Anyway the authors have some concerns in add the other high magnification micrographs with the EDS analysis. In particular, if the other micrographs and EDS analysis were added as single figures the total number of the figures would be too high for the paper. On the other hand, the further required micrographs and EDS analysis can be add in Figure 5 and 8. But in this case the dimension of the images can be too small for being representative and useful: in fact the images of the coatings at high magnification were present in figure 4 and 7. The high magnification micrographs in figure 5 and 8 gives an example of the composition and the EDS results which can be obtained in the different phase identified in the BSE micrographs with different gray shadow. We propose to let the figure in this arrangement, but if there are other reason that we did not understand, please let us known and we will try to adjust in a more suitable way.

9) Try to be more consistent with abbreviations. In some cases it`s YbDS/YbMS and on other cases it`s DS/MS. Use the same in the manuscript.

A double check of the manuscript was carried out in order to remove mistakes in the abbreviation.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The issues have been addressed satisfactorily

Reviewer 3 Report

Most of the suggested improvements were implemented. The manuscript is ready for publication.

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