Cation self-diffusion plays a key role in the microstructure evolution of a wide range of materials, including oxide nuclear fuels. Growing evidence indicates that small defect clusters can make a substantial contribution to cation transport in these oxides. Quantifying this contribution is nevertheless challenging because of complex defect chemistry, strong correlations between cation and anion migration, and the existence of multiple competing migration mechanisms. In this work, we compute bulk cation self-diffusion coefficients in stoichiometric UO2 and PuO2 by explicitly accounting for small vacancy clusters (cation-anion divacancies and Schottky defects) in addition to isolated cation vacancies. Our approach combines a systematic exploration of cluster migration pathways using ART-nouveau with the calculation of cluster transport coefficients through the KINECLUE code, which rigorously incorporates the influence of local atomic environments and kinetic correlations on defect migration. These transport coefficients are then coupled with equilibrium cluster concentrations to obtain self-diffusion coefficients directly comparable with experimental data. We find that small vacancy clusters are significantly more mobile than isolated cation vacancies and dominate the overall diffusion process. In UO2, the resulting self-diffusion coefficients are consistent with the most reliable experimental datasets, whereas in PuO2 the predictions are discussed in light of the limited data currently available. Although vacancy clusters exhibit higher mobility in PuO2, the overall self-diffusion coefficient is lower than in UO2 because of the larger cation vacancy formation energy predicted by our defect model. Beyond actinide oxides, this work demonstrates how defect clusters can be systematically integrated into diffusion calculations and provides transferable insights and input data for fuel behavior models.

In this paper, we employ atomic kinetic Monte Carlo (AKMC) simulations to get insight into the kinetics of Fe-Cr interdiffusion in nanometric multilayer materials, and the relevant information that can be extracted from the evolution of the experimental X-ray diffraction (XRD) spectrum. For this purpose, we develop an elastic model to obtain the interplanar spacing for a given composition profile derived from AKMC simulation, and then we simulate the corresponding XRD spectrum and compare it with the experimental one. We find a very good agreement between the two, which validates our modeling procedure. Then we put some effort into trying to relate specific features of the XRD spectra with phenomena occurring at the atomic scale, mostly the decay of satellite peak intensities over time. The interdiffusion coefficients extracted from the XRD spectra are underestimated in the Fe-rich phase and overestimated in the Cr-rich phase, but more or less within one order of magnitude of the values obtained from standard measurements. Extracting more quantitative kinetic information directly from the experimental XRD spectra is rather difficult without resorting to a modeling study.

Steels are among the technologically and economically most relevant materials. Key innovations in important sectors of human society such as mobility, energy and safety, are currently based on alloying of Fe with other transition-metal elements such as Mn, Cr, or Co. Due to strong impacts and conceptual challenges related to magnetism, however, the fundamental understanding and the ability to computationally design these steels in high-throughput approaches lags behind other classes of alloys. In this article, we will provide a substantial review of the role of magnetism, magnetic excitations and transformations for alloy thermodynamics, point defects, interfaces and kinetics. This will be achieved by combining insights from different methods: Ab initio simulations have the advantage that the magnetic ground state is intrinsic part of the electronic minimization. Due to the coarsening of the many-electron structures and therewith magnetic interactions, tight-binding methods can handle larger system sizes. Effective interaction models provide the freedom to exploit more sophisticated magnetic interactions. The performance of these methods in terms of magnetic properties of Fe alloys will be evaluated by providing state-of-the-art results for their sensitivity to magnetism. Furthermore, dedicated experiments will be discussed to complete the understanding of magnetic effects in Fe alloys and to validate the modeling strategy.

This study investigates the thermodynamics and kinetics of the Ni-Cr system, focusing specifically on the kinetics of the order-disorder phase transformation in the Ni-33at.%Cr alloy. Combining density functional theory, CALPHAD-type models, and experimental diffusion data, we introduce and validate an efficient pair interaction model (PIM) and use it in Monte Carlo simulations. Our results include a detailed phase diagram of Ni-Cr in face-centered cubic structure and kinetic models that delineate the behavior of solid solutions at high temperatures and ordered structures at low temperatures. The simulations shed light on tracer diffusion and ordering kinetics within Ni-33at.%Cr, demonstrating good agreement with existing experimental data. Furthermore, our simulation-driven insights prompt a reevaluation of certain aspects of related experimental studies concerning the apparent ordering activation enthalpies and growth kinetics. We also provide a thorough discussion on the strengths of our models and features for future improvement.

This study examines the thermodynamics and kinetics of the face-centered cubic Ni-Cr-Fe system, focusing on the order-disorder phase transformation in Ni0.67(1-x)Cr0.33(1-x)Fex (x = 0-0.1) alloys. A pair interaction model (PIM) is developed, with a significant portion based on density functional theory (DFT) calculations and CALPHAD models for binary Ni-Cr and Ni-Fe alloys and further adjusted using experimental order-disorder transformation temperatures and diffusion data. Monte Carlo simulations using this PIM yield detailed phase diagrams and kinetic insights into the ordering process. The simulations reveal that adding up to 10 at.% Fe extends the incubation time by slowing down the atomic diffusion, while slight deviations in Ni-Cr ratio have minimal impact on the ordering kinetics. Although additional experimental data would be required-especially at low temperature and high Fe content-for further validation of the model, our results match reasonably well with the available experimental data on ordering incubation times, capturing the alloy's key characteristics.

Predicting atomic diffusion in concentrated magnetic systems is challenging due to thermal magnetic effects and complex magnetochemical interplay. We propose an efficient approach via kinetic Monte Carlo using ab initio parametrized models. We demonstrate its accuracy in the case of Fe-Ni alloys, where we successfully predict and explain the weak composition dependence of diffusion coefficients due to a compensation of distinct contributions of their constituents. The diffusion-behavior difference between the paramagnetic and the magnetic ground states is elucidated, evidencing the role of magnetic disorder.

Most of the phase transformations modifying the microstructure, thereby the materials properties, are controlled by the diffusion of atoms. The rate but also the selection of phase transformations depend on the concentration of lattice point defects (PDs), because substitutional atoms exchange with PDs to diffuse and PDs are non-conservative species. During manufacturing or in use, whenever PD diffusion and creation/annihilation reactions at extended defects in the microstructure are slower than the kinetics of the microstructure, these PDs may not have their equilibrium concentration. A departure of PDs from local equilibrium can be transient under thermal conditions, or permanent in materials driven out of equilibrium as under irradiation. Non-equilibrium PDs can have a dramatic effect on the evolution of the microstructure or even on the stationary microstructure in driven systems. We present an atomic kinetic Monte Carlo (AKMC) method, which is able to tackle the atomic-scale couplings between PD diffusion, annihilation/creation reactions and the kinetics of decomposition of a solid solution into a two-phase microstructure. By introducing PD source-and-sinks (SAS) at specific lattice sites, we control the PD reactions and highlight the role of non-equilibrium quenched-in point defects on the evolution kinetics of short-range order parameters and subsequent second-phase precipitation. Then, we open the discussion on various kinetic phenomena that require taking into account the role of non-equilibrium PDs at different scales of time and space.

Excess point defects created by irradiation in metallic alloys diffuse and annihilate at sinks available in the microstructure, such as grain boundaries, dislocations, or point defect clusters. Fluxes of defects create fluxes of alloying elements, leading to local changes of composition near the sinks and to a modification of the properties of the materials. The direction and the amplitude of this radiation-induced segregation, its tendency to produce an enrichment or a depletion of solute, depend on a set of transport coefficients that are very difficult to measure experimentally. The understanding of radiation-induced segregation phenomena has, however, made significant progress in recent years, thanks to the modeling at different scales of diffusion and segregation mechanisms. We review here these different advances and try to identify the key scientific issues that limit the development of predictive models, applicable to real alloys. The review addresses three main issues: the calculation of the transport coefficients from ab initio calculations, the modeling of segregation kinetics at static point defects sinks—mainly by kinetic Monte Carlo or diffusion-reaction models—and the more challenging task of modeling the dynamic interplay between radiation-induced segregation and sink microstructure evolution, especially when this evolution results from annihilation of point defects. From this overview of the current state-of-the-art in this field, we discuss still-open questions and guidelines for what constitutes, in our opinion, the desirable future works on this topic.

We investigate phase stability and vacancy formation in fcc Fe-Ni alloys over a broad composition-temperature range, via a density functional theory parametrized effective interaction model, which includes explicitly spin and chemical variables. On-lattice Monte Carlo simulations based on this model are used to predict the temperature evolution of the magnetochemical phase. The experimental composition-dependent Curie and chemical order-disorder transition temperatures are successfully predicted. We point out a significant effect of chemical and magnetic orders on the magnetic and chemical transitions, respectively. The resulting phase diagram shows a magnetically driven phase separation around 10--40% Ni and 570--700 K, between ferromagnetic and paramagnetic solid solutions, in agreement with experimental observations. We compute vacancy formation magnetic free energy as a function of temperature and alloy composition. We identify opposite magnetic and chemical disordering effects on vacancy formation in the alloys with 50% and 75% Ni. We find that thermal magnetic effects on vacancy formation are much larger in concentrated Fe-Ni alloys than in fcc Fe and Ni due to a stronger magnetic interaction.

We study the thermodynamic properties of iron-chromium alloys in the framework of the Magnetic Cluster Expansion, a model of effective interactions explicitly taking into account the atomic magnetic moments. Monte Carlo simulations are used to study the magnetic properties and measure the mixing enthalpies of disordered solid solutions. The phase diagram of the Fe-Cr system is established by simulations performed in the canonical and semi-grand canonical ensembles, which require the relaxation of the chemical and magnetic configurations. The effect of magnetism on thermodynamic properties is highlighted via simulations with a fixed spin temperature, in order to impose specific magnetic states. We also propose a simple method to introduce the vibrational entropy in the framework of the Magnetic Cluster Expansion. These simulations allow us to estimate the respective weights of the chemical, magnetic and vibrational contributions and we conclude that they have all a significant effect on the thermodynamics of iron-chromium alloys.

The M4F project brings together the fusion and fission materials communities working on the prediction of radiation damage production and evolution and their effects on the mechanical behaviour of irradiated ferritic/martensitic (F/M) steels. It is a multidisciplinary project in which several different experimental and computational materials science tools are integrated to understand and model the complex phenomena associated with the formation and evolution of irradiation induced defects and their effects on the macroscopic behaviour of the target materials. In particular the project focuses on two specific aspects: (1) To develop physical understanding and predictive models of the origin and consequences of localised deformation under irradiation in F/M steels; (2) To develop good practices and possibly advance towards the definition of protocols for the use of ion irradiation as a tool to evaluate radiation effects on materials. Nineteen modelling codes across different scales are being used and developed and an experimental validation programme based on the examination of materials irradiated with neutrons and ions is being carried out. The project enters now its 4th year and is close to delivering high-quality results. This paper overviews the work performed so far within the project, highlighting its impact for fission and fusion materials science.

An accurate prediction of atomic diffusion in Fe alloys is challenging due to thermal magnetic excitations and magnetic transitions. We investigate the diffusion of Mn in bcc Fe using an effective interaction model and first-principles based spin-space averaged relaxations in magnetically disordered systems. The theoretical results are compared with the dedicated radiotracer measurements of Mn-54 diffusion in a wide temperature range of 773 to 1173 K, performed by combining the precision grinding (higher temperatures) and ion-beam sputtering (low temperatures) sectioning techniques. The temperature evolution of Mn diffusion coefficients in bcc iron in theory and experiment agree very well and consistently reveal a reduced acceleration of Mn solute diffusion around the Curie point. By analyzing the temperature dependencies of the ratio of Mn diffusion coefficients to self-diffusion coefficients we observe a dominance of magnetic disorder over chemical effects on high-temperature diffusion. Therefore, the missing acceleration mainly reflects an anomalous behavior of the Mn solute in the magnetically ordered low-temperature state of the Fe host, as compared to other transition metals.

An accurate prediction of atomic diffusion in Fe alloys is challenging due to thermal magnetic excitations and magnetic transitions. We propose an efficient approach to address these properties via a Monte Carlo simulation, using ab initio-based effective interaction models. The temperature evolution of self- and Cu diffusion coefficients in α-iron are successfully predicted, particularly the diffusion acceleration around the Curie point, which requires a quantum treatment of spins. We point out a dominance of magnetic disorder over chemical effects on diffusion in the very dilute systems.

We present a model of pair interactions on rigid lattice to study the thermodynamic properties of iron-nickel alloys. The pair interactions are fitted at 0 K on ab initio calculations of formation enthalpies of ordered and disordered (special quasirandom) structures. They are also systematically fitted on the Gibbs free energy of the gamma Fe-Ni solid solution as described in a CALPHAD (CALculation of PHAse Diagrams) study by Cacciamani et al. This allows the effects of finite temperature, especially those of magnetic transitions, to be accurately described. We show that the ab initio and CALPHAD data for the gamma solid solution and for the FeNi3-L1(2) ordered phase can be well reproduced, in a large domain of composition and temperature, using first and second neighbor pair interactions which depend on temperature and local alloy composition. The procedure makes it possible to distinguish and separately compare magnetic, chemical, and configuration enthalpies and entropies. We discuss the remaining differences between the pair interaction model and CALPHAD, which are mainly due to the treatment of the short-range order and configurational entropy of the solid solution. The FCC phase diagram of the Fe-Ni system is determined by Monte Carlo simulations in the semigrand canonical ensemble and is compared with experimental studies and other models. We especially discuss the stability of the FeNi-L1(0) phase at low temperature.

The evolution of point defect concentrations under irradiation is controlled by their diffusion properties, and by their formation and elimination mechanisms. The latter includes the mutual recombination of vacancies and interstitials, and the elimination of point defects at sinks. Two models are traditionally used to predict the defect concentration evolution, the standard rate theory (SRT) and the atomistic kinetic Monte Carlo (AKMC). We show in this work a large discrepancy in the defect concentrations between both methods when the average number of defects in the AKMC simulation box is close or lower than one. The reason is that AKMC naturally captures strong space and time correlations between vacancies and interstitials generated by the finite size of the periodic simulation box. These correlations strongly affect the recombination rate and the point defect concentrations. SRT fails to predict such correlations, and the corresponding solution deviates from the more accurate solution given by the AKMC simulation under similar conditions. These finite size correlation effects are strong when the elimination of point defects occurs by recombination only, but can still be significant in the presence of sinks. In order to account for the spacio-temporal correlation in a continuum framework, we introduce a Correlated Pair Theory (CPT). This theory fully takes into account the correlations between vacancy and interstitial pairs and predicts point defect concentrations in good agreement with AKMC simulations. Inversely, if the goal is for the AKMC to reproduce defect concentrations in bulk using small simulation boxes, the naturally occurring correlations need to be corrected. We show here that the CPT can be used to modify the elimination rates in the AKMC simulations, so as to yield point defect concentrations in agreement with SRT.

We report a theoretical study of microstructure, magnetic properties, and their relationship in relatively concentrated Fe-Cr alloys in both Fe- and Cr-rich regions. Annealing of initially random systems at 500 degrees C for times of the order of 10 6 s substantially changes their microstructure. In both systems, solute atoms form clusters with their sizes increasing with time according to power law, with exponent being close to 0.2. For the Fe -32 at. % Cr alloy, magnetization and the Curie temperature increase with increasing annealing time and cluster size. At large simulation times, the Curie temperature approaches its value for Fe -15 at. % Cr, the concentration of completely phase -separated iron -rich alloy. For the Cr-25 at. % Fe alloy, precipitation also results in an increase of magnetization and the Curie temperature, although characteristic times are about one order of magnitude greater.

The diffusion of C in FeCr solid solutions is modelled and compared to experimental data. A set of binding energies and migration barriers for C diffusion in different local chemical environments are first calculated using density functional theory. A pair interaction model is developed in order to reproduce these data and predict the migration barriers in other environments. The diffusion model is then implemented in a kinetic Monte Carlo method to simulate tracer diffusion experiments, using a standard procedure, and internal friction experiments, using a novel method. Simulations of internal friction show a unique Snoek peak in the whole concentration range, between pure iron and pure chromium. The average migration barrier for C diffusion in FeCr alloys is found to increase progressively with the Cr concentration, with a small rate below 6 %Cr. In Cr-rich alloys, the effective migration barrier for C diffusion is found to be larger in tracer diffusion than in the internal friction simulations. We conclude that the effective migration barrier extracted from tracer diffusion is closely related to trapping effects of C atoms in Fe-rich local environments, whereas the migration barrier associated with internal friction is mainly controlled by the migration barriers of the most probable configurations, as it is clearly shown in the Cr-rich domain.