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Modeling Two- and Three-Stage Oxygen Tracer Experiments during High-Temperature Oxidation of Metals with a High Oxygen Solubility

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Abstract

The numerical tool EKINOX-Zr has been upgraded to simulate oxygen tracer experiments during the high-temperature oxidation of a metal with a high oxygen solubility limit. The penetration of 18O tracer is calculated during the dynamic evolution of the ZrO2-x/αZr(O )/βzr system. The numerical approach allows to explicitly take into account the variation of the tracer diffusion coefficient through the oxide scale as a function of the vacancy concentration. A classical two-stages 16O2/18O2 tracer experiment has been simulated. It is shown that a classical fitting procedure on the 18O concentration profile obtained for short-time experiments leads to the identification of the oxygen chemical diffusion coefficient. The second type of tracer experiment is proposed using a three-stages 16O2/18O2/16O2 oxidation. It allows the direct estimation of the diffusion coefficient from the transport of 18O peak in the growing oxide scale.

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Notes

  1. In order to clarify the notations, all the terms “A” linked to 18O will be mentioned as A18. The same convention is followed for the terms linked to the 16O. When a generic term is used, it will be mentioned as A i .

  2. In case of an anionic transport in the oxide scale, the anion flux is predominant, whereas the cation flux is negligible.

  3. The same development can be done for \(\mu_{18}\).

  4. The superscript \(p\) is linked to the metallic slabs whereas the superscript \(q\) is linked to the oxide slabs.

Abbreviations

\(a_{i}^{ }\) :

Chemical activity of the specie \(i\)

\(R\) :

Universal gas constant

\(C_{\text{O}}^{ }\) :

Oxygen concentration

\(R_{18}\) :

Volume ratio of the mix gas 18O2/16O2

\(D_{\text{O}}^{p}\) :

Oxygen diffusion coefficient in the metal

\(T\) :

Temperature

\(D_{\text{ox}}^{q}\) :

Oxygen diffusion coefficient in the oxide

\(X_{i}^{r}\) :

Concentration of the specie \(i\) in the slab \(r\)

\(e\) :

Elementary charge

\(a\) :

Relative electric charge of the oxygen vacancies

\({\text{f}}_{\text{O}}\) :

Correlation factor

\(\Delta t\) :

Numerical time step

\(J_{i}^{r}\) :

Flux of the specie \(i\) from the slab \(r\) to the slab \(r + 1\)

\(\mu_{\text{O}}^{ }\) :

Chemical potential of oxygen

\(K\) :

Equilibrium constant

\(\sigma_{k}^{ }\) :

Electrical conductivity of the specie \(k\)

\(L_{ij}\) :

Crossed diffusion coefficient

\(\varOmega^{r}\) :

Molar volume of the slab \(r\)

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Acknowledgements

The authors want to thank AREVA NP and EDF for their financial support.

Author information

Author notes

  1. Clara Desgranges

    Present address: SAFRAN Tech, rue des Jeunes Bois, 78772, Magny-les-Hameaux, France

  2. Benoît Mazères

    Present address: CU GPS&O, Immeuble Autonéum, Rue des Chevries, 78410, Aubergenville, France

Authors and Affiliations

  1. CIRIMAT, Université de Toulouse, CNRS, INPT, UPS, ENSIACET, 4 Allée Emile Monso, BP-44362, 31030, Toulouse Cedex 4, France

    Benoît Mazères & Daniel Monceau

  2. DEN-Service de la Corrosion et du Comportement des Matériaux dans leur Environnement, CEA, Université Paris-Saclay, 91191, Gif-sur-Yvette, France

    Benoît Mazères & Clara Desgranges

  3. DEN-Service de Recherches Métallurgiques Appliquées, CEA, Université Paris-Saclay, 91191, Gif-sur-Yvette, France

    Caroline Toffolon-Masclet

Authors
  1. Benoît Mazères
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  2. Clara Desgranges
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  3. Caroline Toffolon-Masclet
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  4. Daniel Monceau
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Correspondence to Daniel Monceau.

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Mazères, B., Desgranges, C., Toffolon-Masclet, C. et al. Modeling Two- and Three-Stage Oxygen Tracer Experiments during High-Temperature Oxidation of Metals with a High Oxygen Solubility. Oxid Met 89, 517–529 (2018). https://doi.org/10.1007/s11085-017-9816-3

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  • DOI: https://doi.org/10.1007/s11085-017-9816-3

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