No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
An object kinetic Monte Carlo model for the microstructure evolution of neutron-irradiated reactor pressure vessel steels
Abstract
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 " grey-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 immo-bilization 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.
... A previous study [19] showed that homogeneous nucleation generally does not well predict the experimentally observed MNSP parameters in Cu-free alloys especially at lower Ni, and that some form of cascade MNS defect associated heterogeneous nucleation mechanism is needed. Multiple kinetic Monte Carlo simulations have also suggested that forms of heterogeneous nucleation play a key role in MNSPs [20,21,46]. Monte Carlo simulations [11] show Cu cluster formation in cascade in FeeCu binary alloys. ...
... 7. Heterogeneous nucleation size for MNSP (From Ref. [19]): The fitted parameter value is quite small consistent solute cluster formation during cascade aging. A recent study [46] shows the formation of sub-nanometer dislocation loops in RPVs decorated with MneNieSi. The fitted value corresponds to an 0.6 nm loop radius, which is in agreement with Ref. [46]. ...
... A recent study [46] shows the formation of sub-nanometer dislocation loops in RPVs decorated with MneNieSi. The fitted value corresponds to an 0.6 nm loop radius, which is in agreement with Ref. [46]. 8. Cascade cluster production efficiency factor for MNS (From Ref. [19]): Similar to cascade cluster production efficiency factor for Cu, the fitted parameter is consistent with just a small fraction of cascades (~2%) producing heterogeneous nucleation sites at low solute super saturations. ...
An improved Cluster Dynamics (CD) model of Cu rich and Mn–Ni–Si phase co-precipitation was developed to provide insights on the combined effects of the flux, fluence, temperature and alloy composition on irradiation enhanced precipitation leading to the embrittlement of reactor pressure vessel steels. The CD model was calibrated using a large microstructural database, and key parameters (e.g., interfacial energies) were fitted to minimize the predicted versus measured errors. The CD model was further validated against data not used in the fitting. The CD model predicts that: a) even 0.05% Cu reduces the Mn, Ni, Si precipitation threshold fluence; b) precipitate number densities increase, while their sizes and volume fractions, decrease with increasing flux; c) precipitate number densities and volume fractions increase with decreasing temperature; and, d) most of the matrix Cu precipitates in the early years of vessel service, while MnNiSi precipitates continue to grow up to very high extended life fluence.
... Messina [44] recently proposed that dislocation loops generated in cascade might act as nucleation sites for Mn-Ni precipitates. The key hypothesis is that solute segregation at loops reduces their mobility, with the result that the loop number density is similar to those of the MNSPs. ...
... Thus the model described here builds on earlier studies of the initial formation mechanism of MNSPs [30,31,44,45]. Here the objective is to develop a rigorous physical model for MNSP nucleation, growth and coarsening in low Cu RPV steels up to high fluence based on the underlying thermodynamics and kinetics. ...
... The first model for solute-defect complex formation (Cu-coated nanovoids) was first proposed by Odette [51] and later confirmed by a number of Kinetic Lattice Monte Carlo models of cascade aging [52e54]. While formation on both vacancy and interstitial clusters (nanovoids and loops, respectively) is possible, recent Kinetic Monte Carlo simulations suggest that MNSPs primarily form on loops created in the cascades [30,44]. Further discussion of the rich physics of cascade aging in alloys is beyond the scope of this paper, but it is sufficient to note that large solute cluster complexes, and their solute remnants, likely form in cascades at some frequency that decreases with decreasing size and the corresponding primary knock-on atom recoil energy. ...
Formation of large volume fractions of Mn-Ni-Si precipitates (MNSPs) causes excess irradiation embrittlement of reactor pressure vessel (RPV) steels at high, extended-life fluences. Thus, a new and unique, semi-empirical cluster dynamics model was developed to study the evolution of MNSPs in low-Cu RPV steels. The model is based on CALPHAD thermodynamics and radiation enhanced diffusion kinetics. The thermodynamics dictates the compositional and temperature dependence of the free energy reductions that drive precipitation. The model treats both homogeneous and heterogeneous nucleation, where the latter occurs on cascade damage, like dislocation loops. The model has only four adjustable parameters that were fit to an atom probe tomography (APT) database. The model predictions are in semi-quantitative agreement with systematic Mn, Ni and Si composition variations in alloys characterized by APT, including a sensitivity to local tip-to-tip variations even in the same steel. The model predicts that heterogeneous nucleation plays a critical role in MNSP formation in lower alloy Ni contents. Single variable assessments of compositional effects show that Ni plays a dominant role, while even small variations in irradiation temperature can have a large effect on the MNSP evolution. Within typical RPV steel ranges, Mn and Si have smaller effects. The delayed but then rapid growth of MNSPs to large volume fractions at high fluence is well predicted by the model. For purposes of illustration, the effect of MNSPs on transition temperature shifts are presented based on well-established microstructure-property and property-property models.
... The high-energy neutrons interact with the atom nuclei of the material, creating vacancies and interstitials. Most of the vacancies and interstitials recombine quickly, but some remain and subsequently cause the formation of nanometre-sized clusters containing Cu, Ni, Mn, and Si [1][2][3] . The clusters hinder dislocation movement, causing a hardening, and thereby contribute to embrittlement of the material. ...
In this study, high flux irradiated and surveillance high Ni and Mn and low Cu welds identical to those of the belt-line region of Ringhals R4 were subjected to annealing at temperatures between 390 and 455°C for 24–30 h, in order to study the dissolution of irradiation induced clusters and possible matrix defects using hardness testing and atom probe tomography. It was found that the cluster characteristics did not change during annealing at 390°C, meaning that the size, number density and composition of the clusters, which mainly consist of Ni and Mn, did not change. Thus, the observed decrease in hardness during annealing of the high flux irradiated material is believed to be due to dissolution of matrix defects that were stable at the operating temperature. Cluster dissolution was observed after annealing at 410°C in the high flux irradiated material, leaving around 10% of the original clusters. These clusters contained more Cu and less Ni and Mn than before annealing. The cluster dissolution at temperatures above 400 ˚C correlated with the decrease in hardness. The larger clusters of the surveillance material required a higher temperature or longer time to be dissolved compared to the clusters of the high flux material.
... Shu et al. [32] calculated the migration energy of Fe, Cu and Ni atoms in Fe bulk by using molecular dynamics with the nudged elastic band (NEB) method. Messina and Chiapetto [33] used kinetic Monte Carlo for the simulation of the microstructure evolution of reactor pressure vessel (RPV) steels. Although there are many studies on precipitated phases, there are few on the changes of atomic packing structures in precipitated small size Cu clusters in Fe bulk , the motion of Cu atoms and Fe atoms, and the influence of these Cu clusters on the packing structures in Fe bulk . ...
Understanding of the defect evolution mechanism under irradiation is very important for the research of pressure vessel steel embrittlement. In this paper, the embedded atom method (EAM) based canonical ensemble molecular dynamics (MD) method was used to study the evolution of the stacking structure of different nano-sized Cun (n = 13, 43 and 87) clusters in an Febulk embedded with BCC lattice structure during continuous heating. The mean square displacement, pair distribution functions and atomic structures of Cu atom clusters at the nanometer scale were calculated at different temperatures. The structural changes present apparent differences, for the Febulks contain nano-sized Cu clusters with different atom numbers during heating. For the Febulk–Cu13 system, since the ability to accommodate the atomic Cu in the Fe substrate is lesser, a small number of Cu atoms in BCC lattice positions cannot influence the whole structure of the Fe-Cu system. For the Febulk–Cu43 system, with an increase in temperature, a Cu atomic pile structural change happened, and the strain areas decreased significantly in the Febulk, but a single strain area grew large. For the Febulk–Cu87 system, when the Cu atoms are constrained by the Fe atoms in bulk, only a few of the Cu atoms adjust their positions. With the increase in temperature, strain in the Fe eased.
... The studies cited above are almost exclusively computational, as directly studying the thermodynamic stability of the MNSPs experimentally is challenging in that the kinetics of precipitation at 290 C is very sluggish, and that while increasing the temperature enhances the diffusion rates, it makes MNSPs less thermodynamically stable and especially difficult to nucleate. One approach to addressing the problem is to conduct post-irradiation annealing (PIA) at temperatures above 290 C. Irradiating at 290 C prior to annealing provides a significant volume fraction of precipitates (assisted by cascade cluster enhanced nucleation [19,21]), and annealing at well above 290 C alleviates the slow-kinetics limitation, making it possible to probe the precipitate evolution outside of an irradiation environment. Annealing of RPVs is also of interest as a possible mitigation strategy to reduce precipitate embrittlement, making PIA behavior of important in its own right [22,23]. ...
... wt% Si, but was not so distinct in the stainless steels with 0.43e0.65 wt% Si. As is known, impurities significantly hinder crowdion diffusion [56,57], and Si is an undersized element that traps interstitials in stainless steels. Si could have interfered with the crowdion diffusion between large clusters, and thus, the bimodal size distribution was not observed in alloys with high Si composition. ...
In recent years, modeling studies on the interactions between defect clusters have been extensively conducted to predict the behavior of stainless steels in reactors. However, comparable experimental results are desired to validate existing results and provide guidelines for future modeling. The size of defect clusters is expected to be a key factor influencing cluster interactions. Thus, in this work, the effects of growing clusters on their surrounding microstructure were quantitatively examined by in situ transmission electron microscopy during ion irradiation. To this end, a high-purity 316 L stainless steel model alloy was irradiated by 2 MeV Fe²⁺ to 0.2 dpa at 400 °C and 300 °C separately. At 300 °C, the number density of defect clusters monotonically increased with increasing fluence, whereas at 400 °C, the number density decreased almost immediately after the rapid nucleation regime. This decrease could be explained by the distinct growth of some clusters, which suppressed the nucleation of clusters around them as well as the lifetime of neighboring tiny clusters. Large interstitial-type clusters approximately 6–11 nm in size could be absorbed by neighboring interstitial-type clusters of similar sizes via interstitial crowdion diffusion. The absorption would not occur until both clusters grew large enough to permit a <110> diffusion path between them.
... The number of Cu atoms per cluster is increasing (Fig. 8) even though the Cu concentration of the clusters is decreasing, due to Ni, Mn and Si segregating at a higher rate. There seem to be clusters nucleating without Cu (although it should be noted that the detection efficiency is only 37%), in accordance with results from other studies using APT [27] and Monte Carlo simulations [28,29]. ...
Reactor pressure vessel steel welds are affected by irradiation during operation. The irradiation results in nanometre cluster formation, which in turn affects the mechanical properties of the material, e.g. the ductile-to-brittle transition temperature is shifted to higher levels. In this study, cluster formation is characterised in high Ni (1.58%) low Cu (0.04%) steel welds identical to Ringhals R4 welds, using atom probe tomography in both surveillance material and in material irradiated at accelerated dose rates. Clusters containing mainly Ni and Mn, but also some Si and Cu were observed in all of the irradiated materials. Their evolution did not change drastically during irradiation; the clusters grew and new clusters were nucleated. Hence, both the cluster number density and the average size increased with irradiation time. Some flux effects were observed when comparing the high flux material and the surveillance material. The surveillance material has a lower cluster number density, but larger clusters. The resulting impact on the mechanical properties of these two effects cancel out, resulting in a measured hardness that seems to be on the same trend as the high flux material. The dispersed barrier hardening model with an obstacle strength factor of 0.15 was found to reproduce the increase in hardness. In the investigated high flux materials, the clusters' Cu content was higher.
In this work, the defect evolution in the FeCMnNi model alloy is investigated by the grey-alloy method in an OKMC model. Based on the parameters of the Fe-C system, the influence of Mn and Ni is implicitly considered, and the migration energy of mobile defects is modified. The number density of interstitial clusters and vacancy clusters in simulation has a good agreement with experimental results. We also studied the defect evolution features versus carbon and solutes concentration. The simulation results show that the number density of defect clusters increases with increasing carbon or solutes concentration. The average size of interstitial clusters decreases while the average size of vacancy clusters is hardly affected by increasing impurity/solutes concentration. The defect features do not show a saturation tendency with increasing carbon/solutes concentrations. It also seems the influence of solutes concentration is more sensitive on defect features than carbons concentration in this FeCMnNi alloy.
This article is protected by copyright. All rights reserved.
The objective of this study is to evaluate dose rate effects on microstructure evolution in ferritic-martensitic alloy T91 following neutron or Fe²⁺ irradiation to a common dose (3 dpa) and temperature (500°C). Characterization via TEM and APT is also conducted following Fe²⁺ irradiation to 100 dpa at 500°C. Dislocation loop morphologies are consistent following each irradiation to 3 dpa, with only minor growth observed at 100 dpa. Each irradiation exhibits favorability for a<100> loops over a/2<111>. Si-Mn-Ni-rich and Cu-rich nanoclusters are more coarsely distributed following Fe²⁺ irradiation, while the same solutes exhibit strong evidence of segregation to grain boundaries, dislocation loops, and dislocation lines following both irradiations to 3 dpa. However, after 100 dpa, solutes are likely redistributed. While the invariance theory likely explains dislocation loop evolution with variations in dose rate, it is not sufficient to predict temperature shift requirements for solute cluster evolution at 3 dpa.
This paper introduces the KineCluE code that implements the self-consistent mean-field theory for clusters of finite size. Transport coefficients are obtained as a sum over cluster contributions, each being individually computed with KineCluE. This method allows for the calculation of these coefficients beyond the infinitely dilute limit, and is an important step in bridging the gap between dilute and concentrated approaches. Inside a finite volume of space containing the components of a given cluster, all kinetic trajectories are accounted for in an exact manner. The code, written in Python, adapts to a wide variety of systems, with various crystallographic structures (possibly under strain), defects and solute amount and types, and various jump mechanisms, including collective ones. The code also features a set of useful tools, such as the sensitivity study routine that allows for the identification of the most important jump frequencies to get accurate transport coefficients with minimum computational cost.
We present a systematic analysis, based on ab initio calculations, of concentrated solute arrangements and precipitate phases in Fe-based alloys. The input data for our analysis are the calculated formation and interaction energies of point defects in the iron matrix, as well as the energies of ordered compounds that represent end-members in the 4-sublattice compound energy model of a multicomponent solid solution of Mg, Al, Si, P, S, Mn, Ni, and Cu elements and also vacancies in bcc Fe. The list of compounds also includes crystal structures obtained by geometric relaxation of the end-member compounds that in the cubic structure show weak mechanical instabilities (negative elastic constants) and also the G-phase Mn6(Ni,Fe)16(Si,P)7 having a complex cubic structure. A database of calculated thermodynamic properties (crystal structure, molar volume, enthalpy of formation, and elastic constants) of the most stable late-blooming-phase candidates is thus obtained. The results of this ab initio based theoretical analysis compare well with the recent experimental observations and predictions of thermodynamic calculations employing Calphad methodology.
The interplay between vacancies (V) and interstitial solutes X (X = C, N, and O) and its impact on thermodynamic properties of alpha-Fe solid solutions are studied, starting from first principles calculations. A systematic comparison between the three solutes is performed, investigating X-Fe, X-X, and V -X interactions. In the alpha-Fe lattice, the strength of X-Fe interactions is found to govern the dissolution properties. Next to vacancies, the competition between solute volume effects and X-Fe interactions results in the preference of all the solutes to occupy off-centered sites. Low-energy configurations of small VnXm clusters are calculated for n and m up to 4. They are used to parametrize lattice interaction models at the atomic scale. A detailed analysis of the cluster properties suggests the relevance of many-body terms in these models. The accuracy of the resulting models is verified through their satisfactory prediction of vacancy-solute cluster properties beyond the fitting database. From these models, an entire set of VnXm clusters is generated with a new configurational space exploration method. Statistical treatment of the solid solution including these clusters is then achieved by means of low-temperature expansions, checked against Monte Carlo simulations in some specific conditions. Based on the calculation of equilibrium cluster distributions, it is shown that the solubility limit of oxygen in Fe, hardly measurable experimentally, is largely affected by the presence of small VnOm clusters.
Defect-driven diffusion of impurities is the major phenomenon leading to formation of embrittling nanoscopic precipitates in irradiated reactor pressure vessel (RPV) steels. Diffusion depends strongly on the kinetic correlations that may lead to flux coupling between solute atoms and point defects. In this work, flux coupling phenomena such as solute drag by vacancies and radiation-induced segregation at defect sinks are systematically investigated for six bcc iron-based dilute binary alloys, containing Cr, Cu, Mn, Ni, P, and Si impurities, respectively. First, solute-vacancy interactions and migration energies are obtained by means of ab initio calculations; subsequently, self-consistent mean field theory is employed in order to determine the exact Onsager matrix of the alloys. This innovative multiscale approach provides a more complete treatment of the solute-defect interaction than previous multifrequency models. Solute drag is found to be a widespread phenomenon that occurs systematically in ferritic alloys and is enhanced at low temperatures (as for instance RPV operational temperature), as long as an attractive solute-vacancy interaction is present, and that the kinetic modeling of bcc alloys requires the extension of the interaction shell to the second-nearest neighbors. Drag occurs in all alloys except Fe(Cr); the transition from dragging to nondragging regime takes place for the other alloys around (Cu, Mn, Ni) or above (P, Si) the Curie temperature. As far as only the vacancy-mediated solute migration is concerned, Cr depletion at sinks is foreseen by the model, as opposed to the other impurities which are expected to enrich up to no less than 1000 K. The results of this study confirm the current interpretation of the hardening processes in ferritic-martensitic steels under irradiation.
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 <370 K. 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, < 1 1 1 > and < 1 0 0 >, 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.
Neutron irradiation induces in steels nanostructural changes, which are at
the origin of the mechanical degradation that these materials experience during
operation in nuclear power plants. Some of these effects can be studied by
using as model alloy the iron-carbon system.
The Object Kinetic Monte Carlo technique has proven capable of simulating in
a realistic and quantitatively reliable way a whole irradiation process. We
have developed a model for simulating Fe-C systems using a physical description
of the properties of vacancy and self-interstitial atom (SIA) clusters, based
on a selection of the latest data from atomistic studies and other available
experimental and theoretical work from the literature. Based on these data, the
effect of carbon on radiation defect evolution has been largely understood in
terms of formation of immobile complexes with vacancies that in turn act as
traps for SIA clusters. It is found that this effect can be introduced using
generic traps for SIA and vacancy clusters, with a binding energy that depends
on the size of the clusters, also chosen on the basis on previously performed
atomistic studies.
The model proved suitable to reproduce the results of low (<350 K)
temperature neutron irradiation experiments, as well as the corresponding
post-irradiation annealing up to 700 K, in terms of defect cluster densities
and size distribution, when compared to available experimental data from the
literature. The use of traps proved instrumental for our model.
We describe a new algorithm for Monte Carlo simulation of Ising spin systems and present results of a study comparing the speed of the new technique to that of a standard technique applied to a square lattice of 6400 spins evolving via single spin flips. We find that at temperatures T < Tc, the critical temperature, the new technique is faster than the standard technique, being ten times faster at T = 0.588 Tc. We expect that the new technique will be especially valuable in Monte Carlo simulation of the time evolution of binary alloy systems. The new algorithm is essentially a reorganization of the standard algorithm. It accounts for the a priori probability of changing spins before, rather than after, choosing the spin or spins to change.
The reactor pressure vessel (RPV) steels used in current nuclear power plants embrittle as a consequence of the continuous irradiation with neutrons. Among other radiation effects, the experimentally observed formation of copper-rich defects is accepted to be one of the main causes of embrittlement. Therefore, an accurate description of the nucleation and growth under irradiation of these and other defects is fundamental for the prediction of the mechanical degradation that these materials undergo during operation, with a view to guarantee a safer plant life management. In this work we describe in detail the object kinetic Monte Carlo (OKMC) method that we developed, showing that it is well suited to investigate the evolution of radiation damage in simple Fe alloys (Fe, Fe–Cu) under irradiation conditions (temperature, dose and dose-rate) typical of experiments with different impinging particles and also operating conditions. The still open issue concerning the method is the determination of the mechanisms and parameters that should be introduced in the model in order to correctly reproduce the experimentally observed trends. The state-of-the-art, based on the input from atomistic simulation techniques, such as ab initio calculations, molecular dynamics (MD) and atomic kinetic Monte Carlo, is critically revised in detail and a sensitivity study on the effects of the choice of the reaction radii and the description of defect mobility is conducted. A few preliminary, but promising, results of favorable comparison with experimental observations are shown and possible further refinements of the model are briefly discussed.
It is shown that the dependence of self-interstitial cluster diffusivity in Fe–Cr alloys on Cr concentration correlates with that of swelling in these alloys under neutron irradiation; namely, with increasing chromium concentration the cluster diffusivity first decreases and then increases. The origin of such behaviour lies in a relatively long-ranged, 1 nm, attractive interaction between Cr atoms and crowdions. The minimum diffusivity is realized for 11 at.% Cr, where all crowdions constituting the cluster interact with Cr atoms, but the interaction fields of different Cr atoms do not overlap.
The fine microstructures of medium and medium-high carbon bainitic steels were observed and analyzed by high resolution electron microscope (HREM). The investigation results show that there are retained austenitic films with different appearances and sizes in bainitic ferrite laths. The boundaries of different structure levels are separated and encircled by retained austenitic films. The fine structure units and their sizes of different structure levels in the bainitic ferrite were determined by retained austenitic films. The bainitic ferrite laths are composed of different structure level sublaths, subunits and elementary units (or so called sub-subunits). The dimensions of most sublaths, subunits and elementary units are 25-80 nm, 25-80 nm and 5.0-30 nm, respectively.
Radiation damage of reactor pressure vessel (RPV) ferritic steels has been the subject of intensive study since the 1950s. This is because it was found that neutron irradiation caused degradation in the mechanical properties of the steel, and knowledge of the resultant hardening and embrittlement was required to predict the in-service properties of RPVs. This chapter focuses on the progress made in understanding the underlying radiation damage mechanisms and applying such insight to develop mechanistically based dose–damage relationships (DDRs). These DDRs allow embrittlement of irradiated RPV steels to be assessed as a function of the important irradiation and material variables. It is to be noted that this chapter is concerned with the effects of neutron irradiation over quite a narrow set of irradiation conditions, that is, irradiation temperatures of ∼250–300 °C (although there was interest in irradiation temperatures as low as 160 °C) and irradiation doses typical of in-service exposures (<0.1 dpa).
The strong binding between a vacancy and carbon in bcc iron plays an important role in the evolution of radiation-induced microstructure. Our previous ab initio study points to the fact that the vacancy-carbon (V-C) pair can serve as a nucleus for the solute-rich clusters. Here, we continue the ab initio study by considering the interaction of mixed solute clusters (Mn, Ni and Si) with the V-C pair, and the interaction of typical alloying elements of Fe-based steels (i.e., Mn, Ni, Cu, Si, Cr and P) with di-carbon-vacancy pair (V-C2). We have identified the sequence of growth of Ni, Si and Mn solute-rich clusters nucleating on the V-C pair. The mixed-solute-V-C configurations are found to be less stable clusters than pure-solute-V-C clusters with the energy difference up to 0.22 eV per four atoms. The V-C2 pair is found to be as strong nucleation site for the solute-rich clusters as the V-C pair. Only Si solute atom stands out from the trend showing a weaker affinity to the V-C2 complex by 0.09 eV compared to the attraction to the V-C pair. The overall results point to the importance of taking into account the existence of both V-C and V-C2 complexes in studying the formation of solute-rich clusters in Fe-based steels for nuclear applications.
The radiation embrittlement of low-alloyed reactor pressure vessel steels is partly due to the formation of nanometer-sized solute clusters (Mn, Si, Ni, Cu and P). In order to determine if radiation-induced mechanisms can take part in the solute clustering, an under-saturated binary Fe-1 at.% Mn alloy was irradiated with Fe ions at 400 degrees C. After irradiation, atom probe tomography experiments revealed that a high density of Mn-rich clusters is formed. This observation clearly demonstrates that, under these irradiation conditions, Mn clustering in this model alloy is radiation-induced and not radiation-enhanced. Mn-rich clusters were not distributed homogeneously in the analyzed volume but were heterogeneously precipitated on a planar object, suggesting a grain boundary (GB) or a dislocation loop. In parallel, a rate theory model calibrated on the population of point defect (PD) clusters measured by transmission electron microscopy has shown that the dominant sinks for mobile PDs are PD clusters. Thus Mn clustering could be explained by Mn atoms dragged by mobile PD fluxes towards sinks such as PD clusters or GBs. According to the model, most of the dragging occurs via isolated interstitials. These results are in very good agreement with previous studies, suggesting a correlation of position between solute-rich clusters and sinks.
Atom Probe Tomography has been performed on as-irradiated and post-irradiation annealed surveillance weld samples from Ringhals Unit 3. The weld contains low Cu (0.07 at.%) and high Ni (1.5 at.%). A high number density (∼4 × 1023 m−3) of Ni–Mn–Si-enriched clusters was observed in the as-irradiated material. The onset of recovery was observed during the annealing for 30 min at 450 °C. Much more significant dissolution of clusters occurred during the 10 min 500 °C anneal, resulting in a reduction in mean cluster size and a halving of their volume fraction.
Interstitial carbon, dissolved in bcc matrix of ferritic steels, plays an important role in the evolution of radiation-induced microstructure since it exhibits strong interaction with vacancies. Frequent formation and break-up of carbon–vacancy pairs, occurring in the course of irradiation, affect both kinetics of the accumulation of point defect clusters and carbon spatial distribution. The interaction of typical alloying elements (Mn, Ni, Cu, Si, Cr and P) in ferritic steels used as structural materials in nuclear reactors with a carbon–vacancy complex is analyzed using ab initio techniques. It is found that all the considered solutes form stable triple clusters resulting in the increase of the total binding energy by 0.2–0.3 eV. As a result of the formation of energetically favourable solute–carbon–vacancy triplets, the dissociation energy for vacancy/carbon emission is also increased by ∼0.2–0.3 eV, suggesting that the solutes enhance thermal stability of carbon–vacancy complex. Association of carbon–vacancy pairs with multiple solute clusters is found to be favorable for Ni, Cu and P. The energetic stability of solute(s)–carbon–vacancy complexes was rationalized on the basis of pairwise interaction data and by analyzing the variation of local magnetic moments on atoms constituting the clusters.
Understanding the radiation embrittlement of reactor pressure vessel (RPV) steels is required to be able to operate safely
a nuclear power plant or to extend its lifetime. The mechanical properties degradation is partly due to the clustering of
solute under irradiation. To gain knowledge about the clustering process, a Fe−1.1 Mn−0.7 Ni (at.%) alloy was irradiated in
a test reactor at two fluxes of 0.15 and 9 ×1017 n
E > 1MeV
.m − 2.s − 1 and at increasing doses from 0.18 to 1.3 ×1024 n
E > 1MeV
.m − 2 at 300°C. Atom probe tomography (APT) experiments revealed that the irradiation promotes the formation in the α iron matrix of Mn/Mn and/or Ni/Ni pair correlations at low dose and Mn–Ni enriched clusters at high dose. These clusters
dissolve partially after a thermal treatment at 400°C. Based on a comparison with thermodynamic calculations, we show that
the solute clustering under irradiation can just result from an induced mechanism.
KeywordsMetal and alloys–Solute clusters–Point defects–Neutron irradiation– Irradiation induced segregation
An atomistic Monte Carlo model parameterised on electronic structure calculations data has been used to study the formation and evolution under irradiation of solute clusters in Fe–MnNi ternary and Fe–CuMnNi quaternary alloys. Two populations of solute rich clusters have been observed, which can be discriminated by whether or not the solute atoms are associated with self-interstitial clusters. Mn–Ni-rich clusters are observed at a very early stage of the irradiation in both modelled alloys, whereas the quaternary alloys contain also Cu-containing clusters. Mn–Ni-rich clusters nucleate very early via a self-interstitial-driven mechanism, earlier than Cu-rich clusters; the latter, however, which are likely to form via a vacancy-driven mechanism, grow in number much faster than the former, helped by the thermodynamic driving force to Cu precipitation in Fe, thereby becoming dominant in the low dose regime. The kinetics of the number density increase of the two populations is thus significantly different. Finally the main conclusion suggested by this work is that the so-called late blooming phases might as well be neither late, nor phases.
An extensive database of atomic displacement cascades in iron has been developed using molecular dynamics (MD) simulations. Simulations have been carried out at temperatures of 100, 600, and 900 K, and at energies between 0.10 and 50 keV. The results presented here focus on the simulations conducted at 100 K. A sufficient number of cascades has been completed under each condition of cascade energy and temperature to obtain statistically significant average values for the primary damage production parameters. The statistical analysis has been used to examine the influence of primary knockon direction, simulation cell-size, and lattice heating by the high energy recoil. A surprising effect of primary knockon atom (PKA) direction was observed up to 1 keV, but little effect of lattice heating was detected. We have previously reported preliminary results indicating that the ratio of surviving point defects to the number calculated by the Norgett–Robinson–Torrens (NRT) displacement model appears to pass through a minimum value of about 20 keV. The present analysis supports the statistical significance of this minimum, which can be attributed to the onset of extensive subcascade formation.
A simple procedure is proposed for calculating the number of atomic displacements produced in a damage cascade by a primary knock-on atom of known energy. The formulae have been chosen to give results in close accord with recent computer simulations of radiation damage phenomena. The proposed new standard is compared with other empirical formulae for estimating the number of atomic displacements in a cascade.
The Ringhals Units 3 and 4 reactors in Sweden are pressurized water reactors (PWRs) designed and supplied by Westinghouse Electric Company, with commercial operation in 1981 and 1983, respectively. The reactor pressure vessels (RPVs) for both reactors were fabricated with ring forgings of SA 508 class 2 steel. Surveillance blocks for both units were fabricated using the same weld wire heat, welding procedures, and base metals used for the RPVs. The primary interest in these weld metals is because they have very high nickel contents, with 1.58 and 1.66 wt.% for Unit 3 and Unit 4, respectively. The nickel content in Unit 4 is the highest reported nickel content for any Westinghouse PWR. Although both welds contain less than 0.10 wt.% copper, the weld metals have exhibited high irradiation-induced Charpy 41-J transition temperature shifts in surveillance testing. The Charpy impact 41-J shifts and corresponding fluences are 192 °C at 5.0 × 1023 n/m2 (>1 MeV) for Unit 3 and 162 °C at 6.0 × 1023 n/m2 (>1 MeV) for Unit 4. These relatively low-copper, high-nickel, radiation-sensitive welds relate to the issue of so-called late-blooming nickel–manganese–silicon phases. Atom probe tomography measurements have revealed ∼2 nm-diameter irradiation-induced precipitates containing manganese, nickel, and silicon, with phosphorus evident in some of the precipitates. However, only a relatively few number of copper atoms are contained within the precipitates. The larger increase in the transition temperature shift in the higher copper weld metal from the Ringhals R3 Unit is associated with copper-enriched regions within the manganese–nickel–silicon-enriched precipitates rather than changes in their size or number density.
Evolution of high-energy displacement cascades in iron has been investigated for times up to 200 ps using molecular dynamics simulation. The simulations were carried out using the MOLDY code and a modified version of the many-body interatomic potential developed by Finnis and Sinclair. Previously reported results have been supplemented by a series of 10 keV simulations at 900 K and 20 keV simulations at 100K. Results indicate that the fraction of the Frenkel pairs escaping in-cascade recombination is somewhat higher and the fraction of the surviving point defects that cluster is lower in iron than in materials such as copper. In particular, vacancy clustering appears to be inhibited in iron. Many of the larger interstitial clusters were observed to exhibit a complex, three-dimensional morphology. Apparent mobility of the crowdion and clusters of crowdions was very high.
Plant specific surveillance programs that ideally include all relevant materials and materials combinations that are subjected to neutron irradiation during operation address the degradation due to irradiation of the reactor pressure vessel material for nuclear electric power plants. Plant specific surveillance programs are not unique to the two power plants treated in this study. The current Swedish regulatory system does, however, call for a fairly rigid approach within the surveillance program. In the Swedish case, this means that there is a plant specific predetermined inspection/test program that has to be followed in order to verify the operability of the power plant and also to verify the operational limits with respect to pressure/temperature effects on a repetitive basis. The two pressurized water reactor plants Ringhals 3 and 4 have in common that the weld metal used for the butt welds of the reactor pressure vessel is a high nickel type material, above the current limits of the NUREG Reg. Guide 1.99, rev. 2. In the original state, the high nickel content provides excellent fracture toughness in the unirradiated material condition and a low ductile-to-brittle transformation temperature (DBTT). It has, however, been highlighted in several studies that high nickel materials exhibit a very large DBTT shift as a consequence of irradiation, and also that the precipitates that form during the irradiation are not as easily controlled during a heat treatment to remove the irradiation damage as are the copper rich clusters. This paper will present the current state of the art regarding these effects as observed in the weld metal specimens. The paper will present the results from the Charpy V notched and fracture mechanics specimen test encapsulated in the Ringhals Units 3 and 4 surveillance programs. The results from the Ringhals Units 3 and 4 surveillance programs show that there is a need for corrective action to be taken in order to ensure 60 y of operability for the two power plants. Copyrighl
Primary defect formation in bee iron has been extensively investigated using the methods of molecular dynamics (MD) and Monte Carlo (MC) simulation. This research has employed a modified version of the Finnis-Sinclair interatomic potential. MD was used in the simulation of displacement cascades with energies up to 40 keV and to examine the migration of the interstitial clusters that were observed to form in the cascade simulations. Interstitial cluster binding energies and the stable cluster configurations were determined by structural relaxation and energy minimization using a MC method with simulated annealing. Clusters containing up to 19 interstitials were examined. Taken together with the previous work, these new simulations provide a reasonably complete description of primary defect formation in iron. The results of the displacement cascade simulations have been used to characterize the energy and temperature dependence of primary defect formation in terms of two parameters: (1) the number of surviving point defects and (2) the fraction of the surviving defects that are contained in clusters. The number of surviving point defects is expressed as a fraction of the atomic displacements calculated using the secondary displacement model of Norgett-Robinson-Torrens (NRT). Although the results of the high energy simulations are generally consistent with those obtained at lower energies, two notable exceptions were observed. The first is that extensive subcascade formation at 40 keV leads to a higher defect survival fraction than would be predicted from extrapolation of the results obtained for energies up to 20 keV. The stable defect fraction obtained from the MD simulations is a smoothly decreasing function up to 20 keV. Subcascade formation leads to a slight increase in this ratio at 40 keV, where the value is about the same as at 10 keV. Secondly, the potential for a significant level of in-cascade vacancy clustering was observed. Previous cascade studies employing this potential have reported extensive interstitial clustering, but little evidence of vacancy clustering. Interstitial clusters were found to be strongly bound, with binding energies in excess of 1 eV. The larger clusters exhibited a complex, D structure and were composed of 〈111〉 crowdions. These clusters were observed to migrate by collective 〈111〉 translations with an activation energy on the order of 0.1 eV.
The reaction-rate-theory approach is widely used in analyzing dynamic radiation effects at elevated temperatures. The estimation of the various sink loss terms is a central ingredient of such analyses. These estimates have not always been made in a self-consistent manner. A general approach will be presented yielding a unified set of loss terms for the various sink geometries.RésuméL'approche par la théorie de la vitesse de réaction a été utilisée largement pour analyser les effets dynamiques d'irradiation aux températures élevées. L'estimation des différents termes de perte par piégeage est un argument fondamental pour une telle analyse. Ces estimations n'ont pas toujours été faites d'une manière logique. Une approche générale sera présentée qui conduit à une série logique de termes de perte pour les géométries différentes des pièges.ZusammenfassungDie reaktionskinetische Näherung ist bei der Analyse dynamischer Bestrahlungseffckte bei höheren Temperaturen weit verbreitet. Die Abschätzung der verschiedenen Verlustterme für die Senken ist ein Hauptbestandteil einer derartigen Analyse. Diese Abschätzungen sind nicht immer widerspruchsfrei durchgeführt worden. Es wird eine allgemeine Näherung mitgeteilt, die einen widerspruchsfreien Satz von Verlusttermen für die Geometrie verschiedener Senken liefert.
A simple form of multi-ion interaction has been constructed for the purpose of atomistic simulation of transition metals. The model energy consists of a bonding term, which is the square-root of a site density ρi, summed over atoms i, and a repulsive pairwise term of the form The site density ρi is defined as sum over neighbouring sites j of a cohesive potential (R ij). Both V and are assumed to be short-ranged and are parameterized to fit the lattice constant, cohesive energy and elastic moduli of the seven body-centred-cubic (b.c.c.) transition metals. The result is a simple model which, unlike a pair-potential model, can account for experimental vacancy-formation energies and does not require an externally applied pressure to balance the “Cauchy pressure”.
Using a Monte Carlo technique, a simulation study is made of vacancy migration in the binary ordered alloys AB (simple cubic) and B3A (face-centred cubic). The resulting self-diffusion is calculated and in the first case compares very favourably with the existing experimental results of Kuper et al. for a body-centred binary alloy. Quite different results are predicted for an alloy of form B3A and it is hoped that comparison with experiment will establish the importance of the isolated-vacancy mechanism as the means for producing self-diffusion.
Understanding the behavior of reactor pressure vessel (RPV) steels under irradiation is a mandatory task that has to be elucidated in order to be able to operate safely a nuclear power plant or to extend its lifetime. To build up predictive tools, a substantial experimental data base is needed at the nanometre scale to extract quantitative information on neutron-irradiated materials and to validate the theoretical models. To reach this experimental goal, ferritic model alloys and French RPV steel were neutron irradiated in a test reactor at an irradiation flux of 9 × 1017 nm−2 s, doses from 0.18 to 1.3 × 1024 nm−2 and 300 °C. The main goal of this paper is to report the characterization of the radiation-induced microstructural change in the materials by using the state-of-the-art of characterization techniques available in Europe at the nanometre scale. Possibilities, limitations and complementarities of the techniques to each other are highlighted.
The mechanisms of defect production in displacement cascades in α-iron have been investigated by computer simulation. Cascades of up to 5 keV in energy have been simulated by molecular dynamics in crystals with atomic interactions described by a many-body potential. The effects of lattice temperature have been studied by using block temperatures of either 100 or 600 K. 80 cascades have been modelled overall. The morphology of cascades during the collisional phase changes at about 1–2 keV, due to the collective nature of atomic displacements at higher energy. This transition is reflected in the relaxation time during the subsequent recombination phase, and it also decreases the efficiency factor for defect production. This factor is similar in size to that obtained from recent modelling of copper, an fcc metal. Although the cascade zone contains a large number of displaced atoms, true melting was not observed in α-Fe, and vacancy clustering did not occur in the thermal spike phase. Interstitial clustering has been analysed, and found to be less pronounced than in copper. One large cluster was observed to grow by interstitial movement during the thermal spike, and visual analysis has shown that it formed a perfect dislocation loop: it was not nucleated by the Eyre-Bullough mechanism, however. Statistics on the cascade parameters are presented, and comparisons with work on other crystal structures are drawn where possible.
The radiation induced microstructure was examined by Transmission Electron Microscopy in Fe, FeCu, FeMnCuNi, FeMnNi and a Reactor Pressure Vessel steel that were neutron irradiated to 0.026, 0.051, 0.10 and 0.19 dpa at 300 °C. The effect of dose and composition on defect accumulation and microstructure evolution was investigated. The damaged microstructure consisted in the presence of dislocation loops of interstitial type. The presence of voids was also studied in pure iron. Results on density, size and Burgers vector of radiation induced dislocation loops showed that the evolution of the interstitial component of the neutron irradiation induced microstructure was strongly affected by the presence of solutes such as Cu, Mn and Ni. Density and size increased with increasing dose in all the materials, while the effect of solutes is clearly to decrease the size of defects compared to pure iron. It has been observed that, for the same irradiation dose, the defect size decreases as the material becomes more complex, with the extreme case of the RPV steel where no defects were observed at any of the irradiation doses studied.
The nuclear reactor core is contained in a steel vessel, which is not replaceable during the lifetime of the reactor. It is therefore of crucial importance to make sure that the material properties under irradiation remain adequate to fulfil the expected structural duties. In order to actually predict the behaviour of the material, models are needed based on the microstructural variations observed by state-of-the-art experimental examination. To identify the physical phenomena leading to the microstructural changes, several model alloys and steels are neutron irradiated and subsequently examined. Four different techniques are used by different European laboratories on the same material, to detect, identify and quantify different irradiation-induced defects. In this work, the attention is focused on the use of the positron annihilation spectroscope and the quantification of its results. The results of the four techniques are also compiled together in a complementary way for the full understanding of the microstructural changes during irradiation. Based on this knowledge, an attempt is made to predict the hardening mechanisms in the investigated materials under irradiation.
The sink strength (SS) for three-dimensionally (3D) versus one-dimensionally (1D), or mixed 1D/3D, migrating defects in irradiated materials has attracted much attention in the recent past. Analytical expressions have been developed and a "master curve" approach proposed to describe the transition from purely 1D to purely 3D defect migration. Object kinetic Monte Carlo methods were subsequently used to corroborate the theoretical expressions. Although good agreement was generally found, the ability of this technique to reach the 1D migration limit has been questioned. We show that this technique can reproduce the theoretical expressions for the SS in the whole range of conditions explored. Despite the limited size of the OKMC simulation-box, the method is suitable to describe microstructure evolution of irradiated materials for any defect migration pattern, including fully 1D migrating defects, and to allow for the effect of extended microstructural features, larger than the simulation-box, such as grain boundaries.
- R Stoller
R. Stoller, J. Nucl. Mater. 233, 999-1003 (1996).
Assessment of stability and mobility of SIA and vacancy clusters in target ternary alloy
- N Anento
- N Castin
- A Serra
- L Malerba
N. Anento, N. Castin, A. Serra, and L. Malerba, Assessment
of stability and mobility of SIA and vacancy clusters in target
ternary alloy, Tech. Rep. D1-3.16, PERFORM 60 FP7 project
(grant agreement no. FP7-232612), 2013.
- W Meyer
- H Neldel
W. Meyer and H. Neldel, Z. Tech. Phys. 12, 588 (1937).
Private communication
- M Konstantinovic
M. Konstantinovic. Private communication, 2016.
- A Bakev
- D Terentyev
- E E Zhurkin
- D Van Neck
A. Bakev, D. Terentyev, E. E. Zhurkin, and D. Van
Neck, Nucl. Instrum. Methods Phys. Res. B 352, 47-50
(2015).
- R Stoller
- A Calder
R. Stoller and A. Calder, J. Nucl. Mater. 283, 746-752
(2000).
Private communication
- B Radiguet
B. Radiguet. Private communication, 2015.
Analytical TEM examination of RPV weld metal microstructure Tech. Rep. VTT-R-01951-10 VTT Technical Research Centre of Finland
- W Karlsen
W. Karlsen, Analytical TEM examination of RPV weld metal
microstructure, Tech. Rep. VTT-R-01951-10, VTT Technical Research Centre of Finland, 2010.
- D Terentyev
- L Malerba
- A V Barashev
D. Terentyev, L. Malerba, and A. V. Barashev, Philos. Mag.
Lett. 85, 587-594 (2005).
- P Efsing
- C Jansson
- G Embring
- T Mager
P. Efsing, C. Jansson, G. Embring, and T. Mager, J. ASTM
Int. 4, 1–12 (2007).
- M Finnis
- E Sinclair
M. Finnis and E. Sinclair, Philos. Mag. A 50, 45 (1984).
- C Barouh
- T Schuler
- C.-C Fu
- M Nastar
C. Barouh, T. Schuler, C.-C. Fu, and M. Nastar, Phys. Rev. B
90, 054112 (2014).
- S D Catteau
- H P Van Landeghem
- J Texeira
- J Dulcy
- M Dehmas
- S Denis
- A Redjaïmia
- M Corteaux
S. D. Catteau, H. P. Van Landeghem, J. Texeira, J. Dulcy,
M. Dehmas, S. Denis, A. Redjaïmia, and M. Corteaux, J.
Alloys Compd. 658, 832-838 (2016).
- Z Chang
- D Terentyev
- N Sandberg
Z. Chang, D. Terentyev, and N. Sandberg, J. Nucl. Mater.
461, 221-229 (2015).
- M Hern Andez-Mayoral
M. Hern andez-Mayoral and D. G omez-Brice~ no, J. Nucl.
Mater. 399, 146–153 (2010).