Mathematical Modeling of Phase Separation and Branching Process of the Film Structure during Binary Thin Film Deposition

Reviewer’s comments

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Reviewer 1

The article “The phase separation and branching mechanism of the film structure during binary thin film deposition” introduced a mathematical model to simulate the branching during thin film growth. It discovers that the branching structures are closely related to the diffusivity and sticking coefficient. The modeling method was well described, and the conclusion is clearly drawn. After careful consideration, the reviewer recommends a publication of this work in Coatings after addressing the following questions to improve the quality of the manuscript.

1. It is recommended to show some 3D visualization of the branched structures along with the cross-section images for a more intuitive demonstration.

3d images and their descriptions have been added to the manuscript (see Figures 6 and 7 and lines 465-540).

1. The parameters used for simulation are vital, so please cite some references to show the sources of these numbers.

The sources of the parameters have been cited and the additional discussion have been added (see lines 205-217).

1. The temperature would also change the diffusivity and absorption during material growth. Also, temperatures affect the number of point defects in the solid matrix, which would also affect the diffusion during crystal growth. Please add this information and explain how the temperature would affect the branching.

The discussion how the substrate temperature would affect the branching, based on present and previous works, have been added to the manuscript (see lines 541-557).

1. Atom diffusion could be anisotropic due to the anisotropic lattice structure. Please elaborate if the anisotropy would affect the simulation results.

Yes, diffusion anisotropy due to anisotropic lattice structure can affect simulation results. Anisotropic affect is considered in our previous works. But in this work we analyze isotropic nature in order to show mechanisms of branching structure formation in growing films. The diffusion anisotropy can have quantitative but not qualitative effect..

Reviewer 2

The title of the manuscript is NOT informative. It should contain “mathematical modelling”

The title of the manuscript has been changed.

There are some expressive, punctuation, and grammatical errors in the manuscript e.g.

Line 27: “attracted a tremendous” should be corrected to “attracted tremendous”

Line 27: “over past few” should be corrected to “over the past few”

Lines 33-34: “preparation of nanostructures, composed of those substances,” should be corrected to “preparation of nanostructures composed of those substances” please remove the comma.

Lines 38-39: “nanoparticles and could inhibit their” should be corrected to “nanoparticles. It could inhibit their”

Line 39: “coalescence, which makes the encapsulation” should be “coalescence, making the encapsulation”

Line 45: The sentence “There has been a number of recent works dedicated to the simulation of the growth of nanostructured thin films [10–21]. “ could be rephrased as “There have been many recent works dedicated to the simulation of the growth of nanostructured thin films [10–21].”

Line 52: “were a main objective” should be “were the main objective”

Line 57” “compositions promotes the development” should be “compositions promote the development”

These are examples of the errors, and there are many others. Authors should revise the manuscript comprehensively.

Those and many other errors have been corrected. Any changes are marked throughout the manuscript.

In all Figure captions, the word Figure should be in bold.

The word Figure has been made in bold in all Figure captions.

Reviewer 3

In this study, the authors adopted a mathematical model to explore the mechanism and the factors leading to the phase separation and the formation of the branching structures with nanocolumns extending from larger clusters formed on the substrate to the surfaces of the grown film. The modeling results revealed the mechanism can be divided into two main steps. Totally speaking, this work is valuable in revealing and explaining mechanism leading to the formation of branching morphologies, but at the same time the paper needs to be further revised according to the following comments.

1. In Section 2, Materials and Methods, there are 7 equations in this section. However, the descriptions for these equations are insufficient. If an equation is from a published paper, the citation for this equation should be explicit; if an equation is derived by authors, the derivation process should be given in details. For example, For Equation (1), does it come from Ref. [24] or be deduced by authors, it seems to be unclear. Similar problems may be found in the description for other equations. In other words, new methods and protocols should be described in detail while well-established methods can be briefly described and appropriately cited. In addition, there is only subsection 2.1, but no subsection 2.2, so please check it.

The additional references to the sources of respective equations have been added to the manuscript (see lines 112, 116, 124, 136, 167, 177).

The additional texts highlighting the similarities and differences of different parts of the present and previous model have been added to the manuscript (lines 111-114, 167, 177, and 188-190).

The issue with subsection 2.1 has been corrected.

2. At the beginning of Section 3, authors say “To investigate and determine factors resulting in the growth of branching structures, a series numerical experiments was performed.”, and then followed by Figures 1-5 and the corresponding discussions. However, the reviewer thought it is insufficient for a complete study. In other words, at least, the authors should give one of numerical experiments in details, to clearly show how the numerical results (or the data from the Figures) are obtained, thus interested readers may replicate and make the further study.

One of numerical experiments have been made available in details in Figure 7, where 3d plots of structures formed at different growth times are presented. The description of Figure 7 has also been added to the manuscript (see lines 484-540).

3. The first paragraph in Introduction is very long and the readers may be tired of reading so long paragraph and are difficult to understand why the study is necessary to be done. The reviewer suggested that this paragraph be divided into several small paragraphs, according to the logic relation of problems proposed and the existed works.

The introduction has been divided into the three smaller paragraphs.

4. In the Conclusions, the concluding remarks should be given point by point, such as (1), (2), (3), …, thus interested readers may easily understand the main results obtained in this study.

Conclusions have been made given point by point.

5. At lines 188-191, basic values of parameters used in calculations should be given in the form of table, to agree well with the style of scientific papers.

Values of parameters used in calculations have been made available in the form of table (see line 204).

6. There are some format and typo issues. For example, the new paragraph should be retracted arrangement. Typo may be found at lines 113 and 121. If an equation is referred to, it should be cited as “Equation (n)”, but not “Eq. (n)”, please check them and revise all.

Those and many other format ant typo issues have been corrected.

Any changes are marked throughout the manuscript.

7. The title name does not fit the journal style, the first letter of some words should be capital letter, please check it.

The first letter of some words has been made capital letter.