Crystallographic Orientation Dependence of Nitrogen Mass Transport in Austenitic Stainless Steel

Round 1

Reviewer 1 Report

I am aware, the presented problem is hard to easy-way present. The number of equations may be disconcerting for some readers while their reading text. However, I do not see another way to precisely describe the presented phenomena aspects as well.
What I would like to recommend for authors, is to consider a wider presentation and commenting of the literature, which they refer to in the manuscript.

Author Response

Corrections are made considering a wider presentation and commenting of the literature.

 

Reviewer 2 Report

The manuscript entitled Crystallographic orientation dependence of nitrogen mass transport in austenitic stainless steel, gives a model approach to investigate the mechanism of 316L austenitic stainless steel (ASS) saturation with nitrogen during plasma nitriding process, which is still an up to date concept in the field of thermo-chemical processes. Authors by using finite-difference simulation have confirmed that interesting effects take place at the ASS surface when plasma conditions vary, which highly confirms plasma nitriding experiments realized for ASS. The model was realized for the following process conditions: T = 400⁰C, τ = 3 hours, nitrogen concentration V_N, 3.9·10^-5 m³/mol, hydrogen concentration V_H 1.6·10⁻⁵ m³/mol. The structure of the nitrogen-saturated austenite crystal lattice has not yet been fully explained and there are various hypotheses on this subject, which is why the authors' research is also a new approach to these issues, which is highly appreciated by the reviewer. The authors cite past literature accordingly and have significant achievements related to the subject of the manuscript, mainly in analyzing the mechanisms of nitrogen transport in ASS related to anisotropy of diffusion and stresses in the substrate lattice under influence of hydrogen. The observations have been well documented by simulations results and have a good quality. Generally, the research work was done properly and the goal of the investigation was reached. However, before publishing process starts, the authors in the following points should improve some aspects to present their statements and results more clearly:

1. English language and style check is required, especially in the following verses (8, austenitic / 16 to take / 72 formula / 154 place / 174 not taking)
2. An important aspect of austenitic steels plasma nitriding is also the participation of chromium in the formation of the nitrided layer and the precipitation of chromium nitrides, also at low temperature.
   It would be particularly important in further research to include in the model the effect of chromium in steel and occurring in the structure of austenite, affecting of course the state of stress in austenite cell.
3. Comprehensive knowledge of phenomena occurring both in the plasma and at solid / gas interface is important and necessary for the proper control of the plasma nitriding process. However, technological parameters as temperature, current/voltage parameters, pressure, composition and flow rate of the gas mixture are also very important. Their settings depend on the phase composition of the nitrided layer and the desired finish effect. Therefore, it would be important for the Authors to indicate the relationship between the simulation carried out and the actual process parameters that the Authors verify and observe during the simulation. The combination of such results will be validation of simulation results, important for industrial applications, and thus the possibility of obtaining nitrided layers with assumed properties on asutenitic steels. It is worth mentioning in the article.
4. In plasma processes, oxygen inhibits the thermodynamic activity of nitrogen on the surface of austenitic steels, therefore the presence of oxygen is minimized or eliminated. Assuming the presence of oxygen in the plasma associated with the process of hydrogen etching (sputtering) in the authors' model, one should take into account its amount in the process and indicate the effect of such amount on reactions occurring in the plasma. This will answer the reviewer’s question of whether oxygen should be fully taken into account in the model.
5. The conclusions in the article are too general. I suggest to re-edit the conclusions and extend the description of the impact of research on phenomena and processes in nitrogen – hydrogen plasma conditions. It should also be emphasized that the results presented in the paper can be used to optimize the process of plasma nitriding in ASS and control the morphology of nitrided layers when there is dynamic change of atmosphere.

Apart from the remarks above, I conclude that manuscript overall is of very good quality and there are no more corrections that I would like to comment on. The manuscript is clearly written and should be of great interest to the readers, especially for plasma nitriding researchers. I recommend the article for publication in Metals (ISSN 2075-4701) Scientific Journal.

Author Response

 

1. Text of manuscript was revised according to suggestions and observations of Reviewers.

2 It is a good suggestion further to include influence of Cr and some chromium nitride formation even at low temperature, where this process is not significant, but some influence may be observed.

3. We agree it is important aspect. Technological parameters as temperature, current/voltage parameters, pressure, composition and flow rate of the gas mixture are also very important are indirectly related with parameters used in model such as adsorption sticking coefficient, desorption rate, rate constants of heterogeneous chemical reactions on the surface, diffusion coefficient (depends on temperature), fluxes of various particles to the surface. Relation between technological parameter and calculation parameter is quite obvious.
4. The amount of oxygen in plasma is involved into the model through the relative flux of oxygen to the surface. The values of all fluxes of oxygen, hydrogen and nitrogen are presented in table 1 as i_O2, i_H2 and i_N2. It is seen that flux of oxygen is quite low comparing with others.

5.Text of manuscript at end of section “3. Results and Discussion”) which summarizes the work was appended:

 

In this study it is shown that anisotropic nature of lattice stresses influences the different penetration of nitrogen and hydrogen in the differently orientated grains. The grain orientation dependent penetration of nitrogen and hydrogen is also influenced by anisotropic nature of the processes on the surface such as adsorption and heterogeneous chemical reactions. Most important aspect is that the inclusion of anisotropy of the surface processes into the model explains experimental observations, i.e. that the both, penetration depth and the surface concentration of nitrogen in ASS increase in order (100)>(110)>(111).  Model also explains the role and influence of hydrogen in plasma nitriding process. Hydrogen enhances nitrogen diffusion by reducing the diffusion barrier formed by the oxygen adsorbed on the steel surface during nitriding process (oxygen is a common contamination element in plasma chambers, directly affecting the nitriding process) and natural oxide, whose thickness depends on the pre-history of the sample. Hydrogen also influences on the diffusion of nitrogen, because it creates additional lattice stresses and enhances the process of stress induced diffusion. Here is a mutual effect: hydrogen increases the diffusion of nitrogen and in the opposite nitrogen increases the diffusion of hydrogen. Proposed model can be used to optimize the nitriding process of ASS and control the morphology of nitride layers when there is dynamic change of atmosphere.

 

Conclusions are modified.

Reviewer 3 Report

This article reports on the modelling of nitrogen adsorption and diffusion by taking into account crystallographic anisotropy. It is interesting to consider an anisotropic adsorption of the reactive species. The level of English in this article is good. The reported results are interesting. Before publication, the following remarks must be taken into account:

 

• It is not clear what the authors want to show in this paper. It would be necessary to specify in the introduction and in the discussions what is new, compared to the previous papers of authors 25 and 26. It would be necessary to try to project on the consequences in term of process of these calculations. What would be the conditions to test experimentally to check the validity of the model for instance? The paper ends a little abruptly and it would be good to make a few sentences of summary and perspectives.
• I do not like that the authors suggest that both the stresses and the deformations can be possible without proposing an interaction model between the grains. Without mentioning it, the authors use a Reuss type interaction model, which allows them to introduce the consideration of elastic anisotropy coupled to crystallography. In the Reuss model, the stresses do not vary from one grain to another, it is the deformation that varies (J. F. Nye, ‘‘Physical properties of crystals’’, Oxford University press, Oxford, NY 1979, D. N. Lee, Thin Solid Films 2003, 434, 183). The authors have simply to change the sentence line 59.
• Although this is an interesting working hypothesis, I find that a linear coupling between the stress and the nitrogen concentration is too simplistic. The referee is well aware of the difficulty of finding a better approach but he advises the authors to read the following publication in which a more general relationship is possessed (W. C. Johnson, Acta Mater. 2000, 48, 433). In this approach, it is necessary to distinguish elastic deformation and composition deformation. This remark does not require modification of this article but a discussion would be appreciated. See Larché, Cahn and Voorhees (F.C. Larché, J.W. Cahn, “The effect of self-stress on diffusion in solids”, Acta Metall., 30 (1982) 1835, F.C. Larché, J.W. Cahn, “The interactions of composition and stress in crystalline solids”, Acta Metall., 33 (1985) 331, F.C. Larché, P.W. Voorhees, “Diffusion and stresses: basic thermodynamics”, Defect and Diffusion Forum, 129-130 (1996) 31.).
• In what kind of units are the concentration expressed in relation 2. Surface content are required for the surface, while volume content is needed for diffusion. Is it possible to have some explanations? In equations 8 the N variation is not expressed and alos the oxygen flux. Flux of NH and initial densities of N2, H2 and O2 are missing in table 1. The boundary conditions for diffusion are not given.
• The surface model is interesting but raises many questions. With plasmas, other species such as nitrogen, hydrogen and atomic oxygen are produced. They are not directly taken into account in this model. They are all the same considered via reactions of dissociation of surface of the associated molecules. The authors should say that this is a way of considering the possible adsorption of atoms. In such an approach it is not clear why a radical (NH) is introduced. The authors also postulate the presence of an oxide film (0.5 micrometers), but it is well known that it is not possible to nitride stainless steels at this temperature in the presence of an oxide film. The authors must comment on this fact.
• When considering anisotropy, surface nitrogen concentrations drop. I do not quite understand why and comments on this point would be welcome. Line 240, it is explained that a deeper diffusion of nitrogen is explained by the diffusion of hydrogen. Why does hydrogen diffuse more strongly in the anisotropic model? Are the areas under the curves in Figures 4 and 6 constant? In other words, do we introduce the same quantity of elements while considering or not the anisostropy.

 

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

 

Page 3, line 94, A vector is equal to a scalar!

Page 3, line 112, it must be said that the x-axis is the diffusion axis.

Page 5, line 173, “if to not to take” is not so nice

Page 6, line 209, replace 3.1 and 3.3 by 2.1 and 2.3 to be in accordance with figure2

What is the meaning of 1.1 and 2.1 lines overlap in figure 2?

Line 253, replace “have” by “are”?

Line 266, replace “as result”, by “as a result”

Line 320 the reference to Dahm must be removed it merge with Mingolo.

Author Response

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

 

In this paper the anisotropy of surface processes such as adsorption and heterogeneous chemical reactions is incorporated into the model, which was not previously done. This aspect is important, and it is shown that if the anisotropic nature of adsorption and surface chemical reactions is not taken into account, the results contradict with experimental observations, considering kinetics of nitrogen surface concentration.

 

Text of manuscript at end of section “3. Results and Discussion”) which summarizes the work was appended:

 

In this study it is shown that anisotropic nature of lattice stresses influences the different penetration of nitrogen and hydrogen in the differently orientated grains. The grain orientation dependent penetration of nitrogen and hydrogen is also influenced by anisotropic nature of the processes on the surface such as adsorption and heterogeneous chemical reactions. Most important aspect is that the inclusion of anisotropy of the surface processes into the model explains experimental observations, i.e. that the both, penetration depth and the surface concentration of nitrogen in ASS increase in order (100)>(110)>(111).  Model also explains the role and influence of hydrogen in plasma nitriding process. Hydrogen enhances nitrogen diffusion by reducing the diffusion barrier formed by the oxygen adsorbed on the steel surface during nitriding process (oxygen is a common contamination element in plasma chambers, directly affecting the nitriding process) and natural oxide, whose thickness depends on the pre-history of the sample. Hydrogen also influences on the diffusion of nitrogen, because it creates additional lattice stresses and enhances the process of stress induced diffusion. Here is a mutual effect: hydrogen increases the diffusion of nitrogen and in the opposite nitrogen increases the diffusion of hydrogen. Proposed model can be used to optimize the nitriding process of ASS and control the morphology of nitride layers when there is dynamic change of atmosphere.

 

 

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

 

“A straightforward interpretation of strains in terms of stresses can be obstructed if the single crystallites composing the specimen are elastically anisotropic. A so-called grain interaction model is needed to describe the distribution of stresses and strains over the crystallographically differently oriented crystallites in the specimen. In our case, for the calculation of mechanical elastic constants of bulk polycrystals from single-crystal elastic compliances we use the Reuss grain-interaction model, i.e. the stress tensor for each crystallite is assumed to be equal to the mechanical stress tensor [28]. By taking to account Reuss grain-interaction model [28]…”

 

 

List of References was appended:

[28] Reuss, A. (1929). Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . ZAMM - Zeitschrift Für Angewandte Mathematik Und Mechanik, 9(1), 49–58. doi:10.1002/zamm.19290090104

 

Text of manuscript (section “2. Mass Transport Model”) was appended:

“It is important to note that, 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. Hence, 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 goal for our future investigations.”  

 

We used relative concentrations C_rel=C_abs/A (A surface area). But even if to model with absolute concentration units would be m^-2 for diffusion also, as diffusion goes on from layer to layers and in layer concentration is in m^-2.

Text of manuscript (section “2. Mass Transport Model”) was appended: “…(symbolizes the relative concentration of interstitials in a metallic lattice)…”

In the set of equations 8 the N variation is expressed, it is the last equation dC_N/dt

Flux of NH now is shown in table 1. Initial densities of N2, H2 and O2 are not needed, as we use constant flux of those gases during all process

 

Boundary conditions are given in line 131 near eq.(7) i.e. Φ_{0 int} (x≠0, t) = 0 and Φ_{0 int} (x=0, t) ≠ 0

 

Nitrogen , hydrogen and oxygen are taken not directly in order to create more realistic model because for nitriding is used N2H2 gas mixture plasma. NH radicals are always observed in nitrogen/hydrogen plasma.  Yes we absolutely agree that it is not possible to nitride stainless steels at this temperature in the presence of an oxide film, that why the hydrogen is necessary. Hydrogen removes oxide layer and nitriding becomes possible.

 

Reason for nitrogen surface concetration drop is coefficient A_hkl in eq.(8).

In isotropic case it is the same for all orientation. In the case of anisotropifor some orientation befoms less than 1 ant it resultas indrop od surface concetration. Only for orientation 100 it remains the same what why curves of 100 in Fig, 2 overlap. For that reason the areas under the curves in Figures 4 and 6  are not constant because of different adsorption

 

In the anisotropy case parameter Xstress is higher eq.(6) which result stronger diffusion both nitrogen and hydrogen

 

Text of manuscript was revised according to suggestions and observations of Reviewer.

1.1 and 2.1 lines overlap in figure 2 and it means that these curves completely correspond

 

Page 3, line 94, A vector is not equal to a scalar. Nabla operator itself is vector and according to the standards it is not necessary to put vector sign onto nabla, despite in some literature we can see vector onto nabla. The Equation (4) In line 94 means flux of particles (vector ) relation with gradient of chemical potential (also vector). So vector equals to vector. Taking this into account we removed vector sign from nabla in formula (1) (here we have divergence of vector what is scalar)

Round 2

Reviewer 3 Report

The authors have answered to the question and it is OK for publication

Author Response

Thank you