An Overview on Atomistic Mechanisms of Heterogeneous Nucleation

Round 1

Reviewer 1 Report

This is an excellent paper that really draws together the story of the authors investigations over the last 5-10 years.  Much of the work has been published individually, although there are also new contributions provided here.  However, bringing together the pieces into a systematic descripton of nucleation is very valuable.  They have broken the nucleation process down into a three layer mechanism which is useful for an in-depth understanding of the process even if it may be a little pedantic for description of industrial systems.  One thing that I really like, which the authors did not draw out, is how it can be used to enlighten the discussion of intermediate phases such as the TiB2-Al3Ti-Al system.  The supposed Al3Ti could be better understood as a templating layer rather than a separate phase.  

Some comments for the authors to consider:

1. line 295.  The TiB2 interface is called impotent with a 4.3% misfit when the paper considers misfits from -12.5 to 12.5%.  It seems it is actually in the top third of potencies according to the paper. 

2.  There is a lot of use of f as a symbol.  It is misfit, fraction solid, etc.  This can make it a little confusing.  On line 618, fraction of solid atoms is introduced but not explained.  I wonder whether the description on line 757-8 needs to be provided back at 618 as I think this is a different meaning to what most people would understand by it.

3.  line 913.  I am not sure that there is no barrier to nucleation.  Clearly some undercooling is required to get to the nucleation temperature.  I think that the important point is that when this nucleation temperature is achieved nucleation is deterministic rather than stochastic. Some further thought to how to describe this could help make sure the nuance required is maintained.  

 There are some typographical errors that I have noted in the marked up version.  

Author Response

We would like to thank Reviewer 1 for his/her effort to review our manuscript, and for his/her constructive and positive comments. Here are our rely to the comments and suggestion raised by Reviewer 1:

• “One thing that I really like, which the authors did not draw out, is how it can be used to enlighten the discussion of intermediate phases such as the TiB2-Al3Ti-Al system.  The supposed Al3Ti could be better understood as a templating layer rather than a separate phase.”

We agree with the reviewer1 that Al₃Ti could be better understood as a templating atomic layer. We firstly identified the Al₃Ti 2DC (2 dimensional compound) on (0001) TiB₂ in HRTEM observation, and later found that the Al₃Ti 2DC, formed during prenucleation, serves as the new terminating layer of the TiB₂ substrate. This is consistent with our three-layer nucleation mechanism.

• “ line 295.  The TiB2 interface is called impotent with a 4.3% misfit when the paper considers misfits from -12.5 to 12.5%.  It seems it is actually in the top third of potencies according to the paper.”

We agree with the reviewer 1. We have deleted the “impotent” in the revised manuscript. Potency of a substrate can only be described in relative terms in the context of competition between different types of solid particles. For instance, in a system that contains 3 types of solid particles (A, B and C), nucleation occurs on A first and then on B but not on C. In this case, we refer A as potent, B as less potent and C as impotent. TiB₂ with Al₃Ti 2DC (0.09% misfit) is potent (more potent than oxide particles), and TiB₂ (-4.22% misfit) is impotent (more impotent than oxide particles).

• “ There is a lot of use of f as a symbol.  It is misfit, fraction solid, etc.  This can make it a little confusing. On line 618 (line 610), fraction of solid atoms is introduced but not explained.  I wonder whether the description on line 757-8 needs to be provided back at 618 as I think this is a different meaning to what most people would understand by it.”

In this manuscript, f denotes misfit, and f_s denotes solid fraction. We agree with the point of the reviewer 1, but this symbol has been consistently used in all our previous publications. We firstly introduced solid fraction (f_s) in line 610, rather than Line 618, in the manuscript, where f_s has been explained. We have adopted his/her suggestion that the description (to identify solid atoms with local bond-order analysis) on line 757-8 has better to move to Line 610-11. In most of the cases we have used “misfit” rather than “f”, fraction of solid atoms rather than “f_s” in the revised manuscript.

• “3.  line 913.  I am not sure that there is no barrier to nucleation.  Clearly some undercooling is required to get to the nucleation temperature.  I think that the important point is that when this nucleation temperature is achieved nucleation is deterministic rather than stochastic. Some further thought to how to describe this could help make sure the nuance required is maintained.”

We believe that there is no barrier to nucleation. The undercooling for the nucleation is to reach a critical level of atomic ordering at the liquid/substrate interface for the systems with varied misfits, i.e., precursor, and this is achieved in the prenucleation. The precursor then triggers the heterogeneous nucleation at the corresponding nucleation undercooling. We discussed this problem in more detailed in another manuscript (Men, H.; Fang, C. M.; Fan, Z. Prenucleation at the liquid/substrate interface: An overview. Metals 2022, in this special issue.), submitted to the same Special Issue of metals

Reviewer 2 Report

There are some empty lines between 232 to 243 and 545 to 550

If you can, just arrange the text……this is a recommendation ….that is all……

This is an excellent paper. Manuscript grammar is good and the content is very relevant for the journal Metals. The topic treated of heterogeneous nucleation is well described. Examples are appropriate and explanations are well driven. I am sure this paper will be accepted immediately for publication.

I really want to say congratulations to the authors this is a very nice paper.

Author Response

We would like to thank Reviewer 2 for his/her effort to review our manuscript, and for his/her constructive and positive comments.

Reviewer 3 Report

Dear authors.

A suggestion regarding to your discussion on the bounds of the surfce tension and intefacial tension  roles on page 34:

1. Can you schematize, using up-down arrows to indicte the effects that the rasing of a variable has on the rest of the others? This approach will facilitate the undertanding of those parragraphs. Otherwise it becomes tedious an long story. 

2. Regarding your discussion on the Young´s equation, please add some comments regarding the role of the misfit strain energy on the template mechanism. Talking about the lattice misfit makes sense, tough, the contribution of the strain energy must be directly related with f or fr. 

Thanks and it has been a pleasure to review your work.

Author Response

We would like to thank Reviewer 3 for his/her effort to review our manuscript, and for his/her constructive comments. Here are our rely to the comments and suggestion raised by Reviewer 3:

“A suggestion regarding to your discussion on the bounds of the surface tension and interfacial tension roles on page 34:

1. Can you schematize, using up-down arrows to indicate the effects that the raising of a variable has on the rest of the others? This approach will facilitate the understanding of those paragraphs. Otherwise it becomes tedious a long story. 
2. Regarding your discussion on the Young´s equation, please add some comments regarding the role of the misfit strain energy on the template mechanism. Talking about the lattice misfit makes sense, tough, the contribution of the strain energy must be directly related with f or fr.” 

In our manuscript, only interfacial energies of liquid/solid, liquid/substrate and solid/substrate are our concern for the heterogeneous nucleation. In this case, Young’s equation is not applicable, as we stated in the discussion of Section 5.3. The misfit strain energy related to f or f_r has been included in the calculation of the interfacial energy of solid/substrate in equation 12, and the interfacial energy of solid/substrate increases with increasing f or f_r. We discussed its role on the prenucleation and nucleation (i.e., templating mechanism) in Section 5.3, where the atomic ordering in the liquid at interface (prenucleation) degrades with increasing f and the potency of the substrate deteriorates with increasing f or f_r due to decreasing in the templating capability.

In addition, heterogeneous nucleation is a complicated process, which involves a large number of variables that operate at different levels. This makes it difficult to sketch the influence of individual variable in 2D for a multi-dimensional problem.

Reviewer 4 Report

The manuscript is a great summary of heterogeneous nucleation at the atomic level with well thought out simulations and results. My comments are minor.

The term misfit itself seems to indicate just a deviation. How does it have a sign? Line 389 and 439 seem to be the explanation but this should be much earlier in the manuscript when the negative misfit is first mentioned.

Figure 4 appears to be an instance where no structural templating occurs and the 2D nucleus appears directly above the substrate. Figure 6 and 7 show 3 layers must form on the substrate in order for the 2D nucleus to be present. What dictates the path in each case? Is it because Figure 6 and 7 have a misfit of -8%? What is the misfit in Figure 4? Can small misfits result in direct formations of 2D nuclei without structural templating?

Place equations in line 51 on separate lines and space them out from the main text. Please include the Young’s equation (line 52) or include a reference to it.

Line 127: rewrite to: The initial dimensions were 48[112̅] x 30[1̅10] x 15[111] atoms for the liquid and 48[112̅] x 30[1̅10] x 6[111] atoms for the substrate, with the total number of atoms in the system 128 being 5040.

Check reference 54. I was only able to find this reference with the same name but by different authors. https://doi.org/10.1103/PhysRevB.68.024102. Did the authors mean to refer to this publication? https://doi.org/10.1039/B517931A

For equation 5, what do n and m represent? They appear in AMR2 but are not defined there as well. It appears to be the number of atoms in a row (from Figure 3 caption) for each element but it is not clear.

Is figure 6d supposed to show L1 and L0 layers? The label “L” is not present in Figure 6a but “L0” is.

Include example systems in Figure 25.

Figure 17 is missing a,b,c,d, labels.

The authors provide a nice example of amorphous surfaces but would a similar result occur with substrates that have very large misfits with the solid? Would they behave similar to 3D amorphous structures where the solid forms homogenously?

With heterogeneous nucleation being deterministic, wouldn’t that lead one to think that grain refiners should be much more efficient than they actually are? Typically grain refiners are only 1-2% efficient with most nucleating particles not contributing to grain refinement at all. A good refiner with small misfit should then provide many nucleating sites but experimentally this is not known to be the case. Is this where solute then plays a role?

Author Response

We would like to thank Reviewer 4 for his/her effort to review our manuscript, and for his/her constructive comments and suggestions. Here are our rely to the comments and suggestion raised by Reviewer 4:

• The term misfit itself seems to indicate just a deviation. How does it have a sign? Line 389 and 439 seem to be the explanation but this should be much earlier in the manuscript when the negative misfit is first mentioned.

According to our definition of misfit (Ref. 33. Fan, Z. An epitaxial model for heterogeneous nucleation on potent substrates. Metall. Mater. Trans. A 2013, 44, 1409-1418.), the solid is subject to tensile and compressive stress, respectively, for the substrate with negative and positive misfits. The new definition helps to clear the confusions in the literature. More importantly, the sign of misfit becomes indictive of nucleation mechanisms, as we have fully discussed in the paper.

• Figure 4 appears to be an instance where no structural templating occurs and the 2D nucleus appears directly above the substrate. Figure 6 and 7 show 3 layers must form on the substrate in order for the 2D nucleus to be present. What dictates the path in each case? Is it because Figure 6 and 7 have a misfit of -8%? What is the misfit in Figure 4? Can small misfits result in direct formations of 2D nuclei without structural templating?

Yes, the misfit is dictating factor. As we stated in the text, the formation (112) Al₃Ti 2DC changes the impotent (0001) TiB₂ surface (the original substrate with -4.22% misfit) into an extremely potent TiB₂/Al₃Ti 2DC substrate (the new substrate with 0.09% misfit). We had added further explanation in caption of Figure 4.

• Place equations in line 51 on separate lines and space them out from the main text. Please include the Young’s equation (line 52) or include a reference to it.

It is a good suggestion to put equation in line 51 on separate line. However, for the conciseness of the manuscript we rather like to keep the equation in line 51 in the main text (This manuscript already has 19 equations). A reference has been included in line 52 for Young’s equation.

• Line 127: rewrite to: The initial dimensions were 48[112̅] x 30[1̅10] x 15[111] atoms for the liquid and 48[112̅] x 30[1̅10] x 6[111] atoms for the substrate, with the total number of atoms in the system 128 being 5040.

The number of dimensions for the simulation system is atomic plane, and so we like to keep the original one.

• Check reference 54. I was only able to find this reference with the same name but by different authors. https://doi.org/10.1103/PhysRevB.68.024102. Did the authors mean to refer to this publication? https://doi.org/10.1039/B517931A

It is an error for the title of paper, and we had changed it to “Todorov, I.T.; Smith, W.; Trachenko, K.; Dove, M.T. DL_POLY_3: new dimensions in molecular dynamics simulations via massive parallelism. J. Mater. Chem. 2006, 16, 1911-1918”.

• Is figure 6d supposed to show L1 and L0 layers? The label “L” is not present in Figure 6a but “L0” is.

“L” is “L0” in Figure 6d, and we had change it.

• Figure 17 is missing a,b,c,d, labels.

The (a-f) labels in Figure 17 had been included.

• The authors provide a nice example of amorphous surfaces but would a similar result occur with substrates that have very large misfits with the solid? Would they behave similar to 3D amorphous structures where the solid forms homogenously?

No, substrates with large misfit would not lead to homogeneous nucleation. As we showed in “Section 4.4. Heterogeneous nucleation on a substrate with large misfit”, a CSL forms at the interface and transforms the original substrate into a considerable potent nucleant. This is consistent with experimental observation.

• With heterogeneous nucleation being deterministic, wouldn’t that lead one to think that grain refiners should be much more efficient than they actually are? Typically grain refiners are only 1-2% efficient with most nucleating particles not contributing to grain refinement at all. A good refiner with small misfit should then provide many nucleating sites but experimentally this is not known to be the case. Is this where solute then plays a role?

Yes. We agree that only 1-2% grain refiner particles contribute to grain refinement. However, this low efficiency of grain refiner particles is an outcome of progressive grain initiation and limited by the recalescence. According to our new framework, heterogeneous nucleation is deterministic and occurs on all nucleant particles at the corresponding nucleation temperature. After nucleation, only 1-2% such nucleant particles can successfully initiate new grains, and the rest of particles would not participate grain initiation. Therefore, it is important not to confuse grain initiation with nucleation.