Simulation of the Dynamics of Supersonic N-Crowdions in fcc Lead and Nickel
Gotthard Seifert
Round 1
Reviewer 1 Report
The authors present a theoretical study (molecular dynamics) about the formation of so called crowdions in the crystal lattices of lead and nickel. They apply state-of-the-art molecular dynamics methodology using the LAMMPS software package. The interatomic forces are described by embedded atom (EAM) potentials. The simulation protocol is adequately described. The simulations seem to be done properly. The weakest point is probably the EAM-potential. Especially the short range repulsive part might not describe the interactions correct. However, I cannot propose a better one.
The discussion adequately explains the results. The conclusions are somewhat tenuous. Especially the final remark about the practical impact of the simulations for lead need a bit more explanation.
Altogether, I can recommend the publication of the paper after considering the hints mentioned above.
Author Response
First, we would like to thank the Reviewers for the time they spent evaluating our manuscript and for their helpful critical comments. We provide our step-by-step response below, along with a description of the revisions made to the manuscript. All changes are marked in red for the convenience of Reviewers and Editors. Reviewer 1 wrote: The weakest point is probably the EAM-potential. Especially the short range repulsive part might not describe the interactions correct. However, I cannot propose a better one. Our response: Indeed, the accuracy of the results obtained by the molecular dynamics method directly depends on the quality of the interatomic potential used in the study. It is also true that the repulsive part of the potential is significant in modeling collision cascades. The potentials that we used in our study were taken from the LAMMPS repository without any modifications. To justify the use of these potentials, we calculate the energy of the colliding atoms. The maximum initial velocity of the atoms in our simulation is 150 Å/ps, which gives a maximum collision energy of about 230 eV for lead and 70 eV for nickel. Cascades generated by ions with such energies are considered as low-energy cascades, and the repulsive part of the potentials plays a less important role than for high-energy cascades. In the Section 2 Materials and Methods the following discussion was added: It is well-known that the repulsive part of the potential is significant in modeling collision cascades. The potentials that we used in our study were taken from the LAMMPS repository without any modifications. To justify the use of these potentials, we calculate the energy of the colliding atoms. As stated above, the maximum initial velocity of the atoms in our simulations is 150 Å/ps, which gives a maximum collision energy of about 230 eV for lead and 70 eV for nickel. Cascades generated by ions with such energies are considered as low-energy cascades [48], and the repulsive part of the potentials plays a less important role than for high-energy cascades. Reviewer 1 wrote: The conclusions are somewhat tenuous. Especially the final remark about the practical impact of the simulations for lead need a bit more explanation. Our response: We agree. We have made several additions to the conclusions: To highlight the difference in dynamics between supersonic 1- and 2-crowdions, the following text has been added: In all metals studied in previous works, supersonic 2-crowdions have shown much better transport properties, since they propagate over longer distances compared to supersonic 1-crowdions. The reason is that the sequence of self-focusing collisions is realized only for atoms colliding with a speed below the threshold value. Very fast collisions of atoms cause defocusing, and an interstitial atom cannot propagate stably along a close-packed atomic row; its directed motion is destroyed and energy is transferred to many atoms in the lattice [38]. In a supersonic 1-crowdion, only one atom moves at a high speed, while in a 2-crowdion, two atoms have a high speed, which means that the maximum energy of a 2-crowdion can be about twice that of a 1-crowdion. Having a higher energy, the 2-crowdion propagates over a greater distance at a velocity below the critical one. To support the idea that lead absorbs radiation better than nickel, we added the following: Indeed, due to the instability of the motion of supersonic 2-crowdions in lead, their ability to carry high-energy interstices over long distances is limited, and their energy is rapidly dissipated in the crystal lattice in the form of thermal vibrations.
Reviewer 2 Report
This manuscript reports molecular dynamics simulations (with embedded atom potentials) of so-called 1- and 2-crowdions in fcc lead and nickel with an emphasis on the effects of initial velocity and temperature. The results provide a plausible causal linkage between the softer repulsive interatomic potential in lead, relative to other metals like nickel, and lead's well-known resistance to radiation damage via shorter propagation distances for supersonic 2-crowdions in particular.
The work is complete and of fundamental interest for nuclear materials science. I am a bit surprised that the authors have opted to submit to this journal rather than a journal focused on computational and/or nuclear materials, but nevertheless, the work fits within the scope of the journal. I believe it is publishable, but the authors should first address the following minor concerns and suggestions:
(1) The description "the close-packed direction" in the third paragraph of the manuscript is a bit confusing; there are multiple such directions in the fcc structure, so even changing this to "a close-packed direction" would be clearer. The specific meaning is elucidated later in the computational details.
(2) In the Materials and Methods section, the authors briefly discuss finite-temperature simulation but don't specify whether the T = 297 K simulations are performed in the same NVE ensemble as before (but with initial velocities sampled from a Maxwell-Boltzmann distribution at 297 K) or if they actually use an NVT ensemble. If the latter, what thermostat and settings were used?
(3) Also in Materials and Methods, a formula and masses are provided for 1-crowdion kinetic energies, but not for the 2-crowdion. I would argue that the 2-crowdion is the less obvious case of the two, so the analogous formula used for the 2-crowdion energetics should also be provided and discussed.
(4) In the discussion of Figure 3b, I found the explanation that the "energy radiation rate for 2-crowdion is smaller due to its particular internal structure" to be an incomplete, or at least unsatisfying, justification for the observation. What about the internal structure causes the lower energy radiation rate and greater propagation distance? (I suppose it is the stiffer interatomic potential, but this should be clarified to contrast with the results for lead).
(5) Ideally, the manuscript body should spell out more clearly that the plots in Figures 5-7 include one curve per atom, hence the very large number of (otherwise unlabeled) curves in the figures. I would argue that this is less obvious at first glance than the authors understandably -- as folks studying these systems intensively -- may think.
(6) In the discussion of Fig. 7, it is the relative magnitudes of the vertical axes, not the shapes of the velocity component curves, that show the larger transverse component of the velocities for the 2-crowdion. In this context, I recommend adding "the vertical axes" within the phrase "It can be seen from Fig. 7", as the common instinct is to look for evidence in the shape of the curves rather than the scale of the axes (especially since the plots use different axis scales).
(7) Finally, it should be specified in section 3.3 whether the results shown and discussed in Figure 8 are from a single MD run, and whether additional runs were performed to assess the reproducibility and variance in these results.
Author Response
First, we would like to thank the Reviewers for the time they spent evaluating our manuscript and for their helpful critical comments. We provide our step-by-step response below, along with a description of the revisions made to the manuscript. All changes are marked in red for the convenience of Reviewers and Editors.
Reviewer 2 wrote:
(1) The description "the close-packed direction" in the third paragraph of the manuscript is a bit confusing; there are multiple such directions in the fcc structure, so even changing this to "a close-packed direction" would be clearer. The specific meaning is elucidated later in the computational details.
Our response: We agree. Indeed, there are six close-packed directions in the fcc lattice. We have substituted the article “the” with the indefinite article “a” at the first mentioning and have added the following text to the second paragraph of Sec. 2:
There are six close-packed directions in the fcc lattice, <110>, <-110>, <101>, <-101>, <011>, and <0-11>.
(2) In the Materials and Methods section, the authors briefly discuss finite-temperature simulation but don't specify whether the T = 297 K simulations are performed in the same NVE ensemble as before (but with initial velocities sampled from a Maxwell-Boltzmann distribution at 297 K) or if they actually use an NVT ensemble. If the latter, what thermostat and settings were used?
Our response: In response to this meaningful comment, the following clarification was added to the Materials and Methods section (lines 76-80):
“For some cases, the effect of temperature T=297 K is also analyzed. In this case, the initial velocities selected from the Maxwell-Boltzmann distribution at the desired temperature were introduced, and the NVE ensemble was used. The NVT ensemble cannot be used in our simulations because the thermostat normalizes the velocities of the atoms in the crowdion core and affects its natural motion.”
(3) Also in Materials and Methods, a formula and masses are provided for 1-crowdion kinetic energies, but not for the 2-crowdion. I would argue that the 2-crowdion is the less obvious case of the two, so the analogous formula used for the 2-crowdion energetics should also be provided and discussed.
Our response: Below Eq. (1) we have added an important description "where N=1 or 2 for 1- or 2-crowdion,"..., which was missed.
(4) In the discussion of Figure 3b, I found the explanation that the "energy radiation rate for 2-crowdion is smaller due to its particular internal structure" to be an incomplete, or at least unsatisfying, justification for the observation. What about the internal structure causes the lower energy radiation rate and greater propagation distance? (I suppose it is the stiffer interatomic potential, but this should be clarified to contrast with the results for lead).
Our response: Yes, we believe that the main reason for the difference in the dynamics of supersonic crowdions in Ni and Pb is mainly due to the difference in the repulsive parts of their potentials, as shown in Fig. 2. The discussion of this point has been edited as follows (lines 129-137):
“Note that the 2-crowdion initiated with the velocity Vx0 has initial energy two times greater than the 1-crowdion launched with the same velocity, see Eq. (1). The 2-crowdion propagation distance in lead at Vx0=40 and 50 A/ps is also approximately twice the 1-crowdion propagation distance, see Fig. 2(a). On the other hand, the propagation distance of a supersonic 2-crowdion in Ni is about five times greater than that of a supersonic 1-crowdion, see Fig. 2(b). This means that in lead the energy radiation rate of the 2-crowdion is approximately equal to the radiation rate of the 1-crowdion, but in Ni it is much lower. This difference in the rate of energy radiation of supersonic crowdions in Ni and Pb can be caused by the difference in the repulsive parts of their potentials, see Fig. 2.”
(5) Ideally, the manuscript body should spell out more clearly that the plots in Figures 5-7 include one curve per atom, hence the very large number of (otherwise unlabeled) curves in the figures. I would argue that this is less obvious at first glance than the authors understandably -- as folks studying these systems intensively -- may think.
Our response: We agree. The following text has been edited:
In the caption of Fig. 5: “A curve is plotted for each atom in the row.”
“All curves in (a) have one maximum, and in (b), in the regime of motion of 2-crowdion, each curve has two maximums, as shown for the curve highlighted in red.”
In the text (lines 152-157):
“One curve per atom is plotted.”
“The qualitative difference in the dynamics of supersonic 1- and 2-crowdions lies in that each curve in (a) has one maximum, and in (b), for 2-crowdion, each curve has two maximums, as shown for the curve highlighted in red. After the 2-crowdion is destroyed, it transforms into 1-crowdion with Tn(t) curves having single maximum.”
(6) In the discussion of Fig. 7, it is the relative magnitudes of the vertical axes, not the shapes of the velocity component curves, that show the larger transverse component of the velocities for the 2-crowdion. In this context, I recommend adding "the vertical axes" within the phrase "It can be seen from Fig. 7", as the common instinct is to look for evidence in the shape of the curves rather than the scale of the axes (especially since the plots use different axis scales).
Our response: We agree. The following text has been edited (line 188):
“the vertical axes of”
(7) Finally, it should be specified in section 3.3 whether the results shown and discussed in Figure 8 are from a single MD run, and whether additional runs were performed to assess the reproducibility and variance in these results.
Our response: We agree. The following text has been added (lines 200-202):
“The results shown in Fig. 8(a) are from a single MD run, but they are representative as laterally moving supersonic 1-crowdions were observed in almost every run.”
