Tony Montesin

Near-coincidence lattice method for the determination of epitaxy strains during oxidation of metals

Abstract A theoretical method is proposed to evaluate the strains due to epitaxy between a metal and its oxide. Based on Bollmann’s approach of two adjoining grains, it uses the quantitative texture analysis of the two materials separated by the phase boundary. Our study of the Zr/ZrO 2 and Mo/MoO 3 systems reveals strong correlations between the criterion of best fit proposed by Bollmann and the orientation distribution function obtained by a quantitative texture analysis. The results of this study are used in a thermo-mechano-chemical simulation of the oxidation process of zirconium, which leads to this observation: two different zirconia orientations induce two different oxidation kinetics.

A thermodynamic approach of the mechano-chemical coupling during the oxidation of uranium dioxide

The aim of the present work is to introduce a thermodynamic model to describe the growth of an oxide layer on a metallic substrate. More precisely, this paper offers a study of oxygen dissolution into a solid, and its consequences on the apparition of mechanical stresses. They strongly influence the oxidation processes and may be, in some materials, responsible for cracking. To realize this study, mechanical considerations are introduced into the classical diffusion laws. Simulations were made for the particular case of uranium dioxide, which undergoes the chemical fragmentation. According to our simulations, the hypothesis of a compression stress field into the oxidised UO2 compound near the internal interface is consistent with the interpretation of the mechanisms of oxidation observed experimentally.

Simulation of Metal/Oxide Interface Mobility: Effects of Mechanical Stresses on Geometrical Singularities

During the last decade, an increasing importance has been given to the feedback of mechanical stresses on the chemical diffusion and, further, on corrosion. Many works point the active role of stresses on the material ageing especially on their negative consequences leading to the damaging of structures. Based on a theoretical study and using numerical tools and experimental results our previous works [1, on stress/diffusion coupling, highlight the strong influence of stress field on the diffusion process. The aim of the present paper is to describe the influence of some particular morphologies of the metal/oxide interface on both diffusion and oxidation process. The oxidation is assumed to be driven by a mass conservation law (Stefans law) while the diffusion coefficient of oxygen in metal is locally influenced by the stress field. The stability of a waved-shape interface is studied in both cases: simple diffusion and coupled stress/diffusion process. In this purpose we have developed an original numerical model using a virtual metal/oxide interface of a mono-material with oxygen concentration-dependent parameters, which allows to operate easily with any shape of interface and to use simple finite element meshes. Furthermore, in order to underline in a more obvious way the consequences of mechanical stress on the diffusion process, a particular geometry is studied.

Mechanical Stresses: Inhibitor of Catalyst of High Temperature Oxidation?

Oxidation of metals is a complex reaction in which mechanical and chemical phenomena occur. A dynamic and macroscopic model is developed in order to simulate oxidation kinetics of a metal. It includes the stress/diffusion coupling in the bulk and the interfacial phenomena at metal/oxide interface. Its application to the Zr/ZrO 2 system shows the important role of stress field distribution in oxide on kinetic behavior. According to the sign of stress gradient in the oxide scale, the oxidation rate can speed up or slow down. The calculated kinetic curves could he fitted using a k p .t 1/n law where n and kp vary all over the process, like for the experimental kinetic curves.

Pre-Stressed Sub-Surface Contribution on Bulk Diffusion in Metallic Solids

Our recent modelling works and corresponding numerical simulations realized to describe the UO2 oxidation processes confirm the theory showing that an applied mechanical strain can strongly affect the local oxygen diffusion in a stressed solid. This result allows us to assume that stress field, previously applied at the surface of a metallic sample on several microns, will delay the degradation during its oxidation. Considering this hypothesis, we implemented a FEM simulation code developed in our laboratory to numerically investigate some different stress fields applied on a sample sub-surface, that might significantly modify the volume diffusion of oxygen during the oxidation process. The results of our simulations are presented and discussed from the perspective to study the consequences of a surface mechanical treatment on the durability of a metallic material.

Internal Interface Strains Effects on UO2/U3O7 Oxidation Behaviour

The growth of a U3O7 oxide layer during the anionic oxidation of UO2 pellets induced very important mechanical stresses due to the crystallographic lattice parameters differences between UO2 and its oxide. These stresses, combined with the chemical processes of oxidation, can lead to the cracking of the system, called chemical fragmentation. We study the crystallographic orientation of the oxide lattice growing at the surface of UO2, pointing to the fact that epitaxy relations at interface govern the coexistence of UO2 and U3O7. In this work, several results are given: - Determination of the epitaxy relations between the substrate and its oxide thanks to the Bollmann’s method; epitaxy strains are deduced. - Study of the coexistence of different domains in the U3O7 (crystallographic compatibility conditions at the interface between two phases: Hadamard conditions). - FEM simulations of a multi-domain U3O7 connected to a UO2 substrate explain the existence of a critical thickness of U3O7 layer.

Specific Aspects of Internal Corrosion of Nuclear Clad Made of Zircaloy

In PWR, the Zircaloy based clad is the first safety barrier of the fuel rod, it must prevent the dispersion of the radioactive elements, which are formed by fission inside the UO2 pellets filling the clad. We focus here on internal corrosion that occurs when the clad is in tight contact with the UO2 pellet. In this situation, with temperature of 400 °C on the internal surface of the clad, a layer of oxidised Zircaloy is formed with a thickness ranging from 5 to 15 µm. In this paper, we will underline the specific behaviour of this internal corrosion layer compared to wet corrosion of Zircaloy. Simulations will underline the differences of stress field and their influences on corresponding dissolved oxygen profiles. The reasons for these differences will be discussed as function of the mechanical state at inner surface of the clad which is highly compressed. Differences between mechanical conditions generated by an inner or outer corrosion of the clad are studied and their influences on the diffusion phenomena are highlighted.

An Interfacial Thermodynamic Model for the Oxidation Kinetics of a Metal: Epitaxial Stress Effects

The goal of this work was to introduce a novel thermodynamic approach for the oxidation of metals, which has been developed by considering the methods of non-equilibrium thermodynamics. Our proposition allows the linking between some elementary mechanisms (e.g., diffusion, mechanics) for determining the evolution of the oxidation process of the system. To demonstrate the validity of our approach, we developed a numerical analysis for the oxidation of zirconium. Our results allowed us to determine both the oxidation kinetics and the influence of the epitaxial tensor during the process. The kinetics obtained showed the different behaviours observed experimentally at different time scales.

Self-Induced Stress and Matter Transport Interactions during Metal Oxidation

Zirconium and nickel high-temperature oxidation is approached by the mechanochemical aspect, in order to evaluate the influence of stress-free strains on the oxidation rate by a theoretical way. The formulation of the matter transport uses a coupling between both composition and stress fields to associate the mechanical strains with the reactional process. The reactivity is treated at the mesoscopic level. The epitaxial strains are taken into account in the mechanical behaviour of the oxide scale. The simulated oxidation kinetics are qualitatively in accordance with the experimental ones. Our study confirms the significant role of stresses localized near the metal/oxide interface on the oxidation kinetics. Our conclusions consolidate the necessity to associate mechanics and diffusion in a realistic modelling of the metal oxidation.

Characterization of Oxygen-Enriched Layers of TA6V, Titanium, and Zirconium by Scanning Microwave Microscopy

A technique based on scanning microwave microscopy (SMM) has recently been developed to analyze solid solutions of light elements. This technique consists in local measurements of effects produced by electrical conductivity variations produced by light elements solutions in metals. The penetration of the microwaves into the metals depends on their frequency and the material parameters. Information regarding the local conductivity of the material at different depths can be recorded using various frequencies. In this paper, SMM measurements of the oxygen-enriched zone are presented for several materials: TA6V, pure Ti, and pure Zr. Comparisons with concentration measurements made by nuclear reaction analysis allow one to affirm that for all the materials investigated here the phase shift measured by SMM is proportional to the oxygen concentration dissolved into the metal. Calibration functions are proposed for each material and frequency used. After calibration, the SMM can be used to measure local enrichments.