The Instability Criterion for Bicrystal at Nanoscale

Round  1

Reviewer 1 Report

This article investigates the applicable limit of instability criterion in atomic scale in the dislocation emission at high temperatures and explores the beginning in the plasticity of bi-crystal. The simulation and analysis are fine, and the results and discussion sound well. My comments are as follows.

(1)  English expression is unsatisfied. I recommend the check by native English speaker.

(2)  In section 3:  The authors should carefully observe the instability mode. For an example, is the mode of instability at 200K different from those at lower temperatures?

(3)  The eigen vector, which corresponds with the minimum eigen value, gives the instability mode. The authors should analyze the relation the mode and the atomic rearrangement during the instability.

Author Response

The point-by-point response to the reviewer’s comments is attached in the Word file.

Author Response File: Author Response.docx

Reviewer 2 Report

In this paper, authors describe the plastic yield of bicrystals by the introduction of an instability criterion. 

The mathematical description of the criterion is accurate and results are clearly presented. 

Some minor revisions are required:

In the Simulation methods section, authors must add ALL parameters used in the simulation (timestep, parameters for the minimization, etc...) in order to allow interested readers to reproduce this study. This is a very important point. 

Please add a reference at "This criterion is successsfully applied in the simulation of tensile deformation..."

The sentence "Establish an atomic model, define the atomic center of mass..." is not clear. Please rephrase it.

Equation 24 notation in my pdf is superimposed to the equation. Check the proofs.

There is a Chinese word (时)before equation 27.

Check the sentence "all the above expressions are programming into Matlab" and add the reference and the version for Matlab used.

Check the sentence "Among the function of potential energy of ...".

Just before section 4.2 correct the sentence beginning with "And the simulation cell...". 

Rephrase the sentence "...the minimum energy value decreases initially".

A major concern on this study is the effect of the temperature on the prediction of the instability criterion. Neglecting thermal vibrations is the best way in this study and authors showed that over 200K the plastic yield cannot be predicted. In order to improve the quality of the manuscript, authors should describe a possible way to extend the criterion to higher temperatures: improve the coefficients of the potential by quantum simulations? Change the potential function or the simulation parameters? Just few words are required.

In section 4.3, the fig. 10b describing the tensile stress vs displacement is quite interesting. Just watching the graph it seems that when the displacement is 6.2A a sort of rearrangement of the system is happened. The same happens at 8.5A. From this graph it seems that the stress drop is at 9.6A. Authors should better describe what happens during this simulation which is different from the previous. From the eigenvalues it is clear where the plastic deformation begins.

Author Response

The point-by-point response to the reviewer’s comments is attached in the Word file.

Author Response File: Author Response.docx

Reviewer 3 Report

This ms presents a (possibly) interesting study that establishes the reliability of structural instability criteria on the base of semiempirical potential simulations.

The introduction and motivation of the ms are quite well written and appealing. However, at the present stage, the quality of presentation of the results is poor. Several important information seem to be missing. In some cases, the explanation of the computational approach suggests that the methods used are highly questionable. Before I can express a clear opinion on this work, I need the authors to properly address all issues mentioned below.

1) What are the different colors of atoms representing in Fig. 1? I do not see it explained in the text. Also, it is unclear how the crack is modeled. I do not see any crack in the supercell. The authors say that “A crack is preset at the left of model to control the dislocation nucleation site.” How exactly is this done? I can understand from the text that part of the box is maintained fixed, while another part not… however, this is all confused. Please improve and give more details (perhaps referring to the coloring in the figure) on how calculations are done.

2) Later in the text, the authors say that they perform finite-temperature simulations. I assume these to be molecular dynamics simulations (MD). If yes, please provide all information necessary for your results to be reproducible by peers. Simulation timestep, themodynamic ensemble, thermostat used, simulation time, and size of the simulation box (it is not sufficient to show it in a figure).

3) Related to the previous point, the authors say that the simulation box is “free” in x and y, but periodic in z. Please indicate in Fig. 1 the Cartesian axes. Please also indicate to which crystallographic direction these correspond to.

4) If I understand correctly figure 1, the system is periodic in the direction orthogonal to the page, which should be the [111] direction for a fcc crystal. The authors say that their system is 2-dimensional (which I interpret as the supercell is a (111) monolayer). This is however incorrect! One could not reproduce the fcc symmetry of Al by just replicating one (111) lattice layer! The [111] stacking sequence of fcc crystals is of A-B-C type! Indeed, by looking at the figure, it seems that there are (at least) 3 atomic layers in the direction orthogonal to the page. Please make clarity!!

5) Again related to point (4). The results are unreliable in case the authors are using only 3 atomic layers along the direction orthogonal to the page. These would not be sufficient to accommodate realistic lattice vibrations nor realistic deformation mechanisms.

6) In Fig. 2. The total energy and displacement are extensive properties, while the stress is an intensive property. Please use only intensive properties: energy per atom and strain (percentage) in your plot. If you still want to keep the displacement (I see it used in the text), please use strain on upper horizontal axes of Fig. 2.

7) Related to the previous point, the authors say that “a displacement of 0.01 Å” was used. I do not demand (unless the authors want to) that displacements are changed with strain throughout the text. However, please state here to which strain 0.01 Å corresponds to.

8) Regarding the empirical potential use. I recommend informing readers (several seem unaware of this issue) that empirical and semiempirical potentials may, in some cases, yield artifacts (unphysical behavior). Nevertheless, molecular dynamics simulations based on accurate ab initio density-functional calculations of interatomic forces are unfeasibly time consuming to study deformation and fracture for systems larger than a few hundreds atoms [D.G. Sangiovanni, Inherent toughness and fracture mechanisms of refractory transition-metal nitrides via density-functional molecular dynamics, Acta Materialia 151 (2018) 11.]

Author Response

The point-by-point response to the reviewer’s comments is attached in the Word file.

Author Response File: Author Response.docx

Round  2

Reviewer 3 Report

The authors have satisfactorily amended all my criticisms and suggestions. The ms has significantly improved during revision. The authors have also satisfactorily answered my concern regarding the reliability of their model, by pointing at the work by Kitamura and coworkers. In my opinion the ms can be accepted.