State-of-the-Art Diffusion Studies in the High Entropy Alloys

Round 1

Reviewer 1 Report

       In this paper, an extensive overview of the various diffusion studies in high entropy alloys (HEAs) is presented. The review is certainly useful and worth publishing after some revision is done. The revision must answer/reflect the following points of concern.

1.       Both tracer and interdiffusion coefficients depend of course on the vacancy concentration.

The theoretical discussion should include some comments about the possible change of the vacancy concentration as a function of alloy composition.

       2. In reference [28] of the paper, a quasi-binary experimental approach to study and interpret interdiffusion in multicomponent systems (like HEAs) was used. The results of this study have caused some long-standing discussion in the literature. The main opponent of this study is Aloke Paul, who has published several papers ([37, 39] in the present paper) that criticized [28]. The authors of the present review seem to be quite in favour of the authors of [37, 39]. However, I believe that the review must be re-written in a more balanced, neutral way. This is because 1) the pseudo-binary experimental approach for the investigation of interdiffusion in HEAs (introduced by Aloke Paul as an alternative to the quasi-binary approach) has its own major draw-backs; and 2) the negative points about the interpretation of the results in [28] have already been resolved in other papers, some of which have been mentioned in the present paper.

         Indeed, the quasi-binary approach [28], when the general flux equations are considered, yields good approximations to well-defined diagonal elements of standard interdiffusion matrices. The pseudo-binary approach [39], on the other hand, can only provide an approximation to some weighted average of those diagonal terms. It is almost impossible to predict the rule of averaging of those terms in the pseudo-binary approach.

        Furthermore, the use of the pseudo-binary approach must be done with great caution. In [67], this approach was used for the estimation of the thermodynamic quantity (product of the thermodynamic and Manning factors) of 4 and 5-component alloys. The reference point for this product, in a standard binary alloy, is unity. However, in the pseudo-binary version in the multicomponent alloys, the reference point is NOT unity but is very different. For example, it is about 2.5 in the 5-component alloy and about 2 in the 4-component alloy. This was pointed out in a very recent paper [Scripta  Mat., vol.  172,  pp.  110 – 112, doi:10.1016/j.scriptamat.2019.07.013]. Table 8 in the present paper must be described as an erroneous one and the corrected one must be used (the corrected table is given in [Scripta  Mat., vol.  172,  pp.  110 – 112, doi:10.1016/j.scriptamat.2019.07.013].) The correct conclusion then is that CoCrFeMnNi is indeed very close to being an ideal system.

       At first glance, the theoretical arguments in [37] against all the results in [28] are serious. However, for the particular case of the CoCrFeMnNi alloy that was used there, all these arguments simply don’t work! Now is the time to accept it. In [76, 77] it was shown that all the self-diffusivities, apart from one for Ni, are approximated quite well in this study ([28]) using the quasi-binary approach. Only the Ni self-diffusion coefficient should be corrected by about a factor of 0.5. This success of the quasi-binary approach is due to the fact (shown by the independent tracer diffusion experimental studies as well [65, 66]) that in this system the self-diffusivities of all 5 components are all well within only one order of magnitude. This means that correlation effects are very slight and the corresponding correlation factors are fairly close to unity.

       What is more is that the choice of the quasi-binary couples in [28] was made with the use of components that have the closest self-diffusion coefficients! This is an important lesson that should be taken from the study in [28]. In my opinion, the present paper should admit this and stop being unnecessarily negative about the quasi-binary experimental approach.

       3. In addition to the above, it should be noted in Table 1 that the composition of the 5-component HEA (CoCrFeMn_0.5Ni) in [28] is different from the equiatomic composition (CoCrFeMnNi) that was used in the majority of the other papers.

       4. Minor point. The English grammar could be improved here and there.

Author Response

Dear Reviewer 1, thank you for your time and comments. Below, you will find the answers to the questions raised in the review.

Comments and Suggestions for Authors

       In this paper, an extensive overview of the various diffusion studies in high entropy alloys (HEAs) is presented. The review is certainly useful and worth publishing after some revision is done. The revision must answer/reflect the following points of concern.

1. Both tracer and interdiffusion coefficients depend of course on the vacancy concentration.

The theoretical discussion should include some comments about the possible change of the vacancy concentration as a function of alloy composition.

Additional comments concerning the mechanism of diffusion in high entropy alloys were added in Section 2.

2. In reference [28] of the paper, a quasi-binary experimental approach to study and interpret interdiffusion in multicomponent systems (like HEAs) was used. The results of this study have caused some long-standing discussion in the literature. The main opponent of this study is Aloke Paul, who has published several papers ([37, 39] in the present paper) that criticized [28]. The authors of the present review seem to be quite in favour of the authors of [37, 39]. However, I believe that the review must be re-written in a more balanced, neutral way. This is because 1) the pseudo-binary experimental approach for the investigation of interdiffusion in HEAs (introduced by Aloke Paul as an alternative to the quasi-binary approach) has its own major draw-backs; and 2) the negative points about the interpretation of the results in [28] have already been resolved in other papers, some of which have been mentioned in the present paper.

         Indeed, the quasi-binary approach [28], when the general flux equations are considered, yields good approximations to well-defined diagonal elements of standard interdiffusion matrices. The pseudo-binary approach [39], on the other hand, can only provide an approximation to some weighted average of those diagonal terms. It is almost impossible to predict the rule of averaging of those terms in the pseudo-binary approach.

        Furthermore, the use of the pseudo-binary approach must be done with great caution. In [67], this approach was used for the estimation of the thermodynamic quantity (product of the thermodynamic and Manning factors) of 4 and 5-component alloys. The reference point for this product, in a standard binary alloy, is unity. However, in the pseudo-binary version in the multicomponent alloys, the reference point is NOT unity but is very different. For example, it is about 2.5 in the 5-component alloy and about 2 in the 4-component alloy. This was pointed out in a very recent paper [Scripta  Mat., vol.  172,  pp.  110 – 112, doi:10.1016/j.scriptamat.2019.07.013]. Table 8 in the present paper must be described as an erroneous one and the corrected one must be used (the corrected table is given in [Scripta  Mat., vol.  172,  pp.  110 – 112, doi:10.1016/j.scriptamat.2019.07.013].) The correct conclusion then is that CoCrFeMnNi is indeed very close to being an ideal system.

       At first glance, the theoretical arguments in [37] against all the results in [28] are serious. However, for the particular case of the CoCrFeMnNi alloy that was used there, all these arguments simply don’t work! Now is the time to accept it. In [76, 77] it was shown that all the self-diffusivities, apart from one for Ni, are approximated quite well in this study ([28]) using the quasi-binary approach. Only the Ni self-diffusion coefficient should be corrected by about a factor of 0.5. This success of the quasi-binary approach is due to the fact (shown by the independent tracer diffusion experimental studies as well [65, 66]) that in this system the self-diffusivities of all 5 components are all well within only one order of magnitude. This means that correlation effects are very slight and the corresponding correlation factors are fairly close to unity.

       What is more is that the choice of the quasi-binary couples in [28] was made with the use of components that have the closest self-diffusion coefficients! This is an important lesson that should be taken from the study in [28]. In my opinion, the present paper should admit this and stop being unnecessarily negative about the quasi-binary experimental approach.

The studies of Tsai et al. [28], are certainly of a very high value, as they represent the first ever experimental approach to the diffusion studies in HEAs. Furthermore, the quantitative data obtained by the Taiwanese team indeed compares well with the available literature data collected since its publication in 2013. However, while we do not disagree with the general idea behind the quasi-binary approach, its execution in this particular study [28] is in our opinion controversial, even though the resulting data is not far from the one obtained by the other authors. The problem in our opinion does not lie in the question of the ideality of the CoCrFeMnNi system, as indeed, many studies have supported that the distribution of elements in this particular alloy can be treated as random (the suggested reference paper by Murch and Belova was added to the text in the section concerning the reference [67] and a comment was added). On the other hand, it should be mentioned that both thermodynamic databases and commonly used Miedema’s scheme approximation indicate a prominent interaction between Mn and Ni [49, 72], which cannot be easily neglected during the diffusion analysis [72,73]. Still, the approximation that the tracer and intrinsic diffusivities are equal can be treated as acceptable. Furthermore, we definitely agree that the planning of an experiment in the work of Tsai et al. was excellent, with a very thoughtful selection of the elements within each of the pairs, which allowed minimizing the uphill effects. The problem, as noted by Paul in [37], is in the fact that the procedure applied by Tsai et al. is not self-consistent.

It is not possible to apply any Boltzmann-Matano/Sauer-Fraise based formalism unless the assumption that the total sum off interdiffusion fluxes is equal zero (diffusion+drift). The idea of Tsai et al. that from each quasi-binary profile two different interdiffusion coefficients can be obtained, simply contradicts this most basic assumption. Furthermore, if one assumes that for each quasi-binary element we obtain a different interdiffusion coefficient, the assumption that the intrinsic diffusivities can be approximated from the values of interdiffusivities is also not correct. Both these issues are completely independent from the fact whether the system is ideal or not and are simply a matter of the diffusion formalism. Further criticism of Paul was directed towards the fact that the normalization procedure was no performed by Tsai et al. Again, this issue contradicts the assumption of the zero overall interdiffusion flux and as a result must be considered a serious drawback of this study. To summarize, we are not negative about the quasi-binary approach itself, but rather about its poor execution, from the theoretical point of view, in this particular case. As mentioned before, the resulting errors are relatively small, which can be largely attributed to a very good experiment planning of the Taiwanese team, however, it does not take away from the mentioned theoretical deficiencies of the applied methodology.

We agree that the overall success and relatively good agreement of the data with further studies, obtained by Tsai et al., deserve recognition, therefore additional comments were added to the text to reflect this view.

3. In addition to the above, it should be noted in Table 1 that the composition of the 5-component HEA (CoCrFeMn_0.5Ni) in [28] is different from the equiatomic composition (CoCrFeMnNi) that was used in the majority of the other papers.

The information was included in the Table 1.

4. Minor point. The English grammar could be improved here and there.

Additional grammar and spelling check was performed.

Submission Date

29 December 2019

Date of this review

15 Jan 2020 08:52:29

Reviewer 2 Report

This is an extended and very detailed review of all original works done so far in the field of diffusion in high-entropy alloys. The literature is properly cited (see a comment below), all works are analysed in chronological order and the conclusions are sound. The manuscript can be published "as it is".

However I have an optional comment to the review of theoretical studies. Very recently several papers were published on positron annihilation measurements of vacancies in CoCrFeMnNi HEAs and DFT-based calculations of vacancy formation and migration energies (group of Araki). It is worth to comment these works.

And probably the first ever work of Kulkarni with co-workers on the application of Morral's body-diagonal method has to be mentioned, ever as a note added in proof. 

Author Response

Dear Reviewer 2, thank you for your time and comments. Below, you will find the answers to the questions raised in the review.

The manuscript is a very valuable contribution to diffusion, in this case for diffusion in high entropy alloys. Therefore, I recommend its publication, also motivated by the immense efforts by the authors to report on the state of knowledge of this topic. Now to two aspects which are not clear for me.

The first, more or less, trivial request concerns Table 4: last section: There are two entries for Ni in CoCrFeMnNi with totally different data – is this a misprint?

Yes, there was a mistake, which was corrected in the revised version.

Second, I have a basic question! The authors work with diffusion of, obviously, only substitutional elements. Such a diffusion process is only possible, if vacancies are available. I could not find any comment on this aspect, or in other words, "where are the vacancies?" – for details see "Handbook of Solid State Diffusion", e.g. Vol. 1, 2017, Paul, Divinski. This aspect (vacancies – yes or no!??) must be clarified before publication (see also a detailed study in Acta Mat., 54, 3043-3053, 2006).

Additional information regarding the mechanism of diffusion in high entropy alloys was added in Section 2.

Submission Date

29 December 2019

Date of this review

03 Feb 2020 09:15:58

Reviewer 3 Report

The manuscript is a very valuable contribution to diffusion, in this case for diffusion in high entropy alloys. Therefore, I recommend its publication, also motivated by the immense efforts by the authors to report on the state of knowledge of this topic. Now to two aspects which are not clear for me.

The first, more or less, trivial request concerns Table 4: last section: There are two entries for Ni in CoCrFeMnNi with totally different data – is this a misprint?

Second, I have a basic question! The authors work with diffusion of, obviously, only substitutional elements. Such a diffusion process is only possible, if vacancies are available. I could not find any comment on this aspect, or in other words, "where are the vacancies?" – for details see "Handbook of Solid State Diffusion", e.g. Vol. 1, 2017, Paul, Divinski. This aspect (vacancies – yes or no!??) must be clarified before publication (see also a detailed study in Acta mater., 54, 3043-3053, 2006).

Author Response

Thank you for positive revue.

We made all suggested changes/misprits.

Comment on the vacancies in HEA was added in the final text.