Modeling of corrosion by the cellular automata method: taking into account diffusion in solution and heat transfer.

The materials’ degradations caused by corrosion is a major issue in industry. Their experimental study in the laboratory, necessary in most cases, often proves difficult to perform. It also has its limits, because the processes involved generally take place over long periods of time and in complex environments, which are therefore difficult to reproduce. In this context, modeling is a powerful and complementary approach to the experimental approach, insofar as it is likely to lead to the development of predictive numerical tools and/or interpretation aids.
Modeling by the cellular automata (CA) method, proposed in this thesis, is used in fields as varied as physics, biology, chemistry and social sciences.
It consists of paving a space with a network of identical cells, each being characterized at time t by a state (which is part of a predefined set of possible states) whose temporal evolution is calculated by means of rules of transition which take into account the states of neighboring cells. Its main asset is to explore the spatio-temporal dynamics of simplified representations of systems likely to be very complex in reality.
Significant advances in corrosion modeling using the CA method have been made over the past ten years at CEA/DPC/SCCME/LECA. 3D extension of existing 2D models has in particular been successfully achieved, as well as the coupling of spatially separated anodic and cathodic reactions. This made it possible to study with the same model the competition between generalized corrosion and different types of localized corrosion. 3D models of intergranular corrosion have also been developed.
In the thesis proposed here, it will be a question of developing a CA model allowing the study of corrosion processes in which the diffusion of corrosive species in solution and/or a temperature that is both variable in time and inhomogeneous in space may prove to be dimensioning (pitting and crevice corrosion, evolution of macroscopic defects). We will take advantage of two main features: firstly the equations governing diffusive transport and heat transfers are similar (they will be simulated using 3D random walks), secondly the AC method is particularly suitable for the study of phenomena involving time-dependent interfaces/boundaries.
The model developed will be implemented in C language and CUDA, in order to perform simulations on mixed CPU/GPU computers (parallel programming on graphics cards). Code development will therefore be the main activity, with simulations being performed on dedicated CEA and ENSCP machines. In order to validate the results provided by the model, reference will be made to experimental results selected from the literature and from SCCME/LECA data.

Understanding of corrosion mechanisms and means of mitigating corrosion in a NaCl-ThCl4-UCl3 salt. Application to future molten salt fuel and coolant reactors

The molten salt reactor concept is based on dissolving the fuel in a molten salt. This liquid fuel concept is highly innovative and in many respects represents a break with current reactors, which are all based on the use of a solid fuel and a fluid coolant. Recently, the emergence of American start-ups proposing this innovative concept and the major effort made in China have revived interest worldwide in studying this technology, which offers a number of advantages, both real and potential, over the use of solid fuel, particularly in terms of incineration and intrinsic safety. To build a feasibility demonstrator for this breakthrough concept, extensive research is needed to acquire data and justify the behaviour of the containment barriers, primarily the metal barrier in contact with the salt. In the case of molten salt reactors, the structural materials, nickel-based alloys, are chosen to optimise their behaviour in terms of corrosion and high temperature. Corrosion of the materials is one of the critical points to be overcome when building this reactor. A detailed understanding of the corrosion mechanisms of the alloy chosen as the structural material, on the one hand, and of the chemistry of the ternary salt NaCl-ThCl4-UCl3 envisaged, on the other hand, are necessary to predict the material corrosion rate over the lifetime of the demonstrator. These studies will enable several corrosion mitigation methods to be developed. Each of these processes will be tested and evaluated under nominal conditions and then aggravated.
The first part will be devoted to understanding the corrosion mechanisms of the alloy and the chemistry of the NaCl-ThCl4-UCl3 salt. To this end, tests will be carried out at the IPN in Orsay and the corrosion mechanisms and chemistry studies will be established using electrochemical techniques and microstructural characterisation of corroded samples (thermogravimetry, SEM, TEM, XPS, Raman, GD-OES, etc.). Secondly, material protection tests using different types of salt redox control will be carried out and then tested in nominal and aggravated environments.
This approach will make it possible to meet a major and ambitious corrosion control challenge for an innovative energy process.

Study of the production of martensitic stainless steel 13-4 by Laser Metal Deposition: influence of process parameters, powder characteristics and post-treatments on microstructure and mechanical properties at fracture

Additive manufacturing processes are now widely studied for numerous applications in the nuclear industry. The aim of the studies dedicated to optimising the Laser Metal Deposition (LMD) metal additive manufacturing process for the production and shaping of a 13-4 martensitic stainless steel is to obtain a material with mechanical properties at fracture, particularly in terms of impact strength, that comply with the specifications for use. This work explores the complex relationships between the microstructural characteristics (phase present, granular structure, texture, precipitation, etc.) induced by the process and the resulting mechanical performance.
Additive manufacturing, in particular the LMD process, offers multiple advantages in terms of design flexibility and customisation of metal components. However, obtaining mechanical properties at fracture that meet specifications is a major challenge, particularly for high-temperature applications in corrosive environments.
This thesis focuses on the optimisation of the LMD process to ensure that components manufactured from 13-4 martensitic stainless steel exhibit microstructural characteristics and mechanical performance appropriate to their intended applications, with particular emphasis on impact properties. Determining the optimum process parameters, including the characteristics of the powders and associated post-treatments, the analysis of the microstructure, and the correlation between the microstructure and the mechanical properties constitute a major challenge for the complete control of this process.

Study of fracture toughness - microstructure relationships of new high performance oxide dispersion strengthened steels

ODS steels are considered for the development of components for fourth generation reactors. They offer high tensile and creep strength and good resistance to irradiation [1-3]. This high level of reinforcement is accompanied by a reduction in ductility and toughness. Tube shaping changes the microstructure, so the properties of the material in its final form should be evaluated. The work of B. Rais [4] made it possible to compare the different tests and to develop a test and an analysis method for measuring toughness on thin tubes.

This present PhD will use this new test to evaluate the toughness of various ODS grades. Varied microstructures from historical and recent productions will assessed to identify the mechanisms, the key parameters driving toughness and to identify the microstructural parameters which drive the response of the material. In this work we will be interested in ferritic / martensitic grades, some of which come from a manufacturing process which is the subject of a patent application [5-6] and for which we observe for the first time remarkable properties in resilience, associated with good hot mechanical properties.

The study will be based on a comparison of experience and finite element modeling. This applied research work will allow the student to acquire solid skills in fracture mechanics and fine characterization of materials (SEM, EBSD, etc.). A good understanding of the mechanical properties/microstructure relationships will make it possible to understand the origin of the observed properties and to propose new optimizations on the microstructures to improve the mechanical behavior and/or the shaping of the material.

Student profile: Engineer or M2 Mechanics/Materials

On the role of the elastic deformation field on the formation of irradiation defects in pure metals

In the context of extending the operational lifetime of nuclear power plants (NPPs), currently operating in France, a materials ageing surveillance strategy is in place. It is essential for ensuring their mechanical properties. During the operation of the plant, materials are subjected to irradiation. Under this exposure, the internal structure of materials evolves, leading to the creation of numerous defects that degrade macroscopic properties and may result in a limitation of the long-time operation (LTO) of components. The proposed work is a fundamental study conducted on model materials, aiming to better understanding the behavior under irradiation of metallic alloys. It will contribute to the predictive modelling of materials, covering defects created at the nanoscale up to the level of nuclear components.

The irradiation of materials with high-energy particles such as neutrons, ions, or electrons generates a large number of defects called point defects (PD). These mobile PDs can migrate and aggregate to form 2D or 3D-objects like prismatic loops or cavities respectively. They can also be eliminated at PD sinks. The system is then submitted to PDs flows directed towards these sinks. These flows are then responsible for phenomena such as radiation-induced segregation (RIS) or precipitation (RIP) of solute atoms [1] [2]. The presence of clusters of PDs and of PD flows alters the microstructure and can deteriorate the physical response of the irradiated materials. In particular, the formation of prismatic loops degrades the mechanical properties of materials as they can impede dislocations and induce embrittlement [3]. In a previous study, we focused on vacancy defects in the form of cavities and investigated the facetting of defects formed in a weakly anisotropic metal, aluminum, using in-situ irradiations in a high-resolution transmission electron microscope (HRTEM).
The work aims to go further in the role of the elastic deformation field on the morphology of irradiation defects. More precisely, it aims to carry out a systematic study on different metals with different anisotropy coefficients. We have chosen reference metals with body-centered cubic (BCC) and face-centered cubic (FCC) structures with low or high anisotropy coefficients. The study will concern Cr and Fe with a BCC structure, and Al and Cu with a FCC structure and may be extrapolated to alloys of higher complexity such as high entropy alloys (HEA). The work will be mainly experimental but will also include a theoretical part. The effects of the crystal anisotropy on the morphology of prismatic loops will be carried out by phase field modelling [4]. The spatial arrangement of the loops will be studied by Object Kinetic Monte-Carlo (OKMC) simulations [5], as recently done in aluminium.
The work will be mainly experimental. We will studied [100]-oriented single crystals to avoid any surface effect on the shape of the objects formed. They will be irradiated with heavy ions at temperatures normalized with respect to their melting temperature either in-situ within the Jannus Orsay platform, or ex-situ within the Jannus Saclay platform [6]. Loops will be imaged by conventional TEM or STEM with a FEI Tecnai and Jeol NeoARM type microscopes. The latter is equipped with a double spherical aberration corrector. The work will be carried out within the framework of the joint research laboratory (LRC) MAXIT.
The work will also include a modelling part. The effects of crystallographic anisotropy on the morphology of prismatic loops will be investigated using a phase-field code [4]. The spatial arrangement of the loops will be studied using Object Kinetic Monte Carlo (OKMC) [5], as recently done in aluminum.
This work follows a 2-year postdoctoral fellowship scheduled to conclude in December 2023, during which deep learning (DL) approaches were developed to accelerate the automatic detection of defects created under irradiation [7]. The utilization of these approaches will significantly enhance the statistical robustness and precision of the results.

Advantage for the student: The PhD is situated in a laboratory composed by 25 researchers and approximately 25 students (PhD, postdoctoral fellows), creating a simulating scientific environment. The activities involve both experimental and simulation sides, offering the opportunity to interact with experts from both sides.

[1] M. Nastar, L. T. Belkacemi, E. Meslin, et M. Loyer-Prost, « Thermodynamic model for lattice point defect-mediated semi-coherent precipitation in alloys », Communications Materials, vol. 2, no 1, p. 1-11, mars 2021, doi: 10.1038/s43246-021-00136-z.
[2] L. T. Belkacemi, E. Meslin, B. Décamps, B. Radiguet, et J. Henry, « Radiation-induced bcc-fcc phase transformation in a Fe3%Ni alloy », Acta Materialia, vol. 161, p. 61-72, 2018, doi: https://doi.org/10.1016/j.actamat.2018.08.031.
[3] M. Lambrecht et al., « On the correlation between irradiation-induced microstructural features and the hardening of reactor pressure vessel steels », Journal of Nuclear Materials, vol. 406, no 1, p. 84-89, 2010, doi: http://dx.doi.org/10.1016/j.jnucmat.2010.05.020.
[4] A. Ruffini, Y. Le Bouar, et A. Finel, « Three-dimensional phase-field model of dislocations for a heterogeneous face-centered cubic crystal », Journal of the Mechanics and Physics of Solids, vol. 105, p. 95-115, août 2017, doi: 10.1016/j.jmps.2017.04.008.
[5] D. Carpentier, T. Jourdan, Y. Le Bouar, et M.-C. Marinica, « Effect of saddle point anisotropy of point defects on their absorption by dislocations and cavities », Acta Materialia, vol. 136, p. 323-334, sept. 2017, doi: 10.1016/j.actamat.2017.07.013.
[6] A. Gentils et C. Cabet, « Investigating radiation damage in nuclear energy materials using JANNuS multiple ion beams », Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 447, p. 107-112, mai 2019, doi: 10.1016/j.nimb.2019.03.039.
[7] T. Bilyk, A. M. Goryaeva, E. Meslin, M.-C. Marinica, Quantification of radiation damage in high entropy alloys by deep learning approach, 2-7/10/2022, MMM2022, Baltimore, USA

Impact of irradiation parameters on the alpha’ phase formation in oxide dispersion strengthened steels

Ferritic-martensitic oxide dispersion strengthened steels (ODS steels) are materials of great interest in the nuclear industry. Predominantly composed of iron and chromium, these materials can become brittle due to the precipitation of a chromium-rich phase, called a', under irradiation. This phase, known to be sensitive to irradiation conditions, provides an ideal topic for a deeper exploration of the capability to emulate neutron irradiation with ions. Indeed, while ion irradiations are frequently used to understand phenomena observed during neutron irradiations, the question of their representativeness is often raised.

In this thesis, we aim to understand how the irradiation parameters can affect the characteristics of the a' phase in ODS steels. To do so, various ODS steels will be irradiated under different conditions (flux, dose, temperature, and type of particles, such as ions, neutrons, electrons), and subsequently analyzed at the nanoscale. The a' phase (size, chromium content) obtained for each ion irradiation condition will be compared to the one after neutron irradiation.

Synthesis, characterization and modeling of (Mn,Co)3O4 thin films applied to corrosion layers and spintronics

Spinel-type transition metal oxides (AB2O4) appear spontaneously during the generalized corrosion of steels or alloys in aqueous or gaseous environments at high temperatures. This spinel phase forms a continuous corrosion layer and thus regulates corrosion processes by controlling conductivity and material transport between the material and the oxidizing medium. They are also applied voluntarily as protective coatings against degradation phenomena. In particular, the Mn-Co-O spinel system is very promising as protective conductive layers on ferritic stainless steel used to fabricate interconnects in solid oxide fuel cells for green hydrogen production. The composition of the spinel phase determines the protective performance of the coatings. This feature is particularly delicate for materials used in high-temperature electrolyzers, as electronic transport must be optimal (high electrolysis), but must not be accompanied by material transport (low cation diffusion).
In contrast, electronic transport properties of spinel-type transition metal oxides are generally not well understood. Measurements are made on complex corrosion layers (or coatings) of variable composition, low crystallinity, complex microstructure and low thickness. Furthermore, spinel oxides exhibit magnetic properties and composition-dependent cationic disorder that are usually ignored, even though they have a strong impact on electronic transport. The properties highlighted here are the ones that also hold significant importance within the field of spintronics. Thus, tuning the chemical composition of these spinel-structured oxides (normal, inverse or mixed) offers a wide range of magnetic (ferrimagnetic, antiferromagnetic) and electronic (semimetallic, semiconductor, insulator) properties. In particular, CoMn2O4 is expected to exhibit a complex magnetic configuration [1], mainly related to the arrangement of Co2+ and Mn3+ cations in interstitial sites, which needs to be analyzed in detail. Unlike corrosion layers, these physical studies require the synthesis of thin films of well-controlled composition and high crystallinity.
The aim of the thesis is to build up knowledge of physicochemical and structural properties of (Mn,Co)3O4 in order to contribute to the elaboration of Mn-Co-O phase diagrams and electronic transport models based on the relationship between order/disorder, magnetic properties and resistivity of (Mn,Co)3O4. Eventually, the whole (Fe,Cr,Mn,Co)3O4 system will be also considered. The study will be carried out on thin films of perfectly controlled composition and high crystallinity, and will be enhanced by numerical simulations. The experimental and theoretical work will be based on the results of previous studies on (Ni,Fe,Cr)3O4 epitaxial thin films [2,3].
The thesis will be divided as follows:
- Growth of thin films and multilayers by MBE (Molecular Beam Epitaxy) (J.-B. Moussy)
- Spectroscopic characterization using XPS (X-ray photoemission spectroscopy) (F. Miserque)
- Fine structure characterization by DRX and X-ray absorption (XMCD) (P. Vasconcelos)
- Modeling of core-level spectra (XPS, XAS and XMCD) and atomistic modeling (A. Chartier)
- Magnetic characterization by SQUID/VSM magnetometry and electric transport characterization (J.-B. Moussy)

[1] Systematic analysis of structural and magnetic properties of spinel CoB2O4 (B= Cr, Mn and Fe) compounds from their electronic structures, Debashish Das, Rajkumar Biswas and Subhradip Ghosh, Journal of Physics: Condensed Matter 28 (2016) 446001.
[2] Stoichiometry driven tuning of physical properties in epitaxial Fe3-xCrxO4 thin films, Pâmella Vasconcelos Borges Pinho, Alain Chartier, Denis Menut, Antoine Barbier, Myrtille O.J.Y. Hunault, Philippe Ohresser, Cécile Marcelot, Bénédicte Warot-Fonrose, Frédéric Miserque, Jean-Baptiste Moussy, Applied Surface Science 615 (2023) 156354.
[3] Elaboration, caractérisation et modélisation de films minces et multicouches à base d’oxydes (Ni,Fe,Cr)3O4 appliquées à la corrosion et à la spintronique, A. Simonnot, thèse en cours.

Experimental study and modelling of high temperature oxidation of Cr coated zirconium alloy substrate

This thesis concerns the research and development of materials more resistant in extreme conditions at high temperature. It is more specifically dedicated to the development of a new concept of nuclear fuel cladding : Cr coated Zr-based claddings. The purpose of this work is to adpat the Ekinox-Zr code, initially developped for the description of diffusion phenomena in uncoated Zr claddings, to Cr-coated Zr-based claddings and create a new code : “Ekinox-Zr-Cr”. This work will be divided into two parts : a modelling/simulation one and an experimental one dedicated to the determination of the diffusion coefficients of Cr, Zr and O species inside the different phases of the system. These data constitute essential parameters for the modelisation. High temperature oxidation experiments on Cr-coated claddings will also be used in order to improve our knowledge on the different mechanisms involved and compare them to the results obtained with the Ekinox-Zr-Cr code created during this study.

Delayed hydride cracking (DHC) of nuclear fuel cladding: experiments, modelling and numerical simulations of microstructure effects

Corrosion of nuclear fuel cladding by the water in the primary circuit as it passes through the reactor leads to hydriding. Delayed hydride cracking (DHC) is likely to occur later, during dry storage. Such cracking requires a pre-existing defect and a thermo-mechanical history that enables the following iterative mechanism to be set in motion: hydrogen diffusion, precipitation of hydrides at the crack tip and rupture of the embrittled zone. During a previous thesis carried out in the host laboratory, an original procedure combining experiments and numerical simulations using finite elements was used to determine the toughness of unirradiated relaxed Zircaloy-4 cladding in the event of DHC, and to report on the effect of mechanical loading and temperature on the incubation time and cracking speed between 150°C and 250°C. The aim of this thesis is to apply this procedure to a more modern cladding material (recrystallised M5) and to develop fine-scale microstructure modelling that can account for the effects of texture (crystallographic and morphological), propagation direction and plane, and irradiation on DHC.
Corrosion of nuclear fuel cladding by the water in the primary circuit as it passes through the reactor leads to hydriding. Delayed hydride cracking (DHC) is likely to occur later, during dry storage. Such cracking requires a pre-existing defect and a thermo-mechanical history that enables the following iterative mechanism to be set in motion: hydrogen diffusion, precipitation of hydrides at the crack tip and rupture of the embrittled zone. During a previous thesis carried out in the host laboratory, an original procedure combining experiments and numerical simulations using finite elements was used to determine the toughness of unirradiated relaxed Zircaloy-4 cladding in the event of DHC, and to report on the effect of mechanical loading and temperature on the incubation time and cracking speed between 150°C and 250°C. The aim of this thesis is to apply this procedure to a more modern cladding material (recrystallised M5) and to develop fine-scale microstructure modelling that can account for the effects of texture (crystallographic and morphological), propagation direction and plane, and irradiation on DHC.

Experimental characterisation and numerical simulation of intergranular oxide fracture: Application to Irradiation Assisted Stress Corrosion cracking

Metal alloys used in industrial applications can form oxide layers in the presence of a corrosive environment. These oxides may be distributed on the surface and/or localized at the grain boundaries. In the latter case, the oxidized grain boundaries may experience brittle fracture under mechanical loading, potentially leading to intergranular cracking of the material. This mechanism is, for example, a possible scenario for the failure of austenitic stainless steel bolts used in the internals structure of Pressurized Water Reactors (PWRs). Under the effect of mechanical loading, neutron irradiation and the presence of a corrosive environment, these bolts fail through a phenomenon known as irradiation-assisted stress corrosion cracking. To model this phenomenon, we need to determine the fracture properties of intergranular oxides, and to take into account the coupling between cracking, oxidation and irradiation. In this thesis, experimental and numerical work will be combined. Firstly numerical simulations based on the variational approach to fracture approach will be assessed in order to design micro-beam micromechanics experiments aimed at reliably determining the fracture properties of oxides, and also to study the couplings between cracking, oxidation and irradiation. In particular, the cracking-oxidation coupling that prefigures the transition between initiation and propagation will be investigated in detail. These experiments will then be carried out on model and industry-relevant steels, and interpreted using numerical simulations. Finally, all the results obtained in this work will be incorporated into simulations of polycrystalline aggregates, in order to assess the possibility of quantitatively predicting intergranular cracking in the context of irradiation-assisted stress corrosion.
By the end of the PHD, the doctoral student will have acquired both experimental skills - micromechanical tests - and numerical skills - numerical simulations of fracture - at the cutting edge of the state of the art and applicable to a large number of problems in the mechanics of materials.
A Master's 2 / end-of-studies internship preparatory to the PHD is available in 2024.

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