Dynamic Response of Nanoscale He Bubbles in Single Crystal Al during Release from a High-Pressure State

Round 1

Reviewer 1 Report

Dear Editor,
The authors studied the dynamic response of a He bubble in single crystal aluminum using the molecular dynamics method. I did not have any technical concerns; however, there were many grammatical mistakes and sentences that did not make sense. There are too many, so I highlighted only the initial few. Before I recommend the manuscript for publication, I want the authors to address them.

•           Lines 17, 18, 19 : We find that the growth of He bubble significantly impedes the surroundsurrounding void nucleation, and meantime reduces the spall strength before release melting, while this effect is gradually negligible if release to liquid state.

•           Line 30, 31, 32 : Therefore, understanding the evolution behavior of He in metals ~~shows very importance ~~ is very important in the research field of mechanical properties of irradiated materials.

•           Line 36, 37, 38: This is because that it is difficult to control the preparation of He bubble samples without introducing other defects, and the detailed in-situ observation under extreme conditions is also very hard.

•           The first paragraph in the section titled simulation details is hard to follow. For example, “The above 84 models are relaxed by energy minimization using the conjugate gradient method, followed by equilibration using the NPT ensemble with reference to different Hugoniot states, which are obtained from the MD simulations on shock waves with the above model of Al.”

•           Figure 1 is also confusing to me. Because when I see the results, it appears to me that there is only one He bubble in the simulation cell; however, based on the figure, it appears that there are two He bubbles in the simulation cell.

•           Why would there be a difference in response between the bubbles located at the center of the simulation cell compared to those not located at the center of the cell? What does the simulation cell represent, a bulk Al or a chunk of Al with 6 surfaces? Because figs. 13 and 14 show a bubble bursting. A better description of their simulation cell is important to interpret/understand results correctly.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript by Wei-Dong Wu and Jian-Li Shao entitled “Dynamic response of nanoscale He bubbles in single crystal Al during release from shocked state” according to the authors is devoted to “the deformation and release path of the nanoscale He bubble in metal from high pressure state”. In fact, the manuscript presents results of the classical molecular dynamics simulations of rather small (100x100x180 fcc unit cells – ~7.2 mln. atoms) MD system of single orientation ([100] along ‘release direction’) with a single helium bubble of 10 nm placed in three positions released from artificially constructed ‘Hugoniot’ states. The MD simulations are poorly described. It is highly required to clarify the MD simulations details. The conclusions made in the manuscript based on the simulation results in my opinion are artifacts of the simulations themselves rather than reflections of real physical phenomena. In the following you will find my concerns and criticism substantiating my decision.

 

The title of the manuscript is misleading. It states “…during release from shocked state”. However, in fact there are no shocked compressed states from which the release occurs in the presented simulations. The authors used as initial states for release simulations artificially constructed ‘Hugoniot’ states.

 

In the abstract in line 12 the authors introduced terms ‘symmetric and asymmetric release’ of He bubble. From the content of the manuscript, I understood that by the ‘symmetric and asymmetric release’ of He bubble authors meant not more than the position of the bubble relative to center of the MD sample. Thus, the introduction of the terms is not justified.

 

In line 16 of the abstract (and throughout the manuscript) the authors misspelled “Carnhan-Starling model”. It should be Carnahan.

 

The study of shock compression, release and following spallation of single- and polycrystal materials via large-scale classical molecular dynamics simulations has long story with well justified methods of the simulations. There are many atomistic simulations papers in which shocked compressed states of single- and polycrystal metallic materials, pure elemental and alloys, without and with various defects (including helium bubbles) are generated by a rigid piston or via counter strike of MD sample parts. However, the authors decided to use release from artificially constructed ‘Hugoniot’ states rather than to perform shock compression and following release simulations. There is no justification of such choice, and, in my opinion, this introduced undesirable and unphysical artefacts to the simulations. From the introduction section it is not clear what new problems are addressed and what new results in comparison for example with the refs. [23-28] are obtained.

 

As I mentioned above the MD simulations are poorly described. First of all, the MD simulation samples are too small in all directions. 180 fcc unit cells along the ‘release direction’ would give enormous strain rates upon release, while 100 fcc unit cells (40 nm) across mean that the 10 nm He bubble is very close to the free surface (if free surface or rigid wall boundary conditions are used) or feel its periodic images (if periodic boundary conditions are used). Sufficiency of such small MD samples for the release and spallation simulations should be justified. In my understanding, these are insufficient. By the way, it is not clear from the manuscript which boundary conditions were used in each stage of the simulations. As I understood from the manuscript during the relaxation and preparation of the ‘Hugoniot’ states the authors used periodic boundary conditions and then free boundaries along the z direction and periodic boundary conditions in the x and y directions in order to have one-dimensional release from the compressed and heated ‘Hugoniot’ states. But this is only my guess. It is not clear why authors used for the simulations 10 nm in size He bubbles. What are 10 nm He bubbles? Are those bubbles made by deleting of Al atoms within 10 nm in diameter and then placing there He atoms? How many He atoms? What is He concentration in He bubble (1/m^3 or number of Helium atoms per deleted Al atoms)? What is the pressure inside the bubbles at the ambient conditions? Do the parameters of the bubbles satisfy Carnahan-Starling model mentioned by the authors? My guess they would not! How typical are those 10 nm bubbles for the experimental observations? It is not clear from the manuscript how the authors obtained Hugoniot state parameters: are those E, P, and V in each ‘Hugoniot’ state satisfying the Rankine–Hugoniot conditions for the used EAM potential or they are taken as external parameters from the Hugoniot adiabat of some equation of state? In other words, did the author used some sort of Hugoniostat in the simulations or just set the parameters (V and T) according to some EoS?

 

My main concern is the preparation of ‘Hugoniot’ states for the simulations of the release. As I understood from the manuscript the initial states were constructed by triaxial compression and heating of the zero-pressure state in periodic (or rigid wall) boundary conditions. After that the boundary conditions along the ‘release direction’ (z) was replaced by free boundary conditions.

It means that the triaxially compressed states without shear stresses were unphysically and enormously fast (due to small size of the samples) released uniaxially. Thus, all the shear stresses, plasticity and unusual deformations are artifacts of the fast release of triaxially compressed sample along the single direction. If the authors would used accurate simulations of plane wave compression and following release they would get plasticity, maybe, ‘cold melting’, overheating, jets etc. during the shock compression phase and the following releases would be different from the described in the manuscript. Thus, the void growth, bubble deformations, jets and following spallation are artifacts of the simulations rather than real physical phenomena.

 

The comparison of the pressure in He bubbles with the hard-sphere equation of state by Carnahan and starling is irrelevant. The Carnahan-Starling model is for free gas, while He atoms in nanometer-sized bubbles in metals are in potential well. The artificially introduced ‘hardening coefficient’ is obviously not a constant and it depends on initial state, probably, temperature. The ‘hardening coefficient’ characterizes the pressure of the metal lattice (lattice elastic strength) on the gas inside the bubbles. Thus, the pressure in He bubbles does not satisfy the Carnahan-Starling EoS.

 

In conclusion, I do not recommend the manuscript for publication in its present form. Although I admit that I could interpret the presented simulations details in the wrong way, however if I got them right the conclusions are based on artifacts of the simulations and not related to real physical phenomena. Moreover, there are no new insights in the field of the nanometer sized inert gas bubbles impact on dynamic strength properties of metals in the manuscript.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf