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Metallurgical and Materials Transactions A
Published in: Metallurgical and Materials Transactions A 2/2012

01-02-2012

The Shape of Nitrogen Concentration-Depth Profiles in γ′-Fe4N1–z Layers Growing on α-Fe Substrates; the Thermodynamics of γ′-Fe4N1–z

Authors: T. Woehrle, A. Leineweber, E. J. Mittemeijer

Published in: Metallurgical and Materials Transactions A | Issue 2/2012

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Abstract

An unusual, concave curvature is observed in experimental nitrogen concentration-depth profiles in the surface region of γ′-Fe4N1–z layers obtained during nitriding pure iron at 823 K and 843 K (550 °C and 570 °C). It can be shown by the simulation of nitrogen concentration-depth profiles in γ′-layers, adopting the thermodynamic Wagner-Schottky approach applied to γ′-Fe4N1–z , that this concave character is caused by the strong concentration dependence of the Gibbs energy of the γ′-phase, which is counterintuitive in recognition of the very small homogeneity range of γ′ iron nitride. Thereby, for γ′-layers with low porosity, a previous suggestion ascribing the concave shape to the additional uptake of nitrogen through porous grain-boundary channels is rendered less likely.
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Appendix
Available only for authorised users
Footnotes
1
The observation of seemingly hyperstoichiometric γ′ may be ascribed to systematic experimental errors such as the detection of adsorbed nitrogen at the specimen surface.[23]
 
2
Porosity is caused by the metastability of the γ′-phase with respect to pure iron and molecular nitrogen gas at normal nitriding temperature and pressure, leading to the precipitation of N2 gas, predominantly at grain boundaries in the surface adjacent region of the compound layer.[27,45,47]
 
3
The parabolic growth law is expected to be exactly valid in the case of local equilibrium at both interfaces of the layer and either a completely nitrogen-saturated α-iron substrate or an initially unsaturated substrate of infinite thickness. In the following text, the case of a fully nitrogen-saturated substrate will be adopted because of the relatively fast saturation of the up to 2 mm thick α-iron substrates at the nitriding conditions applied (cf. Table I).
 
4
The self-diffusion coefficient normally is written as \( D_{\text{N}}^{(\gamma^{\prime} )*} = M_{\text{N}}^{(\gamma^{\prime} )\prime } c_{\text{N}}^{(\gamma^{\prime} )} , \) where \( M_{\text{N}}^{(\gamma^{\prime} )\prime } = y_{\text{Va}}^{(\gamma^{\prime} )} M_{\text{N}}^{(\gamma^{\prime} )} \).
 
5
Assuming the mobility in both sublattices to be different the total flux of nitrogen through the γ′ layer is given by the sum of the fluxes in sublattices I and in sublattice II. According to Ref. 27, it holds that \( M_{\text{N}}^{(\gamma^{\prime} )} = M_{\text{N}}^{II} + M_{\text{N}}^{\text{III}} \).
 
6
In quasi-steady-state diffusion, the depth variation of the local concentration gradient \( \partial c_{\text{N}}^{(\gamma^{\prime} )} /\partial x \) is balanced by a concentration dependence of the intrinsic diffusion coefficient \( D_{\text{N}}^{(\gamma^{\prime} )} \) (here: because of the thermodynamic factor) such that the flux of nitrogen through the γ′-layer \( J_{\text{N}}^{(\gamma^{\prime} )} \) remains constant and independent of depth (cf. Eq. [4]). Then, the local concentration gradient within the γ′-layer is directly proportional to the reciprocal of the diffusion coefficient. This quasi-steady-state diffusion assumption in γ′ could be validated by numerical calculations (see Section IV) and is only an acceptable approximation of reality because of the small homogeneity range of γ′ together with the large nitrogen concentration difference of the γ′ layer and the α-iron substrate.
 
7
The exact solution for case (2) would be a complementary error function[17] that, in view of the narrow concentration variation over the compound layer thickness and the large concentration difference between layer and substrate, leads to an approximately linear concentration-depth profile.
 
8
The concentration-depth profiles obtained from adopting the Langmuir-type approach and the HS approach, for calculation of the thermodynamic factor, are in qualitative agreement with those obtained from adopting the WS approach and show in principle the same concave shape (results not shown here).
 
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Metadata
Title
The Shape of Nitrogen Concentration-Depth Profiles in γ′-Fe4N1–z Layers Growing on α-Fe Substrates; the Thermodynamics of γ′-Fe4N1–z
Authors
T. Woehrle
A. Leineweber
E. J. Mittemeijer
Publication date
01-02-2012
Publisher
Springer US
Published in
Metallurgical and Materials Transactions A / Issue 2/2012
Print ISSN: 1073-5623
Electronic ISSN: 1543-1940
DOI
https://doi.org/10.1007/s11661-011-0870-1

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