Ab-Initio Studies of the Micromechanics and Interfacial Behavior of Al3Y|fcc-Al
Round 1
Reviewer 1 Report
This study uses DFT to analyze interface properties between Al and Al3Y, a subject which is of relevance for particle reinforced Al composites containing Y. The DFT methodology used is standard yet sound. The study is, with some minor exceptions, carefully conducted and the methods are, again with some exceptions, well described. Overall the paper leaves a positive impression.
Specific criticisms are as follows:
1) The methods used for cleavage calculations are well described. Both rigid separation and intermediate relaxation (with outermost layers kept rigid) are studied. The results show that the relaxed model -- while the overall separation energy of course is significantly higher -- has a softer response with a lower critical stress and a wider critical interface. The presentation of these results and the accompanying discussion of the critical configurations is commendable. However, the same is not true for the calculation of stacking fault energies. What are the boundary conditions here? Do you rigidly displace AlY vs Al in the directions shown in Figure 13, or do you only constrain and displace the outermost layers of atoms, and then relax? Here a precise description of the methodology is mandatory.
2) The authors evaluate, for interface cleavage, both the energies and the corresponding derivatives (ie separation stresses). This is good, because in a fracture mechanics theory both quantities matter. However, they fail to do the same for interface shear where, besides the SF energies, also their derivatives with respect to the lateral displacement are important. In the context of dislocation nucleation, the former define the Peierls energy while the latter define the Peierls stress. Both quantities are of equal importance, since the first defines the barrier for plasticity initiation by thermal activation while the latter defines the critical stress for plasticity initiation at zero temperature. The same considerations apply to interfaces, where the derivative of SF energy wrt SF displacement (ie the interfacial shear stress) defines the critical condition for interface sliding at zero temperature. This quantity should also be computed and shown, ie the curves in Figure 13 should be complemented by matching cruves of interfacial shear stress vs SF displacement.
3) The discussion of interface shear properties is based exclusively on the Rice ratio, ie the ratio of separation energy over maximum SF energy. However, the 'stress ratio' of critical stress for interface separation over maximum interfacial shear stress is at least as important. Also note that the conclusions may differ, for instance, for [010]/[010] the <100> direction may well have the lower stress ratio but the much higher Rice ratio.
4) Generally it would be desirable to map out the entire SF energy surface and not only its high symmetry directions. Only in this manner one can be sure that the relevant saddle points which govern dislocation nucleation are covered.
Minor points:
in the text below Eq. (16), a SF energy is given as 0.07 J/m2 which is surely a typo.
In the final paragraph of Section 3, it is stated that all DR values are below 1. However, the opposite is correct according to Table 6.
Please conduct a thorough proofreading since I have surely not identified all glitches of this kind.
Author Response
Dear reviewer
Thank you for you comments. The responds are in the attached file. And please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In the work under review, methods of density functional theory are used to study the structural, mechanical, and electronic properties of the Al3Y/Al interface.
The topic of the work is relevant. The literature review contains references to modern works. We can recommend, at the discretion of the authors, related topics:
Microstructure design to achieve optimal strength, thermal stability, and electrical conductivity of Al-7.5wt.%Y alloy. Materials Science and Engineering: A. Volume 852, 5 September 2022, 143700. https://doi.org/10.1016/j.msea.2022.143700;
Ab initio investigation on preferred orientation at the Al/Al3(Zr,Y) interface in Al–Zr–Y alloy. Journal of Applied Physics 131, 225111 (2022); https://doi.org/10.1063/5.0090591;
Phase interface induced stacking faults in Al-7.5Y alloy revealed by in-situ synchrotron X-ray diffraction and ex-situ electron microscopy. Materials Characterization. Volume 179, September 2021, 111322. https://doi.org/10.1016/j.matchar.2021.111322.
There are several questions and comments.
1. Section 2. Computation. One of the important questions in the theory of the density functional is the choice of the exchange-correlation functional. This is necessary to be able to repeat the above calculation results. The authors point to the use of the "Perdew-Burke-Ernzerh [32, 33] (PBE) scheme". Usually in DFT, the abbreviation PBE is used to indicate the corresponding functionality. Is it exchange-correlation functional? Is "Perdew-Wang-91" also functional? Please explain and provide a link. "Local-density ap-proximation (LDA) method" - you must specify the specific form of the functional in this approximation. It can be recommended to expand this section so that it is possible to carry out repeated calculations with the specified parameters.
2. Section 2.1. In formula (1) "? are energies". However, in formulas (7) - (13) this symbol is used to indicate the chemical potential. This needs to be clarified or changed.
3. Table 2. References [27], [36] refer to the elastic constants of Al, but not Al3Y. For Al3Y one should use, for example, [Phase stability, electronic, elastic and thermodynamic properties of Al-RE intermetallics in Mg-Al-RE alloy: A first principles study. Journal of Magnesium and Alloys 3 (2015) 197-202. http://dx.doi.org/10.1016/j.jma.2015.08.003]. It is necessary to specify the dimension of elastic constants and modules (GPa)
4. Table 3. “Layer distances” Can the distance be measured in %. Need to change the name
5. Figure 6, 7, 8. For the partial density of states (PDOS), you must specify the units of measurement.
6. Figure 9, 10, 11. The term “electronic structure” is used. Would it be correct to use electron density or deformation charge density?
7.Conclusions. “hybrid orbitals were found to have formed” This is not a good physical expression.
In general, the manuscript should be recommended for publication, after appropriate clarifications.
Author Response
Dear reviewer
Thank you for your comments. All the responds are in the attached file. And please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have addressed my main concerns. I have no further issues.
