Numerical modeling of interstitial diffusion in binary systems. Application to iron nitriding

Belmonte, T.; Gouné, Mohamed; Michel, H.

doi:10.1016/s0921-5093(00)01830-x

Cited by 47 publications

(29 citation statements)

References 16 publications

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“…[3,8,9,21,22,[27][28][29][30][31][32][33][34][35][36] The evaluation of the N mobility is usually based on the timeand temperature-dependent ␥Ј-or /␥Ј-layer-thicknesses. Various methods have been developed, or standard methods have been adapted, to these processes, in order to determine diffusion coefficients from the kinetic data.…”

Section: Discussionmentioning

confidence: 99%

Phase transformations in iron-nitride compound layers upon low-temperature annealing: Diffusion kinetics of nitrogen in ▓- and γ′-iron nitrides

Liapina

Leineweber²,

Mittemeijer

2006

Metall Mater Trans A

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The /␥Ј-iron nitride (-Fe 3 N 1ϩx , ␥Ј-Fe 4 N) compound double layers with thicknesses of about 10 m were grown on pure ␣-Fe, by gas nitriding at 823 K, followed by quenching. The specimens were subsequently annealed at significantly lower temperatures, in the range of 613 to 693 K, for different periods of time. These heat treatments led to a redistribution of N, within the compound layer as well as between the compound layer and the adjacent ferrite, inducing thickness changes in the -and ␥Ј-sublayers. The microstructure and sublayer-thickness changes were analyzed by light microscopy and X-ray diffraction (XRD). The experimentally observed time and temperature dependences of the layer-thickness changes were compared with the results obtained from numerical simulations, by adopting a model based on volume diffusion in the -and ␥Ј-phases and on local equilibrium at the phase interfaces. In this manner, the intrinsic diffusion coefficient of N in the -phase and the integral diffusion coefficient of N in the ␥Ј-phase were determined for the applied range of annealing temperatures.

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Section: Discussionmentioning

confidence: 99%

Phase transformations in iron-nitride compound layers upon low-temperature annealing: Diffusion kinetics of nitrogen in ▓- and γ′-iron nitrides

Liapina

Leineweber²,

Mittemeijer

2006

Metall Mater Trans A

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“…At the inner section, nitrogen concentration is decreased rapidly to a lower value. The hardness profiles after nitriding are calculated by experimental regression equation (4) and shown in Fig. 6 for SCr420H steel.…”

Section: Resultsmentioning

confidence: 99%

“…Their model considered the diffusion of nitrogen in ferrite and development of iron nitride layer on the surface simultaneously. Then, Goune et al, 3 and Belmont et al, 4 constructed a realistic diffusion-precipitation model to describe the volume diffusion of nitrogen in ferrite and the simultaneous precipitation of fine scale alloying element nitrides in the diffusion zone. Furthermore, Kamminga, Janssen 8,9 presented a model for the calculation of nitrogen depth profiles in nitrided steel based on precipitation and trapping, and the calculations agreed well with experimental nitrogen depth profiles for nitrided Fe-Mn (1.62 wt.% Mn) and Fe-V (0.55 wt.% V) alloy.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Phase Composition and Nitrogen Concentration During the Nitriding Process in Low-Alloy Steel

Deng

2016

Mat. Res.

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A diffusion/transformation coupled model has been developed which combines finite difference (FD) model with a phenomenological model. The composition of the different iron-nitrogen(Fe-N) hardening phase can be regard as a function of nitriding time and nitrogen concentration. The diffusion model and transformation model are linked by the limiting nitrogen solubilities and the effective diffusion coefficients. The effect of alloy elements (Cr, Mo, Mn, V, Ni etc.) is considered by introducing an alloy coefficient for limiting nitrogen solubilities and diffusion coefficient. The diffusion/transformation model can predict nitrogen concentration, phase composition and hardness distribution. The model is employed to simulate the nitriding process of SCr420H low-alloy steels. The simulated nitrogen concentration and hardness profiles are consistent with the measured ones. In addition, the predicted depth distributions of iron-nitrogen phase agree well with the available experimental results. Therefore, the comparison shows the reliability of the coupled model. It can be applied to improve the nitriding process parameters.

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“…In the porous SE, when the permeability becomes sufficiently small, the mean free path of the molecules becomes comparable to the pore size, and the collisions of the molecules with the walls start to significantly affect the transport process via Knudsen diffusion. To assess the potential importance of this effect in modelling gas transport processes through the porous electrodes, consider that the molecules of gas flow come in contact with the SE and reach TPB among the gas, YSZ and SE by diffusion in accordance with Fick's second law [37] that is expressed as a parabolic type equation:…”

Section: Resultsmentioning

confidence: 99%

Mathematical model of electrochemical gas sensors with distributed temporal and spatial parameters and its transformation to models of the real YSZ-based sensors

Zhuiykov

2006

Ionics

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The activity in the field of computer-aided optimum design in engineering of electrochemical gas sensors has been increasing steadily over the last decade. A vast range of models exist today, varying in complexity and in the number of assumptions employed. However, the emphasis in a majority of the models has been either on the transport processes or on the electrochemical processes. This manuscript presents a complete mathematical model of electrochemical gas sensors, represented as a system of the partial differential equations of parabolic and hyperbolic types and the algorithm of transfer from the complete model to models of specific sensors. A complete mathematical model shows that the physic-electro-chemical processes occurring in the electrochemical gas sensors can be described more accurately. Presented mathematical model together with the proposed algorithm provides a decision-making tool for better optimal design of the solid electrolyte gas sensors. An example of transfer from a complete model to real model of the yttria-stabilized zirconia (YSZ)-based potentiometric gas sensors has been shown for the YSZ-based oxygen sensor with Pt sensing electrode (SE) and metal-metal oxide (Me-MeO) reference electrode (RE). Verification of the adequacy of the mathematical model to real gas sensor has been evaluated by the Fisher criterion.

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Numerical modeling of interstitial diffusion in binary systems. Application to iron nitriding

Cited by 47 publications

References 16 publications

Phase transformations in iron-nitride compound layers upon low-temperature annealing: Diffusion kinetics of nitrogen in ▓- and γ′-iron nitrides

Phase transformations in iron-nitride compound layers upon low-temperature annealing: Diffusion kinetics of nitrogen in ▓- and γ′-iron nitrides

Prediction of Phase Composition and Nitrogen Concentration During the Nitriding Process in Low-Alloy Steel

Mathematical model of electrochemical gas sensors with distributed temporal and spatial parameters and its transformation to models of the real YSZ-based sensors

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