Melting Thresholds of Materials Irradiated with a Wide Class of Pulsed Electron Beams

Round 1

Reviewer 1 Report

The presented article presents very interesting material describing the influence thermal processes during irradiation and the prediction their suitability for certain applications. The article is written in a comprehensible manner. I have only a few minor important comments regarding the formal requirements of the submitted article.

  The autors of article mention 40 literary sources, which, however, are cited in a very unconventional way (e.g. [1-33], source 37 is not cited at all).

Some of the abbreviations used are not fully explained (eg BF line 207) even if they are used in the text before, but without explanation (abbreviations should always be explained at the moment they are used in the text for the first time).

Author Response

First of all, I would like to express my deep gratitude to all the reviewers for the work they have done, not only studying the manuscript in detail, but also making valuable comments. This says of their deep understanding of the problems that are raised in the work. I tried to take into account all the comments as much as possible, and improve the manuscript in terms of both its essence and perception. Hope the manuscript has got better.

Reviewer 1

The presented article presents very interesting material describing the influence thermal processes during irradiation and the prediction their suitability for certain applications. The article is written in a comprehensible manner. I have only a few minor important comments regarding the formal requirements of the submitted article.

• The authors of article mention 40 literary sources, which, however, are cited in a very unconventional way (e.g. [1-33], source 37 is not cited at all).

I have changed the presentation of the references in a more conventional way and enhanced their number to 52.

• Some of the abbreviations used are not fully explained (eg BF line 207) even if they are used in the text before, but without explanation (abbreviations should always be explained at the moment they are used in the text for the first time).

All the abbreviations including BF (beam factor) are now explaining in the text before their further using.

Reviewer 2 Report

This paper analyzes the melting thresholds of different materials under electron beam irradiation through theoretical derivation. The research content may have practical value in engineering. But there is a lack of eye-catching innovation points. Because the author's discussion is entirely based on theoretical derivation, without verifying the theory. It is recommended to conduct experimental verification of the theory to make the paper more rigorous and reliable.

1. The expression of publicity in the text is not uniform. Does different publicity have different meanings? If so, it is recommended to provide an explanation. If not, it is recommended to unify.

2. Different materials have different physical and chemical properties. It is recommended to supplement experimental research to determine the applicability of the theoretical model.

3. In the discussion section, it is recommended to cite previous research, including theoretical derivation and experimental research. Highlight the superiority and innovation of the theory proposed in this article by comparing theoretical models. Verify the accuracy of the model by citing experimental research.

Minor editing of English language required

Author Response

Reviewer 2.

First of all, I would like to express my deep gratitude to all the reviewers for the work they have done, not only studying the manuscript in detail, but also making valuable comments. This says of their deep understanding of the problems that are raised in the work. I tried to take into account all the comments as much as possible, and improve the manuscript in terms of both its essence and perception. Hope the manuscript has got better.

This paper analyzes the melting thresholds of different materials under electron beam irradiation through theoretical derivation. The research content may have practical value in engineering. But there is a lack of eye-catching innovation points. Because the author's discussion is entirely based on theoretical derivation, without verifying the theory. It is recommended to conduct experimental verification of the theory to make the paper more rigorous and reliable.

1. The expression of publicity in the text is not uniform. Does different publicity have different meanings? If so, it is recommended to provide an explanation. If not, it is recommended to unify.

I tried to make expression of publicity in the text more uniform by correcting a terminology in the text, conclusions in section Conclusions, and enhancing the Sections of Introduction, and Materials and Methods.

2. Different materials have different physical and chemical properties. It is recommended to supplement experimental research to determine the applicability of the theoretical model.
3. In the discussion section, it is recommended to cite previous research, including theoretical derivation and experimental research. Highlight the superiority and innovation of the theory proposed in this article by comparing theoretical models. Verify the accuracy of the model by citing experimental research.

Concerning points 2-3 I completed the Discussion Section by the following paragraphs

It should be noted that this paper is devoted not so much to the development of any theoretical model for calculating temperature fields and melting thresholds of materials, since the implemented one is based on the well-known one-dimensional non-stationary heat equation (17). Rather, it is about a methodological approach to the use of a specific source of PEBs for certain industrial applications. The presented list of sources of PEBs can be expanded. Accordingly, the range of BFs for additional ones should be calculated using formula (1). Then, the calculated BFs lines should be plotted on Fig. 1 in the ‘BF–MF’ phase space. This enables to understand which of the Z1–Z3 regions, corresponding to the mixed volume or surface heating source, fall to these PEBs. In other words, a range of the g type of heating criterion is determined for certain sources of PEBs. As discussed above, this makes it possible to draw conclusions about the possibility of using PEBs for the required applications firstly. Secondly, the relative MMT and EMMT values for these sources of PEBs can be directly estimated (without calculations) using the data shown in Fig. 2. Moreover, their multiplying on the coefficients presented in formulas (17), (22), (27), and (28), real (not relative) values of MMT (for γ≫1 and γ≪1 cases) and EMMT (for cases γ≫1 and γ≪1), respectively, can be determined.

Experimental verification of the presented analytical model and the calculated results is an important component of the study. However, it should be stated that such examinations are a separate and very difficult task. Nevertheless, it is possible to test the accuracy of the presented model using previously published data. For example, in work [52], the experimentally determined EMMT values for bulk Cu and the 316 stainless steel are 5.0–5.5 and 2.0–2.5 J/cm², respectively. In this case, irradiation has been carried out with a source of PEBs with parameters close to those for the ‘RITM’ facility at a τ pulse duration of ~2.5 µs. It follows from Fig. 1 that this case corresponds to the γ≪1 range. Fig. 2 shows that the EMMT value for Cu (yellow column) is 3.45 J/cm² at τ~1.0 µs. In accordance with formula (28) and taking into account that the τ experimental value is 2.5 times larger, it is necessary to multiply the EMMT value by . As a result, we get EMMT ≈5.45 J/cm² for Cu, which correlated well with the experimental data.

For the 316 stainless steel, its EMMT value is more difficult to determine because this material is not represented in Fig. 2. Nevertheless, an estimation can be obtained, given that all properties of this steel are close to those of pure iron (except for thermal conductivity, which is approximately four times lower). It follows from Fig. 2 that the EMMT value of Fe (yellow column) is 2.24 J/cm² at τ~1.0 µs. As in the previous case, it is necessary to multiply this value by  in accordance with formula (28). Considering that the thermal conductivity is four times lower, it should be also divided by two. As a result, EMMT ≈1.77 for the 316 stainless steel, which satisfactorily agrees with the experimental data.

Reviewer 3 Report

The considerations presented in the work are based on correct physics. They may be very useful as a guide for those planning electron beam experiments, as well as analysing them. The work can be published with minor corrections as follows.

Some variables and parameters used in the formulas have not been defined before use. Undoubtedly, most are standard or have been specified in the cited reference [34], but they should be defined anyway. This will improve the readability of the work.

This reviewer thinks, it would be very helpful to provide the definitions of MF and BF, perhaps even at the very beginning of the text around tables 1 and 2, where they appear for the first time. However, I leave the decision on this matter to the author. At least for clarity of considerations in formula (22) it is worth adding explicitly:

gamma = … = BF/MF

In the right hand of formula (19) we have T_0(x) but should be T_0(0) or even T_0

The text below equation (22) reads: It follows from expression (22) that the values of gamma are positive in all cases. This is redundant, as gamma positivity follows from its definition in (2).

Author Response

Reviewer 3

First of all, I would like to express my deep gratitude to all the reviewers for the work they have done, not only studying the manuscript in detail, but also making valuable comments. This says of their deep understanding of the problems that are raised in the work. I tried to take into account all the comments as much as possible, and improve the manuscript in terms of both its essence and perception. Hope the manuscript has got better.

The considerations presented in the work are based on correct physics. They may be very useful as a guide for those planning electron beam experiments, as well as analyzing them. The work can be published with minor corrections as follows.

Some variables and parameters used in the formulas have not been defined before use. Undoubtedly, most are standard or have been specified in the cited reference [34], but they should be defined anyway. This will improve the readability of the work.

I agree. Now almost all variables and parameters are defining at the beginning of the manuscript in the Materials and Methods section

This reviewer thinks, it would be very helpful to provide the definitions of MF and BF, perhaps even at the very beginning of the text around tables 1 and 2, where they appear for the first time. However, I leave the decision on this matter to the author. At least for clarity of considerations in formula (22) it is worth adding explicitly:

gamma = … = BF/MF

I agree. Now I have provided the definitions of MF and BF in the Materials and Methods section

In the right hand of formula (19) we have T_0(x) but should be T_0(0) or even T_0

Yes, I have corrected the last term in formula (19) which now have the form T₀^.. Due to introducing two additional formulas for MF and BF, the formula (19) now has number (21).

The text below equation (22) reads: It follows from expression (22) that the values of gamma are positive in all cases. This is redundant, as gamma positivity follows from its definition in (2).

I agree and have deleted the extra words.

Reviewer 4 Report

Dear Author and Editor,

In review, I received a manuscript draft entitled »Melting thresholds of materials irradiated with a wide class of pulsed electron beams” considered for publication in the MDPI journal “Coatings”.

The author is exploring the following PEBs: SOLO, RITM, GASA-1, DUET, GESA-2, TEU-500 and SINUS-7, with acc. voltages from 5 kV to 1000 kV, with pulse duration from 0.05 – 300 mus. The author classifies the PEBs and analyzes the thermophysical properties, namely calculating by HEATPACK-1.0 the dynamics of temperature fields under irradiation.

The abstract / introduction needs a sentence or two on to clarify how this manuscript fits the “Coatings” aim and scope. In the current version, I do not see a direct connection. I understand this is submitted to a special issue on this topic, but think about the casual reader. 

The considered e- sources need to be further described (I guess they are all located in The Institute of High-Current Electronics. At least short info on where and how are available for experiments. Without the information on availability and access, the value of the performed calculation is reduced on the internal work report…)

L62: The software Heatpack 1.0 should be explained in ref 34 and 35, but references do not consider the software package. Please elaborate on the software package used for simulations. If not available for general use, then it should be properly referenced. One of the important aspects is the reproducibility of the scientific results...     

L74: based on which criterion these targets were selected?

L77: Why BaseM has to be introduced – for what purpose?

L84: are plates here considered as grains? The grain boundary (GB) plays a crucial role in heat transfer – how is this effect considered in the “plates” scenario? If the effect of GBs cannot be assessed, then the simulation of single-crystal would be more suitable considering the stated theoretical values in Table 1.

L137: based on scanning electron microscope electron-beam interaction (0.1 – 30 kV), the e-beam energy transfer is far more efficient than stated in the manuscript (“up to 40% is reflected”). Can the author justify or reference this value?

Page 5: how do the executed calculations differ from the Monte Carlo simulation of electron-matter interaction volume? There are several different physics models for e-matter interaction widely adopted, and differences and similarities should be clearly underlined in this section.   

From this part onward, I suggest the editor to consider the recommendation also from other Reviewers.

Author Response

Reviewer 4

First of all, I would like to express my deep gratitude to all the reviewers for the work they have done, not only studying the manuscript in detail, but also making valuable comments. This says of their deep understanding of the problems that are raised in the work. I tried to take into account all the comments as much as possible, and improve the manuscript in terms of both its essence and perception. Hope the manuscript has got better.

In review, I received a manuscript draft entitled »Melting thresholds of materials irradiated with a wide class of pulsed electron beams” considered for publication in the MDPI journal “Coatings”.

The author is exploring the following PEBs: SOLO, RITM, GASA-1, DUET, GESA-2, TEU-500 and SINUS-7, with acc. voltages from 5 kV to 1000 kV, with pulse duration from 0.05 – 300 mus. The author classifies the PEBs and analyzes the thermophysical properties, namely calculating by HEATPACK-1.0 the dynamics of temperature fields under irradiation.

The abstract / introduction needs a sentence or two on to clarify how this manuscript fits the “Coatings” aim and scope. In the current version, I do not see a direct connection. I understand this is submitted to a special issue on this topic, but think about the casual reader. 

I agree. I inserted the phrase into the Introduction.

It should be noted that PEBs are widely used for surface modification: 1) for surface cleaning from inclusions, its homogenization and smoothing; and 2) as a tool for the formation of highly adhesive coatings (surface alloys) by mixing of molten both preliminary deposited films and the surface layers of substrates.

The considered e- sources need to be further described (I guess they are all located in The Institute of High-Current Electronics. At least short info on where and how are available for experiments. Without the information on availability and access, the value of the performed calculation is reduced on the internal work report…)

I agree. I hope I have inserted enough materials concerning the PEBs and their availability.

In this paper, the main focus is on source of PEBs, which are among the most promising for industrial applications (in the author’s opinion). In particular, the ‘RITM’ source of PEBs is considered, which has been developed at the Institute of High Current Electronics of the Siberian Branch of the Russian Academy of Sciences [9–22]. Back in the early 2000s, the license for its industrial production has been sold to the Japanese ‘SODICK’ company that has produced the ‘PIKA PF32A Finish Machine’ industrial analogue. This equipment is used all over the world for both scientific and industrial purposes [23, 24]. In Russia, the ‘RITM-SP’ machine (manufactured by OOO ‘Microsplav’ company) is available for experiments at the Tomsk Regional Center for Collective Use of the Tomsk Scientific Center of the Siberian Branch of the Russian Academy of Sciences (https://ckp-rf.ru/catalog/ckp/3058/). In Europe, such machine is installed in the Laboratory of Surface Engineering and Applied Electrochemistry ‘Roberto Piontelli’ of Politecnico di Milano University (https://www.cmic.polimi.it/en/ricerca/elenco-gruppi-di-ricerca/surfacelab/). Designed by the Efremov Institute of Electrophysical Apparatus (St. Petersburg, Russia) in collaboration with Karlsruhe Institute of Technology (Germany), the ‘GESA’ source of PEBs is available both in Russia and Germany [25–27]. One of the potential applications of the ‘GESA’ setup is the processing of gas turbine engine blades. The ‘SOLO’ source of PEBs is also widely used for scientific purposes [28–32]. It is an integral part of the ‘UNIKUUM’ complex of unique electrophysical equipment of Russia [33] (https://ckp-rf.ru/catalog/usu/434216/). The ‘TEU-500’ source of PEBs, developed at Tomsk Polytechnic University [34–36], the ‘DUET’ one by the Institute of High-Current Electronics [37–39] and the ‘SINUS-7’ facility [40–43] are also of great interest for a number of scientific and technological applications.

L62: The software Heatpack 1.0 should be explained in ref 34 and 35, but references do not consider the software package. Please elaborate on the software package used for simulations. If not available for general use, then it should be properly referenced. One of the important aspects is the reproducibility of the scientific results...     

I added the desirable information.

Computer simulation of the dynamics of temperature fields under irradiation with PEBs has been carried out using the ‘HEATPACK-1.0’ software package. The software package is a registered commercial product, the copyright owner is the Tomsk Scientific Center of the Siberian Branch of the Russian Academy of Sciences. The physical model, on the basis of which this software package has been developed, is described in details in [44, 46].

L74: based on which criterion these targets were selected?

Metals were chosen as targets, which are most often used as substrates when coatings are applied to them by electron beam processing.

L77: Why BaseM has to be introduced – for what purpose?

The BaseM material is a virtual pseudo-metal that does not exist in nature. Its properties are collective and close to some average values of a wide class of real metals and alloys. Its properties are using as the measuring units. For instance, in Figure 2 the MMT values of all metals are presented in Abr. Units, where the MMT of the BaseM is taken as the unit of measurement. It is useful for results presentation.

L84: are plates here considered as grains? The grain boundary (GB) plays a crucial role in heat transfer – how is this effect considered in the “plates” scenario? If the effect of GBs cannot be assessed, then the simulation of single-crystal would be more suitable considering the stated theoretical values in Table 1.

In our calculation we operate with such property of materials as heat conductivity. Table value of heat conductivity automatically considering the influence of the grain boundaries. In Table 2 the properties are given that are close to a single-crystal. If we want to calculate the MMT and EMMT for polycrystalline structure, we just have to use the properties (especially a heat conductivity) for polycrystalline structure.

L137: based on scanning electron microscope electron-beam interaction (0.1 – 30 kV), the e-beam energy transfer is far more efficient than stated in the manuscript (“up to 40% is reflected”). Can the author justify or reference this value?

I added the desirable information.

For elements with a low nuclear charge, the reflected part of the electron beam energy is low but it may reach up to 40% for ones characterized by high nuclear charge values [47].

Page 5: how do the executed calculations differ from the Monte Carlo simulation of electron-matter interaction volume? There are several different physics models for e-matter interaction widely adopted, and differences and similarities should be clearly underlined in this section.   

The electron energy loss function normalized by r its extrapolated range (depth of penetration) f(x/r,t), and depth of penetration of electrons r may be can be obtained in different ways. One of them is the Monte Carlo calculation method, the other one, which we use here, is semi-empirical. In the latter case, the formulas for the above functions are obtained in the form of polynomials by interpolation of experimental data. The accuracies of both methods are approximately equal, but for analytical calculations it is preferable to use the semi-empirical approach.

From this part onward, I suggest the editor to consider the recommendation also from other Reviewers.