# Generative deep-learning modeling and machine-learning potentials for the calculation of atomic-scale transport properties in disordered uranium-plutonium mixed oxides

Machine learning (ML) is now commonly used in materials science to enhance the predictive capabilities of physical models. ML interatomic potentials (MLIP) trained on electronic-structure calculations have become standard tools for conducting efficient yet physically accurate molecular dynamics simulations. More recently, unsupervised generative ML models are being explored to learn hidden property distributions, and generate new atomic structures according to these distributions. This is useful for chemically disordered solid solutions, whose properties depend on the distribution of chemical species in the crystal lattice. In such cases, the number of possible configurations is so large that exhaustive sampling is beyond the capability of conventional methods. An example is U-Pu mixed oxides (MOX), a type of nuclear fuel that can significantly reduce the volume and radiotoxicity of spent-fuel waste. High-entropy alloys are another class of disordered materials that are promising candidates for radiation-resistant nuclear materials.

The goal is to combine MLIPs and generative methods to address atomic transport properties in MOX. The candidate will use in-house ML generative tools to generate representative atomic configurations and build an ab initio database. They will use this database to train a new MLIP for MOX, leveraging the experience gained from developing analogous MLIPs for the pure UO2 and PuO2 oxides. Finally, they will apply the MLIP to calculate atomic diffusion coefficients, crucial for predicting irradiation-induced microstructure evolution and in-reactor behavior.

The work will be conducted at the Nuclear Fuel Department (IRESNE, CEA Cadarache), within a scientific environment characterized by a high level of expertise in materials modelling, and in close collaboration with other CEA teams in the Paris region specialized in ML methods. Results will be disseminated through scientific publications and participation in international conferences

# Calculation of the thermal conductivity of UO2 fuel and the influence of irradiation defects

Atomistic simulations of the behaviour of nuclear fuel under irradiation can give access to its thermal properties and their evolution with temperature and irradiation. Knowledge of the thermal conductivity of 100% dense oxide can now be obtained by molecular dynamics and the interatomic force constants[1] at the single crystal scale, but the effect of defects induced by irradiation (irradiation loop, cluster of gaps) or even grain boundaries (ceramic before irradiation) remain difficult to evaluate in a coupled way.

The ambition is now to include defects in the supercells and to calculate their effect on the force constants. Depending on the size of the defects considered, we will use either the DFT or an empirical or numerical potential to perform the molecular dynamics. AlmaBTE allows the calculation of phonon scattering by point defects [2] and the calculation of phonon scattering by dislocations and their transmission at an interface have also recently been implemented. Thus, the chaining atomistic calculations/AlmaBTE will make it possible to determine the effect of the polycrystalline microstructure and irradiation defects on the thermal conductivity. At the end of this post-doc, the properties obtained will be used in the existing simulation tools in order to estimate the conductivity of a volume element (additional effect of the microstructure, in particular of the porous network, FFT method), data which will finally be integrated into the simulation of the behavior of the fuel element under irradiation.

The work will be carried out at the Nuclear Fuel Department of the CEA, in a scientific environment characterised by a high level of expertise in materials modelling, in close collaboration with other CEA teams in Grenoble and in the Paris region who are experts in atomistic calculations. The results will be promoted through scientific publications and participation in international congresses.

References:

[1] Bottin, F., Bieder, J., Bouchet, J. A-TDE

# Multiphysics modeling of an experimental sintering furnace

In the scope of the development and improvement of the performance of low-carbon energy sources, the CEA has a software platform for modeling the behavior of nuclear fuel from its manufacture to its use in the reactor. Sintering, a key step in fuel fabrication is the heat treatment process used to consolidate and densify nuclear fuel to form the solid solution U1_yPuyO2-x. The sintering cycle generally comprises a rise in temperature with a linear ramp, a constant temperature plateau and a controlled cooling, with possibly a continuous adaptation of the oxygen potential through the oxidation-reduction buffer imposed by the H2 over H2O ratio of the carrier gas to reach the target oxygen-metal ratio. A first modeling of an industrial sintering furnace was carried out using the OpenFOAM software suite and the C++ finite elements library DIFFPACK. A second step aims to validate the models used in the simulation of this industrial furnace based on a separate effects approach and the modeling of a laboratory sintering furnace. This post-doctorate will be carried out at CEA Cadarache within the multiscale modeling laboratory (LM2Cà of the fuel studies department. This work will be carried out in close collaboration with the teams of experimenters from the Solid Chemistry and Actinide Materials Development Laboratory (LSEM) of CEA Marcoule who are developing and operating the experimental furnace. The collaboration will focus on the modeling input data (furnace geometry, temperature and atmospheric conditions) and the measurements to be compared with the simulation data. The post-doctoral student will evolve in a stimulating environment, within a dynamic laboratory where about fifteen doctoral and post-doctoral students are already working, in contact with experts in fuel physics modeling and in collaboration with experimenters. The work can be enhanced by presentations at conferences and the writing of articles.

# Modeling of the Fission gas behaviour in a 4th generation nuclear fuel at low power level

French alternative energies and atomic energy commission (CEA) is still studying a sodium fast reactor (SFR) core with intrinsic safety [1]. In this reactor core, low linear heat rate induce a significant fission gas retention in the fuel. It is mandatory to describe accurately the thermomechanics of this concept in order to confirm its safety.

Current model used in the CEA as fuel performance code for SFR, GERMINAL, is based on an empirical approach which the calibration database is centered on fuel pins irradiated at a high linear heat rate, and also a low gas retention. This fellow aims to extend to SFR fuels an existing gas model, MARGARET, which has been developed for the pressurized water reactor (PWR) fuels. On issue will be the restructuring phenomenon, which is far more relevant in SFR than in PWR, this topic is raised in [4].

First step of the work will consist in the integration of the MARGARET gas model in the GERMINAL code throughout the PLEIADES platform. This task will need to couple variables associated to the resolution of equilibriums in various physics (thermal, mechanical, and gas swelling) in order to build the coupling scheme.

Second step of the work will be focused on the analysis of the mechanisms contributing to the gas swelling, using the post-irradiation experiments realized in the CEA Cadarache facility (LECA - Laboratoire d’Examens des Combustibles Actifs). Image analysis tools would be used in order to characterize the porosity distribution in the fuel. Based on these observations, it will be necessary to make the calibration of the MARGARET model in order to give a good assessment of the gas swelling and of the porosity distribution. Depending on the results, a second year dedicated to the extension of this gas model for the power transients would be possible.

# Improvement by thermodynamic calculations of the modeling for the joint oxyde-gaine and the fuel cladding chemical interaction into the fuel performance code GERMINAL

This work is proposed in the frame of studies on the physico-chemical behaviour of the (U,Pu)O2 fuel during irradiation considered for the future reactors of 4th generation. Indeed, this kind of fuel is subject in particular to two specific specific phenomena that can have an impact on its behaviour:

- the formation of a JOG (Joint Oxyde-Gaine), a fission products layer localised between the external surface of the fuel pellet and the inner surface of the cladding material ;

- the FCCI (Fuel-Cladding Chemical Interaction), which leads to the formation of a corrosion layer on the internal surface of the clad containing fission products and elements constituting the cladding material.

The goal is this work is to improve the modelling of the JOG and of the FCCI into the fuel performance code (FPC) GERMINAL, dedicated dedicated to the calculation of the thermo-mechanical and physico-chemical behaviour of fast reactor fuel irradiated in normal and off-normal conditions. For that purpose, the candidate will work on the dedicated calculation scheme of GERMINAL which uses the thermochemical software OpenCalphad and on the comparison of the JOG and of the internal cladding corrosion widths obtained to experimental observations obtained for some irradiation experiments. Complementary stand-alone thermodynamic calculations will be performed with the TAFID, thermodynamic database on nuclear materials developed in an international framework, in order to analyse the thermochemistry JOG/FCCI versus parameters of interest.

This work will be performed in collaboration with a team specialised in thermodynamic modelling, in charge of the TAFID project. The student will thus have the opportunity to exchange on his results in a collaborative frame with international partners. In addition, he will be able to highlight his work through publications and presentations at conferences.

# Micro-scale modelling of the mass transfer induced by a vaporization-condensation process in a ceramic material under thermal gradient

The post-doctoral work concerns the mechanism of mass transfer induced by evaporation-condensation under a thermal gradient. In nuclear fuels, the presence of porosities, the very high temperatures combined with the strong thermal gradient activate this evaporation-condensation phenomenon. This results in a displacement of porosities towards the central hot part and a transfer of material in the opposite direction towards the external cold part. This phenomenon is currently modeled by a 2D homogenized approach at the fuel pellet scale in which the material transfer is computed by solving the advection equation coupled to the heat equation by the finite element method.

The post-doctoral fellow will have to set up a microscopic modeling of the vapor phase transfer phenomenon. This work will allow to improve the simulation of free volumes associated to cracks and thus, to justify the assumptions of the velocity law of porosities migration used in the 2D homogenized model.

The work to be carried out is decomposed in two main steps which are on the one hand, the formulation and the numerical implementation of the constitutive equations of the microscopic model, and on the other hand, the justification of the homogenized model. The post-doctoral fellow will work at the CEA Cadarache site in the framework of a collaboration between the research teams of the Department of Fuel Studies and the IUSTI of Aix-Marseille University on the simulation of material transfer in the vapor phase under a thermal gradient. A major advance expected from this work is to take into account the evolution of the geometry of porosities, induced by the material transfer, with techniques for tracking the movement of solid-gas interfaces. The results will be valorized by publications in scientific journals and participation in conferences.

# Application of the Hybrid-High-Order (HHO) method for the treatment of non-local effects in crystal plasticity via a micromorph approach

Describing the behavior of materials at the crystalline scale is the subject of much academic research, and is of growing interest in industrial R&D studies. Classically, this description is based on behavior laws describing the local evolution of the material's microstructural state: (visco-)plastic deformation, dislocation density, etc.

The main driving force behind this evolution is resolved shear stress, the projection of the stress tensor on the slip systems.

The formalism of these local constitutive equations (as opposed to non-local constitutive

equations discussed hereafter) is now well established, whether we are considering

infinitesimal or finite transformations, and benefits from special support within the MFront code generator. Thanks to MFront, those constitutive equations can be used in various mechanical solvers at CEA (Manta, Cast3M , Europlexus , AMITEX_FFTP ) and EDF

(code_aster, Manta, Europlexus ).

However, the use of local constitutive equations does not allow to account for many effects.

The aim of the post-doc is to develop a robust numerical strategy for reliably solving

structural problems using non-local crystal plasticity laws, and guaranteeing the

transferability of the constitutive equations between the CEA and EDF codes.