Isochronal annealing of electron-irradiated dilute Fe alloys modelled by an ab initio based AKMC method: Influence of solute-interstitial cluster properties

The evolution of the microstructure of dilute Fe alloys under irradiation has been modelled using a multiscale approach based on ab initio and atomistic kinetic Monte Carlo simulations. In these simulations, both self interstitials and vacancies, isolated or in clusters, are considered. Isochronal annealing after electron irradiation experiments have been simulated in pure Fe, Fe-Cu and Fe-Mn dilute alloys, focusing on recovery stages I and II. The parameters regarding the self interstitial - solute atom interactions are based on ab initio predictions and some of these interactions have been slightly adjusted, without modifying the interaction character, on isochronal annealing experimental data. The different recovery peaks are globally well reproduced. These simulations allow interpreting the different recovery peaks as well as the effect of varying solute concentration. For some peaks, these simulations have allowed to revisit and re-interpret the experimental data. In Fe-Cu, the trapping of self interstitials by Cu atoms allows experimental results to be reproduced, although no mixed dumbbells are formed, contrary to the former interpretations. Whereas, in Fe-Mn, the favorable formation of mixed dumbbell plays an important role in the Mn effect.     

An object Kinetic Monte Carlo Simulation of the dynamics of helium and point defects in tungsten

In the near surface of plasma facing materials, high concentrations of hydrogen and helium isotopes can build up, which will interact with the point defects resulting from the bombardment of the surface as well as with the impurities of the materials. It is important to develop an understanding of the evolution of W microstructure in such conditions and to be able to model this evolution. The task is very complex, as many elements have to be included in the model which must be all parameterized correctly. Isochronal annealings experiments are simple experiments which can help in the making of more complicated models. In this work, an object Kinetic Monte Carlo technique parameterized on ab initio calculations as been used to model He desorption in W. The He atoms and the self interstitial atoms have been found to be very mobile but they can bind quite strongly with impurities such as carbon or molybdenum atoms. The evolution of the number of defects in the Kinetic Monte Carlo simulation was found to be in good agreement with the resistivity changes observed during an He desorption experiment of above threshold He implantation in a thin wire of tungsten.     

Stability and mobility of Cu-vacancy clusters in Fe-Cu alloys: A computational study based on the use of artificial neural networks for energy barrier calculations

An atomistic kinetic Monte Carlo (AKMC) method has been applied to study the stability and mobility of copper-vacancy clusters in Fe. This information, which cannot be obtained directly from experimental measurements, is needed to parameterise models describing the nanostructure evolution under irradiation of Fe alloys (e.g. model alloys for reactor pressure vessel steels). The physical reliability of the AKMC method has been improved by employing artificial intelligence techniques for the regression of the activation energies required by the model as input. These energies are calculated allowing for the effects of local chemistry and relaxation, using an interatomic potential fitted to reproduce them as accurately as possible and the nudged-elastic-band method. The model validation was based on comparison with available ab initio calculations for verification of the used cohesive model, as well as with other models and theories.     

Simulation of radiation damages in molybdenum by combining molecular dynamics and OKMC

In this paper,radiation defects in bcc molybdenum with the primary knock-on atom(PKA) energies of2-40 keV are simulated by the molecular dynamics.The binding energy of single point defect-to-defect clusters increases with the cluster size.The stabiUty and mobility of point defects and defect clusters are analyzed.The interstitial-type clusters are found to be easily migrating along the 111 direction with low barriers(0.01-0.10 eV).Then,the object kinetic Monte Carlo is used to gain insight into the long-term defect evolution in the cascade.The simulation results indicate that Stage I almost occurs at annealing temperature of 100K,which corresponds to the correlated recombination resulting from the motion of small interstitial clusters(n ≤2).The formation of substage partly as result of the small vacancy clusters motion.At about 460 K,the Stage II starts because of uncorrected recombination due to an emitting mechanism of larger clusters.Size distribution of the clusters at the cascade quenching stage is positively correlated with the PKA energies,affecting notably the subsequent annealing process.     

Ab initio calculations of self-interstitial interaction and migration with solute atoms in bcc Fe

The embrittlement of pressure vessel steels under radiation has been long ago correlated with the presence of solute Cu. Indeed the atom probe and the small angle neutron scattering, principally, have revealed the formation of Cu clusters under neutron flux in reactor pressure vessel (RPV) steels and dilute FeCu alloys. Other solutes such as Ni, Mn and Si which are also found within the clusters, are now suspected to contribute to the embrittlement. The interactions of these solutes with radiation induced point defects need thus to be characterized properly in order to understand the elementary mechanisms behind the formation of these clusters. We have investigated by ab initio calculations based on the density functional theory the interactions of self-interstitials with solute atoms in dilute FeX alloys (X = Cu, Mn, Ni or Si). Different possible configurations of solute-dumbbell complexes have been studied. Their binding energies are discussed, as well as their relative stability. The migration of dumbbells with a solute atom in their vicinity was also investigated. All these results are compared to some experimental ones obtained on dilute FeX model alloys. Our results indicate that for Mn solute atoms, diffusion via an interstitial mechanism is very likely.     

MD and OKMC simulations of the displacement cascades in nickel

The molecular dynamics(MD) method was used to investigate the displacement cascades with primary knock-on atom(PKA) energies of 2-40 keV at 100 and600 K.The migration energy of defects and their clusters was calculated by nudged elastic band(NEB) method.Object kinetic Monte Carlo(OKMC) was used to simulate the evolution of defects in Ni under annealing.In each annealing stage,the recombination mechanism was discussed and evolution of the defects under different cascade conditions was compared.It was found that the defects generated in high-temperature cascades are more stable than those in the low-temperature cascades.In addition,almost all the defects are annihilated during annealing process at low PKA energy.At PKA energy of 20-40 keV,however,a large number of defects would remain after annealing.     

Kinetic Monte Carlo simulations of radiation induced segregation and precipitation

Kinetics of radiation induced segregation and precipitation in binary alloys are studied by Monte Carlo simulations. The simulations are based on a simple atomic model of diffusion under electron irradiation, which takes into account the creation of point defects, the recombination of close vacancy-interstitial pairs and the point defect annihilation at sinks. They can reproduce the coupling between point defect fluxes towards sinks and atomic fluxes, which controls the segregation tendency. In pure metals and ideal solid solutions, the Monte Carlo results are found to be in very good agreement with classical models based on rate equations. In alloys with an unmixing tendency, we show how the interaction between the point defect distribution, the solute segregation and the precipitation driving force can generate complex microstructural evolutions, which depend on the very details of atomic-scale diffusion properties.     

The effect of Cr concentration on radiation damage in Fe-Cr alloys

Displacement cascades in Fe-Cr alloys were studied using molecular dynamics computer simulations. We considered random Fe-5Cr and Fe-15Cr alloys, as well as Fe-10Cr alloys with and without Cr-rich precipitates. In the simulations two versions of a two-band embedded atom method potential were used, and the cascades were induced by recoils with energies up to 20 keV. We found that the average number of surviving Frenkel pairs and the fraction of vacancies and self-interstitials in clusters was approximately the same in pure Fe and random Fe-Cr alloys (regardless of Cr concentration). A noticeable effect of the presence of Cr in the Fe matrix was only observed in the enrichment of self-interstitials by Cr in Fe-5Cr. The calculated change in the short range order parameter showed that Fe-5Cr tends towards ordering (negative short range order parameter) and Fe-15Cr towards segregation (positive short range order parameter) of Cr atoms. In simulations with the Cr-rich precipitate, enhanced cascade splitting and segregation of self-interstitial defects created inside the precipitates towards the precipitate-matrix interface region was observed. The number of Frenkel pairs and their clustered fraction was not affected by the presence of the precipitate.     

Kinetic Monte Carlo model of defect transport and irradiation effects in La-doped CeO2

A generalized Kinetic Monte Carlo code was developed to study oxygen mobility in UO₂ type nuclear fuels, using lanthanum doped CeO₂ as a surrogate material. Molecular Statics simulations were performed using interatomic potentials for CeO₂ developed by Gotte, Minervini, and Sayle to calculate local configuration-dependent oxygen vacancy migration energies. Kinetic Monte Carlo simulations of oxygen vacancy diffusion were performed at varying lanthanum dopant concentrations using the developed generalized Kinetic Monte Carlo code and the calculated configuration-dependent migration energies. All three interatomic potentials were found to confirm the lanthanum trapping effect. The results of these simulations were compared with experimental data and the Gotte potential was concluded to yield the most realistic diffusivity curve.     

Effects of solute atoms on evolution of vacancy defects in electron-irradiated Fe-Cr-based alloys

The evolution of vacancy-type defects in Fe-Cr alloys (13-16 at.% Cr) undoped and doped with C, N, Au, or Sb and in conventional ferritic-martensitic steel (∼13% Cr) has been investigated using positron annihilation spectroscopy under electron irradiation at room temperature and subsequent stepwise annealing. Small vacancy clusters are formed in the undoped Fe-16Cr alloy, which anneal out between 320 and 550 K. It is shown that oversized substitutional solute atoms (Sb, Au) in the Fe-Cr alloy interact with vacancies and form complexes, which are stable up to 600 and 420 K, respectively. It is found that the accumulation of vacancy defects considerably increases in the alloys and the steel with an enhanced content of interstitial impurities. It is shown that this effect is related to the formation of vacancy-carbon complexes. It is known that chromium in iron decreases the diffusion mobility of carbon. Therefore, the structure of vacancy-carbon complexes and the kinetics of their annealing in Fe-Cr alloys differ from those in the Fe-C system.     

Formation energy of vacancies in FeCr alloys: Dependence on Cr concentration

A modified version of the concentration-dependent model (CDM) potential (A. Caro et al., Phys. Rev. Lett. 95 (2005) 075702) [1] has been developed to study defects in Fe-Cr for different Cr concentrations. A comparison between this new potential and DFT results for a variety of point defect configurations is performed in order to test its reliability for radiation damage studies. The effect of Cr concentration on the vacancy formation energy in Fe-Cr alloys is analyzed in detail. This study shows a linear dependence of the vacancy formation energy on Cr concentration for values above 6% of Cr. However, the formation energy deviates from the linear interpolation in the region below 6% Cr concentration. In order to understand this behavior, the influence of the relative positions between Cr atoms and vacant sites on the vacancy formation energy has been studied.     

Irradiation induced clustering in low copper or copper free ferritic model alloys

In order to determine the formation mechanism of solute cluster in ferritic steels under irradiation, Cu and Cu free ferritic model alloys (FeCuMnNiP and FeMnNiP) were irradiated with electrons and ions. Their microstructures were characterized by atom probe tomography and the evolution of the population of point defects was estimated with a model of cluster dynamic. The comparison between experimental results and predictions of the model suggests that the formation of the solute clusters is heterogeneous, on the point defect clusters. The comparison between the experimental results obtained on these two alloys shows that the absence of copper slows down the kinetics of precipitation. Moreover, by comparing the results obtained on the FeCuMnNiP alloy with previous results obtained on binary alloy FeCu, it appears that the presence of manganese, nickel and/or phosphorus slows down the kinetics of precipitation. Finally, the comparison between this study and results obtained by other authors on similar alloys irradiated with neutrons reveals a strong flux effect on the kinetic of precipitation of solute clusters.     

The microstructure of neutron-irradiated Fe-Cr alloys: A small-angle neutron scattering study

The effect of Cr on the irradiation-induced microstructure of neutron-irradiated Fe-Cr alloys is not yet known in detail. Small-angle neutron scattering was applied in order to provide the characteristics of nm-sized defects averaged over macroscopic volumes. Results are reported for a set of Fe-Cr alloys of Cr levels of 2.5, 5, 9 and 12.5 at.%, irradiated at 300 °C up to neutron exposures of 0.6 and 1.5 dpa. We have found that the incoherent magnetic scattering of the unirradiated alloys exhibits a systematic variation with the Cr content and that there is an irradiation-induced increase of the coherent magnetic scattering for each of the irradiated conditions. The effect of Cr on size and type of irradiation-induced scatterers is discussed. For 12.5 at.%Cr, the scatterers are unambiguously identified as α′ particles. For 2.5 and 5 at.%Cr, the scatterers are tentatively interpreted as clusters enriched with alloying Cr and impurity C. For 9 at.%Cr, a mixture of both kinds of scatterers explains the experimental findings.     

Modelling radiation-induced phase changes in binary FeCu and ternary FeCuNi alloys using an artificial intelligence-based atomistic kinetic Monte Carlo approach

We apply a novel atomistic kinetic Monte Carlo model, which includes local chemistry and relaxation effects when assessing the migration energy barriers of point defects, to the study of the microchemical evolution driven by vacancy diffusion in FeCu and FeCuNi alloys. These alloys are of importance for nuclear applications because Cu precipitation, enhanced by the presence of Ni, is one of the main causes of hardening and embrittlement in reactor pressure vessel steels used in existing nuclear power plants. Local chemistry and relaxation effects are introduced using artificial intelligence techniques, namely a conveniently trained artificial neural network, to calculate the migration energy barriers of vacancies as functions of the local atomic configuration. We prove, through a number of results, that the use of the neural network is fully equivalent to calculating the migration energy barriers on-the-fly, using computationally expensive methods such as nudged elastic bands with an interatomic potential. The use of the neural network makes the computational cost affordable, so that simulations of the same type as those hitherto carried out using heuristic formulas for the assessment of the energy barriers can now be performed, at the same computational cost, using more rigorously calculated barriers. This method opens the way to properly treating more complex problems, such as the case of self-interstitial cluster formation, in an atomistic kinetic Monte Carlo framework.     

Overview of the RPV-2 and INTERN-1 packages: From primary damage to microplasticity

In the framework of the European project PERFECT, four multiscale simulation packages dedicated to the prediction of evolution of material properties were developed. Among them, the RPV-2 and INTERN-1 are two simulation sequences of similar structure dealing with radiation damage in the reactor pressure vessel and the reactor internal structures, respectively. Both start at the atomic scale, where the neutron spectrum of the specified reactor is used to determine the energy distribution of the primary knocked-on atoms (PKA). A database of molecular dynamics results is then used to integrate the instantaneous production of defect clusters resulting from the displacement cascades initiated by each PKA. Depending on the type of calculation chosen to model long-term diffusion and reactions of defect clusters, precipitates and mixed-clusters, this primary damage enters either in rate equations or in Object Kinetic Monte Carlo simulations. The later correspond to a more accurate (but also more computationally demanding) physical model for diffusion as positions of objects on a lattice are explicitly treated. Finally, the increase of critical resolved shear stress is estimated from these cluster distributions either using an analytical model, taking into account the self and mutual dipole interactions of dislocations pinned on randomly dispersed unshearable obstacles, or by simulating the glide of a single dislocation line in its main slip system. Dislocation dynamics simulations were already used to validate some of the assumptions of the latter models, and will be fully integrated in the next versions of the packages.     

FeCr合金中Cr含量对微观结构影响的原子尺度模拟研究

低温辐照脆化是影响铁素体/马氏体（F/M）钢服役的主要问题之一。F/M钢低温辐照脆化的主要机理是辐照产生的纳米缺陷（如位错环、α′相(富Cr团簇)等）阻碍位错运动。本文利用分子动力学方法和迈氏蒙特卡罗方法对F/M钢模型材料--FeCr合金（Fe7%Cr、Fe9%Cr、Fe14%Cr）中Cr元素析出成团簇及在位错环上偏析的机理进行研究，并分析Cr团簇析出与合金成分的关系以及位错环尺寸、位错环类型和合金中Cr含量对位错环上Cr偏析量的影响。模拟结果表明：热力学模拟后，高Cr含量（>9%)的FeCr合金中会析出Cr团簇，且基体内Cr含量越高，析出的Cr团簇尺寸越大；在所研究的3种FeCr合金中，受位错环张应力场作用，合金元素Cr均会在位错环的外围偏析，且FeCr合金中Cr含量越高，Cr在位错环上偏析量越高。低Cr的FeCr合金中Cr对其辐照硬化的影响需考虑位错环上Cr偏析的影响，高Cr的FeCr合金中Cr元素对其辐照硬化的影响需综合考虑Cr团簇及位错环上Cr偏析。     

Structure, energetics and thermodynamics of copper-vacancy clusters in bcc-Fe: An atomistic study

A combination of on-lattice simulated annealing based on Metropolis Monte Carlo simulations and off-lattice relaxation by Molecular Dynamics is applied in order to determine the structure and energetics of coherent copper-vacancy clusters in bcc-Fe. The most recent interatomic potential for Fe-Cu alloys is used. About 150 clusters consisting of up to 200 monomers (vacancies or copper atoms) are investigated. The atomic structure and the formation energy of the most stable configurations as well as their total and monomer binding energy are calculated. All clusters show facets which correspond to the main crystallographic planes. In the case of mixed clusters a core-shell structure is found where Cu atoms coat the outer surface of vacancy clusters. These findings are in agreement with previous theoretical results and with indications from measurements. For small clusters the total binding energy determined in this work shows a good agreement with literature data obtained by first-principle calculations. For further application in rate theory and object kinetic Monte Carlo simulations compact and physically-based fit formulae are derived from the atomistic data for the total and the monomer binding energy. The fit is based on the classical capillary model and the core-shell structure of the mixed clusters is explicitly taken into account. An atomistic nucleation model is established, and for typical irradiation conditions the nucleation free energy of pure vacancy and pure copper clusters as well as the critical size for cluster formation are estimated.