Crystal Chemistry and Physical Properties of A Quaternary Intermetallic Compound, θ-(Al0.8718Cu0.0256Si0.1026)13Fe4
Round 1
Reviewer 1 Report
The Article is devoted to theoretical investigation of intermetallic compound, θ-(Al0.8718Cu0.0256Si0.1026)13Fe4 which appears during casting of commercial Al metals and alloys. Basing on first-principles density-functional theory, and thermodynamics and statistical analysis the Authors estimate a stability of this compound and its bulk modulus. Results of study gives new information about formation and phase transformation of θ-phase during casting. The Article is well and clearly written. I have no critical comments and think the Article can be published as it is.
Author Response
We thank Reviewer 1 very much for the careful reading and good understanding of our work. We also improved the language in the text.
Reviewer 2 Report
The authors presented extensive theoretical work on a computational study of the substitution effects in the Al-rich region of the Al13Fe4 alloy system. Modeling and analysis of a complex Cu-containing Al-based intermetallic system were aimed toward the study of chemical ordering in the monoclinic phase with different Si content. The main goal was to numerically simulate the structural and electronic properties in order to understand how local substitutions in Al positions affect the stoichiometric lattice. Thus, this work may provide additional insight into possible ways to optimize the formation of Al-rich quaternary intermetallic compounds. It may be recommended that the authors revise the manuscript according to the suggestions/comments listed below.
1) The analysis, which is a key aspect of the study and therefore very important for understanding, is not performed completely. In particular, the work examines the structural stability of the model, which has a low-symmetric lattice, but does not consider the details of the elastic constants (Born criteria), and does not check the behavior of the low-lying vibrational modes of the phonon spectrum.
2) It is well known from the DFT+U method that a number of electronic characteristics are sensitive to intra-atomic (on-site) Coulomb repulsion (U). In this context, it would be interesting to explain why the authors used the Stoner approach for iron atoms and the Hubbard model for copper atoms, respectively, in their simulations.
3) Bader's charge analysis (Tables 1 and 2):
- Why do the calculated Bader charges differ markedly for symmetrically equivalent lattice positions? Is this an inhomogeneous effect or is it caused by the computational scheme when only the valence charges were used in the PAW calculations and not the total charge summing the core and valence charges? In this case, since Figure 4 indicates the absence of a pseudo-gap, the presented bonding scheme is irrelevant to the model of an intermetallic system, since it contains strongly reduced iron.
- Why is the structural hierarchy of copper such that it is accommodated in the 2c Wyckoff positions of the lattice model? Is this accommodation structurally stable?
- Spin-polarized calculations were used in the simulations. Why is the magnetic moment of iron atoms not listed in Table 2? It would be interesting to relate the electron configuration of iron, chosen from the effective Bader charges (electron counting), to the magnetic characteristics.
4) It would be interesting to check the Al-Al bond changes in the model quaternary composition of the Al-based intermetallic system.
5) Table 4: In the context of local chemical pressures and bond optimizations, it would be interesting to understand the crystal-chemical origin of the volume effect.
6) Page 1, lines 42 and 43: "... with 20 different atomic species (15 Al and 5 Fe)". This phrase seems unclear in a crystallographic sense.
7) Page 12, lines 339 and 340: "This compound exhibits a chemically ionic, metallic, and covalent triple nature." This sentence seems confusing in a crystal-chemical sense.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 3 Report
The authors studied structural and mechanical properties of the quaternary Al-Cu-Fe-Si system from first principles. The methods they use correspond to the present state of the art approaches, and the computational settings seem to be appropriate to give correct and trustworthy results. The presentation of the results obtained is clear and comprehensive.
There are only some minor corrections (typos) that should be made:
· unify the quotation marks in the caption of Fig. 1
· two dots at the end of the caption of Fig. 3, Fig. 5, Fig. 6and Table 4
Author Response
We appreciate the careful reading and positive feedback of Reviewer 3. We checked the references, improved the English language and unified and clarified the quotation marks in the caption of Figure 1 in detail and deleted the extra dots in the Figures and Table 4.
Round 2
Reviewer 2 Report
The authors have revised their manuscript. However, not all of the issues raised in the previous report have been addressed and further improved. The manuscript has some potential. It could be suggested that readers will expect that the authors will provide more details on the results presented. In this context, all the results could be well structured, clearly explained, and discussed.
Answer | Commentary on the response
(A1) This answer seems rather indefinite. For information, in theoretical modeling of macroscopic elastic properties, the analysis of the bulk (B) modulus is sufficient only for highly symmetric systems of the cubic lattice type (isotropic material model). In the case of a low-symmetric crystal lattice, there is a fundamental question whether it is possible to limit the analysis to the bulk (B) module for the elastic (or macroscopic stability of the equilibrium geometry of this lattice and, accordingly, not to check other possible acoustic-phonon instabilities. In this context, the comparison of the authors' results with the work of R. A. Cowley (Phys. Rev. B 1976, 13, 4877) would be very reasonable.
(A2) This answer is rather irrelevant. The question was why the DFT model of intermetallic alloy assumes that the KS electronic states of copper atoms are renormalized by in-situ Coulomb repulsion, while the KS electronic states of iron atoms are considered delocalized?
(A3) This answer is irrelevant. For information, the grid-based Bader analysis algorithm, which implements the AIM approach, is used as a post-processing method to investigate charge density distributions calculated numerically in the employed DFT scheme. It is known from the PAW-PP calculations methodology that computations of effective Bader charges are based on total charges (which are the sums of the core and valence charges). If only valence charges are used, there can be a false effect of unphysical separation into electron-rich and electron-poor spatial regions. In particular, the result that iron atoms are easily reduced to stable Fe3- anions is chemically curious, because iron with a high negative charge density is a completely uncharacteristic feature in the inorganic crystal chemistry of iron compounds.
(A3_1) From the point of view of crystal chemistry, this answer is incorrect. This means that the local charge density distributions are different at sites with the same point symmetry. However, this is only possible when the DFT calculations are not yet finished and the model system remains in a state of waiting for further charge redistribution.
(A3_2) The answer about the 2c Wyckoff positions is irrelevant. The reader might expect more details on this issue from the authors, since the reader would not seek understanding of this issue in the authors' previous studies.
(A3_3) The answer contradicts the results of the work. Since the Fe atom has a magnetic moment, the Fe3- anion can also contain uncompensated spins.
(A4) No analysis of these distances has been included in the paper.
(A5) The answer is unclear.
(A7) Already from the title of the work it is obvious that this answer is completely incomprehensible.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
The authors did not provide a constructive revision of their manuscript. Nor did they give a more detailed elaboration of their findings. In particular, the real picture of the ground state of the electronic subsystem is not sufficiently investigated. Figure 3 seems uninformative. Figure 4 lacks significant information - does not show the electronic states of Al. The effects of p-d hybridization are not considered. In this context, the results cannot be considered properly structured, clearly explained, and well reasoned.
Answer | Commentary on the response
Re1) The response discusses stability issues concerning some high-symmetry directions, but completely ignores inspection for other essential instabilities associated with transverse acoustic modes. But this approach can be appropriate only for cubic lattices with higher symmetry (i.e., when an isotropic material model is considered). More details on this issue can be found in R. A. Cowley, Phys. Rev. B 1976, 13, 4877. In particular, as emphasized in this paper, there is a direct connection between macroscopic stability against homogeneous deformations and positive eigenvalues of the matrix of elastic constants. Thus, the authors' answer can be regarded as rather unclear.
Re2) The DFT model of intermetallic alloy used in this work assumes that the KS electronic states of copper atoms are subject to in-situ Coulomb repulsion, while the KS electronic states of iron atoms are delocalized. Following these assumptions, the authors performed DFT calculations. The reviewer's criticism was that such a picture (i.e., why just the 3d electrons of copper are considered strongly correlated) was not well explained in the text in a clear physical way. Unfortunately, the authors' response is disappointing and does not add any clarity on this issue.
Re3) The authors' answer cannot be considered acceptable. The procedure and analysis of the calculated data look defective. According to the reviewer's comment, the authors were asked to carefully re-analyze the charge density distributions calculated numerically in the DFT scheme used. According to an opinion of the reviewer, the values of Bader effective charges reported for the DFT model of an intermetallic alloy seem to be incorrect. For more information, the authors may read the following information: "Code: Bader Charge Analysis," published online by the Henkelman group, https://theory.cm.utexas.edu/henkelman/code/bader/ , section "Note for VASP users".
Re3_1) The authors' response cannot be accepted as argumentative. The reviewer's comment comes from the principle of periodicity of the crystal lattice and the role of point symmetry in respect to the crystallographic sites of the unit cell. In fact, the authors' results contradict these key properties of crystal lattices.
Re3_3) This issue remains unclear. In particular, the reviewer's comment stated: "The answer contradicts the results of the work. Since the Fe atom has a magnetic moment, the Fe3- anion can also contain uncompensated spins." In their response, the authors claim that "... the Fe atoms here have no uncompensated electrons.". However, a simple count of electrons shows that the electronic configuration of the ground state of Fe3- anionic iron could be [Ar].3d9.4s2. This is one of the reasons why the reviewer wrote in a previous report: "It is known from the PAW-PP calculations methodology that computations of effective Bader charges are based on total charges (which are the sums of the core and valence charges). If only valence charges are used, there can be a false effect of unphysical separation into electron-rich and electron-poor spatial regions. In particular, the result that iron atoms are easily reduced to stable Fe3- anions is chemically curious, because iron with a high negative charge density is a completely uncharacteristic feature in the inorganic crystal chemistry of iron compounds." This point is very important because several results contain this artifact.
Re7) The reviewer's comment was - This sentence ("This compound exhibits a chemically ionic, metallic, and covalent triple nature.") seems confusing in a crystal-chemical sense. In the crystal chemistry context, the arguments presented in the response look inconsistent and fall outside the chemical rules. The central point is that the simple (naive) mechanistic unification of three different kinds of chemical bonding within a whole model system seems incorrect, since such a construction does not correspond to the methodology and generally accepted procedures of quantum chemistry. In particular, the work lacks a clear analysis of the real electron density distributions and the investigation of their macroscopic stability.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
