Abstract
Previous studies have shown that the numerical model EKINOX-Zr was able to simulate with accuracy oxide growth and oxygen diffusion into the matrix during high-temperature oxidation of Zy-4. In this study, the aim of the development was to evaluate if the observed effect of hydrogen cladding content on the increase of oxygen solubility in the high-temperature βZr was only a thermodynamic effect. Previous experimental studies have shown that hydrogen induces an evolution of equilibrium oxygen concentration at the αZr/βZr interface. The present work showed that EKINOX-Zr linked with the thermodynamic database Zircobase reproduced the evolution induced by hydrogen during the high-temperature steam oxidation. However, the results showed also that additional studies are necessary to better understand hydrogen behavior during high-temperature oxidation of Zr.
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Abbreviations
- EPMA:
-
Electron probe micro analyse
- \( \frac{dx_{i}}{dt} \) :
-
is the metal/oxide interface velocity
- \( \frac{dx_{j}}{dt} \) :
-
is the αZr/βZr interface velocity
- \( PBR = 1,56 \) :
-
is the Pilling–Bedworth ratio between Zr metal matrix and the associated oxide
- \( D_{ox} \) :
-
is the oxygen coefficient diffusion in the oxide
- \( D_{\alpha } \) :
-
is the oxygen coefficient diffusion in αZr(O)
- \( D_{\beta } \) :
-
is the oxygen coefficient diffusion in βZr
- \( J \) :
-
is the oxygen flux
- \( c \) :
-
is the oxygen concentration
- \( t \) :
-
is the time
- \( J_{{V_{k} }}^{n} \) :
-
is the anionic vacancy flux from slab n to n + 1
- \( D_{{V_{k} }}^{n} \) :
-
is the anionic vacancy diffusion vacancies in the slab n
- \( X_{{V_{k} }}^{n+1} \) :
-
is the anionic vacancy concentration in the slab n
- \( \Upomega^{n} \) :
-
is the molar volume of the slab \( n \)
- \( e^{n} \) :
-
is the thickness of the slab \( n \)
- \( X^{n}_{{V_{K} }} = \frac{{dX^{n}_{{V_{K} }} }}{dt} \) :
-
is the rate of change of the anionic vacancies concentration
- \( \gamma \) :
-
is linked with the oxide type MOγ
- \( C_{\frac{ox}{vap}} \) :
-
is the oxygen boundary concentration in the oxide at the steam/oxide interface
- \( C_{\frac{ox}{\alpha}} \) :
-
is the oxygen boundary concentration in the oxide at the metal/oxide interface
- \( C_{\frac{\alpha}{ox}} \) :
-
is the oxygen boundary concentration in αZr(O) at the metal/oxide interface
- \( C_{{\frac{\alpha }{\beta }}} \) :
-
is the oxygen boundary concentration in αZr(O) at the αZr(O)/βZr interface
- \( C_{{\frac{\beta }{\alpha }}} \) :
-
is the oxygen boundary concentration in βZr at the αZr(O)/βZr interface
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Acknowledgments
The authors would like to thank J.-C. Brachet and V. Vandenbergh from CEA Saclay for their helpful discussions. This study was funded by AREVA and EDF.
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Mazères, B., Desgranges, C., Toffolon-Masclet, C. et al. Contribution to Modeling of Hydrogen Effect on Oxygen Diffusion in Zy-4 Alloy During High Temperature Steam Oxidation. Oxid Met 79, 121–133 (2013). https://doi.org/10.1007/s11085-012-9335-1
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DOI: https://doi.org/10.1007/s11085-012-9335-1