First-Principles Study on the Elastic Mechanical Properties and Anisotropies of Gold–Copper Intermetallic Compounds

Round 1

Reviewer 1 Report

The authors present an excellent theoretical study of elastic properties of three Au-Cu intermetallic compounds, in particular Au3Cu, AuCu and AuCu3. The study is clearly motivated and the authors neatly explain the importance of their work. The quantum-mechanical calculations are excellently performed and their technical details are listed in detail. The manuscript is also very well structured and its English is perfect – it was very smooth reading for me.

As far as the results are concerned, the authors mention previous theoretical studies of elastic properties of the Au-Cu intermetallics and the present results are in agreement with the previously published values. Importantly, in contrast to these previous studies, the authors of the current manuscript provide a very detailed analysis of elastic anisotropy of a number of elastic properties, e.g., Young’s modulus, shear modulus and the Poisson ratio. In particular the anisotropy of shear modulus and Poisson ratio are very rarely seen in the literature. Importantly, the authors do not only present directional dependences but also provide complete and quite complicated mathematical relations of the directional dependences of shear modulus and the Poisson ratio. Therefore, I expect that this paper will be studied and cited in the future not only because of the elastic parameters of the Au-Cu intermetallics but also because of the complicated equations mentioned in this manuscript.

My very minor criticism is related to the following two facts:

1) It would nice if all the three structure visualized in Fig. 1 are rotated by the same angle and the coordination system on the right-hand side is rotated in the same way – as it is now it is not mistake, it would be just nicer if it is rotated in the same way.

2) It seems to me that there is mistake in the figure caption of Fig. 2 where (it seems to me that) the sub-figure 2b visualizes the Young’s modulus  and not the bulk modulus as currently written … but I can be wrong – I just suggest that the authors check it.

To summarize, I recommend this manuscript to be accepted for publication.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript 'First-principles...' by J. Wang et al. investigates the elastic properties of three intermetallic compounds (IMC); AuCu3, AuCu, and Au3Cu3, using density-functional theory (DFT).
Au-Cu IMC's has been shown interest by the scientific community over the years, but their mechanic properties have not been studied theoretically in a systematic fashion before, it seems. 
The manuscript is nicely written, and seem to use sound methods, and could be a useful reference in the future for materials researchers. However, there are some issues that have to be clarified before acceptance:

1) The Au-Cu IMC's are known to be difficult cases for DFT. The (somewhat simplified) reason is that the LDA is good for heavier elements (like Au) and GGA is better for lighter elements (like Cu). Therefore, when you
try to model a compound like Au-Cu, it is hard to find a suitable functional (see for example Zhang et al., PRL 112, 075502 (2014) and Tian et al., PRL 117, 066401 (2016)). This issue is not mentioned in the manuscript. Can the authors argue for the use of the PBE-GGA in their calculations?

2) Usually, many k-points are needed to get well-converged elastic constants. The k-meshes that were used in the manuscript looks somewhat small (though I must say I am not familiar with how CASTEP constructs k-meshes). Did the authors check
for convergency of the elastic constants with respect to the number of k-points?

3) On line 71, there is no need to mention the maximum number of iterations. I assume all calculations were converged?

4) In the caption of Figure 2, the labelling between (b) and (c) seems to be mixed up. 
On a similar note, Figures 2 and 5 would benefit from having the chemical formula written out next to the plots, this would improve readability.

5) Some typos:

56: Posson's -> Poisson's
70: A -> AA (angstrom)
81: It -> They
202: Tetragonal -> tetragonal
208: Young's -> Young's modulii
349: Telaxation -> Relaxation

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have answered the questions to my satisfaction. I can recommend the manuscript for publication.