Trapping Capability of Small Vacancy Clusters in the α-Zr Doped with Alloying Elements: A First-Principles Study

Round 1

Reviewer 1 Report

The authors address the trapping of alloying elements in bi-vacancy and tri-vacancy in hcp-Zr using first-principles calculations. However, the manuscript seems not to be carefully written. For instance, the formation energies of the vacancy clusters are incorrectly quoted from the previous publication of some authors. There are also other issues about this study that should be tackled as follows.

 

1.       The coordinate axis and their orientations in Figs. 1 and 2 are not shown.

2.       In section 2, “Methodology”, the setting for the VASP calculations is not fully clear. E.g. the volume and the shape of the models were kept or not, spin-polarized or not?

3.       There are various inequivalent configurations for the bi-vacancies and tri-vacancies in hcp-Zr. Why did the authors choose the vacancy configurations as shown in Fig. 1?

4.       In Eq. (2) on lines 86-89, page 3,  the alloying elements X=Sn, Fe, Cr, and Nb seem to act as interstitial atoms in the model of E_{NZr, X}. Why do the alloying elements tend to form interstitial atoms, but not substitutional atoms in hcp-Zr?

 

5.       On line 81, page 3, the formation energies of bi-vacancy and tri-vacancy in hcp-Zr are 2.11 and 0.32 eV, respectively. However, the formation energies could contradict the data in Figs. 4 and 5 in Ref. [19] (Sampedro et al. Nucl. Istrum. Meth. B 2013, 303, 46-50). The formation energy of mono-vacancy is 2.11 eV in Fig. 4 in Ref. [19]. Using the binding energies of bi-vacancy and tri-vacancy in Figs. 4 and 5 in Ref. [19], the formation energies could not be 2.11 and 0.32 eV. 

Author Response

Point 1: The coordinate axis and their orientations in Figs. 1 and 2 are not shown.

Response 1: Thanks for your suggestions. The coordiante axis and their orientations are added in Fig. 1 and 2 which are shown in our revised manuscript.

Point 2: In section 2, “Methodology”, the setting for the VASP calculations is not fully clear. E.g. the volume and the shape of the models were kept or not, spin-polarized or not?

Response 2: Thanks for your suggestions. the volume and the shape of the models were relaxed during the structural opimization, and spin-polarized is not used in this structure opitmization in our manuscpit, which are marked in red color, as shown in our revised manuscript.

Point 3: There are various inequivalent configurations for the bi-vacancies and tri-vacancies in hcp-Zr. Why did the authors choose the vacancy configurations as shown in Fig. 1?

Response 3: Thanks for your comments. Wo have chose the vacany configurations as shownin Fig. 1, due to we got the stable configurations of small vacancy clusters (two/three vacanies) by First-principels calculations in our previous cooperated work, which could be find in Ref. 12 in our manuscript. Based on these stable vacany configurations, we continue doing this work about trapping capability of small vacancy clusters in the α-Zr doped with alloying elements using First-prinicples study.

Point 4: In Eq. (2) on lines 86-89, page 3, the alloying elements X=Sn, Fe, Cr, and Nb seem to act as interstitial atoms in the model of E_{NZr, X}. Why do the alloying elements tend to form interstitial atoms, but not substitutional atoms in hcp-Zr?

 Response 4: Thanks for your comments. In Eq. (2) on lines 86-89, page 3, the alloying elements X=Sn, Fe, Cr, and Nb are used to substitutional atoms in the model of E_{NZr, X}. Because the atomic voulme of the alloying elements is more than the volume of interstitial site in α-Zr.

Point 5: On line 81, page 3, the formation energies of bi-vacancy and tri-vacancy in hcp-Zr are 2.11 and 0.32 eV, respectively. However, the formation energies could contradict the data in Figs. 4 and 5 in Ref. [19] (Sampedro et al. Nucl. Istrum. Meth. B 2013, 303, 46-50). The formation energy of mono-vacancy is 2.11 eV in Fig. 4 in Ref. [19]. Using the binding energies of bi-vacancy and tri-vacancy in Figs. 4 and 5 in Ref. [19], the formation energies could not be 2.11 and 0.32 eV.

Response 5: Thanks for your comments. As you said, the formation energy of mono-vacancy is 2.11 eV in hcp-Zr. We are sorry for givinging the wrong data of formation ernegy of bi-vacancy and tri-vacancy in hcp-Zr. We have recalculated the the data of formation ernegy of bi-vacancy and tri-vacancy in hcp-Zr, which are 3.90 and 6.23 eV, repectively, marked in red color in our revised manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

The article "Trapping Capability of Small Vacancy Clusters in the α-Zr Doped with Alloying Elements: A First-Principles Study" is devoted to the study of the processes of modeling structural defects in zirconium doped with various elements (Sn, Fe, Cr and Nb). Undoubtedly, the results presented by the authors are of high scientific novelty and practical significance, and are also promising for practical research. In general, the presented results of the study can be accepted for publication after the authors provide answers to all the questions raised by the reviewer during the reading of the article.

 

1. In the abstract, the authors need to more clearly state the purpose and relevance of this work.

2. The authors should clarify exactly how they chose the conditions for modeling structural defects in the crystal lattice, as well as justify the choice of the number of vacancy defects in the simulation.

3. What is the reason for such a strong difference in energy when an element changes in the structure of the Vn-X complex?

4. The authors should explain the choice of alloyed elements for the modification of zirconium.

5. The change in electron density depending on the simulation conditions should be further explained.

6. Conclusion requires significant revision.

Author Response

Point 1: In the abstract, the authors need to more clearly state the purpose and relevance of this work.

 Response 1: Thank you for your useful suggestions. In order to more clearly state the purpose and relevance of this work, we have carefully revised the content of the abstract in our revised manusciprt, which marked in red color.

Point 2: The authors should clarify exactly how they chose the conditions for modeling structural defects in the crystal lattice, as well as justify the choice of the number of vacancy defects in the simulation.

Response 2: Thank you for your useful comments. In nuclear reactors, they are subjected to a fast neutron flux, leading to the creation of a large number of point defects, both vacancies and self-interstitials. These point defects then diffuse and can be trapped by the different sinks of the them, or can cluster to form larger defect, such as vacancy and interstitial clusters. In this work, small vacancy culsters as one importatnt clusters trapped with doped alloying elements, which are prime importance for modeling the kinetic evolution and formation mechanism of the microstructure of vacancy-alloying element complexes under irradiation and of the associated macroscopic behavior.

Point 3: What is the reason for such a strong difference in energy when an element changes in the structure of the Vn-X complex?

Response 3: Thank you for your useful comments. For such as strong difference in energy when an element changes in the structure of the Vn-X complex, ity may due to the diffrence between the atomic volume, electronegativity and electronic propreties of the doped elements. Furthermore, this may be related to the binding energies of small vacancy clusters with these elements. Thus, it would be useful to know the effect of different dopants on vacancy diffusion.

Point 4: The authors should explain the choice of alloyed elements for the modification of zirconium.

Response 4: Thank you for your comments. The choice of alloyed elements for the modification of zirconium is based on the development of new Zr alloys for the pressurized water reactor (PRW) that contains the alloying element of Sn, Nb, Fe, Cr. For example, the element of Sn is used to solution soild strengthing, the alloying element of Nb is enhacing the corrosion resistance and soultion solid strengthing, and so on.

Point 5: The change in electron density depending on the simulation conditions should be further explained.

Response 5: Thank you for your useful suggestions. In this stage, the stablility of structures of bri-vacancies or tri-vacancies doped with alloying elements are judged by the total density of state (TDOS) and combined with the corresponding Fermi level of the system. It would be useful to confer the trapp capability of the small vacancy cluster with doped alloying elements in the α-Zr.

Point 6: Conclusion requires significant revision.

Response 6: Thank you for your useful suggestions. We have cafrefully revised the conclusion in our revised paper, which marked in red color.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

On lines 90-93, if X in the model with the energy of E_{NZr, X} is a substitutional atom as the authors' reply, the last term in Eq. (2), “E_{NZr}” should be the energy of V_{1}. Then, Eq.(2) represents the energy change by transferring a substitutional X atom to one of the vacancy sites in V_{n}. The removal of the substitutional X leads to a monovacancy model (V_{1}) and the X occupying one of the vacancy sites in V_{n} leads to a V_{n-1}-X, which leads to the energy change from  “V_{n-1}-X + V_{1}” to “V_{n} + V_{NZr, X}”. Thus, the binding energy defined in Eq.(2) includes not only the energy change by adsorbing a substitutional X to the vacancy cluster but also the energy change by emitting a vacancy from the vacancy cluster.  In short, I do not believe this study and suggest rejecting the manuscript. 

Author Response

Point 1: On lines 90-93, if X in the model with the energy of E_{NZr, X} is a substitutional atom as the authors' reply, the last term in Eq. (2), “E_{NZr}” should be the energy of V_{1}. Then, Eq.(2) represents the energy change by transferring a substitutional X atom to one of the vacancy sites in V_{n}. The removal of the substitutional X leads to a monovacancy model (V_{1}) and the X occupying one of the vacancy sites in V_{n} leads to a V_{n-1}-X, which leads to the energy change from  “V_{n-1}-X + V_{1}” to “V_{n} + V_{NZr, X}”. Thus, the binding energy defined in Eq.(2) includes not only the energy change by adsorbing a substitutional X to the vacancy cluster but also the energy change by emitting a vacancy from the vacancy cluster.  In short, I do not believe this study and suggest rejecting the manuscript.

 Response 1: Thank you very much for your comments. We are very sorry about the definition of Eq (2) in our manuscript. We are totally agree with your comments “On lines 90-93, if X in the model with the energy of E_{NZr, X} is a substitutional atom as the authors' reply, the last term in Eq. (2), “E_{NZr}” should be the energy of V_{1}. Then, Eq.(2) represents the energy change by transferring a substitutional X atom to one of the vacancy sites in V_{n}. The removal of the substitutional X leads to a monovacancy model (V_{1}) and the X occupying one of the vacancy sites in V_{n} leads to a V_{n-1}-X, which leads to the energy change from  “V_{n-1}-X + V_{1}” to “V_{n} + V_{NZr, X}”.” And we have changed our previous Eq. (2) to , which is marked in red color in our revised manuscript. Furthermore, we have recalculated all the trapping energies for Vn-X (in eV), here n = 2 or 3, which are marked in Table 1 in our revised manuscript. We have studied the comments carefully and made the suggested changes/corrections. We hope that we now produced a more balanced and better account of our work.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors answered all the questions posed, the article can be accepted for publication.

Author Response

Thanks for your careful and helpful comments on the original manuscript.