Predicting thermodynamic properties of defects in medium-entropy alloys from the atomic scale through statistical learning
The properties and behaviour of materials under extreme conditions are essential for energy systems such as fission and fusion reactors. However, accurately predicting the properties of materials at high temperatures remains a challenge. Direct measurements of these properties are limited by experimental instrumentation, and atomic-scale simulations based on empirical force fields are often unreliable due to a lack of precision.This problem can be solved using statistical learning techniques, which have recently seen their use explode in materials science. Force fields constructed by machine learning achieve the degree of accuracy of {it ab initio} calculations; however, their implementation in sampling methods is limited by high computational costs, generally several orders of magnitude higher than those of traditional force fields. To overcome this limitation, two objectives will be pursued in this thesis: (i) to improve active statistical learning force fields by finding a better accuracy-efficiency trade-off and (ii) to create accelerated free energy and kinetic path sampling methods to facilitate the use of computationally expensive statistical learning force fields.
For the first objective, we improve the construction of statistical learning force fields by focusing on three key factors: the database, the local atomic environment descriptor and the regression model. For the second objective, we will implement a fast and robust Bayesian sampling scheme to estimate the anharmonic free energy, which is crucial for understanding the effects of temperature on crystalline solids, using an adaptive bias force method that significantly improves convergence speed and overall accuracy.We will apply the methods developed to the calculation of free energy and its derivatives, physical quantities that give access to the thermo-elastic properties of alloys and the thermodynamic properties of point defects. To do this, we will use algorithmic extensions that allow us to sample a specific metastable state and also the transition paths to other energy basins, and thus to estimate the free energies of formation and migration of vacancy defects. The thermodynamic quantities calculated will then be used as input data for kinetic Monte Carlo methods, which will make it possible to measure the diffusion coefficients in complex alloys as a function of temperature.
One aim will be to try to relate the atomic transport properties to the complexity of the alloy. Since our approach is considerably faster than standard methods, we will be able to apply it to complex alloys comprising the elements W, Ti, V, Mo and Ta at temperatures and compositions that have not been studied experimentally.
Oxide-clad joint and internal corrosion layer modelling in GERMINAL using experimental data provided by different characterisation techniques
This work will be done in the frame of studies on the thermo-mechanical and physico-chemical behaviour behaviour of the « uranium and plutonium mixed oxide fuel » during irradiation currently considered for the future reactors of 4th generation. Because of its particularly hight thermal level during irradiation this kind of fuel is subject to several physical and chemical phenomena duringf its stay in reactor. Those one can have a strong impact on the behaviour of the whole fuel element (pellet and clad), but we can focus on two specific phenomena that take place at middle and high burnup :
- the formation by evaporation-condensation of a fission products layer between the external surface of the fuel pellet and the inner surface of the cladding material at middle burnup, designed as JOG for Joint Oxyde-Gaine;
- the formation of a corrosion layer on the internal surface of the clad, containing fission products and elements constituting the cladding material at high burnup, and resulting from the FCCI (Fuel-Cladding Chemical Interaction),
The occurence of this two phenomena is a limiting factor for increasing the burnup. Thus it is important de be able to estimate quite precisely the chemical composition of the fuel pellet and of the fuel-to-clad gap during irradiation. Previous experimental work had shown that the JOG consisted mainly of caesium, molybdenum and oxygen, with the presence of other elements such as tellurium and barium. Observations have also shown the presence of chromium, iron and nickel, along with other volatile fission products (VFP), in areas of ROG. These observations were backed up by thermodynamic calculations, which led to the assumption that the JOG consisted mainly of caesium molybdate Cs2MoO4. However, until recently, there had been no direct evidence of the presence of this compound. Recently, more detailed characterisation methods carried out as part of a current thesis on (U,Pu)O2 fuel samples confirmed quantitatively that the JOG was mainly made up of Cs, Mo and O, but also of I and Ba distributed in several phases. Other elements were detected and measured in localised areas, namely Te, Zr as well as U and Pu. With regard to corrosion, phases based on Fe, Te and Pd were observed, as well as the joint presence of Cr and O.
At the same time, work was started on modelling the axial redistribution of caesium, with a view to improving the description currently used in GERMINAL. The chemical element inventory at a given axial dimension has a first-order effect on the calculated JOG thickness and ROG thickness.
The aim of this thesis is to improve the description and modelling of JOG and ROG formation in the GERMINAL scientific calculation tool (OCS), which is dedicated to calculating the thermo-mechanical and physico-chemical behaviour of 4th generation reactor fuel irradiated under nominal and/or incidental conditions.
To this end, research will be developed in three areas:
- Further development of the radial migration methodology adopted in the GERMINAL code through comparison with existing and recently obtained experimental results. This is based on a coupling with a thermochemistry module in which several hypotheses for the release of volatile fission products created in the pellet towards the pellet-cladding gap can be considered.
The aim of this PhD subject consists in improving the JOG and FCCI modeling into the fuel performance code (FPC) GERMINAL, dedicated to the calculation of the thermo-mechanical and physico-chemical behaviour of the 4th generation reactors’ fuel irradiated in normal and off-normal conditions. For that purpose, an acurrate experimental caractherization of some irradiated fuel samples, to which the PhD student will contribute, will be elaborated and coupled to a thermodynamic approach. The research will be based on the two items :
- Determination and experimental identification of the chemical elements and phases located into the fuel pellet, into the gap and at the fuel-to-clad interfaces at the end of the irradiation using the implementation of microprobe-SIMS-SEM/FIB techniques, by combining elemental and isotopic analysis results with microscopic observations.
- Comparison of the results with thermodynamic calculations: type and local quantities of the chemical phases formed in the fuel pellet as well as the phases constituting the JOG and those resulting from the FCCI.
Thus, based on those results, it will be possible to evaluate precisely the chemical composition of the irradiated fuel, of the JOG and of the corrosion compounds by using the FPC GERMINAL, from which the input inventory in chemical elements will be estimated in function of burnup at the different radial and axial localisations.
The PhD student will be attached both to a multi-scale modeling group and to an experimental team having sophisticated tools. Furthermore, academic or international collaborations are possible, in particular in the frame of the OECD/NEA with the development of the TAFID database. The student will have the opportunity to enhance the skills learned in the field of nuclear materials characterisation as well as in the field of thermodynamic calculations and irradiated fuel behaviour simulation.
To this end, the research will be developed along three lines:
- Further development of the radial migration methodology adopted in the GERMINAL code through comparison with existing and recently obtained experimental results. This is based on a coupling with a thermochemistry module in which several hypotheses for the release of volatile fission products created in the pellet towards the pellet-cladding gap can be considered.
- Further development of a [simplified] model for the axial redistribution of caesium and, by extension, of volatile fission products, leading to an initial implementation in the GERMINAL code for testing and preliminary validation of the axial inventories estimated by calculation by comparison with experimental results,
- Finally, thermodynamic calculations to determine the nature and local quantity of the chemical phases formed in the fuel pellet and the constituent phases of the JOG and ROG will be carried out on the basis of the axial inventories estimated by the GERMINAL code.
This will enable a more accurate assessment of the chemical composition of the irradiated fuel, the JOG and the ROG products as a function of the burn-up rate using the GERMINAL OCS as a function of time at the various radial and axial locations.
The PhD student will be integrated into the fuel behaviour study and simulation group(IRESNE Institute, CEA CAdarache) which has or is developing various simulation tools, and will also be able to interact with a characterisation laboratory with cutting-edge experimental tools. Academic and international collaborations are also possible, particularly within the OECD/NEA framework with the development of TAFID database. These will enable the PhD student to make the most of the skills he or she has acquired in the field of characterisation of nuclear materials, as well as in thermodynamic calculations and simulation of the physico-chemical behaviour of irradiated nuclear fuel.
Design of asynchronous algorithms for solving the neutron transport equation on massively parallel and heterogeneous architectures
This PhD thesis work aims at designing an efficient solver for the solution to the neutron transport equation in Cartesian and hexagonal geometries for heterogeneous and massively parallel architectures. This goal can be achieved with the design of optimal algorithms with parallel and asynchronous programming models.
The industrial framework for this work is in solving the Boltzmann equation associated to the transportof neutrons in a nuclear reactor core. At present, more and more modern simulation codes employ an upwind discontinuous Galerkin finite element scheme for Cartesian and hexagonal meshes of the required domain.This work extends previous research which have been carried out recently to explore the solving step ondistributed computing architectures which we have not yet tackled in our context. It will require the cou-pling of algorithmic and numerical strategies along with programming model which allows an asynchronousparallelism framework to solve the transport equation efficiently.
This research work will be part of the numerical simulation of nuclear reactors. These multiphysics computations are very expensive as they require time-dependent neutron transport calculations for the severe power excursions for instance. The strategy proposed in this research endeavour will decrease thecomputational burden and time for a given accuracy, and coupled to a massively parallel and asynchronousmodel, may define an efficient neutronic solver for multiphysics applications.
Through this PhD research work, the candidate will be able to apply for research vacancies in highperformance numerical simulation for complex physical problems.
Nucleation, Growth, and Multi-Scale Structural Properties of Colloidal Nanoparticles of Actinide Oxides (Pu, U, Th)
Nanocrystalline oxides possess unique physicochemical properties, modulated by their size and local structure, making them promising for various technological applications. However, actinide oxide nanoparticles remain underexplored due to their radioactivity and toxicity. Nonetheless, studies dedicated to these species are growing, driven by environmental and industrial considerations, particularly for their involvement in current and future nuclear fuel cycles. This thesis focuses on plutonium, a key element in nuclear reactors. Its behavior in solution is complex, particularly due to hydrolysis reactions that lead to the formation of highly stable colloidal PuO2 nanoparticles. Although these species are now better described, the mechanisms leading to their formation remain largely unexplored.
The ambitious goal of this thesis is to uncover the fundamental mechanisms involved in the formation of these nanoparticles by adopting a systematic approach that combines a wide range of experimental parameters. These include the synthesis medium, temperature, reactant concentration, reaction time, and the contribution of sonochemistry. The focus will be on studying the nucleation and growth stages of these nanoparticles, as well as their structural properties in relation to the physicochemical conditions that influence their formation. Studies will be conducted at ICSM with Th, U, and Zr as analogs, and at the Atalante facility for Pu. In addition to standard laboratory techniques necessary for characterizing these systems, complementary experiments will be carried out on synchrotron lines (SOLEIL and ESRF) to thoroughly investigate the structural and reactive properties of these species and their precursors.
Superlattices for the characterization of diffusion under irradiation at the atomic scale
Metal alloys used in nuclear applications are subjected to relatively low temperatures (below 450°C) for long periods of time (more than 10 years). At these temperatures, the kinetics of the diffusion-controlled microstructure transformations are slow. The appearance of certain undesirable phases, likely to embrittle the material, can occur after several years of service. Therefore, diffusion coefficients play a crucial role as input data for modeling the evolution of these microstructures using phenomenological models. However, experimental determination of diffusion coefficients at low temperatures (T < 600°C) is extremely tricky, especially because of the need to characterize nanometric diffusion lengths, a difficulty made all the more difficult in the presence of irradiation.
With the development of chemical analysis by transmission electron microscopy (TEM) and atom probe tomography (APT), it is now possible to experimentally access very small diffusion lengths and thus determine low-temperature diffusion coefficients using superlattices, which consist of stacking nanometric layers of different chemical compositions. We can even characterize the effect of irradiation on diffusion by performing ion irradiations, enabling us to simulate the changes caused by neutron irradiation without activating the materials. The aim of this thesis is to develop a methodology and characterize diffusion under and outside irradiation in a ternary system of interest (Ni-Cr-Fe), representative of the steels and high-entropy considered in the nuclear industry.
This thesis is an opportunity to work with cutting-edge experimental techniques, in close collaboration with a team of theoretician in the same department, as well as with teams specializing in the development of superlattices at UTBM in Belfort and CINAM in Marseille.
Deterministic neutron calculation of soluble-boron-free PWR-SMR reactors based on Artificial Intelligence
In response to climate challenges, the quest for clean and reliable energy focuses on the development of small modular reactors using pressurized water (PW-SMR), with a power range of 50 to 1000 MWth. These reactors aimed at decarbonizing electricity and heat production in the coming decade. Compared to currently operating reactors, their smaller size can simplify design by eliminating the need for soluble boron in the primary circuit water. Consequently, control primarily relies on the level of insertion of control rods, which disturb the spatial power distribution when control rods are inserted, implying that power peaks and reactivity are more difficult to manage than in a standard PWR piloted with soluble boron. Accurately estimating these parameters poses significant challenges in neutron modeling, particularly regarding the effects of the history of control rod insertion on the isotopic evolution of the fuel. A thesis completed in 2022 explored these effects using an analytical neutron model, but limitations persist as neutron absorbers movements are not the only phenomena influencing the neutron spectrum. The proposed thesis seeks to develop an alternative method that enhances robustness and further reduces the calculation biases. A sensitivity analysis will be conducted to identify key parameters, enabling the creation of a meta-model using artificial intelligence to correct biases in existing models. This work, conducted in collaboration with IRSN and CEA, will provide expertise in reactor physics, numerical simulations, and machine learning.
AI based prediction of solubilities for hydrometallurgy applications
Finding a selective and efficient extractant is one of the main challenges of hydrometallurgy. A comprehensive screening is impossible by the synthesis/test method due to the high number of possible molecules. Instead, more and more studies use quantum calculations to evaluate the complexes stabilities. Still, some important parameters such as solubility are lacking in this model.
This project thus aims to develop an AI based tool that provides solubility values from the molecular structure of any ligand. The study will first focus on 3 solvants: water, used as a reference as AI tools already exist, 3 M nitric acid to mimic nuclear industry applications and n-octanol, organic solvent used to measure the partition coefficient logP. The methodology follows 4 steps:
1) Bibliography on existing AI tools for solubility prediction yielding the choice of the most promising method(s)
2) Bibliography on existing databases to be complemented by the student's in-lab solubility experiments
3) Code generation and training of the neural network on the step 2 databases
4) Checking the accuracy of the predictions on molecules not included in the databases by comparing the calculated results with in-lab experiments
Systematic study of the neutron scattering reactions on structural materials of interest for nuclear reactor applications
Elastic and inelastic scattering reactions on structural materials have a significant impact on the simulation of neutron transport. The nuclear data of structural materials of interest for nuclear reactors and criticality studies must be known with good precision over a wide incident neutron energy range, from a few tens of meV to several MeV. The thesis proposal aims to carry out a systematic study of the scattering reactions above the resolved resonance range up to 5 MeV. In this energy range, neither the R-Matrix formalism nor the statistical Hauser-Feshbach model are valid for structural materials. A new formalism will be developed by using high-resolution measurements of the scattering angular distributions. This work will focus more precisely on measurements already done at the JRC-Geel facility (sodium [1], iron [2]) and will be extended to other elements studied within the framework of the IAEA/INDEN project, such as copper, chromium and nickel. As part of this thesis, the experimental database will be complemented by new measurements on the copper isotopes (Cu63 and Cu65). The measurements will be carried out at JRC Geel GELINA facility with the ELISA detector. Concerning the copper isotopes, integral benchmarks from the ICSBEP database revealed several issues in the nuclear data libraries, which provide contradictory integral feedbacks on the nuclear data of U235. For example, the ZEUS benchmarks, which is routinely used to study the capture cross section of U235 in the fast neutron energy range, are very sensitive to the nuclear data of copper. This type of benchmark will provide an ideal framework for quantifying the impact of any new formalism developed to evaluate the nuclear data of structural materials.
This study will allow the PhD student to develop skills in experimental and theoretical nuclear physics, as well as in neutron physics. The results will be communicated to the JEFF working group of the Nuclear Energy Agency (OCDE/AEN).
[1] P. Archier, Contribution à l’amélioration des données nucléaires neutroniques du sodium pour le calcul des réacteurs de génération IV, Thèse, Université de Grenoble, 2011.
[2] G. Gkatis, Study of neutron induced reaction cross sections on Fe isotopes at the GELINA facility relevant to reactor applications, Thèse, Université Aix-Marseille, 2024.
Behavior of nanocavities under mechanical loading: from understanding physical mechanisms to homogenizing nanoporous materials
Nanocavities - typically a few nm to a few tens of nm in size - are often observed in metals, for example in high-temperature applications due to the condensation of vacancies or in metal alloys used in nuclear reactors due to irradiation. The presence of these nanocavities degrades the mechanical behaviour of materials and contributes to fracture. It is therefore necessary to determine the physical mechanisms associated with the behaviour of these nanocavities under mechanical loading and to obtain homogenised models describing the macroscopic behaviour of these nanoporous materials. The results available in the literature remain limited to date, particularly with regard to the representativeness of the simulations carried out and the models proposed for the applications of interest. This includes for example considering crystal defects surrounding the cavities, the effect of cyclic loading and the localisation of nanocavities at grain boundaries. The objectives of this thesis are therefore to determine the behaviour of nanocavities under mechanical loading and the associated physical mechanisms by considering realistic situations with respect to applications, to develop physically-based analytical models to describe the behaviour of nanocavities under mechanical loading, and finally to propose homogenised models adapted to nanocavities that can be used to simulate the failure by growth and coalescence of cavities. The targeted applications are those related to metal alloys under irradiation, but the elements of understanding obtained and the models developed could be used in a broader context. In order to achieve these objectives, Molecular Dynamics (MD) simulations will be performed, analysed from the elastic theory of dislocations and used to propose relevant homogenised models for nanoporous materials.
Study of the transitions of flow regimes in post-burnout
Dispersed two-phase flows are part of many fluid systems such as the cooling of nuclear reactors. Depending on the heat flux in the reactor core, the flow rate, the subcooling or the pressure, different flows may occur: single phase, bubbly or annular flows (with a liquid film on the wall and a vapour core).
During a loss of primary coolant accident, the reactor core, containing the fuel rods, increases in temperature until the boiling crisis when the heat flux is high enough. The different regimes of two-phase flows that occur in this type of accident are illustrated in figure 1. A vapour film appears rapidly and thermally insulates the rods, while some liquid remains in the centre of the flow. The rods are dried up, thus their surface are cooled down by the single vapour, and the heat exchange at the wall is reduced [1], which corresponds to the « inverted annular film boiling » flow. When the liquid gradually vaporises, the vapour film thickens and the induced turbulence tends to form waves at the vapour-liquid interface, and to destabilise the interface until the formation of liquid slugs (inverted slug film boiling). Then, the evaporation and fragmentation of these slugs lead to the formation of a dispersed flow with droplets (dispersed film boiling).
The transitions of flow regimes in this configuration are not well-identified [1], [2] although their understanding is significant to study the cooling of a nuclear reactor core. One of the main obstacles in experimental studies is that the walls need to be strongly heated up in order to form and maintain a vapour film, which leads to opaque test sections. Thus, a direct visualisation is particularly complex to obtain, as much as measuring local parameters such as temperature and velocity fields. The experimental results available in the literature on this topic are insufficient to develop a physical model [1], [3], [4], [5].
As a first step towards an accurate identification of the regime transitions, this thesis focuses on the single effect of the hydrodynamics, by coupling experimental and analytical approaches. In order to clarify the physics of the different phenomena, the configuration of a liquid flow inside a gas flow is proposed. Indeed, the interface deformation and the gas and liquid velocities may influence the transition from one regime to another [6], [7]: the smooth interface is therefore perturbed by waves (Kelvin-Helmholtz instabilities) and droplets could be entrained from the interface. A parametric analysis is considered by varying the gas and liquid flow rates and the thickness of the gas film, in order to observe these different phenomena and to understand the influence of each parameter on the regime transitions. An experimental facility has recently been conceived at DM2S/STMF/LE2H to study these transitions by a visualisation of the interface deformations, and may be adapted with new measurements or new methodology if necessary.
Dimensionless numbers will be identified or defined from the experimental results to describe the phenomena. Then, the regime transitions will be characterized, based on these dimensionless numbers, in order to establish a diagram of the transitions of flow regimes.
The combination of the results obtained in this thesis will enable to reinforce the physical models used in the system code CATHARE, developed at CEA for thermal-hydraulic studies about nuclear safety. This thesis presents a strong academic interest thanks to an innovative experimental facility and production of original results. Besides, it also presents an interest on the industrial level since it contributes to enhance the expertise of significant phenomena in the demonstration of nuclear reactor safety.
References:
[1] M. Ishii et G. De Jarlais, « Flow visualization study of inverted annular flow of post-dryout heat transfer region », Nuclear Engineering and Design, 1987.
[2] G. De jarlais, M. Ishii, et J. Linehan, « Hydrodynamic stability of inverted annular flow in an adiabatic simulation », Argonne National Laboratory, CONF-830702-9, 1983.
[3] T. G. Theofanous, « The boiling crisis in nuclear reactor safety and performance », International Journal of Multiphase Flow, vol. 6, no 1, p. 69-95, févr. 1980, doi: 10.1016/0301-9322(80)90040-3.
[4] N. Takenaka, T. Fujii, et others, « Flow pattern transition and heat transfer of inverted annular flow », Int. J. Multiphase Flow, 1989.
[5] M. A. El Nakla, D. C. Groeneveld, et S. C. Cheng, « Experimental study of inverted annular film boiling in a vertical tube cooled by R-134a », International Journal of Multiphase Flow, vol. 37, p. 37-75, 2011.
[6] Q. Liu, J. Kelly, et X. Sun, « Study on interfacial friction in the inverted annular film boiling regime », Nuclear Engineering and Design, vol. 375, 2021.
[7] K. K. Fung, « Subcooled and low quality film boiling of water in vertical flow at atmospheric pressure », PhD Thesis, Argonne National Laboratory, 1981.