Modification of Precipitate Coarsening Kinetics by Intragranular Nanoparticles—A Phase Field Study

Round 1

Reviewer 1 Report

1. The subject of the article is of current interest and in line with the profile of the journal. The authors prove a good knowledge of the field. Recognizing some of the limitations of their research in the chapter on conclusions is a positive aspect.
2. In the introductory chapter, a definition of what is meant by "precipitate coarsening" might be useful to the less knowledgeable reader of the subject.
3. In the case of equation (1), the meanings of all symbols must be included (in their current form, explanations for the symbols r and v seem to be missing. The statement remains valid also for the symbols used in equation (2). The three equations written after equation (1) could be given serial numbers.
4. Although the authors mention the use of the bibliographic source [19] for writing equations (1), (2) and the other three equations included after equation (2), there are some differences between the ways of writing equations (1) and (2) in manuscript and in the paper [19]. For example, the constant dimension H seems to have been introduced by the authors, and this should be emphasized (for example, it could be written “The authors of this paper propose the introduction of a dimensional constant H, to ...”.
5. The software used to produce the histograms could be specified. Is it the same Image J software?
6. Definitions of the symbols r* and t* could be introduced, possibly justifying if it is a quantity considered conventionally dimensionless because the paper does not specify the units of measurement for radius r* and time t*.
7. Even if they are considered to be well known, explanations of the symbols R and T used in equation (13) could be introduced in the article.
8. By diminishing the components (subfigures) of some figures, it is possible that all the components of the figure are on the same page (the cases in Figures 3 and 6).
9. Are there limits to the growth of the average precipitate radius R³ versus time? Should growth slow down at some point?
10. In the case of the concluding chapter (lines 421 and 422) “the precipitate size distribution and the coarsening rate can be affected by nanoparticles.”, the precipitate size distribution and the coarsening may in fact be affected by the presence and of some characteristics of nanoparticles?
11. The equations do not appear to be numbered in the usual order. There are equations (1) and (2), equation (3) and equations (8) - (12) seem to be missing.
12. Some aspects of editing the article are presented below. The identifiers a and b used to include the names of the authors immediately after the title of the article must be included as exponents.

Generally, a space is required after each punctuation mark. For example, a free space is required after the colon, before the email address of the corresponding author.

The recommendation that bibliographic references be given numbers as used in the text of the article is not strictly followed. Thus, for example, the paper [8] does not appear to have been used, and it must be placed between the citations of the papers [7] and [9].

In line 120, a free space could be placed between the components of the wording "alloys[19]".

In both equation (2) and line 139, the symbol H could be written in italics. Italic characters could also be used for other symbols in the paper (see symbols t, n, D, etc.).

After equation (5), a comma could be placed, and the explanations of the symbols placed after equation (5) could start using the word "where" (it could be written "where Li and MC have kinetic coefficients, ...". The above statement remains valid for other equations included in the paper, for example, the word “where” included after equation (7) could start with a lowercase letter.

Throughout the work, after each abbreviation "i.e." a comma should be placed.

In line 269, the initials of the authors' first names are not required and a white space must be included immediately after each dot (write "Wu et al. [27], Wang et al. [28]", instead of "X. Wu et al. al.[27], T. Wang et al.[28]”, etc.).

In line 289, it is possible to write “ure 6a”, instead of “ure6a”, in line 291, Figures 6b and 6c. ” instead of “Figs.6b and 6c.”, in line 338 “stresses [5]”, instead of “stresses[5]” etc.

The way of including bibliographic references in the list at the end of the article does not follow the journal's recommendations in this regard (https://www.mdpi.com/journal/metals/instructions). Thus, in the case of journal articles, the initials of the authors' first names are written after the last name and are separated from the last name by commas, the titles of the articles are not written in quotation marks, the abbreviations "vol." and "no." are not used, the year of publication is written immediately after the abbreviated name of the journal and using bold characters, etc. It is recommended to mention all the authors of the work; the way of writing only the first author and using the abbreviation "et al." for the other co-authors is considered rude.

The instructions for authors do not seem to recommend the use of abbreviations for the word "Figure”.

Author Response

Please see attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors,

I believe that for the article to be published, a few inaccuracies should be corrected.

Figures 4, 7-9, 12 and 13 show histograms of the PSD along with a Probability Density Function (PDF) plots. The histogram is constructed on an absolute scale showing the number of particles belonging to a class. The PDF diagram cannot be made to the same scale, so these drawings need to be adjusted, namely - adding a second dimensionless scale for probability density.

The line 262 says that the PSD curves shown in Figures 4 and following "maintained the unimodal skewed shape". However, the bell curves in these figures appear to be symmetric. This needs to be clarified.

Digitizing of the graphics results shows that the mean values of the particle radius R for the bell curves shown in Figs. 7d, 8d, 9d, 12d, and 13d (for 20000 s) differ by more than 10% from the same values estimated from Fig. 6a. It seems that this discrepancy is not solely due to the accuracy of the processing of the graphical results. Please check and comment for me.

The law of what statistical distribution was used to plot the PDFs in your manuscript? What are the parameters of each PDF shown in the paper?

What is the basis for choosing the proposed relationship g(η_nano) - lines 157-158?

Please, correct the typos:

line 74: 300 nm

line 120: alloys [19]

line 133: add the missing equation number (3)

Author Response

Please see the attachment

Author Response File: Author Response.pdf