First-Principles Study of Rare-Earth Doping Effects on Nitrogen Adsorption and Diffusion in Chromium

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Comments, Questions, and Suggestions for the Authors

1. p. 5, line 190. Why is no comparison made between the obtained elastic moduli and published data? The values reported in Table 1 differ substantially from experimental measurements (e.g., at 4.2 K). What is the reason for this?
2. p. 5, line 191. Why do you consider adsorption of an atomic nitrogen species rather than a nitrogen molecule (N₂)? Atomic nitrogen would arise only after N₂ adsorption and dissociation.
3. p. 5, lines 194–208. The real surface structure clearly differs from the ideal (110) plane. You state that surface relaxation was calculated. In addition to out-of-plane atomic displacements, were there in-plane (lateral) shifts within the surface layers? How do Ce and La atoms affect the surface structure? How does the relaxed surface differ from that shown in Fig. 2? Do the adsorption energies in Table 2 include full surface relaxation? How does the surface structure evolve as the concentration (coverage) of adsorbed nitrogen increases?
4. p. 5, lines 202–204. “A clear inverse correlation is observed between the nitrogen–surface distance (h_N–S) and the magnitude of the adsorption energy: nitrogen atoms closer to the surface exhibit more negative adsorption energies.” Not all entries in Table 2 support this statement.
5. p. 5, lines 215–216. The conclusion that “subsurface doping (Cr_La^sub and Cr_Ce^sub) marginally weakens nitrogen adsorption” is not clearly justified. According to Table 2, the adsorption energies for subsurface doping at LB3 are compared to the pristine surface. Please clarify the like-for-like comparison and the basis for this conclusion.
6. p. 6, line 219. The in-text reference to Figure 3 appears to be incorrect.
7. p. 6, lines 226–233. This passage is contradictory. On one hand, “the d-band center of Ce in the surface-doped system is located further from the Fermi level relative to subsurface doping.” On the other, “a d-band center closer to the Fermi level typically indicates stronger hybridization … enhancing adsorption strength,” and you attribute stronger metal–nitrogen interactions to surface-layer Ce. Please reconcile these statements.
8. p. 6, Table 2, lines 243–244. The term “Final Site” is not explained. Please define it and clarify how it is used in the analysis.
9. p. 7, line 258. Why is the calculated activation energy not compared with literature data on nitrogen diffusion in chromium?
10. p. 8, line 275. Correct the notation to Cr(110).
11. p. 8, line 285. Why is the calculated vacancy formation energy in chromium not compared with published values?
12. p. 9, line 301. What is the physical reason for the apparent long-range repulsion between vacancies and RE atoms?
13. p. 9, line 328. Why is the nitrogen diffusion barrier near Ce (1.89 eV) significantly higher than near La (1.19 eV)? Since La is larger, a higher barrier near La might be expected; please explain this trend.
14. The presence of rare-earth (RE) elements leads to vacancy localization near RE atoms. This should slow chromium self-diffusion but may increase RE mobility. It would be useful to comment on this point. In addition, the influence of RE elements on nitrogen diffusion should diminish for RE–vacancy pairs; please discuss.
15. The manuscript should more clearly define the authors’ contribution to understanding how RE atoms affect chromium nitridation. You examine the effects of La and Ce on nitrogen adsorption and incorporation from the surface into the bulk, as well as on bulk nitrogen diffusion in chromium. The slowing of nitrogen diffusion by larger RE atoms (via compressive local strain and reduced interstitial free volume) is expected. Moreover, adsorption/incorporation results are susceptible to the surface structure, which evolves from the initial chromium surface to chromium nitride during nitridation. This limits the generality of the conclusions. Once a nitride layer forms, additional effects arise—on defect structure, electronic structure of the nitride, nitrogen transport through the nitride layer, and properties of the nitride/metal interface. Please delineate these limitations and the scope of your conclusions more explicitly.

 

Comments for author File: Comments.pdf

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript entitled “Atomistic Study on the Effect of Rare Earth Doping on Nitrogen Adsorption and Diffusion in Cr Systems: Insights into Corrosion-Resistant Nitridation Modification” primarily focuses on the investigation of premature corrosion failure of chromium-based coatings under specific environmental conditions. The essence of this work is directly related to the influence of cerium and lanthanum additives on nitrogen adsorption and diffusion in the produced chromium coatings. The authors suggest that this nitriding effect plays a significant role in the early-stage corrosion of the formed surfaces, the prevention of which is crucial for selecting an optimal surface protection strategy.

This manuscript is written in proper scientific English and fully conforms to the structure characteristic of a research article. Nevertheless, I would like to draw the authors’ attention to several aspects that are more discussion-oriented in nature.

In the introduction, the authors present a clear and specific motivation for the forthcoming study; however, the rationale behind the choice of additives for chromium coating modification remains undefined. Why were lanthanum and cerium selected for alloying? Why not yttrium, scandium, or other lanthanides? What are the potential, cheaper, and technologically simpler alternatives for the modification of corresponding chromium coatings?

On the other hand, the elements selected for alloying or substitution should correspond to the fundamental atomic size similarities associated with the chromium atom parameters and the tetrahedral and octahedral voids in its cubic lattice. The theoretical calculations presented by the authors show only limited agreement with the experimental results.

Why did the authors choose the body-centred cubic (Im3̅m) structure for their calculations? Why were the primitive cubic (Pm3̅n), face-centred cubic (Fm3̅m), or hexagonal (P6₃/mmc) crystalline structures, which are also known for metallic chromium, disregarded?

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

Currently, the work contains many inaccuracies and ambiguities that need to be fixed in the corrected version. Here are some of them.

1. The title and abstract do not correspond to the work done, this concerns the lack of mention of the DFT method on which the entire work is based, which leads the reader into confusion, expecting to see an experimental paper. It is recommended to rewrite the abstract in accordance with the rules for authors.
2. The font on some figures should be enlarged.
3. Figure 6. Migration energy barriers for Cr atom diffusion via the vacancy mechanism in (a)  undoped, (b) Ce-doped, and (c) La-doped Cr systems. Figure 7.Energy barriers for nitrogen diffusion between adjacent octahedral interstitial sites in (a) pure (b) Ce-doped, and (c) La-doped Cr. “Cr systems” and “pure Cr” are the same things?
4. Line 248. Catalytic Influence of RE Doping on Nitrogen Penetration into Cr (110). Line 249-251 To elucidate the catalytic role of RE doping in nitrogen diffusion during the initial stage of nitriding, the energy barriers for nitrogen penetration from the Cr (110) surface into the subsurface region were calculated using the CI-NEB method.  – Catalysis is a chemical process in which the catalytic substance influences the reaction rate, thereby controlling the reaction path without being consumed. Therefore, the catalytic effect can only be discussed on the rate of formation of a solid layer of nitrides, and not on Nitrogen Penetration into Cr.
5. What meaning do the authors to Nitrogen Penetration into Cr?
6. What is the relationship between the subsurface region thickness and the thickness of the protective Cr-based coating?
7. It is recommended to provide a list of references according to the MDPI template standard. It is also advisable to specify the DOI indexes for each ref.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Dear authors, your article on modeling the influence of the rare earth elements Ce and La on the chromium nitriding process is purely theoretical in nature and may be of interest to relevant specialists. In my opinion, the quality of the manuscript could be improved by correcting some inaccuracies. When editing, please consider the opinion expressed below.

General point of view

1. Dear authors, I hope you agree that we must consider the readership when preparing this article. Who is your work intended for? Who do you think will be interested in your modeling methodology and the results you obtained? The phrase "The findings are expected to guide the design of Cr-based coatings with enhanced nitrogen utilization and superior corrosion resistance" (lines 102-104) could be interpreted as an answer to my question. However, the article lacks any practical recommendations on how to do this. I encourage you to consider this.
2. Your work lacks information on the corrosion resistance of nitrided chromium, so I recommend removing this term from the title. A possible title for the work would be "Modeling the Effect of Rare Earth Elements on the Chromium Nitriding Process."
3. It seems that you are modeling chromium as a semi-infinite medium. However, in the introduction, you indicated that chromium is applied to the metal surface as a film to protect it from corrosion. Furthermore, you state that "The findings are expected to guide the design of Cr-based coatings with enhanced nitrogen utilization and superior corrosion resistance" (lines 102-104). It would be helpful to specify under what conditions your results can be applied to a chromium film. Specifically, the question could be phrased differently: "Are your results applicable to a chromium film 50-100 nm thick?"
4. It is well known that the increase in corrosion resistance of chromium (Cr) during nitriding occurs due to the formation of chromium nitride (CrN or Cr2N). Your phrase "...the formation of a hard, stable CrN/Cr2N 43 surface layer..." (lines 46-44). When modeling this process, we can imagine that the CrN film grows as a result of a chemical reaction occurring at the CrN-Cr interface. Three stages can be distinguished: adsorption of N2 molecules on the surface of the growing CrN film and dissociation, diffusion of N atoms through the CrN layer to the CrN-Cr interface, and the chemical reaction of CrN formation. Most likely, this is how you envision this process. Of course, I do not exclude other models. However, in your manuscript, the nitriding model is described extremely unclearly. In one place, you write "... elements regulate nitrogen (N) adsorption and diffusion behavior in Cr during the early stages of nitriding..." (lines 17-18), in another "... significantly enhances N adsorption strength from -3.23 eV to -3.559/-3.645 eV..." (lines 21-22). Here it should be noted that an energy greater than 3.0 eV describes a chemical bond rather than adsorption. I advise you to describe the nitriding model more clearly.
5. If nitriding is a method for improving corrosion resistance, the quality of your work would be significantly improved if you were able to correlate the obtained modeling results with the actual effect of the rare earth elements Ce and La on the corrosion resistance of nitrided chromium films.
6. Your article is purely theoretical in nature and only tangentially related to the topic of corrosion. Perhaps another journal would be more suitable for publication?

 

Abstract

1. You describe your results in great detail, but the purpose of the study is not clearly stated. Please specify it.
2. Readers working in this or a related field are always interested in learning about the novelty of your results. What new insights have you gained? Please answer this question briefly. You can describe this in more detail in the conclusion.
3. Some terminology cannot be considered correct. These include, first and foremost, "Surface RE doping on Cr(110…" (line 21). Clearly, in your problem, doping is performed from the surface, so I recommend removing the term "Surface." In another case, you write "…subsurface doping slightly weakens the adsorption…" (line 23). The term "subsurface" is not quantitative. It would be advisable to clarify it.

 

1. Introduction

You've provided a fairly detailed analysis of the problem. However, in this section, it would be advisable to:

1) replace references [1] and [2], as these papers lack information on "Chromium (Cr)-based coatings..." (lines 36-38);

2) clarify the meaning of "...enhanced nitrogen utilization..." (line 103).

 

2. Calculation Details

The calculation is presented in detail and clearly, but judging by its details, you assume the medium in which diffusion occurs is monocrystalline. However, the chromium film is clearly polycrystalline. Please note that in such a medium, the diffusion of nitrogen atoms along grain boundaries can play a dominant role.

 

3. Results and Discussion

 

3.1. Bulk Properties of Cr Doped with RE

 

See comment 3 in the general view and comment to section 2

1.  

3.2. Adsorption Properties of Nitrogen Atom on Cr (110)

 

See comment 3 in the general view and comment to section 2

 

3.3. Catalytic Influence of RE Doping on Nitrogen Penetration into Cr (110)

 

See comment 3 in the general view and comment to section 2

 

3.4. Influence of RE Doping on Nitrogen and Vacancy Diffusion Behavior in Bulk CrI agree.

 

See comment 3 in the general view and comment to section 2

 

4. Conclusions

 

1. This section is consistent with the main text. However, I recommend that you indicate how your results relate to the corrosion resistance of a particular material.
2. Please note the novelty of your results.

 

References

1. Please replace references 1 and 2, as these papers lack information on chromium based 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors provided detailed answers to all the comments, as well as revised the text of the manuscript. The paper is now recommended for acceptance.

Author Response

Thank the Reviewer #3 for recommending the acceptance of our manuscript. 

Reviewer 4 Report

Comments and Suggestions for Authors

Dear authors, thank you for understanding some of my wishes and advice. However, questions regarding the content of certain sections of the manuscript remain unanswered. Please provide your comments on the entire review.

General point of view

1. I agree
2. I agree
3. I agree
4. I agree
5. I agree
6. I agree

 

Abstract

1. There is no answer
2. There is no answer
3. There is no answer

 

1. Introduction

 

1) There is no answer

2) There is no answer

 

2. Calculation Details

There is no answer

 

3. Results and Discussion

 

3.1. Bulk Properties of Cr Doped with RE

There is no answer

 

3.2. Adsorption Properties of Nitrogen Atom on Cr (110)

There is no answer

 

3.3. Catalytic Influence of RE Doping on Nitrogen Penetration into Cr (110)

There is no answer

 

3.4. Influence of RE Doping on Nitrogen and Vacancy Diffusion Behavior in Bulk CrI agree.

There is no answer

 

4. Conclusions

 

1. There is no answer
2. There is no answer

 

References

1. There is no answer

Author Response

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Author Response File: Author Response.pdf

Round 3

Reviewer 4 Report

Comments and Suggestions for Authors

Dear authors, thank you for understanding some of my wishes and advice. Good luck!

Abstract

1. I agree
2. I agree
3. I agree

 

1. Introduction

 

1) I agree

2) I agree

 

2. Calculation Details

I agree

 

3. Results and Discussion

 

3.1. Bulk Properties of Cr Doped with RE

I agree

 

3.2. Adsorption Properties of Nitrogen Atom on Cr (110)

I agree

 

3.3. Catalytic Influence of RE Doping on Nitrogen Penetration into Cr (110)

I agree

 

3.4. Influence of RE Doping on Nitrogen and Vacancy Diffusion Behavior in Bulk CrI agree.

I agree

 

4. Conclusions

 

1. I agree
2. I agree

 

References

1. I agree