Clara Desgranges

Depletion and Voids Formation in the Substrate During High Temperature Oxidation of Ni-Cr Alloys

A numerical model to treat the kinetics of vacancy annihilation at the metal/oxide interface but also in the bulk metal has been implemented. This was done using EKINOX, which is a mesoscopic scale 1D-code that simulates oxide growth kinetics with explicit calculation of vacancy fluxes. Calculations were performed for high temperature Ni–Cr alloys oxidation forming a single chromia scale. The kinetic parameters used to describe the diffusion in the alloy were directly derived from an atomistic model. Our results showed that the Cr depletion profile can be strongly affected by the cold work state of the alloy. In fact, the oversaturation of vacancies is directly linked to the efficiency of the sinks which is proportional to the density of dislocations. The resulting vacancy profile highlights a supersaturation of vacancy within the metal. Based on the classical nucleation theory, the possibility and the rate of void formation are discussed.

Low Temperature Oxidation of Pure Iron: Growth Kinetics and Scale Morphologies

Isothermal oxidation of pure iron has been performed in air at atmospheric pressure between 260°C and 500°C. Growth kinetics are accurately analysed and scale morphologies are investigated by SEM and TEM observations. The calculation of the variations of the parabolic rate constant kp with scale thickness allows a better understanding of scale growth mechanisms involved at this intermediate temperature range, which have been poorly investigated up to now. These results are discussed with the objective of long term behaviour for long term interim storage of some nuclear waste containers.

Simulation of the β→α(O) Phase Transformation due to Oxygen Diffusion during High Temperature Oxidation of Zirconium Alloys

The EKINOX numerical code, formerly developed to simulate high temperature oxidation of Ni alloys, has been recently adapted to solve out the issue of high temperature oxidation of Zirconium alloys. This numerical code is a one dimensional model that simulates the growth of an oxide layer using a specific algorithm for moving boundaries problem. In order to simulate the oxygen diffusion inside Zr alloys, an adaptation of the EKINOX code was necessary. It consisted in adding, first, a non-null oxygen equilibrium concentration in the substrate and second, a new interface in order to simulate the β/α(O) phase transformation due to oxygen diffusion. In this study, EKINOX has also been coupled with the thermodynamic database for zirconium alloys ZIRCOBASE (thermocalc formalism) in order to obtain accurate concentrations values in each phases (considering local equilibrium at each interface). The present paper illustrates the simulation ability of the code by comparing experimental and calculated oxygen diffusion profiles corresponding to different cases, from isothermal oxidations at high temperature (900 < T < 1250°C) to the study of dissolution kinetics of a pre-transient oxide layer under a neutral environment. The influence of pre-hydriding from a few hundreds up to thousands weight-ppm is also derived from the calculations.

Numerical Model for Oxide Scale Growth with Explicit Treatment of Vacancy Fluxes

In the framework of research on behaviour of nuclear waste containers, to evaluate the effects of possible evolution of experimental conditions, as well as evolution of parameters controlling oxidation rate during long-term interim storage, a numerical model has been developed in order to take into account non-stationary states. To anticipate effects like cold working of the metal on the scale growth kinetics and risks of scale detachment by over saturation of vacancies at the metal/oxide interface in the course of scale growth, the model is based on the calculation of chemical species, but also vacancies profiles evolution in the oxide and the metal following a simple time integration. An original numerical treatment is proposed to easily describe elimination of vacancies by introducing sink strength in the metal. The first calculations are presented and discussed.

Contribution to Modeling of Hydrogen Effect on Oxygen Diffusion in Zy-4 Alloy During High Temperature Steam Oxidation

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.

Chemical Evolution in the Substrate due to oxidation: A Numerical Model with Explicit Treatment of Vacancy Fluxes

To get a better understanding of oxidation behavior of Ni-base alloys in PWR primary water, a numerical model for oxide scale growth has been developed. The final aim of the model is to estimate the effects of possible changes of experimental conditions. Hence, our model has not been restricted by the classical hypothesis of quasi-steady state and can consider transient stages. The model calculates the chemical species concentration profiles, but also the vacancy concentration profiles evolution in the oxide and in the metal as a function of time. It treats the elimination of the possible supersaturated vacancies formed at the metal/oxide interface by introducing a dislocation density at the interface and in the metal bulk. This latter density can be related to the cold-working state. Its effect on the vacancy profile evolution is studied in the case of a pure metal. Eventually an extension of the present model to the oxidation of Ni-base alloys is discussed regarding a recent vacancy diffusion model adjusted on Ni-base alloys.

Effects of Compression Tests on Point Defects in Pure Ni and Ni-16wt%Cr Model Alloys

On Ni and Ni-16wt%.Cr model-alloys compressed at 30 % and 60 % deformation, point-defects and dislocations concentrations are respectively characterized by positron annihilation spectroscopy and x-ray diffraction analysis. The positron results show that only mono-vacancies are formed during compressive test The X-ray results allows us to quantify the dislocation concentration in the systems. Saturation of defect densities is observed in measurements for these high deformation rates. In support to the experimental work, an homogeneous kinetic model is used to characterize point-defect – dislocation interactions to estimate the kinetics of vacancy restoration to equilibrium concentration.