Object Kinetic Monte Carlo Model Research Articles

Readdressing nanocavity diffusion in tungsten

In nuclear fusion (ITER and the future DEMO), those components that face the plasma are exposed to high temperature and irradiation which, in the long term, modifies their thermal and mechanical properties and tritium retention. Tungsten is a candidate material and is the subject of many studies of microstructure evolution under various irradiation and temperature conditions. One milestone is the characterization of its defect properties. We here readdress the diffusion of nanocavities on broad ranges of size and temperature and compare it with dissociation, a competing process during nanocavity growth. First, at the atomic scale, we used molecular dynamics to explore the variety of elementary events involved in the nanocavity diffusion. Second, an experimental study of ion-irradiated samples, annealed at different temperatures up to 1,773 K, revealed the creation and growth of nanocavities on transmission electron microscopy images. Third, we performed multi-objective optimization of the nanocavity diffusion input of our object kinetic Monte Carlo model to reproduce the experimental results. Finally, we applied a sensitivity analysis of the main inputs of our model developed for these particular conditions—the source term which combines two cascade databases and the impurities whose interaction with the defects is characterised with a supplemented database of density functional theory calculations. Three domains of nanocavity size were observed. The first is the small vacancy clusters, for which atomistic calculations are possible and dissociation is negligible. The second is the small nanocavities, for which we provide new diffusion data and where a competition with the dissociation can take place. The third domain is the large nanocavities, for which, in any case, the dissociation prevents their existence above 1,500 K in the absence of a stabilizing interface.

Modelling of zirconium growth under irradiation and annealing conditions

Modelling zirconium growth under irradiation is a difficult task due to the different types of defects formed which all contribute to the macroscopic deformation. An Object Kinetic Monte Carlo model parameterized using state-of-the-art atomic-scale calculations and experimental data is presented. It is able to reproduce a good macroscopic deformation, the coexistence of all types of defects: 〈a〉 interstitial and vacancy loops, 〈c〉 vacancy loops and the alignments of 〈a〉 loops parallel to the basal plane. A large parametric study is performed in order to understand thoroughly in which conditions these microstructural features can be observed. The model is then applied to study flux effects and the microstructure evolution during annealing. It can be concluded that 〈a〉 loop alignments are phenomena which are very sensitive to the flux. During annealing, the defects can recover in a non-monotonous way and 〈a〉 loops inside the alignments disappear at last, which illustrates their strong stability.

Implantation and desorption of H isotopes in W revisited by object kinetic Monte Carlo simulation

As the leading candidate of plasma-facing materials, tungsten is expected to withstand the influx of D-T plasma in future fusion reactors, which is known to cause damages to tungsten surface and give rise to T fuel retention. In this work, based on accurate density functional theory parameterization, we carried out a series of object kinetic Monte Carlo (OKMC) simulations to study the retention behavior of H isotopes in W. By directly comparing our simulations with existing experiments, we show that the OKMC model can accurately describe H implantation and desorption behavior in W, with excellent agreements found between experimental/simulated H annealing curves, thermal desorption spectra, and fluence dependence. Our OKMC model reveals primary trapping sites of H in these experiments, provides deeper understanding for experimental results, and offers quantitative theoretical assessment for H implantation and desorption in W.

Vacancy-solute clustering in Fe–Cr alloys after neutron irradiation

Vacancy-solute clustering in neutron irradiated Fe–Cr alloys with various concentrations of Cr and minor solutes (Ni, Si and P) were studied by using coincidence Doppler broadening spectroscopy and small angle neutron scattering techniques. The results from both experiments, supported by an object kinetic Monte Carlo model, show in a very consistent way the existence and formation of vacancy-CrNiSiP clusters that play detrimental role in irradiation hardening. Similar solute cluster number density of about 30–50 ×1016cm−3 and an average diameter of about 1 nm were estimated for all alloys containing minor solutes, irrespectively of the chromium content. In Fe9Cr ferritic and Fe9Cr ferritic/martensitic alloys, with significantly reduced concentration of minor solute elements, the main defects are vacancy clusters, with an average cluster size of about 10 and 2 vacancies, respectively. Large concentration of α’-precipitates was observed in Fe14Cr(NiSiP). However, both vacancy clusters and α’-precipitates provide significantly less impact to hardening in comparison to vacancy-CrNiSiP clusters. The fact that vacancy clustering in Fe9Cr ferritic alloy resembles that of pure iron suggests that Cr solutes may play lesser role in irradiation hardening of ferritic alloys and steels than previously believed.

A coupled rate theory-Monte Carlo model of helium bubble evolution in plasma-facing micro-engineered tungsten

A multiscale model of helium bubble evolution in plasma-facing materials is developed. The model links different stages of helium bubble evolution: deposition, nucleation, growth, motion, and coalescence. Helium deposition is simulated with the SRIM Monte Carlo program to give spatial information on helium and displacement damage distributions near the surface. This deposition profile is then introduced into a space-dependent rate theory of bubble nucleation and growth to describe the early stages of the distribution and size of helium bubbles. The coarsening stage of bubble evolution as a result of whole bubble motion, interaction, and coalescence is modeled by a new Object Kinetic Monte Carlo (OKMC) model, for which initial conditions are taken from the mean-field rate theory calculations. The model is compared to experimental data on low-energy helium plasma interaction with micro-engineered tungsten (W), and on high-energy helium ion deposition in flat W samples. Novel features of the multiscale model include: (1) space-dependent rate theory; (2) OKMC model of bubble motion in stress and temperature fields; and (3) application of the model to micro-engineered materials, and comparison with experiments on the same time-scale. At low helium ion energy, it is found that the mechanism of trap mutation is essential in achieving good agreement with experimental measurements. On the other hand, good agreement with experiments at high incident ion energy and temperature showed the importance of bubble coalescence and coarsening as main mechanisms. The results of the model are compared with experiments on flat W surfaces irradiated at high ion energy (30 keV), and with micro-engineered W, where the surface is coated with high-density micro-pillars at low ion energy (around 100 eV). The predicted average bubble radius and density are in qualitative agreement with experimental results.

Object kinetic Monte Carlo model for neutron and ion irradiation in tungsten: Impact of transmutation and carbon impurities

We upgrade our object kinetic Monte Carlo (OKMC) model, aimed at describing the microstructural evolution in tungsten (W) under neutron and ion irradiation. Two main improvements are proposed based on recently published atomistic data: (a) interstitial carbon impurities, and their interaction with radiation-induced defects (point defect clusters and loops), are more accurately parameterized thanks to ab initio findings; (b) W transmutation to rhenium (Re) upon neutron irradiation, impacting the diffusivity of radiation defects, is included, also relying on recent atomistic data. These essential amendments highly improve the portability of our OKMC model, providing a description for the formation of SIA-type loops under different irradiation conditions. The model is applied to simulate neutron and ion irradiation in pure W samples, in a wide range of fluxes and temperatures. We demonstrate that it performs a realistic prediction of the population of TEM-visible voids and loops, as compared to experimental evidence. The impact of the transmutation of W to Re, and of carbon trapping, is assessed.

Kinetic Monte Carlo simulation of phase-precipitation versus instability behavior in short period FeCr superlattices

The structural evolution of FeCr superlattices has been studied using a quasi-atomistic Object Kinetic Monte Carlo model. Superlattices with different spatial periods have been simulated for anneal durations from few hours to several months at 500°C. Relatively-long period superlattices stabilize into Fe-rich and Cr-rich layers with compositions close to those of bulk α and α′ phases. In contrast, superlattices with very short periods (4, 5, 6nm) are observed to undergo instability and, for long annealing times, evolve into three-dimensionally decomposed regions, in qualitative agreement to recent experimental observations. The instability onset is delayed as the spatial period increases, and it occurs via interface roughness. This evolution can be explained as a minimization of the free-energy associated to the α/α′ interfaces. A comprehensive description of the evolution dynamics of FeCr-based structures is obtained with our model.

Nanostructure evolution of neutron-irradiated reactor pressure vessel steels: Revised Object kinetic Monte Carlo model

This work presents a revised set of parameters to be used in an Object kinetic Monte Carlo model to simulate the microstructure evolution under neutron irradiation of reactor pressure vessel steels at the operational temperature of light water reactors (∼300°C). Within a “grey-alloy” approach, a more physical description than in a previous work is used to translate the effect of Mn and Ni solute atoms on the defect cluster diffusivity reduction. The slowing down of self-interstitial clusters, due to the interaction between solutes and crowdions in Fe is now parameterized using binding energies from the latest DFT calculations and the solute concentration in the matrix from atom-probe experiments. The mobility of vacancy clusters in the presence of Mn and Ni solute atoms was also modified on the basis of recent DFT results, thereby removing some previous approximations.The same set of parameters was seen to predict the correct microstructure evolution for two different types of alloys, under very different irradiation conditions: an Fe-C-MnNi model alloy, neutron irradiated at a relatively high flux, and a high-Mn, high-Ni RPV steel from the Swedish Ringhals reactor surveillance program. In both cases, the predicted self-interstitial loop density matches the experimental solute cluster density, further corroborating the surmise that the MnNi-rich nanofeatures form by solute enrichment of immobilized small interstitial loops, which are invisible to the electron microscope.

An object kinetic Monte Carlo model for the microstructure evolution of neutron‐irradiated reactor pressure vessel steels

This work presents a full object kinetic Monte Carlo framework for the simulation of the microstructure evolution of reactor pressure vessel (RPV) steels. The model pursues a “gray‐alloy” approach, where the effect of solute atoms is seen exclusively as a reduction of the mobility of defect clusters. The same set of parameters yields a satisfactory evolution for two different types of alloys, in very different irradiation conditions: an Fe–C–MnNi model alloy (high flux) and a high‐Mn, high‐Ni RPV steel (low flux). A satisfactory match with the experimental characterizations is obtained only if assuming a substantial immobilization of vacancy clusters due to solute atoms, which is here verified by means of independent atomistic kinetic Monte Carlo simulations. The microstructure evolution of the two alloys is strongly affected by the dose rate; a predominance of single defects and small defect clusters is observed at low dose rates, whereas larger defect clusters appear at high dose rates. In both cases, the predicted density of interstitial loops matches the experimental solute‐cluster density, suggesting that the MnNi‐rich nanofeatures might form as a consequence of solute enrichment on immobilized small interstitial loops, which are invisible to the electron microscope.

Simulation of nanostructural evolution under irradiation in Fe-9%Cr[sbnd]C alloys: An object kinetic Monte Carlo study of the effect of temperature and dose-rate

This work explores the effects of both temperature and dose-rate on the nanostructural evolution under irradiation of the Fe-9%CrC alloy, model material for high-Cr ferritic/martensitic steels. Starting from an object kinetic Monte Carlo model validated at 563K, we investigate here the accumulation of radiation damage as a function of temperature and dose-rate, attempting to highlight its connection with low-temperature radiation-induced hardening. The results show that the defect cluster mobility becomes high enough to partially counteract the material hardening process only above ∼290°C, while high fluxes are responsible for higher densities of defects, so that an increase of the hardening process with increasing dose-rates may be expected.

Primary damage in tungsten using the binary collision approximation, molecular dynamic simulations and the density functional theory

The damage produced by primary knock-on atoms (PKA) in W has been investigated from the threshold displacement energy (TDE) where it produces one self interstitial atom–vacancy pair to larger energies, up to 100 keV, where a large molten volume is formed. The TDE has been determined in different crystal directions using the Born–Oppenheimer density functional molecular dynamics (DFT-MD). A significant difference has been observed without and with the semi-core electrons. Classical MD has been used with two different empirical potentials characterized as ‘soft’ and ‘hard’ to obtain statistics on TDEs. Cascades of larger energy have been calculated, with these potentials, using a model that accounts for electronic losses (Sand et al 2013 Europhys. Lett. 103 46003). Two other sets of cascades have been produced using the binary collision approximation (BCA): a Monte Carlo BCA using SDTrimSP (Eckstein et al 2011 SDTrimSP: Version 5.00. Report IPP 12/8) (similar to SRIM www.srim.org) and MARLOWE (RSICC Home Page. (https://rsicc.ornl.gov/codes/psr/psr1/psr-137.html) (accessed May, 2014)). The comparison of these sets of cascades gave a recombination distance equal to 12 Å which is significantly larger from the one we reported in Hou et al (2010 J. Nucl. Mater. 403 89) because, here, we used bulk cascades rather than surface cascades which produce more defects (Stoller 2002 J. Nucl. Mater. 307 935, Nordlund et al 1999 Nature 398 49). Investigations on the defect clustering aspect showed that the difference between BCA and MD cascades is considerably reduced after the annealing of the cascade debris at 473 K using our Object Kinetic Monte Carlo model, LAKIMOCA (Domain et al 2004 J. Nucl. Mater. 335 121).

Effect of Cr content on the nanostructural evolution of irradiated ferritic/martensitic alloys: An object kinetic Monte Carlo model

Self-interstitial cluster diffusivity in Fe–Cr alloys, model materials for high-Cr ferritic/martensitic steels, is known to be reduced in a non-monotonic way as a function of Cr concentration: it first decreases, then increases. This non-monotonic behaviour is caused by a relatively long-ranged attractive interaction between Cr atoms and crowdions and correlates well with the experimentally observed swelling in these alloys under neutron irradiation, also seen to first decrease and then increase with increasing Cr content, under comparable irradiation conditions. Moreover, recent studies reveal that C atoms dispersed in the Fe matrix form under irradiation complexes with vacancies which, in turn, act as trap for one-dimensionally migrating self-interstitial clusters. The mobility of one-dimensional migrating clusters is considered key to determine swelling susceptibility. However, no model has ever been built that quantitatively describes the dependence of swelling on Cr content, allowing for the presence of C in the matrix. In this work we developed physically-based sets of parameters for object kinetic Monte Carlo (OKMC) simulations intended to study the nanostructure evolution under irradiation in Fe–Cr–C alloys. The nanostructural evolution in Fe–C and in four Fe–Cr–C alloys (containing 2.5, 5, 9 and 12 wt.% Cr) neutron irradiated up to ∼0.6 dpa at 563 K was simulated according to the model and reference experiments were reproduced. Our model shows that the SIA cluster reduced mobility has a major influence on the nanostructural evolution: it increases the number of vacancy-SIA recombinations and thus leads to the suppression of voids formation. This provides a clear framework to interpret the non-monotonic dependence of swelling in Fe–Cr alloys versus Cr content. Our model also suggests that the amount of C in the matrix has an equally important role: high amounts of it may counteract the beneficial effect that Cr has in reducing swelling.

Nanostructure evolution under irradiation in FeMnNi alloys: A “grey alloy” object kinetic Monte Carlo model

This work extends the object kinetic Monte Carlo model for neutron irradiation-induced nanostructure evolution in Fe–C binary alloys developed in [1], introducing the effects of substitutional solutes like Mn and Ni. The objective is to develop a model able to describe the nanostructural evolution of both vacancy and self-interstitial atom (SIA) defect cluster populations in Fe(C)MnNi neutron-irradiated model alloys at the operational temperature of light water reactors (∼300°C), by simulating specific reference irradiation experiments. To do this, the effects of the substitutional solutes of interest are introduced, under simplifying assumptions, using a “grey alloy” scheme. Mn and Ni solute atoms are not explicitly introduced in the model, which therefore cannot describe their redistribution under irradiation, but their effect is introduced by modifying the parameters that govern the mobility of both SIA and vacancy clusters. In particular, the reduction of the mobility of point-defect clusters as a consequence of the presence of solutes proved to be key to explain the experimentally observed disappearance of detectable defect clusters with increasing solute content. Solute concentration is explicitly taken into account in the model as a variable determining the slowing down of self-interstitial clusters; small vacancy clusters, on the other hand, are assumed to be significantly slowed down by the presence of solutes, while for clusters bigger than 10 vacancies their complete immobility is postulated. The model, which is fully based on physical considerations and only uses a few parameters for calibration, is found to be capable of reproducing the experimental trends in terms of density and size distribution of the irradiation-induced defect populations with dose, as compared to the reference experiment, thereby providing insight into the physical mechanisms that influence the nanostructural evolution undergone by this material during irradiation.

Nanostructure evolution under irradiation of Fe(C)MnNi model alloys for reactor pressure vessel steels

Radiation-induced embrittlement of bainitic steels is one of the most important lifetime limiting factors of existing nuclear light water reactor pressure vessels. The primary mechanism of embrittlement is the obstruction of dislocation motion produced by nanometric defect structures that develop in the bulk of the material due to irradiation. The development of models that describe, based on physical mechanisms, the nanostructural changes in these types of materials due to neutron irradiation are expected to help to better understand which features are mainly responsible for embrittlement. The chemical elements that are thought to influence most the response under irradiation of low-Cu RPV steels, especially at high fluence, are Ni and Mn, hence there is an interest in modelling the nanostructure evolution in irradiated FeMnNi alloys. As a first step in this direction, we developed sets of parameters for object kinetic Monte Carlo (OKMC) simulations that allow this to be done, under simplifying assumptions, using a “grey alloy” approach that extends the already existing OKMC model for neutron irradiated Fe–C binary alloys [1]. Our model proved to be able to describe the trend in the buildup of irradiation defect populations at the operational temperature of LWR (∼300°C), in terms of both density and size distribution of the defect cluster populations, in FeMnNi model alloys as compared to Fe–C. In particular, the reduction of the mobility of point-defect clusters as a consequence of the presence of solutes proves to be key to explain the experimentally observed disappearance of detectable point-defect clusters with increasing solute content.

The nanostructure evolution in Fe–C systems under irradiation at 560 K

This work extends our Object Kinetic Monte Carlo model for neutron irradiation-induced nanostructure evolution in Fe–C alloys to consider higher irradiation temperatures. The previous study concentrated on irradiation temperatures <370K. Here we study the evolution of vacancy and self-interstitial atom (SIA) cluster populations at the operational temperature of light water reactors, by simulating specific reference irradiation experiments.Following our previous study, the effect of carbon on radiation defect evolution can be described in terms of formation of immobile complexes with vacancies, that in turn act as traps for SIA clusters. This dynamics is simulated using generic traps for SIA and vacancy clusters. The traps have a binding energy that depends on the size and type of the clusters and is also chosen on the basis of previously performed atomistic studies. The model had to be adapted to account for the existence of two kinds of SIA clusters, 〈111〉 and 〈100〉, as observed in electron microscopy examinations of Fe alloys neutron irradiated at the temperatures of technological interest.The model, which is fully based on physical considerations and only uses a few parameters for calibration, is found to be capable of reproducing the experimental trends, thereby providing insight into the physical mechanisms of importance to determine the type of nanostructural evolution undergone by the material during irradiation.

Object Kinetic Monte Carlo calculations of irradiated Fe–Cr dilute alloys: The effect of the interaction radius between substitutional Cr and self-interstitial Fe

Object Kinetic Monte Carlo models allow for the study of the evolution of the damage created by irradiation to time scales that are comparable to those achieved experimentally. Therefore, the essential Object Kinetic Monte Carlo parameters can be validated through comparison with experiments. However, this validation is not trivial since a large number of parameters is necessary, including migration energies of point defects and their clusters, binding energies of point defects in clusters, as well as the interaction radii. This is particularly cumbersome when describing an alloy, such as the Fe–Cr system, which is of interest for fusion energy applications. In this work we describe an Object Kinetic Monte Carlo model for Fe–Cr alloys in the dilute limit. The parameters used in the model come either from density functional theory calculations or from empirical interatomic potentials. This model is used to reproduce isochronal resistivity recovery experiments of electron irradiated dilute Fe–Cr alloys performed by Abe and Kuramoto. The comparison between the calculated results and the experiments reveal that an important parameter is the capture radius between substitutional Cr and self-interstitial Fe atoms. A parametric study is presented on the effect of the capture radius on the simulated recovery curves.

Multiscale Modeling of Helium-Vacancy Cluster Nucleation under Irradiation: A Kinetic Monte-Carlo Approach

AbstractWe applied ab initio calculation and an object kinetic Monte Carlo modeling to the study of He-vacancy cluster nucleation under irradiation in bcc and fcc Fe, which are surrogate materials for ferritic/martensitic and austenitic steels, respectively. The ab initio calculations provided parameters for the object kinetic Monte Carlo model, such as the migration energies of point defects and the dissociation energies of He and vacancy to He-vacancy clusters. We specially focused on the simulation of high He/dpa irradiation such as He-implantation into the materials and tracked the nucleation of clusters and the fate of point defects such as SIAs, vacancies, and He atoms. We found no major difference of He-vacancy cluster nucleation between bcc and fcc Fe when we ignore the intracascade clustering even if the migration energies of point defects are significantly different between the two crystals.

Object Kinetic Monte Carlo calculations of electron and He irradiation of nickel

We present results of an Object Kinetic Monte Carlo model (OKMC) of nucleation of He–vacancy complexes under irradiation of nickel. This OKMC model has been constructed using the existing atomistic information on migration energies and binding energies of vacancies, self-interstitials and He–vacancy interactions, as well as He migration from embedded atom interatomic potentials. We use this model to first study the different annealing stages of electron irradiated Ni and the influence of impurities in the recovery of damage during isochronal annealing. Then, He desorption from implanted Ni is studied for different doses and compared to existing experimental measurements.

Effect of self-interstitial cluster migration on helium diffusion in iron

The influence of self-interstitial cluster migration on defect evolution in irradiated α-Fe is studied using an object kinetic Monte Carlo model with input from ab initio and molecular dynamics calculations. Helium implantation and desorption is simulated during isothermal annealing under different conditions of temperature and sample thickness. Results are compared with experimental measurements existing in the literature. In particular, the effect of self-interstitial cluster migration on the fraction of He released during annealing is studied. The results of these calculations point towards a strong effect of traps in the nucleation and growth of He-vacancy clusters.