Structural Transition of Vacancy–Solute Complexes in Al–Mg–Si Alloys

Round 1

Reviewer 1 Report

Reviewers' comments:

The authors performed first-principles calculations for layered vacancy–solute complexes with additional Mg atoms in Al–Mg–Si alloys. When five Mg atoms were added to the layered vacancy–solute complex, the central Mg atom completely shifted to the Si layer, and a Mg vacancy was formed in the Mg layer, which indicated that the β-eye is formed upon the addition of Mg atoms. The results  indicate that the layered vacancy–solute complex plays an important role in β-eye formation. In general, the work was carefully done and some interesting results were obtained. It is very helpful for the use of 6000 series Al–Mg–Si alloys. However, this manuscript requires minor revision. I recommend publication after revising following issues.

 

• In introduction, the use of 6000 series Al–Mg–Si alloys for manufacturing automobile body panels 24 has increased because such alloys exhibit hardening characteristics. The authors should be give the detailed reference cites.
• In the last of page 2, a proper explanation should be provided to interpret why the length of the Si–Si bond in the β″-eye is longer than that in the layered VMg4Si8 complex.
• In methods section, “To examine the reproduction of the vacancy–solute complexes from the solid solution in the Al–Mg–Si alloy, we performed the first-principles-based MC simulations at 200 K”. The authors why choose simulations at 200 K? rather than others like 300 K.
• In page 4, to illustrate the bonding between atoms, the authors should give detailed mechanism pictures, e.g., explaining the number of bonds between Mg-Si by charge density.
• In page 4, “There is a steep drop both in the formation energy and the binding energy of the VMg4Si8+Mg5 complex.” the authors need to mention the reason for the steepness.
• In page 5, Figure 5 shows the average lengths of the Mg–Si, Si–Si, and Mg–Mg bonds... The average length of the Mg–Si bond remains almost constant at 2.80 Å, which are obvious larger than those of Si-Si and Mg-Mg, how to explain this phenomenon?
• In page 6, the authors performed the MC simulations, but not provide the details of the calculation settings, e.g. the time step ….
• Some minor errors exist in some paragraphs/sentences and should be polished again carefully.

Author Response

Response to Reviewer 1 Comments

 

Point 1: In introduction, the use of 6000 series Al–Mg–Si alloys for manufacturing automobile body panels 24 has increased because such alloys exhibit hardening characteristics. The authors should be give the detailed reference cites.

 

Response 1: We thank the reviewer for this suggestion. We have added references [1-6] about hardening characteristics in Al-Mg-Si alloys.

 

Point 2: In the last of page 2, a proper explanation should be provided to interpret why the length of the Si–Si bond in the β″-eye is longer than that in the layered VMg4Si8 complex.

 

Response 2: In the β″-eye, to accommodate the Mg-Si bonds in the Si layers, the Si-Si bonds are expanded. We have added a sentence to explain the length of the Si-Si bond.

 

Point 3: In methods section, “To examine the reproduction of the vacancy–solute complexes from the solid solution in the Al–Mg–Si alloy, we performed the first-principles-based MC simulations at 200 K”. The authors why choose simulations at 200 K? rather than others like 300 K.

 

Response 3: To avoid an excessive increase in the potential energy, we employed 200 K for the MC simulations. We have added Appendix A to explain why we employed 200 K for the MC simulations.

 

Point 4: In page 4, to illustrate the bonding between atoms, the authors should give detailed mechanism pictures, e.g., explaining the number of bonds between Mg-Si by charge density.

 

Response 4: We thank the reviewer for this suggestion. Considering the reviewer's suggestion, to evaluate the change in the stability of the β″-eye with increasing Mg atoms, we have calculated the formation energies of the layered VMg₄Si₈+Mg_n (n = 1–5) complexes with the β″-eye arrangement and the results are shown in Fig.6. We have added sentences about the change in the stability of the β″-eye in Lines: 152-161.

 

Point 5: In page 4, “There is a steep drop both in the formation energy and the binding energy of the VMg4Si8+Mg5 complex.” the authors need to mention the reason for the steepness.

 

Response 5: The reason for the steep drop was written in Lines:135-140 in the original manuscript (Lines:141-146 in the revised manuscript) as follows: “The steep decrease in the formation and binding energies of the VMg₄Si₈+Mg₅ complex arises from not only the formation of Mg–Si bonds but also the weakening of the repulsive Mg–Mg interaction.”

 

Point 6: In page 5, Figure 5 shows the average lengths of the Mg–Si, Si–Si, and Mg–Mg bonds... The average length of the Mg–Si bond remains almost constant at 2.80 Å, which are obvious larger than those of Si-Si and Mg-Mg, how to explain this phenomenon?

 

Response 6: The reason why the average length of the Mg-Si bonds is shorter than that of the Mg-Mg and Si-Si is that the Si atoms were outwardly displaced. To clearly show the reason, we have added a sentence: “Therefore, the Si-Si bond is longer than the Mg-Si and the Mg-Mg bonds” In Lines: 140-141.

 

Point 7: In page 6, the authors performed the MC simulations, but not provide the details of the calculation settings, e.g. the time step ….

 

Response 7: We have performed not MD (Molecular Dynamics) but MC (Monte Carlo) calculations. Therefore, additional conditions such as the time step are not required.

 

Point 8: Some minor errors exist in some paragraphs/sentences and should be polished again carefully.

 

Response 8: We have checked and corrected minor errors.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper investigated the structural transition from the vacancy-solute complexes to the β''-eye in 6000 series Al-Mg-Si alloys, using first-principles-based Monte Carlo simulations.
It is an extended investigation, initially published in Materialia by the same authors last year. This work is interesting, and it could be a significant theoretical contribution to understand better the nucleation of vacancy-solute complexes, V(Mg, Si)n, and their structural transitions to β'' structure in Al-Mg-Si alloys. 

This work could be published in Metals if the following questions and suggestions are cleared: 

1. The formation energy of vacancy-solute complexes, V(Mg, Si)n is estimated using one supercell size and expected to vary when a larger supercell is used. How much may the supercell size effect change the results and affect the conclusions of this work? More details about the used β''-Mg5Si6 crystal structure are required. Also, an additional side-view figure is needed in Figure 1.
2. The MC calculations presented in this work are at 200K. The selected temperature (200K) is quite different from the temperature of 473K used in the authors' previous work [Mizuno et al., Materialia 13 (2020) 100853]. I invite the authors to reconsider the same temperature (473K) in this work, not to hamper the flow of understanding of the topic and which is in line with the temperature interval generally used by industrial groups for the heat treatment of Al-Mg-Si alloys [413-573K].
3. Some sections, for instance, in the introduction [lines:25-28] and the computational method [lines:76-93], are entirely copied from the previous paper [Mizuno et al., Materialia 13 (2020) 100853]. The authors are invited to rephrase these sections.  

Author Response

Response to Reviewer 2 Comments

 

Point 1: The formation energy of vacancy-solute complexes, V(Mg, Si)n is estimated using one supercell size and expected to vary when a larger supercell is used. How much may the supercell size effect change the results and affect the conclusions of this work? More details about the used β''-Mg5Si6 crystal structure are required. Also, an additional side-view figure is

 

Response 1: To evaluate the size effect of the supercell, we have calculated the formation energies of VMg₄Si₈+Mg_n (n = 1–5) complexes calculated using the 3 × 3 × 4 supercell. The results are shown in Appendix B. We have confirmed that the increase in the supercell size does not affect the conclusions of the present work. We have added the side-view of Fig.1. as Fig.1(b).

 

Point 2: The MC calculations presented in this work are at 200K. The selected temperature (200K) is quite different from the temperature of 473K used in the authors' previous work [Mizuno et al., Materialia 13 (2020) 100853]. I invite the authors to reconsider the same temperature (473K) in this work, not to hamper the flow of understanding of the topic and which is in line with the temperature interval generally used by industrial groups for the heat treatment of Al-Mg-Si alloys [413-573K].

 

Response 2: In our previous work, to evaluate the concentrations at finite temperatures, we employed 0 K and 473 K to calculate the concentrations of V(Mg,Si)_n. The purpose of the MC simulations in the present work is not to evaluate the influence of finite temperature but to reproduce of the formation of the β″-eye from the solid solution. The influence of the temperature employed in the MC simulations cannot be directly compared to that of the heat treatment of Al-Mg-Si alloys because the difference in the atomic jump frequencies of the solute atoms by temperatures is not considered in the MC simulations. The atomic jump frequencies in the heat treatment increases with increasing temperature. To consider the increase in the atomic jump frequencies with increasing temperature in the MC simulations, we have to increase the number of MC steps in accordance with the temperature, which requires considerably more computational resources. Therefore, we employed relatively low temperature to reproduce the β″-eye formation in the MC simulations. We have added Appendix A about the temperature in the MC simulations.

 

Point 3: Some sections, for instance, in the introduction [lines:25-28] and the computational method [lines:76-93], are entirely copied from the previous paper [Mizuno et al., Materialia 13 (2020) 100853]. The authors are invited to rephrase these sections.

 

Response 3: We thank the reviewer for this suggestion. We have rephrased the sentences used in the previous paper.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have answered all my questions and comments, and the manuscript has been sufficiently improved to be accepted for publication in Metals in its present form.