A Study on the Mechanical Properties of Ni-Al Alloy Based on Molecular Dynamics Simulation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

See Attached file/report

Comments for author File: Comments.pdf

Comments on the Quality of English Language

See Attached file/report

Author Response

Thank you very much for your valuable time and review comments of our manuscript titled “A study on the mechanical properties of Ni-Al alloy based on molecular dynamics simulation.” (ID: Coatings-4081905). Your profound insights have greatly helped us to improve the quality and clarity of this research work. We have made a comprehensive and detailed revision of the manuscript according to each of your suggestions. Now we will state the specific amendments and supplementary explanations to your suggestions one by one as follows.

 

Response to the reviewer’s comments:

Reviewer #1:

The manuscript investigates the tensile mechanical behavior of NiAl and Ni₃Al single-crystal intermetallics at different temperatures using molecular dynamics simulations. The topic is good for high-temperature structural and coating applications, and the atomistic approach is appropriate. However, despite the extensive simulation results, the manuscript requires improvements in motivation, methodological justification, and the depth and consistency of the mechanistic interpretation to strengthen its scientific impact.

Authors’ Response: Thank you very much for your review work, positive comments and very kind recommendation. According to the recommendation, we have tried our best to improve the content of the manuscript.

 

Commnets:

[1] The abstract is largely descriptive and repetitive and it does not clearly articulate the novelty or specific scientific contribution of the study beyond reporting temperature dependent trends. Several statements (such as weakening of mechanical properties with temperature, phase transition before and after fracture) are generic outcomes of MD tensile simulations and are not framed as new insights. So, the authors should explicitly state the new mechanistic insight gained from the simulations, particularly what fundamentally distinguishes the deformation or fracture behavior of NiAl from Ni₃Al and why this matters for high-temperature applications.

Authors’ Response: We totally agree with your opinion and have completely rewritten the Abstract. The new abstract points out the research background and challenges at the beginning and highlights the core scientific contributions at the end. The most important modification is that, we clearly expounded the new mechanism obtained in the re-submitted manuscript.

The following modifications have been added to the Abstract (lines 27-37):

In this study, the tensile mechanical behavior and microscopic mechanism of single crystals NiAl (B2) and Ni₃Al (L12) at different temperatures were systematically studied by the molecular dynamics method. It is found that although the mechanical properties of NiAl and Ni₃Al decrease with the increase of temperature, there are essential differences in their deformation mechanisms: the high temperature strength of NiAl originates from the stable plastic flow dominated by 1/2 <111> screw dislocation. The early softening of Ni3Al is closely related to stacking fault formation, HCP phase transition and the slip of various incomplete dislocations (such as 1/6 <112> Shockley dislocation). Atomic strain analysis shows that the high strain region is highly consistent with the phase transition region. This study reveals the completely different deformation mechanism of the two alloy phases from the atomic scale, which provides a key theoretical basis for the rational selection of Ni-Al alloy for specific high temperature conditions.

[2] The Introduction lacks a clear research gap and justification for the present study, as it mainly summarizes general background and prior work without explicitly identifying what remains unresolved in existing MD or experimental studies on NiAl and Ni₃Al. The authors should clearly state what specific limitation in the literature is being addressed and how their single-crystal, temperature-dependent MD analysis provides new insight beyond previous studies.

Authors’ Response: We highly appreciate this valuable suggestion, which helps us improve the academic rigor and pertinence of the manuscript. According to the comment, we have revised the Introduction section accordingly.

The following modifications have been added to the second paragraph (lines 53-54), the third paragraph (lines 72-80), the fourth paragraph (lines 81-85) and the fifth paragraph (lines 86-93) of the Introduction:

The second paragraph: Previous studies on Ni–Al alloys have primarily focused on alloy design, processing routes, and microstructural strengthening mechanisms. For example,

The third paragraph: However, despite these extensive efforts, several key issues remain insufficiently addressed. Most existing experimental and computational studies concentrate on polycrystalline or nanocrystalline Ni-Al alloys, where grain boundaries and phase interfaces dominate deformation behavior, making it difficult to isolate the intrinsic mechanical response of the crystal lattice itself. Moreover, systematic temperature-dependent investigations of single-crystal NiAl and Ni₃Al under complex loading conditions are scarce, particularly at the atomic scale. In available MD studies, direct comparisons between NiAl and Ni₃Al single crystals remain limited. As a result, the fundamental mechanisms governing temperature-induced changes in elastic–plastic behavior, defect evolution, and crystal structure stability in these two materials are still not fully understood.

The fourth paragraph: Given that single-crystal materials generally exhibit superior high-temperature strength, creep resistance, and fatigue performance compared with polycrystalline counterparts, especially for turbine blades and other hot-end components. Accordingly, conducting systematic, temperature-dependent atomic-scale investigations on single-crystal NiAl and Ni₃Al is of critical significance for gaining in-depth insights into their intrinsic deformation mechanisms.

The fifth paragraph: In this study, molecular dynamics simulations were employed to investigate the biaxial tensile deformation behavior of single-crystal NiAl and Ni₃Al over a wide temperature range. By analyzing stress–strain responses, crystal structure evolution, and defect formation mechanisms at the atomic scale, this study provides new insights into the intrinsic mechanical characteristics and temperature sensitivity of these intermetallic compounds. The results aim to clarify the fundamental differences between NiAl and Ni₃Al single crystals under thermal–mechanical coupling conditions, thereby offering theoretical guidance for the design and application of Ni-Al based single-crystal materials in high-temperature aerospace environments.

 

[3] Seventeen references can be sufficient for a focused MD study. However, in its current form the introduction relies on limited and selectively cited literature, particularly for recent MD studies and mechanistic interpretations of NiAl/Ni₃Al deformation. The authors should expand and better balance the references, especially by including more recent and directly comparable simulation and experimental works, to convincingly establish the research gap and context.

Authors’ Response: Thank you very much for your comments. We have completely updated and expanded the references and added several key documents.

The following modifications have been added to the first paragraph (lines 148-150 and 152-155) and the second paragraph (lines 167-172) in 3.1 Tensile analysis of NiAl:

The first paragraph: The main reason is that the temperature rise intensifies the thermal vibration of atoms, increases the average distance between atoms, and weakens the bonding force between atoms, thus reducing the ability of materials to resist elastic deformation [31,32].

This is because the temperature increases, the binding force between atoms weakens and the lattice energy decreases, which weakens the lattice stability and makes it easier for the system to break through the phase transition energy barrier to produce phase transition [33].

The second paragraph: The main reason is that in the stress concentration area during the pre-fracture tensile process, local strain induces crystal structure rearrangement, and mechanical load promotes the BCC phase to transform into metastable FCC phase and amorphous phase, thus reducing stress concentration and delaying crack propagation. After the crack is formed, the external load is released, and the NiAl system in the BCC lattice is a stable structure with the lowest energy, and the atoms tend to return to this stable phase [34].

The following modifications have been added to the first paragraph (lines 223-231) and the third paragraph (lines 259-269) in 3.2 Tensile analysis of Ni₃Al:

The first paragraph: This is because NiAl is B2-type ordered body-centered cubic structure, Ni and Al atoms occupy the body center and vertex positions respectively, and the atoms in the lattice are relatively tightly packed, so the lattice has a strong intrinsic ability to resist deformation [40]. Ni₃Al is an ordered face-centered cubic structure of L1₂ type. Al atoms occupy the vertex position of the face-centered cubic, and Ni atoms fill all octahedral gaps, and the atomic packing density of its lattice is lower than that of the B2 structure. More crucially, there are a large number of parallel {111} slip planes in the L1₂ structure, and the interlayer bonding force between slip planes is weaker than that between lattices in the B2 structure, so it is easier to have relative slip between layers under the action of external force, which shows lower tensile stress and elastic modulus macroscopically [41].

The third paragraph: This is because NiAl is B2-type ordered body-centered cubic structure, and its effective slip system is mainly <111> {110} at room temperature to moderate temperature, and the number of slip systems is small, and the dislocation is 1/2 <111> total dislocation, so the lattice resistance and antiphase domain boundary (APB) resistance to be overcome in slip are high [42,43]. High resistance will inhibit the initiation and proliferation of dislocations, so the dislocation density is low. On the contrary, Ni₃Al is an ordered face-centered cubic structure of L12 type, with effective slip systems of <110> {111} and <110> {112}, and the number of slip systems is far greater than that of NiAl's B2 structure. At the same time, incomplete dislocation dominates the slip, and the critical cleavage stress (CRSS) required for slip is significantly lower than that of NiAl's total dislocation [44,45]. The low resistance enables NiAl to quickly start a large number of slip systems under a small external stress, which leads to the continuous proliferation of dislocations and directly increases the dislocation density.

 

[4] Modeling and Simulation Details section needs more critical methodological justification in regards to the choice of tensile direction, loading rate, ensemble (NVT during deformation), and simulation time with size effects. The authors should justify these selections, discuss their physical relevance to real deformation conditions, and briefly assess whether the chosen strain rate and boundary conditions could influence the reported mechanical responses and defect evolution.

Authors’ Response: Thank you very much for your suggestion. In the second section, "Modeling and Simulation Details", we have added the demonstrative explanation.

The following modifications have been added to the first paragraph (lines 111-113) of the Modeling and simulation details:

The simulation system adopted the canonical ensemble (NVT) during tensile. NVT ensemble was selected to better control the simulation temperature and study the temperature effect, which is a typical choice for MD simulation with high strain rate and limited computing resources [24].

 

[5] Figure 1 lacks clarity and does not effectively convey the spatial distribution of different atomic species. Due to the large number of atoms, the tensile configuration is difficult to interpret, and Ni and Al atoms cannot be clearly distinguished by color. The authors should simplify the visualization with a reduced model, zoomed region, or clearer color scheme. Or consider removing the figure if it does not add meaningful information.

Authors’ Response: Thank you very much for your suggestion. According to the suggestion, we modified the color matching of the picture and replaced the original picture.

The following modifications have been added to the first paragraph (lines 115) of the Modeling and simulation details:

 

 

[6] While the authors mention the use of LAMMPS and OVITO, the description is largely procedural rather than explanatory, with limited discussion of why these tools and specific analysis methods were chosen or how their settings affect reliability. The authors should briefly clarify the software versions, key input choices, and validation rationale to improve transparency and reproducibility.

Authors’ Response: Thank you very much for your comments. In the second section of Modeling and simulation details, we have added the relevant description.

The following modifications have been added to the first paragraph (lines 96-99) and the fourth paragraph (lines 129-131) of the Modeling and simulation details:

The first paragraph：The reason for choosing LAMMPS is its high efficiency in simulating atomic dynamics of large-scale metal system [19], which can accurately describe the atomic bonding and lattice evolution behavior of the simulated system, and meets the simulation requirements of defect evolution and atomic reconstruction in the tensile process of this study.

The fourth paragraph：OVITO was chosen to carry out structural analysis because its built-in calculation modules are mature and stable.

 

[7] Lattice constants of NiAl (B2) with a ≈ 2.86 Å is reasonable and commonly reported. For Ni₃Al (L1₂) with a = 3.52 Å is somewhat lower than widely reported values of typically 3.56-3.58 Å at room temperature. The authors should justify or reference the chosen lattice constant for Ni₃Al (give the source of the potential, equilibrium value after relaxation, or temperature dependence) to avoid ambiguity and ensure physical consistency.

Authors’ Response: Thank you very much for your suggestion. According to the suggestion, we supplemented the data sources in the manuscript.

The following modifications have been added to the first paragraph (lines 102-104) of the Modeling and simulation details:

In contrast, Ni₃Al possesses a typical face-centered cubic (FCC) crystal structure, with a lattice constant of 3.52 Å [20], values of typically 3.56-3.58 Å at room temperature [21-23].

 

[8] For section 3.1. Tensile Analysis of NiAl: The discussion in this section is largely descriptive and figure-driven, with limited mechanistic interpretation linking the observed stress-strain behavior to specific atomic-scale processes. The authors should more clearly explain how and why the reported phase transitions, dislocation evolution, and amorphization mechanisms control the different deformation stages and the temperature-dependent loss of strength, rather than restating trends visible in the figures.

Authors’ Response: Thank you very much for your suggestion. We have reconstructed this section. According to the suggestion, we have supplemented the explanations of phase transformation, dislocation evolution and amorphization in Section 3.1 (Tensile analysis of NiAl), and at the same time, added relevant references to support the explanation of relevant mechanisms, which enhanced the depth of discussion.

The following modifications have been added to the first paragraph (lines 148-150 and 152-155) and the second paragraph (lines 167-172 in 3.1 Tensile analysis of NiAl:

The first paragraph (lines 148-150 and 152-155): The main reason is that the temperature rise intensifies the thermal vibration of atoms, increases the average distance between atoms, and weakens the bonding force between atoms, thus reducing the ability of materials to resist elastic deformation [31,32].

This is because the temperature increases, the binding force between atoms weakens and the lattice energy decreases, which weakens the lattice stability and makes it easier for the system to break through the phase transition energy barrier to produce phase transition [33].

The second paragraph (lines 167-172): The main reason is that in the stress concentration area during the pre-fracture tensile process, local strain induces crystal structure rearrangement, and mechanical load promotes the BCC phase to transform into metastable FCC phase and amorphous phase, thus reducing stress concentration and delaying crack propagation. After the crack is formed, the external load is released, and the NiAl system in the BCC lattice is a stable structure with the lowest energy, and the atoms tend to return to this stable phase [34].

 

[9] In Section 3.2 (Tensile Analysis of Ni₃Al), there is a clear internal inconsistency in the interpretation of temperature effects. In lines 189-190, the authors state that the deformation resistance and mechanical properties of Ni₃Al decrease with increasing temperature, whereas in lines 206-207 they claim that the deformation resistance “gradually strengthened” as temperature increased. These two statements contradict each other and must be resolved so that the qualitative discussion is fully consistent with the stress-strain results and the overall mechanical interpretation.

Authors’ Response: Thank you very much for your careful and kind comments. According to the suggestion, we have carefully checked and corrected the contradictory statements in the original text, and unified the description of fracture strain in Section 3.2.

The following modifications have been added to the second paragraph (lines 244-245) in 3.2 Tensile analysis of Ni₃Al:

the fracture toughness increased gradually, and the fracture cavity in the system decreased gradually, and the strain should be higher when it was completely fractured.

 

[10] Most figure captions are descriptive but lack critical explanatory detail, and there are no tables summarizing key quantitative results. The authors should revise the captions to clearly define symbols, colors, strain and temperature conditions, and analysis methods used, and consider adding summary tables (like elastic modulus, fracture strain, peak stress) to improve clarity, readability, and comparison across temperatures and between NiAl and Ni₃Al.

Authors’ Response: Thank you very much for your comments. We have completely revised all the problematic illustrations and added the necessary explanatory details.

The following modifications have been added to the third paragraph (lines 188-189) of the 3.1 Tensile Analysis of NiAl and the third paragraph (lines 271-272) of the 3.2 Tensile Analysis of Ni₃Al:

 

Fig. 4. The statistical results of dislocation defects in NiAl after tensile at different temperatures

 

Fig. 9. The statistical results of dislocation defects in Ni₃Al after tensile at different temperatures

 

[11] The authors are requested to merge Figures 5 and 6 or remove one of them, as both convey similar information regarding structural distortion and disorder during tensile deformation. Combining or simplifying these figures would reduce redundancy and improve the clarity and conciseness of the results section. Take care of the captions.

Authors’ Response: Thank you sincerely for making this detailed and important suggestion to improve the conciseness of the manuscript.

Although these diagrams are all related to structural changes, they serve different analysis purposes. The core of the "Atomic Strain Analysis" in Figure 5 (for NiAl) is the visualization of spatial distribution, which aims to visually show the location of strain localization, the formation of shear band and its correlation with phase change region, which is a qualitative and spatial microscopic mechanism display. The "RDF analysis" in Figure 6 provides quantitative and global evidence of structural order change. The evolution of the peak value of RDF curve (such as the decrease of peak intensity and the broadening of peak value) is a key quantitative index to demonstrate the long-range disorder loss and amorphization process of the system. Merging these two kinds of data with different types and dimensions in one picture may blur their independent information, which is not conducive to readers' understanding of the logical chain from "qualitative observation strain concentration" to "quantitative confirmation structure disorder" step by step and at different levels.

 

[12] Again, the authors should merge Figures 10 and 11 or remove one of them, as both describe structural changes in Ni₃Al during tensile deformation and lead to overlapping conclusions. Consolidating these figures would reduce redundancy and improve the clarity and efficiency of the presentation.

Authors’ Response: Thank you sincerely for making this detailed and important suggestion to improve the conciseness of the manuscript. We seriously considered the plan of merging charts. After careful evaluation, we think that the separation of Figure 10 from Figure 11 is based on the following two scientific expressions, in order to provide readers with the clearest information flow.

Although these diagrams are all related to structural changes, they serve different analysis purposes. The core of the "Atomic Strain Analysis" in Figure 10 (for Ni₃Al) is the visualization of spatial distribution, which aims to visually show the location of strain localization, the formation of shear band and its correlation with phase change region, which is a qualitative and spatial microscopic mechanism display. The "RDF analysis" in Figure 11 provides quantitative and global evidence of structural order change. The evolution of the peak value of RDF curve (such as the decrease of peak intensity and the broadening of peak value) is a key quantitative index to demonstrate the long-range disorder loss and amorphization process of the system. Merging these two kinds of data with different types and dimensions in one picture may blur their independent information, which is not conducive to readers' understanding of the logical chain from "qualitative observation strain concentration" to "quantitative confirmation structure disorder" step by step and at different levels.

 

[13] The Conclusions section is very much repetitive of the Results and Discussion and does not clearly articulate the key take-home messages or broader implications of the study. The authors should condense descriptive statements and explicitly highlight the most important mechanistic findings, clearly distinguishing the behavior of NiAl versus Ni₃Al and explaining how these insights inform the design or selection of high-temperature structural or coating materials.

Authors’ Response: Thank you very much for your comments. We have rewritten the conclusion of the fourth section, abandoned the mode of simply repeating the results, and instead extracted the core mechanism discovery and its enlightenment to material design. The new conclusion clearly compares the different behaviors of NiAl and Ni₃Al, and expounds its significance for guiding the development of high-performance Ni-Al-based high-temperature materials and coatings.

The following modifications have been added to the Conclusions (lines 294-305):

In this study, the mechanical properties of single crystal NiAl and Ni₃Al under high temperature tension and their microscopic mechanism were systematically revealed by molecular dynamics simulation. The results show that NiAl's superior high-temperature deformation resistance stems from its stable plastic deformation mechanism dominated by 1/2 <111> screw dislocation, and the early softening of Ni₃Al is closely related to its complex stacking fault, HCP phase transformation and slip dominated by Shockley incomplete dislocation (1/6 <112>). Atomic strain analysis confirms that the high strain region is highly consistent with the phase transition region. The increase of temperature generally weakens the interaction between atoms and promotes the amorphous phase transition. In this study, the completely different deformation mechanisms of Ni-Al based intermetallic compounds are clarified from the atomic scale, which provides an important theoretical basis and design guidance for rational selection and design of Ni-Al based intermetallic compounds for specific high-temperature working conditions (such as high-stress parts or impact-resistant coatings).

 

[14] I find it strange that the manuscript does not quantitatively or qualitatively compare the MD results (elastic modulus, fracture strain, deformation mechanisms, …) with available experimental data for NiAl or Ni₃Al. The authors should include at least a brief comparison with reported experimental trends or values to validate the simulations and strengthen the physical relevance of the conclusions.

Authors’ Response: Thank you very much for your comments. We have added a brief comparison with the experimental data in the corresponding result discussion section.

The following modifications have been added to the first paragraph (lines 148-150 and 152-155) in 3.1 Tensile analysis of NiAl:

The main reason is that the temperature rise intensifies the thermal vibration of atoms, increases the average distance between atoms, and weakens the bonding force between atoms, thus reducing the ability of materials to resist elastic deformation [31,32].

This is because the temperature increases, the binding force between atoms weakens and the lattice energy decreases, which weakens the lattice stability and makes it easier for the system to break through the phase transition energy barrier to produce phase transition [33].

 

[15] The references are adequate in number but weak in balance and integration. Key recent experimental and MD studies directly relevant to tensile deformation, fracture, and temperature effects in NiAl/Ni₃Al are underrepresented, and several cited works are not explicitly linked to the claims they are used to support. The authors should update and better integrate the references, particularly by adding comparative experimental studies and recent MD benchmarks, to strengthen credibility and context.

Authors’ Response: Thank you very much for your comments. This revision has been completed together with the reply to comment 3. While updating and expanding the references, we ensure that each quotation closely corresponds to the specific discussion in this work, which enhances the scientific nature of the argument.

The following modifications have been added to the first paragraph (lines 148-150 and 152-155) and the second paragraph (lines 167-172) in 3.1 Tensile analysis of NiAl:

The first paragraph: The main reason is that the temperature rise intensifies the thermal vibration of atoms, increases the average distance between atoms, and weakens the bonding force between atoms, thus reducing the ability of materials to resist elastic deformation [31,32].

This is because the temperature increases, the binding force between atoms weakens and the lattice energy decreases, which weakens the lattice stability and makes it easier for the system to break through the phase transition energy barrier to produce phase transition [33].

The second paragraph: The main reason is that in the stress concentration area during the pre-fracture tensile process, local strain induces crystal structure rearrangement, and mechanical load promotes the BCC phase to transform into metastable FCC phase and amorphous phase, thus reducing stress concentration and delaying crack propagation. After the crack is formed, the external load is released, and the NiAl system in the BCC lattice is a stable structure with the lowest energy, and the atoms tend to return to this stable phase [34].

The following modifications have been added to the first paragraph (lines 223-231) and the third paragraph (lines 259-269) in 3.2 Tensile analysis of Ni₃Al:

The first paragraph: This is because NiAl is B2-type ordered body-centered cubic structure, Ni and Al atoms occupy the body center and vertex positions respectively, and the atoms in the lattice are relatively tightly packed, so the lattice has a strong intrinsic ability to resist deformation [40]. Ni₃Al is an ordered face-centered cubic structure of L1₂ type. Al atoms occupy the vertex position of the face-centered cubic, and Ni atoms fill all octahedral gaps, and the atomic packing density of its lattice is lower than that of the B2 structure. More crucially, there are a large number of parallel {111} slip planes in the L1₂ structure, and the interlayer bonding force between slip planes is weaker than that between lattices in the B2 structure, so it is easier to have relative slip between layers under the action of external force, which shows lower tensile stress and elastic modulus macroscopically [41].

The third paragraph: This is because NiAl is B2-type ordered body-centered cubic structure, and its effective slip system is mainly <111> {110} at room temperature to moderate temperature, and the number of slip systems is small, and the dislocation is 1/2 <111> total dislocation, so the lattice resistance and antiphase domain boundary (APB) resistance to be overcome in slip are high [42,43]. High resistance will inhibit the initiation and proliferation of dislocations, so the dislocation density is low. On the contrary, Ni₃Al is an ordered face-centered cubic structure of L1₂ type, with effective slip systems of <110> {111} and <110> {112}, and the number of slip systems is far greater than that of NiAl's B2 structure. At the same time, incomplete dislocation dominates the slip, and the critical cleavage stress (CRSS) required for slip is significantly lower than that of NiAl's total dislocation [44,45]. The low resistance enables NiAl to quickly start a large number of slip systems under a small external stress, which leads to the continuous proliferation of dislocations and directly increases the dislocation density.

 

[16] The manuscript contains numerous language and grammatical issues, including difficult and not clear phrasing, inconsistent terminology, and typographical errors, which at times hinder clarity and readability. In addition, sentence structure is often repetitive and very descriptive. A thorough professional English language editing is strongly recommended to improve clarity, coherence, and overall presentation.

Authors’ Response: Thank you very much for your comments. The manuscript has been comprehensively modified and polished with professional software to improve its accuracy, fluency and academic standardization.

 

[17] Finally, the listed keywords are too general and partially redundant with the title. The authors should refine them to include more specific and mechanism-oriented terms. Consider single-crystal deformation, phase transition, dislocation evolution, temperature-dependent tensile behavior, to improve discoverability and alignment with the core contributions of the manuscript.

Authors’ Response: Thanks very much for your kind comment. According to the suggestion, the keyword has been modified to "molecular dynamics simulation, Ni-Al alloy, dislocation evolution, phase transition". The new keywords can better reflect the core content and contribution of the paper.

 

[18] In general, although the authors briefly mention that Ni-Al intermetallics exist in several phases and highlight NiAl and Ni₃Al due to their high melting points and relevance to high-temperature applications, the justification remains incomplete. The manuscript does not clearly explain why these two phases are uniquely suitable for addressing the brittleness and deformation mechanisms targeted in this study, nor why other stable Ni Al phases (Ni₂Al₃, NiAl₃, Ni₅Al₃, …) or alloyed variants were excluded. The authors should explicitly clarify the scientific and mechanistic rationale for focusing exclusively on NiAl and Ni₃Al and describe the scope and limitations of their conclusions in this context.

Authors’ Response: Thank you very much for your comments. we have modified and explained the reasons for choosing NiAl and Ni₃Al in the Introduction.

The following modifications have been added to the first paragraph (lines 45-52) of the Introduction:

As a potential high-temperature structural material, Ni-Al intermetallic compounds mainly exist in five phase states: NiAl, Ni₃Al, NiAl₃, Ni₂Al₃, and Ni₅Al₃ [7,8]. The melting point of common Ni-Al intermetallic compounds can reach up to 1600 ℃, which is on average 300 ℃ higher than that of ordinary Ni-based alloys. Among them, due to the high melting points of NiAl and Ni₃Al, which are 1638 ℃ and 1395 ℃, respectively, they have received widespread attention as a substitute for nickel-based high-temperature alloys in aviation engine blades or thermal barrier coatings [9,10]. Moreover, NiAl not only has high thermal conductivity, but also has good resistance to high-temperature oxidation [11,12].

 

Once again, we sincerely thank you for your valuable time and incisive comments! We hope that this revision has fully responded to all your concerns and substantially improved the quality of the manuscript. I hope our revision can meet the requirements of you and the journal.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

See accompanying file.

Comments for author File: Comments.pdf

Author Response

Reviewer #2:

 

[1] I have difficulty interpreting Figures 4 and 9, which are said to represent dislocation defects ‘after tensile’... The extent of tensile strain is 35% (Fig.4) / 25% (Fig.9), which must mean that the structures have failed.

Authors’ Response: Yes, your understanding is basically consistent with what we want to express. We think that the system has failed at the time of tensile fracture, and the deformation resistance of NiAl and Ni3Al systems is different at 500, 1000 and 1500 K. NiAl system breaks at 35% strain and the structure fails, while Ni3Al system breaks at 25% strain and the structure fails. Therefore, we analyze the defects of this model in order to analyze its failure mechanism. In order to express more accurately and avoid ambiguity, we have put "strain 35%" (for NiAl) and "strain 25%" (for Ni3Al) in the relevant descriptions of Figure 4 and Figure 9 respectively to make it clear that this analysis corresponds to the moment of structural failure.

The following modifications have been added to the third paragraph (lines 188-189) of the 3.1 Tensile Analysis of NiAl and the third paragraph (lines 271-272) of the 3.2 Tensile Analysis of Ni3Al:

 

Fig. 4. The statistical results of dislocation defects in NiAl after tensile at different temperatures

 

Fig. 9. The statistical results of dislocation defects in Ni3Al after tensile at different temperatures

 

[2] In Figure 4 I see some green zones... but no trace of purple <100> or red ‘Other.’ More vectors are defined in Figure 9, but I see only green zones.

Authors’ Response: Thank you very much for your comments. First of all, because of the different types of dislocations produced after the two systems are stretched, the results of dislocation types in Figure 9 are more than those in Figure 4. The results in the manuscript are not clear because of the resolution of the picture, and in addition, because of our negligence, the Other type that does not exist is marked in Figure 4. According to the suggestion, we have replaced the two figures again.

The following modifications have been added to the third paragraph (lines 188-189) of the 3.1 Tensile Analysis of NiAl and the third paragraph (lines 271-272) of the 3.2 Tensile Analysis of Ni₃Al:

 

Fig. 4. The statistical results of dislocation defects in NiAl after tensile at different temperatures

 

Fig. 9. The statistical results of dislocation defects in Ni3Al after tensile at different temperatures

 

[3] I see distances of 325, 187, and 20 Angstroms for panels a-c in Figure 4 and quite different values 968, 693, and 16 in Figure 9, but no explanation of their meaning.

Authors’ Response: Thank you very much for pointing out this important omission. These numbers represent the total length of all identified dislocation lines in the system (unit: angstrom). The description of the manuscript lacks the description of the figures in the picture. According to the suggestion, we added the description in the figure. At the same time, we also added a brief analysis of the variation trend of the total dislocation length with temperature in the paragraphs of section 3.1 and section 3.2 of the manuscript, making it a part of our mechanism explanation.

The following modifications have been added to the third paragraph (lines 188-189) of the 3.1 Tensile Analysis of NiAl and the third paragraph (lines 271-272 and 259-269) of the 3.2 Tensile Analysis of Ni₃Al:

 

Fig. 4. The statistical results of dislocation defects in NiAl after tensile at different temperatures

This is because NiAl is B2-type ordered body-centered cubic structure, and its effective slip system is mainly <111> {110} at room temperature to moderate temperature, and the number of slip systems is small, and the dislocation is 1/2 <111> total dislocation, so the lattice resistance and antiphase domain boundary (APB) resistance to be overcome in slip are high [42,43]. High resistance will inhibit the initiation and proliferation of dislocations, so the dislocation density is low. On the contrary, Ni₃Al is an ordered face-centered cubic structure of L1₂ type, with effective slip systems of <110> {111} and <110> {112}, and the number of slip systems is far greater than that of NiAl's B2 structure. At the same time, incomplete dislocation dominates the slip, and the critical cleavage stress (CRSS) required for slip is significantly lower than that of NiAl's total dislocation [44,45]. The low resistance enables NiAl to quickly start a large number of slip systems under a small external stress, which leads to the continuous proliferation of dislocations and directly increases the dislocation density.

 

 

Fig. 9. The statistical results of dislocation defects in Ni3Al after tensile at different temperatures

 

[4] The response of g(r) to temperature and strain shown in Figures 6 and 11 (especially panels 6b and 11b) might deserve further discussion, particularly in the range 6-8 Angstroms.

Authors’ Response: Thank you very much for your suggestion. According to the suggestion, we supplemented and modified the relevant analysis content.

The following modifications have been added to the fourth paragraph (lines 205-21) in 3.1 Tensile analysis of NiAl:

The results in Fig. 6 (b) indicated that during the strain variation from 0 to 20%, the probability of atomic bonding gradually decreased and the interaction force gradually weakend. After the strain increases from 20% to 30%, the intensity of the first peak of the RDF increases, and the peak shifts to the left. This is because after the occurrence of crack defects (Stage IV), the external forces acting on the atoms in the system gradually decrease, leading to the transformation of the system stress during tension into inter-atomic forces. As a result, the atomic arrangement becomes tighter, the inter-atomic interactions were enhanced, and the bond length gradually shortens [39].

The following modifications have been added to the fourth paragraph (lines 282-288) in 3.2 Tensile analysis of Ni₃Al:

Fig. 11 (b) showed the variation results at 500 K, indicating that at a strain of 0-10%, as the tensile progresses, the bond length between atoms in the system increased, the interaction gradually weakened, the peak position shifted to the right, and the peak strength weakened. When the strain was between 20% and 25%, the state change caused by atomic tension ends due to the breaking of chemical bonds at both ends of the crack in the system. The system contracted, the bond length decreased, the interatomic interaction strengthened, the peak position shifted to the left, and the peak intensity increased.

 

Once again, we sincerely thank you for your valuable time and incisive comments! We hope that this revision has fully responded to all your concerns and substantially improved the quality of the manuscript. I hope our revision can meet the requirements of you and the journal.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

A study on the mechanical properties of Ni-Al alloy based on molecular dynamics simulation

 

1. The abstract addresses an important topic and presents relevant results. Still, it should be refined for clarity, corrected for grammar and usage, and made more concise, with a clearer emphasis on the main findings and their significance.
2. The introduction is well structured and provides strong motivation for studying Ni–Al intermetallic compounds; however, it would benefit from careful language polishing, removal of redundancy, correction of spelling and formatting errors, and a more explicit statement of the research gap and the specific novelty of the present work on single-crystal NiAl and Ni₃Al.
3. The potential energy formula is not clearly defined because the variable r (interatomic distance) is undefined. The authors should explicitly state that r denotes the distance between atoms i and j and clarify all symbols used in the EAM potential equation for completeness and clarity.
4. The results are detailed, but the section would benefit from language refinement, correction of typographical errors, a more precise definition of the Burgers vector, clearer figure-to-text connections, and a more concise interpretation that more explicitly links stress–strain behavior, phase transitions, defect evolution, and atomic strain to the underlying deformation and fracture mechanisms.
5. The conclusions clearly summarize the main findings, but the authors should refine the language and strengthen the findings by making them more concise and quantitative and by better emphasizing the novelty and practical implications of the results for high-temperature applications.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

The English could be improved to make the research more straightforward.

Author Response

Reviewer #3:

 

[1] The abstract addresses an important topic and presents relevant results. Still, it should be refined for clarity, corrected for grammar and usage, and made more concise, with a clearer emphasis on the main findings and their significance.

Authors’ Response: We totally agree with your opinion and have completely rewritten the abstract. The new abstract points out the research background and challenges at the beginning and highlights the core scientific contributions at the end.

The following modifications have been added to the Abstract (lines 24-37):

With the wide application of Ni-Al high-temperature materials, the research on their performance has gradually gained attention. To further develop Ni-Al high-temperature materials, it is necessary to deeply analyze the brittleness mechanism of Ni-Al intermetallic compounds and reveal the essence of the brittleness of Ni-Al intermetallic compounds. In this study, the tensile mechanical behavior and microscopic mechanism of single crystals NiAl (B2) and Ni₃Al (L1₂) at different temperatures were systematically studied by the molecular dynamics method. It is found that although the mechanical properties of NiAl and Ni₃Al decrease with the increase of temperature, there are essential differences in their deformation mechanisms: the high temperature strength of NiAl originates from the stable plastic flow dominated by 1/2 <111> screw dislocation. The early softening of Ni₃Al is closely related to stacking fault formation, HCP phase transition and the slip of various incomplete dislocations (such as 1/6 <112> Shockley dislocation). Atomic strain analysis shows that the high strain region is highly consistent with the phase transition region. This study reveals the completely different deformation mechanism of the two alloy phases from the atomic scale, which provides a key theoretical basis for the rational selection of Ni-Al alloy for specific high temperature conditions.

 

[2] The introduction is well structured and provides strong motivation for studying Ni–Al intermetallic compounds; however, it would benefit from careful language polishing, removal of redundancy, correction of spelling and formatting errors, and a more explicit statement of the research gap and the specific novelty of the present work on single-crystal NiAl and Ni₃Al.

Authors’ Response: Thank you very much for your affirmation and suggestions on this part. We have refined the language of the introduction, corrected spelling and formatting errors, and made the expression more concise and professional. According to the comment, we have revised the Introduction section accordingly.

The following modifications have been added to the second paragraph (lines 53-54), the third paragraph (lines 72-80), the fourth paragraph (lines 81-85) and the fifth paragraph (lines 86-93) of the Introduction:

The second paragraph: Previous studies on Ni–Al alloys have primarily focused on alloy design, processing routes, and microstructural strengthening mechanisms. For example,

The third paragraph: However, despite these extensive efforts, several key issues remain insufficiently addressed. Most existing experimental and computational studies concentrate on polycrystalline or nanocrystalline Ni-Al alloys, where grain boundaries and phase interfaces dominate deformation behavior, making it difficult to isolate the intrinsic mechanical response of the crystal lattice itself. Moreover, systematic temperature-dependent investigations of single-crystal NiAl and Ni₃Al under complex loading conditions are scarce, particularly at the atomic scale. In available MD studies, direct comparisons between NiAl and Ni₃Al single crystals remain limited. As a result, the fundamental mechanisms governing temperature-induced changes in elastic–plastic behavior, defect evolution, and crystal structure stability in these two materials are still not fully understood.

The fourth paragraph: Given that single-crystal materials generally exhibit superior high-temperature strength, creep resistance, and fatigue performance compared with polycrystalline counterparts, especially for turbine blades and other hot-end components. Accordingly, conducting systematic, temperature-dependent atomic-scale investigations on single-crystal NiAl and Ni₃Al is of critical significance for gaining in-depth insights into their intrinsic deformation mechanisms.

The fifth paragraph: In this study, molecular dynamics simulations are employed to investigate the biaxial tensile deformation behavior of single-crystal NiAl and Ni₃Al over a wide temperature range. By analyzing stress–strain responses, crystal structure evolution, and defect formation mechanisms at the atomic scale, this study provides new insights into the intrinsic mechanical characteristics and temperature sensitivity of these intermetallic compounds. The results aim to clarify the fundamental differences between NiAl and Ni₃Al single crystals under thermal–mechanical coupling conditions, thereby offering theoretical guidance for the design and application of Ni-Al based single-crystal materials in high-temperature aerospace environments.

 

[3] The potential energy formula is not clearly defined because the variable r (interatomic distance) is undefined. The authors should explicitly state that r denotes the distance between atoms i and j and clarify all symbols used in the EAM potential equation for completeness and clarity.

Authors’ Response: This point you pointed out is very accurate, which is very important to ensure the rigor and repeatability of the method. We have supplemented the description of formula (1).

The following modifications have been added to the first paragraph (lines 124-125) of the Modeling and simulation details:

and r is the distance between atoms i and j.

 

[4] The results are detailed, but the section would benefit from language refinement, correction of typographical errors, a more precise definition of the Burgers vector, clearer figure-to-text connections, and a more concise interpretation that more explicitly links stress–strain behavior, phase transitions, defect evolution, and atomic strain to the underlying deformation and fracture mechanisms.

Authors’ Response: Thank you very much for your comments. We have completely revised the third section "Results and Discussion". Including the language touch-up of the full manuscript and the correction of all the identified typographical errors. We also supplemented the analysis content of results, which is devoted to organically linking the observed results of stress-strain behavior, phase transformation, defect evolution (such as dislocation) and atomic strain.

The following modifications have been added to the first paragraph (lines 148-150 and 152-155) and the second paragraph (lines 167-172) in 3.1 Tensile analysis of NiAl:

The first paragraph: The main reason is that the temperature rise intensifies the thermal vibration of atoms, increases the average distance between atoms, and weakens the bonding force between atoms, thus reducing the ability of materials to resist elastic deformation [31,32].

This is because the temperature increases, the binding force between atoms weakens and the lattice energy decreases, which weakens the lattice stability and makes it easier for the system to break through the phase transition energy barrier to produce phase transition [33].

The second paragraph: The main reason is that in the stress concentration area during the pre-fracture tensile process, local strain induces crystal structure rearrangement, and mechanical load promotes the BCC phase to transform into metastable FCC phase and amorphous phase, thus reducing stress concentration and delaying crack propagation. After the crack is formed, the external load is released, and the NiAl system in the BCC lattice is a stable structure with the lowest energy, and the atoms tend to return to this stable phase [34].

The following modifications have been added to the first paragraph (lines 223-231) and the third paragraph (lines 259-269) in 3.2 Tensile analysis of Ni₃Al:

The first paragraph: This is because NiAl is B2-type ordered body-centered cubic structure, Ni and Al atoms occupy the body center and vertex positions respectively, and the atoms in the lattice are relatively tightly packed, so the lattice has a strong intrinsic ability to resist deformation [40]. Ni₃Al is an ordered face-centered cubic structure of L1₂ type. Al atoms occupy the vertex position of the face-centered cubic, and Ni atoms fill all octahedral gaps, and the atomic packing density of its lattice is lower than that of the B2 structure. More crucially, there are a large number of parallel {111} slip planes in the L1₂ structure, and the interlayer bonding force between slip planes is weaker than that between lattices in the B2 structure, so it is easier to have relative slip between layers under the action of external force, which shows lower tensile stress and elastic modulus macroscopically [41].

The third paragraph: This is because NiAl is B2-type ordered body-centered cubic structure, and its effective slip system is mainly <111> {110} at room temperature to moderate temperature, and the number of slip systems is small, and the dislocation is 1/2 <111> total dislocation, so the lattice resistance and antiphase domain boundary (APB) resistance to be overcome in slip are high [42,43]. High resistance will inhibit the initiation and proliferation of dislocations, so the dislocation density is low. On the contrary, Ni₃Al is an ordered face-centered cubic structure of L1₂ type, with effective slip systems of <110> {111} and <110> {112}, and the number of slip systems is far greater than that of NiAl's B2 structure. At the same time, incomplete dislocation dominates the slip, and the critical cleavage stress (CRSS) required for slip is significantly lower than that of NiAl's total dislocation [44,45]. The low resistance enables NiAl to quickly start a large number of slip systems under a small external stress, which leads to the continuous proliferation of dislocations and directly increases the dislocation density.

 

[5] The conclusions clearly summarize the main findings, but the authors should refine the language and strengthen the findings by making them more concise and quantitative and by better emphasizing the novelty and practical implications of the results for high-temperature applications.

Authors’ Response: Thank you very much for your comments. We have rewritten the conclusion, abandoned the mode of simply repeating the results, and instead refined the core mechanism discovery and its enlightenment to material design. The new conclusion clearly compares the different behaviors of NiAl and Ni₃Al, and expounds its significance for guiding the development of high-performance Ni-Al-based high-temperature materials and coatings.

The following modifications have been added to the Conclusions (lines 294-305):

In this study, the mechanical properties of single crystal NiAl and Ni₃Al under high temperature tension and their microscopic mechanism were systematically revealed by molecular dynamics simulation. The results show that NiAl's superior high-temperature deformation resistance stems from its stable plastic deformation mechanism dominated by 1/2 <111> screw dislocation, and the early softening of Ni₃Al is closely related to its complex stacking fault, HCP phase transformation and slip dominated by Shockley incomplete dislocation (1/6 <112>). Atomic strain analysis confirms that the high strain region is highly consistent with the phase transition region. The increase of temperature generally weakens the interaction between atoms and promotes the amorphous phase transition. In this study, the completely different deformation mechanisms of Ni-Al based intermetallic compounds are clarified from the atomic scale, which provides an important theoretical basis and design guidance for rational selection and design of Ni-Al based intermetallic compounds for specific high-temperature working conditions (such as high-stress parts or impact-resistant coatings).

 

Once again, we sincerely thank you for your valuable time and incisive comments! We hope that this revision has fully responded to all your concerns and substantially improved the quality of the manuscript. I hope our revision can meet the requirements of you and the journal.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors did a very good job replying to most of the raised points. However, the following points still need attention:

1. The provided line numbers are wrong. I had to compare modifications word line by line. See “The following modifications have been added to the Abstract (lines 27-37):” and many others.
2. Point 4: The added NVT justification addresses temperature control but does not discuss how NVT may suppress stress fluctuations or affect dislocation kinetics during deformation, which should be acknowledged as a limitation.
3. The justification for focusing on NiAl and Ni₃Al is clearer thermodynamically, but the manuscript still does not explicitly state that conclusions are not transferable to Al-rich brittle phases, which should be acknowledged as a scope limitation.

In conclusion, I see that the authors have made substantial and genuine improvements, and most of my  concerns are addressed. Remaining issues are refinement-level (mechanistic precision, quantitative validation, and language tightening) rather than fundamental flaws.

Comments on the Quality of English Language

Please improve. Especially the many added lines in the new version.

Author Response

Response to the reviewer’s comments:

Reviewer #1:

The authors did a very good job replying to most of the raised points.

Authors’ Response: Thank you very much for your review work, positive comments and recognition of our work. Based on your recommendation, we have made the greatest efforts to improve the content of the manuscript.

 

Commnets:

[1]. The provided line numbers are wrong. I had to compare modifications word line by line. See “The following modifications have been added to the Abstract (lines 27-37):” and many others.

Authors’ Response: We sincerely apologize for the inconvenience caused by the incorrect line numbers. This was due to a mistake in the formatting adjustments during the manuscript revision process. In the final version, we have corrected all the line numbers to ensure accurate citations.

 

[2]. Point 4: The added NVT justification addresses temperature control but does not discuss how NVT may suppress stress fluctuations or affect dislocation kinetics during deformation, which should be acknowledged as a limitation.
Authors’ Response: Thank you very much for your comments. The use of the NVT ensemble may indeed suppress stress fluctuations and affect dislocation dynamics, and this should be clearly stated as a limitation of the method.

The following modifications have been added to the first paragraph (lines 117-121) of the Modeling and Simulation Details:

The simulation adopted the canonical ensemble (NVT) to precisely control temperature and study its effect, a standard approach for high-strain-rate MD simulations with limited computational resources [24]. It is acknowledged, however, that the constant-volume constraint of NVT may influence stress fluctuations and dislocation kinetics, a limitation considered in the interpretation of the results [25-27].

 

[3]. The justification for focusing on NiAl and Ni₃Al is clearer thermodynamically, but the manuscript still does not explicitly state that conclusions are not transferable to Al-rich brittle phases, which should be acknowledged as a scope limitation.
Authors’ Response: Thank you very much for your comments. The manuscript mainly focuses on NiAl and Ni3Al single crystals, as they are the key phases in high-temperature applications. However, the conclusions may not directly apply to other Ni-Al intermetallic compounds (such as the Al-rich brittle phase). To clearly define the scope limitations, an explanation was added, emphasizing the limitations of the study.

The following modifications have been added to the fifth paragraph (lines 91-93) of the Introduction:

It should be noted that the findings pertain specifically to the NiAl (B2) and Ni₃Al (L1₂) phases investigated, direct extrapolation to Al-rich brittle phases is not warranted.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper has been improved; however, professional English-language editing is recommended to further enhance clarity, fluency, and readability.

Comments on the Quality of English Language

The English could be improved to make the research more straightforward.

Author Response

Reviewer #3:

Commnets:

[1]. The paper has been improved; however, professional English-language editing is recommended to further enhance clarity, fluency, and readability.

Authors’ Response: Thank you very much for your comments. We have made comprehensive revisions and polishings to the manuscript based on the suggestions, aiming to enhance its accuracy, fluency, and academic standardization.

 

Once again, we sincerely thank you for your valuable time and incisive comments! We hope that this revision has fully responded to all your concerns and substantially improved the quality of the manuscript. I hope our revision can meet the requirements of you and the journal.

Author Response File: Author Response.pdf