The Anisotropic Stress-Induced Diffusion and Trapping of Nitrogen in Austenitic Stainless Steel during Nitriding

Reviewer 3

The level of English in this article is good. The reported results are interesting. Before publication, the following remarks must be taken into account:

No action needed

The authors are recognized in the field of modelling of nitriding of stainless steels. They have published numerous papers in this field. Here they must clearly explain the originality of their approach in this article. To my mind, the originality is related to the fact that many aspects of stainless steel nitriding can be explained by only taking into account elastic anisotropy of stainless steel. It is also necessary to express it in the conclusion that is not well wrtitten. The fact the diffusion coefficient can be taken constant is also an important point.

The anisotropic stress-induced diffusion together with trapping-detrapping was not investigated before. There were just two publications (Sommers group [24,25]) which considered stress-induced diffusion together with trapping-detrapping, but anisotropic aspects were not considered, also are more differences between those and our models (processes on the surface). That is mentioned in the Introduction

I wonder to what extent it is essential to take detrapping into account. Would it not be possible to take into account only the trapping? Some experiments of annealing on nitrided layers (see reference 33 and the papers cited therein) seem to show that the nitrogen having interacted with the chromium is very difficult to destabilize and no longer contributes to the diffusion. In order to begin to answer this question, it would be interesting to have an idea of the importance of the two terms of equation 4 as a function of the nitrogen concentration.

Detrapping is always considered in trapping-detrapping model, the importance was shown by Templier. Martinavicius et. And also Parascandola et al.

For example, in [Parascandola et al. [https://doi.org/10.1016/S0168-583X(97)00844-6] and [Parascandola, S., Möller, W., & Williamson, D. L. (2000).The nitrogen transport in austenitic stainless steel at moderate temperatures. Applied Physics Letters, 76(16), 2194–2196. doi:10.1063/1.126294 ] when investigated the diffusion behaviour of nitrogen implanted AISI 316 by sequential implantation with 14N and 15N isotopes at a temperature around 400 °C. They showed that the firstly implanted 14N could be redistributed after implantation with 15N. This behaviour was interpreted to entail detrapping of the initially trapped nitrogen.

So we cannot neglect detrapping

A major trouble of this work resides in the choice of the experimental data (figures 1 and 4). The authors chose data from Menendez al. (reference 19) which nitrided single crystals of stainless steel. It is not certain that the modelling presented in this article applies to the nitriding of polycrystals made of stainless steels. While it is normal to find different nitrided depths between samples with different orientations, it is much more questionable to say that the nitrogen concentration at a given depth is different from grain to grain for a polycrystalline sample. Authors should clarify this point.

Figure 3 is very particular in that the results presented without TD or SID are not optimized while they are for the model with TD and SID. Would it be possible to optimize models without SID and TD so that the results are better?

Using presented model, we studied the effect of crystallographic orientations of single crystal on nitrogen penetration depth during formation of the expanded austenite in single crystal ASS. If to be very precise for polycrystalline ASS presented model should be modified by taking to account the crystalline texture of sample (which strongly depends on the thermal and mechanical treatments used in the fabrication process). Furthermore, the influence of grain boundary diffusion as well as the role of compressive stresses could also explain why the simulation of nitrogen depth profiles in  polycrystalline ASS is difficult. Moreover, a recent investigation in plasma nitrided polycrystalline ASS steel has demonstrated that nitrogen incorporation into the steel matrix induces not only lattice expansion but also significant lattice rotations. This process modifies the crystallographic texture at the surface and it will very likely affect the nitrogen diffusion since nitrogen diffusion depends on the crystallographic orientation. However, model can be applied for polycrystals also but with some “averages” Influence of grains of polycrystals steel was considered in our previous work

[39]      Moskalioviene, T.; Galdikas, A.; Riviere, J.P.; Pichon, L. Modeling of nitrogen penetration in polycrystalline AISI 316L austenitic stainless steel during plasma nitriding. Surf. Coat. Technol. 2011, 205(10), 3301-3306. https://doi.org/10.1016/j.surfcoat.2010.11.060

About fig. 3. Yes, models can be optimized to get better results. In manuscript this point is discussed and it is said that good fitting can be obtained also only with SID or only with TD, but in fact both processes works simultaneously and this aspect is analyzed in this paper.

We do not understand what the authors want to do at the end of this paper. 2 figures (6 and 7) to show that the diffusion is in root of time, which is normal given that one uses the law of Fick in semi-infinite medium with relatively standard boundary conditions.

The conclusion must be rewritten

Figures (6 and 7) show qualitative and quantitative properties of presented model not just to show that the diffusion is in root of time. We agree that this conclusion is trivial and not important. Fig.7 also shows different penetration depth for different lattice orientation at the same diffusion coefficient.

Conclusions are rewritten

In addition, the following minor points have to be corrected:

Line 57, replace “pace” by “place”

Line 74, there is a problem with the reference number of Oriani, 45 instead of 46.

Line 191, add “A” at the beginning of the sentence.

Corrected

Reviewer 4

Address
=======

The address of the authors should clearly state their country, not

just a ZIP code.

corrected

Syntax
======

- Note the difference between "stress induced diffusion" and
"stress-induced diffusion." In many instances, hyphens are lacking
in the text that are crucial to convey the intended meaning.

Corrections made

Mathematical Typesetting
========================

- Failure to comply with established rules of mathematical typesetting
(according to which only single-letter variables are italicized) and
unnecessarily lengthy variable subscripts make it unnecessarily hard
to read the equations.

We think that equations are written in agreement with rules of mathematical typesetting and requirement of journal

SI Units
========

- "cm" is no SI unit.
- The authors treat "at.%" like a unit. This is wrong. Atom fractions
have no dimension. They are a dimensionless number, i.e. have /no/
unit.
- Correspondingly, e.g. X=451.4 MPa/at.% is wrong. It should be X=45.1
GPa.

X=451.4 MPa/at.% changed to X=45.1GPa.                                                 

Corresponding modifications modifications were done in figure 2

cm is not SI unit but widely used in scientific publications. Diffusion coefficient of solids is better recognized in cm2/s than m2/s

Terminology
===========

- The expression "different crystallographic orientation of [the]
steel lattice" is wrong. Why "crystallographic orientation of the
lattice" and not just "lattice orientation"? However, the relevant
orientation is the crystallographic direction of the /surface/
normal. This is specified by only 2 parameters, while specifying a
lattice orientation requires 3 parameters. The mistake penetrates
the entire paper.

Corrections made to just "lattice orientation"

Physics
=======

- For the relevant intervals of stress and nitrogen level, the effect
(A) of local nitrogen concentration on the diffusion coefficient is
stronger than the effect (B) of stress. If the authors neglect (A),
how can their modeling of (B) be expected to be realistic?

- The concentration dependence of the diffusion coefficient is
mentioned, but it is not appropriately appreciated in this article.

- The prefactor of the diffusion coefficient, D_0, should also vary as
a function of stress. Why is this effect neglected?

- Table 1 specifies C11 of AISI-316L with 4-digit precision.
Considering the considerable range of composition allowed for
AISI-316L, the precision of this value appears to be significantly
exaggerated. All other data should be checked for the same issue.

We do not neglect (A). Concentration dependent diffusion was considered in our previous publications: 

Galdikas, Arvaidas; Moskalioviene, Teresa. Swelling effect on stress induced and concentration dependent diffusion of nitrogen in plasma nitrided austenitic stainless steel // Computational materials science. Amsterdam : Elsevier. ISSN 0927-0256. 2013, vol. 72, p. 140-145. DOI: 10.1016/j.commatsci.2013.02.007

Moskaliovienė, Teresa; Galdikas, Arvaidas. Stress induced and concentration dependent diffusion of nitrogen in plasma nitrided austenitic stainless steel // Vacuum. Oxford : Pergamon-Elsevier. ISSN 0042-207X. 2012, vol. 86, iss. 10, p. 1552-1557. DOI: 10.1016/j.vacuum.2012.03.026.

D_0 is constant in our calculation because Xstress is function of stress. But we do not neglect D_0 dependence on stress and concentration and that is discussed.

The values of C11 of AISI-316L were taken from refs [50] and [51] as is. We did not made any changes

Model Predicition versus Experimental Data
==========================================

- The goodness of match between the profiles predicted by the model
and the experimental data must be quantified.
- The reliability (error bars) of the experimental data need to be
considered in this analysis. This important aspect is entirely
neglected.

Corrections made.

Text of manuscript was appended:

:

 Comparison of the theoretical predictions with experimental data was considered good if the relative deviation of the calculated value from the experimental value was in the range from 0 to 5 %.,

 error bars in figs 1 and 4 were added

Conclusions
===========

- The conclusions are not sufficiently supported by the results.

- Especially, the goodness of match that was accomplished (but not
quantified) by the model that includes trapping does not prove that
"nitrogen traps and trapping-detrapping process play [an] important
role..."
- To prove that, the authors should present (i) the best possible
match that can be obtained /without/ trapping and /with/
concentration dependence of the diffusion coefficient, (ii) the best
possible match that can be obtained /with/ trapping and /without/
concentration dependence of the diffusion coefficient, and (iii)
demonstrate that the match that can be obtained /with/ trapping is
significantly better. "Significantly," in this context, means that
the improvement that can be accomplished by assuming trapping is
substantially greater than the uncertainty (error bars) of the
experimental data.

The fittings without trapping-detrapping and with concentration dependent diffusion coefficient were considered in our previous works

 Galdikas, Arvaidas; Moskalioviene, Teresa. Swelling effect on stress induced and concentration dependent diffusion of nitrogen in plasma nitrided austenitic stainless steel // Computational materials science. Amsterdam : Elsevier. ISSN 0927-0256. 2013, vol. 72, p. 140-145. DOI: 10.1016/j.commatsci.2013.02.007

Moskaliovienė, Teresa; Galdikas, Arvaidas. Stress induced and concentration dependent diffusion of nitrogen in plasma nitrided austenitic stainless steel // Vacuum. Oxford : Pergamon-Elsevier. ISSN 0042-207X. 2012, vol. 86, iss. 10, p. 1552-1557. DOI: 10.1016/j.vacuum.2012.03.026.

This conclusion is confirmed by results presented in figure 3 where are presented profiles without SID and without TD. Both are even qualitatively different from experiment. Only SID +TD profiles qualitatively in agreement with experiment (shows characteristic plateau).

Conclusions are reorganized

Introduction
============

- The introduction includes several mistakes. These will be addressed
when the above (more severe) points have been resolved.

No actions needed

The paper was corrected, taking into the account my comments. However, the description of the nitriding experiment is incomplete. The composition of the nitriding atmosphere is missing. It has to be added.

Text of manuscript (section “3. Results and Discussion”) was appended:

In those experiments the 316L ASS bulk single crystals with [100], [110], and [111] crystalline orientations have been plasma-nitrided for 1.00 h at either 573 or 673 K. The specimens were nitrided in the URANOS reactor [54] where plasma is created by a 13.56 MHz electromagnetic excitation with an incident input power of 700 W. The gas mixture and the total pressure were 60% N₂ + 40% H₂ and 7.5 Pa, respectively. Treatments were performed under floating potential conditions. Detailed description of the sample preparation and plasma conditions are reported in [19, 54]. Nitrogen depth profiles were determined by method of nuclear reaction analysis (NRA).

The authors answered the questions I had asked. However, the modeling relates only to single crystals of stainless steels and is not applicable to polycrystals. This should be specified in the introduction which is not currently the case. It is therefore essential that the authors add one or two sentences in this direction

Sentence added:

The modeling relates to single crystals of stainless steels and is not directly applicable to polycrystals, where lateral diffusion fluxes, grain-to-grain mechanical interaction and different surface conditions play a role.

Abstract
========

Line 11
~~~~~~~

"The model is presented which combines two main mass transport
mechanisms in austenitic stainless steel during nitriding at moderate
temperatures: lattice stress-induced diffusion and
trapping-detrapping."
- This is wrong because is sounds like stress is required for
diffusion. Firstly, only a stress /gradient/ can bias diffusion.
Secondly, diffusion also occurs in the absence of stress. It can
also occur against a stress gradient. The lack of physical
understanding expressed in this sentence is detrimental for a paper
that wants to focus on exactly this topic!
- The mistake repeats in other locations, e.g. Line 76.
- Trapping and detrapping is not a "transport" mechanism.

Abstract was modified:

The model involves diffusion of nitrogen in presence of internal stresses gradient induced by penetrating nitrogen as the next driving force of diffusion after concentration gradient. The diffusion equation takes into account the fact that nitrogen atoms reside in interstitial sites and in trapping sites.

Introduction
============

Line 32
~~~~~~~

"compressive residual stresses"

Line 35
~~~~~~~

"lattice orientations"
- This is still not correct. What you mean -- here and EVERYWHERE else
in the paper -- is the "crystallographic orientation of the surface
normal." To understand this point, consider a grain with a surface
normal parallel to <001>. Now rotate this grain by 20 degrees about
the <001> surface normal. This changes the lattice orientation, but
not the stress level, penetration depth, etc.

corrected

Line 42
~~~~~~~

"strongly dependent"
- How strong is "strongly"?

Corrected

Line 66:
~~~~~~~~

"The γN phase in general is a metastable nitrogen supersaturated solid
solution"
- γN is no phase. Check Gibbs's Phase Rule! It is not metastable,
either. γN is unstable.

We agree, Expanded austenite is essentially not a phase, with a metal lattice different from f.c.c. austenite and it is not separated from austenite by a phase boundary. However, in scientific literature expanded austenite is mainly referred to as “S-phase” or “γ_N-phase”, and that is the reason why we use this terminology in this article.

The clarification (section “1. Introduction”) was inserted:

"Expanded austenite, that will be called γN phase in this paper, is known as a supersaturated solid solution of nitrogen in stainless steel with a disordered fcc structure and a distorted lattice [33]."  

Line 75
~~~~~~~

"The depth profiles calculated with the trapping–detrapping model are
in excellent agreement with the experimental ones [17,38,39]"
- Yes, correct.
- However, the profiles calculated /without/ the trapping–detrapping
model, just based on concentration-dependent diffusion are /also/ in
excellent agreement with the experimental ones [X. Gu, G.M. Michal,
F. Ernst, H. Kahn, A. Heuer, Numerical Simulations of Carbon and
Nitrogen Composition--Depth Profiles in Nitrocarburized Austenitic
Stainless Steels, Metallurgical and Materials Transactions, 45A,
2014, 4268-4279].
- The authors consider the fact that the trapping–detrapping model can
predict observed concentration--depth profiles as a proof for this
madel to be correct. However, other models can predict the
experimental observations equally well. This must be mentioned here
or the authors loose credability as objective scientists.

Text of manuscript  was appended:

Moreover, a concentration-dependent diffusivity model has also been used to describe the behavior of nitrogen in stainless steel. The diffusivity of interstitial atoms in the γ_N phase seems to be dependent on their concentration. For example, Mandl et al. [40] calculated the nitrogen diffusivity from concentration profiles of N-implanted samples and they found that nitrogen diffusivity depends on concentration, with a high value for high nitrogen content and low value for low concentration. It has been hypothesized that the increase of the lattice constant during γ_N phase formation changes the electron density distribution, so that an increase of diffusivity occurs due to the lowered potential barriers between two interstitial sites. This model is also able to explain the carbon diffusivity in austenite [41]. In fact, many efforts have been made in order to explain this enhanced nitrogen diffusion, and several models have been suggested in order to correctly take into account the different phenomena which can influence it, and thus reproduce the experimental profile.

List of References was appended:

[40] Mändl, S.; Scholze, F.; Neumann, H.; Rauschenbach, B. Nitrogen diffusivity in expanded austenite. Surf. Coatings Technol. 2003, 174–175, 1191–1195.

[41] Xiaoting Gu, Gary M. Michal, Frank Ernst, Harold Kahn & Arthur H. Heuer, Numerical Simulations of Carbon and Nitrogen Composition-Depth Profiles in Nitrocarburized Austenitic Stainless Steels,

Metallurgical and Materials Transactions A volume 45, pages4268–4279(2014)

Line 77

~~~~~~~

"chrome-free"

- The name of this element is chromium.

- Chrome is a web browser.

Corrected

Line 81
~~~~~~~

"Generally, the trapping of interstitial components such as hydrogen,
carbon or nitrogen at 82 interstitial positions by dislocation cores,
substitutional impurities or other sort of traps (grain 83 boundaries,
carbide or nitride/matrix interfaces, microvoids and other defects)"
- The introduction contrasts diffusion versus trapping.
- Here, grain boundaries are considered as trapping sites.
- However, there is a wealth of literature on grain boundary
diffusion.

Text of manuscript (section “1. Introduction”) was modified:

Generally, the trapping of interstitial components such as hydrogen, carbon or nitrogen at interstitial positions by different sort of traps can be observed in metal alloys [40-44].

Line 88
~~~~~~~

"He postulates that the vast majority of sites are normal interstitial
sites (NIS). The minor fraction of sites called trapping sites (TS)
provides an energetically favorable environment for occupancy by the
interstitial atoms."
- The concept of "trapping" is generally problematic, especially as
proposed here in the form that nitrogen is trapped in some sites but
not in others. In reality, all that is needed here is to consider
diffusion with different migration energies. When nitrogen is next
to Cr, the migration energy is higher than when nitrogen is
surrounded only by Fe and Ni. Similar considerations apply to
nitrogen near crystal defects. The distinction between trapping and
non-trapping seems artificial. There is a /quantitative/ difference
between nitrogen at Cr and elsewhere (e.g. Fe, Ni), but not a
fundamental, qualitative difference as suggested here.

This aspect can be discussed but trapping – detrapping models are commonly accepted. See comments below

Model
=====

Line 103
~~~~~~~~

"Fick's law"
- Which one? There are 2.

Corrected

…based on Fick's second law…

Equations (2) and (4)
~~~~~~~~~~~~~~~~~~~~~

- (2) shows molar energy RT, popular among chemists.
- (4) shows particle energy kB T, popular among physisists.
- This should be made consistent.

Line 141
~~~~~~~~

"a mechanical model recently proposed in our previous work [29,31]"
- The important assumption here is that of an "infinitely" thick
non-nitrided alloy core that balances the compressive stress in the
nitrogen-rich zone by dilative stress.
- This should also be mentioned in the Introduction.

Corrected

Results and Discussion
======================

Line 176
~~~~~~~~

"Results and Discussion"
- Generally, results are facts that other investigators should be able
to reproduce.
- The Discussion, on the other hand, reflects the interpretation of
the results by the authors.
- Mixing these two important parts of a scientific paper obscures what
is fact and what is interpretation.

We agree, but we think it is more applicable for articles which present experimental results.  

Line 181
~~~~~~~~

"plasma-nitrided for 1 hour"
- hour is no SI unit.
- By convention, "1 hour" means (1.0 +/- 0.5) h. This is likely wrong.
- Consider replacing with 3.6 ks or 1.0 h or 1.00 h.
- Similar in Line 325.

Corrected. All are now SI unites

Line 182
~~~~~~~~

"quartz tube"
- Quartz is crystalline.
- The material used here is called "fused silica."

corrected

Line 187
~~~~~~~~

"Comparison of the theoretical predictions with experimental data was
considered good if the relative deviation of the calculated value from
the experimental value was in the range from 0 to 5 %. "
- Replace with "Comparison of the theoretical predictions with
experimental data was considered good if the relative deviations of
the calculated values from the experimental values was in the range
from 0 to 5 % everywhere."

Replaced, thanks for suggestion

Line 188
~~~~~~~~

"The characteristic plateau, which typical for nitrogen distribution
in plasma nitrided austenitic stainless steels, is well expressed."
- This can be modelled equally well by just assuming
concentration-dependent diffusion. The wording "was made attempt"
(wrong English) does not appreciate the success of competing
approaches.
- Generally, the authors come across as biased toward the trapping
model. They fail to prove that it is actually better than
competing models.
- A scientific paper should focus on facts, not opinions.

For us it is interesting to show influence of chromium. Influence of chromium to distribution of nitrogen take place though the traps 

For example, in [Parascandola et al. [https://doi.org/10.1016/S0168-583X(97)00844-6] and [Parascandola, S., Möller, W., & Williamson, D. L. (2000).The nitrogen transport in austenitic stainless steel at moderate temperatures. Applied Physics Letters, 76(16), 2194–2196. doi:10.1063/1.126294 ] when investigated the diffusion behaviour of nitrogen implanted AISI 316 by sequential implantation with 14N and 15N isotopes at a temperature around 400 °C. They showed that the firstly implanted 14N could be redistributed after implantation with 15N. This behaviour was interpreted to entail detrapping of the initially trapped nitrogen.

We added comment and citation on concentration-dependent diffusion

Line 191
~~~~~~~~

"second Fick’s law"
- Just a comment: This is no law. It is the assumption of a
concentration-independent diffusion coefficient. Compare Ohm's law,
which is the assumption of a voltage-independent resistance.

No action needed

Figure 1
~~~~~~~~

- The fit is /relatively/ poor.
- Fits obtained with just assuming concentration-dependent
diffusion are much better [X. Gu, G.M. Michal, F. Ernst, H. Kahn, A.
Heuer, Numerical Simulations of Carbon and Nitrogen
Composition--Depth Profiles in Nitrocarburized Austenitic Stainless
Steels, Metallurgical and Materials Transactions, 45A, 2014,
4268-4279].
- As I suggested earlier, the goodness of fit should be quantified,
such that the quality of the predictions obtained with different
physical models can be quantitatively compared.

As is mentioned in text of manuscript the fits are with 5% of relative deviation from experimental results.

Suggested citation is added (see comment above)

Conclusions
===========

Line 369
~~~~~~~~

"Numerical modeling to predict the nitrogen concentration evolution"
- Change to "Numerical modeling to predict the temparal evolution of
the nitrogen concentration depth profile"

Replaced, thank for suggestion

Line 370
~~~~~~~~

"Numerical modeling to predict the nitrogen concentration evolution
during expanded austenite4 formation *needs* the incorporation of the
coupling between diffusion, *trapping* and mechanical stress"
- The distinction between diffusion and trapping is diffuse, as
discussed above.
- There is no convincing evidence that the concept of trapping is
needed. The authors appear to be biased, as they ignore equal or
better predicition success of models that to not consider trapping.
- Thus, the conclusions of this paper are (still) not supported by the
data.

Trapping explains the influence of chromium through the traps (also see comments above)

Line 376
~~~~~~~~

"The effect of the nitriding temperature on nitrogen penetration at
moderate temperatures is mainly due to the variation of diffusion
coefficient."
- As opposed to what? It seems trivial that the effect of the
nitriding temperature on nitrogen penetration at moderate
temperatures is mainly due to the variation of the thermal
activation factor of diffusion coefficient. Why is this a conclusion
of this paper?

This conclusion is removed

General Comment
===============

- Several mistakes in the current version communicate an apparent lack
of physical understanding of exactly those concepts that constitute
the central topic of the article -- diffusion, phases, lattice
orientation, element names.
- It is mandatory for the authors to correct these mistakes.
- The authors appear to be biased toward the trapping-detrapping
model. They seem to ignore the success of other models to predict
concentration--depth profiles equally well or better.

Corrections are made.

We do not ignore other models and they are discussed, more discussion on this is extended in corrected manuscript. (see comments above)

Response to Previous Comments
=============================

Thank You
~~~~~~~~~

- Thank you for addressing numerous comments. I believe the paper has
improved.
Mathematical Typesetting
~~~~~~~~~~~~~~~~~~~~~~~~

- Italicizing of mathematical symbols is still wrong across the paper.
- I will not insist on this poin, just want to help.

SI Units
~~~~~~~~

- Yes, cm is often used. So is e.g. ft (feet).
- cm is tolerated by the SI system.
- Still, cm is no SI unit.
- Neither is degree C, nor is hour.
- "Diffusion coefficient of solids is better recognized in cm2/s than
m2/s."
- The strength of the SI system is that conversions are easy.
- If diffusion coefficients are better recognized in cm2/s than m2/s,
this is because some authors prefer to do what we have always done
and resist to any change instead of doing what is right. This
mindset is not likely to support the advance of science.

Terminology
~~~~~~~~~~~

- My comment: "The relevant orientation is the crystallographic
direction of the /surface/ normal. This is specified by only 2
parameters, while specifying a lattice orientation requires 3
parameters. The mistake penetrates the entire paper."
- Author response: "Corrections made to just "lattice orientation."
- This is still wrong -- across the paper. Please see my comment
above.

Physics~~~~~~~

- "We do not neglect (A). Concentration dependent diffusion was
considered in our previous publications."
- Thank you for this response. However, the issue is not resolved --
see comments above.

Conclusions
~~~~~~~~~~~

- "The fittings without trapping-detrapping and with concentration
dependent diffusion coefficient were considered in our previous
works."
- Maybe the data you show in that previous work can justify the
conclusion that the trapping-detrapping model provides better
predictions.
- However, the results in /this/ paper do not justify /this/
conclusion.
- "This conclusion is confirmed by results presented in figure 3 where
are presented profiles without SID and without TD. Both are even
qualitatively different from experiment. Only SID +TD profiles
qualitatively in agreement with experiment (shows characteristic
plateau)."
- "This conclusion is confirmed by results presented in figure 3 where
are presented profiles without SID and without TD. Both are even
qualitatively different from experiment. Only SID +TD profiles
qualitatively in agreement with experiment (shows characteristic
plateau)."
- The fit in the paper cited above, based on concentration-dependent
diffusion only, seem better than any fit you have produced in this
work.
- You have still not provided convincing evidence for your
conclusion that tbe trapping-detrapping model is essential.

We are very thankful for valuable discussion and suggestions, which significantly improved quality of manuscript.