Coupled Modeling of Anisotropic Stress-Induced Diffusion and Trapping of Nitrogen in Austenitic Stainless Steel during Nitriding and Thermal Annealing

Authors are very thankful to Reviewer for valuable suggestions to improve the manuscript.

Reviewer 1

This paper proposed the mathematical kinetic model for the isothermal aneling process of nitrided austenitic stainless steel. The nitrogen diffusion of the nitride layer with three crystal orientations were described. The model was well deduced. However, there existed some places to clarify.

Reviewers' Comments and Suggestions for Authors

Authors comment:

The XRD patterns of nitride layer and annealed layer should be provided. Whether the annealing could change the crystal orientation of as-nitrided layers?

The XRD patterns of nitrided layer and annealed layer are provided in Ref [53] Fig. 1. We included citation.

Text of manuscript (section “3. Results and Discussion”, all changes in the manuscript are marked by “Track Changes” function) was appended:

“It is important to note that, the XRD analysis of virgin, nitrided, and subsequently annealed samples showed the presence of γ_N phase in the nitrided layer and any formation of chromium nitrides has not been detected (see Fig. 1 in Ref. [53]). This is of fundamental importance as nitrogen diffusion during nitriding or annealing can be described by the purposed model.”

In addition, it would be better to provide the N distribution maps for the nitride layer before and after annealing.

The validation of the proposed model has been made by performing the simulations 

on the basis of experimental measurements from literature. Experimental results are taken from Ref. [Martinavičius, A.; Abrasonis, G.; Möller, W.; Templier, C.; Rivière, J.P.; Declémy, A.; Chumlyakov, Y. Anisotropic ion-enhanced diffusion during ion nitriding of single crystalline austenitic stainless steel. J. Appl. Phys. 2009, 105, 93502. https://doi.org/10.1063/1.3120912], where the nitrogen depth profiles were determined by nuclear reaction analysis (NRA) and the N distribution maps were not presented.

In our manuscript we analyze nitrogen depth profiles (or maps) before and after annealing.

Authors are very thankful to Reviewer for valuable suggestions to improve the manuscript.

Reviewer 2

This manuscript is aimed to investigate the mathematical kinetic model for the isothermal aneling process of nitrided austenitic stainless steel surface layers. Although, the authors have been reported some interesting data, the manuscript must be revised. The detailed problems are following:

Reviewers' Comments and Suggestions for Authors

Authors comment:

1) English texting should be fundamentally revised. There are some grammatical mistakes so that some parts of statements are confusing.

Text of manuscript was revised (all changes in the manuscript are marked by “Track Changes” function).

2) The abstract should be re-written again. It is necessary to report the brief of results in this section.

The abstract has been rewritten:

“Nitrogen diffusion is investigated in single crystalline austenitic stainless steel during modified layer formation and thermal annealing. The generalized system of diffusion equations is derived within a thermodynamic framework from Fick's laws which describe the nitrogen flux under multiple driving forces including a concentration gradient and the gradient of hydrostatic stress. Trapping and detrapping phenomena are considered within this model and nitrogen flux is distinguished depending on whether nitrogen is in a lattice or in a trapping site. Furthermore, the effects of anisotropic elasticity in single crystal austenitic stainless steel on the stress field were involved. The proposed model was used to simulate nitrogen transportation process in single crystalline AISI 316L during ion beam nitriding and after isothermal annealing at three different crystalline orientations. Theoretical curves are compared with experimental results taken from the literature. It is shown, that during isothermal annealing, the nitrogen diffusion becomes significantly slower than during nitriding. The diffusion coefficient during annealing process comparing with nitriding process de-creases by factors of 4.3, 3.3, and 2.5 for the orientations (001), (011), and (111), respectively.”

3) It has been mentioned in line 191 that “there are significant differences in the  nitrogen penetration depths and surface nitrogen content for the different crystal orientations”. What is that reason?

Such dependences were considered and explained in our previous works [Moskalioviene, T.; Galdikas, A. Crystallographic Orientation Dependence of Nitrogen Mass Transport in Austenitic Stainless Steel. Metals 2020, 10, 615. https://doi.org/10.3390/met10050615] by the anisotropic nature of the adsorption process due to Gibbs energies for different oriented grains and the internal lattice stress anisotropy, which was determined by taking to account the anisotropy in the Young’s modulus for the fcc crystal.

The main reason is that the nitrogen diffusion is anisotropic due to the effects of the anisotropic stress gradient and the anisotropic effects on the steel surface.

4) The authors must add the microstructure analyses to the manuscript (SEM micrograph from the nitrogenized surface).

The validation of the proposed model has been made by performing the simulations 

on the basis of experimental measurements from literature. Experimental results are taken from Ref. [Martinavičius, A.; Abrasonis, G.; Möller, W.; Templier, C.; Rivière, J.P.; Declémy, A.; Chumlyakov, Y. Anisotropic ion-enhanced diffusion during ion nitriding of single crystalline austenitic stainless steel. J. Appl. Phys. 2009, 105, 93502. https://doi.org/10.1063/1.3120912], where the nitrogen depth profiles were determined by nuclear reaction analysis (NRA) and the structure of the modified surface layer was characterized by XRD.

Text of manuscript (section “3. Results and Discussion”, all changes in the manuscript are marked by “Track Changes” function) was appended:

“It is important to note that, the XRD analysis of virgin, nitrided, and subsequently annealed samples showed the presence of γ_N phase in the nitrided layer and any formation of chromium nitrides has not been detected (see Fig. 1 in Ref. [53]). This is of fundamental importance as nitrogen diffusion during nitriding or annealing can be described by the purposed model.”

The SEM micrographs of nitrided samples, which show different depth penetration at different orientated grain were shown in previous our work ref. [49] (fig.3) and this work is cited in the manuscript. 

Text of manuscript (section “3. Results and Discussion”, all changes in the manuscript are marked by “Track Changes” function) was appended:

“The microstructure of post-nitrided ASS samples was analyzed in our previous work, where the SEM micrographs show very clearly different penetration depths of nitrogen for different orientated grains (see Figure 3 in Ref. [49]).”

Authors are very thankful to Reviewer for valuable suggestions to improve the manuscript.

Reviewer 3

The manuscript is devoted to modeling of the process of isothermal annealing of nitrided surface layers of austenitic stainless steel. The authors are working on a topical issue. But there are a few remarks about the manuscript:

Reviewers' Comments and Suggestions for Authors

Authors comment:

1. It is necessary to add more specifics to the abstract. While the abstract is similar to enumeration of what is done. Authors in the abstract should reflect the best aspects of the manuscript.

The abstract has been rewritten (all changes in the manuscript are marked by “Track Changes” function):

“Nitrogen diffusion is investigated in single crystalline austenitic stainless steel during modified layer formation and thermal annealing. The generalized system of diffusion equations is derived within a thermodynamic framework from Fick's laws which describe the nitrogen flux under multiple driving forces including a concentration gradient and the gradient of hydrostatic stress. Trapping and detrapping phenomena are considered within this model and nitrogen flux is distinguished depending on whether nitrogen is in a lattice or in a trapping site. Furthermore, the effects of anisotropic elasticity in single crystal austenitic stainless steel on the stress field were involved. The proposed model was used to simulate nitrogen transportation process in single crystalline AISI 316L during ion beam nitriding and after isothermal annealing at three different crystalline orientations. Theoretical curves are compared with experimental results taken from the literature. It is shown, that during isothermal annealing, the nitrogen diffusion becomes significantly slower than during nitriding. The diffusion coefficient during annealing process comparing with nitriding process de-creases by factors of 4.3, 3.3, and 2.5 for the orientations (001), (011), and (111), respectively.”

2. In figure 4, commas need to be replaced with dots

The commas have been replaced with dots (in Figures 1, 2, 4 and 6)

3. Conclusions need to be supplemented. Authors should show where research can be used.

Conclusions were modified (section “4. Conclusions”, all changes in the manuscript are marked by “Track Changes” function):

4. Conclusions

Nitrogen diffusion in single crystalline austenitic stainless steel during modified layer formation and thermal annealing has been analyzed by the presented kinetic model. The main conclusions are as follows:

1. During nitriding and post-nitriding annealing of austenitic stainless steels the same diffusion mechanisms take place, the trapping/detrapping and lattice stress induced diffusion.

2. The anisotropic nature of mass transport processes i.e., dependence on crystallographic lattice orientation is observed during both processes, nitriding and post-nitriding isothermal annealing.

3. The trapping-detrapping process has the main influence on the specific distribution depth profile of nitrogen in post-nitrided and post-annealed ASS. However, the lattice stress induced diffusion cannot be excluded.

4. The nitrogen diffusivity during post-nitriding thermal annealing is significantly lower than during nitriding. The diffusion coefficient during annealing process comparing with nitriding process decreases by factors of 4.3, 3.3, and 2.5 for the orientations (001), (011), and (111), respectively.

It follows from above conclusions that the application of the thermal annealing procedure for phase stabilization and stress relaxation of post-nitrided ASS samples leads to significant changes in nitrogen distribution, as well as influences physical and mechanical properties of ASS.

4. The authors should state clearly the limitations of their study.

Text of manuscript (section “2. The Governing Equations of Nitrogen Transport Model”, all changes in the manuscript are marked by “Track Changes” function) was appended:

“It is important to note that, the purposed model can be used to describe the nitro-gen distribution in ASS during the nitriding and thermal annealing processes at temperatures till chromium nitride formation, i.e. at temperature below 450 °C [21-27]. Moreover, for nitrided layers containing the γ_N phase, various types of strains (thermal, compositional, elastic and plastic) can be considered. However, we only take into account anisotropic compositional strain in our model. Therefore, incorporation of the compositional, thermal, plastic and elastic contributions to the strain, induced on austenite lattice due to the formation of the γ_N phase, is the main task for our future investigations.”

As a result, I recommend the paper for publication after minor revision.