Long term solute evolution in RPV steels: experimental and modeling convergence?

Pareige Philippe1, B. Radiguet

1 and Malerba Lorenzo

2

1Groupe de Physique des Matériaux, Normandie Université,

76801 Saint Etienne du Rouvray, France 2Structural Materials Group, Institute of Nuclear Materials Science, SCK•CEN,

The Belgian Nuclear Energy Research Centre, Boeretang 200, 2400 Mol, Belgium

Radiation-induced embrittlement of steels used to build the irreplaceable reactor pressure

vessels (RPV) is the lifetime limiting factor of existing nuclear light water reactors

(LWR). 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. So far, two classes of nano-structural features are considered as the

main contributors to the embrittlement of RPV steels: (a) clusters of solute atoms such as

Cu, Ni, and Mn, generally catalogued as precipitates; and (b) the so-called 'matrix

damage', generally interpreted in terms of clusters of point-defects

In the first class, one can distinguish between Cu-rich precipitates (CRP) and Mn-Ni-rich

precipitates (MNP). The formation of the latter, which might also not contain Cu, is

favoured by low(er) temperature and high Ni (and Mn and Si) content. MNP without Cu

are detected only at sufficiently high neutron fluence, not only in (low-Cu) RPV steels,

but also in FeMnNi model alloys. Today, the large amount of experimental works in this

field of irradiated materials (vessel steels, model alloys, ferritic-martensitic steels,…)

brings a lot of information on the behavior of solutes or impurities in bcc iron under

irradiation. Common trends are observed and often explained or validated with numerical

modeling.

Back to RPV steels, there is a belief that precipitates rich in Mn and Ni, once nucleated,

will rapidly grow to large volume fractions. For these reasons, they are more commonly

denoted as late blooming phases (LBP). Their appearance has been associated with the

possibility of a sudden and unexpected increase of embrittlement above a certain dose,

that cannot be predicted by current commonly used empirical correlations.

In this paper, insight gained lately from atomistic simulation and experimental results on

the possible mechanism of formation of “dislocation obstacles” are described. Strong of

this, a discussion of up to what extent the lateness and the blooming of these phases

should be really considered a concern for nuclear power plants will be engaged. The

modeling/experimental parallel suggests that these features start forming at early dose by

heterogeneous nucleation on point-defect clusters and are therefore intimately connected

with matrix damage, thereby following the same trend as the latter in terms of kinetics of

formation versus dose.

Self-interstitial clusters with C15 Laves phase structure in bcc iron

M.C. Marinica, R. Alexander, L. Dezerald, L. Ventelon, F. Willaime

CEA, DEN, Service de Recherches de Métallurgie Physique, 91191 Gif-sur-Yvette,

France

The morphology adopted by small self-interstitial atom (SIA) clusters in metals under

irradiation cannot be resolved by experimental techniques. Molecular Dynamics

simulations of cascades have shown that while most SIA clusters adopt the standard loop

geometry and are highly mobile, a large remaining fraction is immobile [1]. Using a

combination of Density Functional Theory (DFT) and empirical potential calculations we

show that in iron a particular family of these immobile clusters has an unusual three

dimensional periodic structure corresponding to the C15 Laves phase. These C15

aggregates are highly stable compared to the conventional 2D loops and they exhibit

large antiferromagnetic moments with respect to the bcc matrix [2].

DFT calculations show that in iron the formation

energies of C15 SIA clusters are lower by 1.5 eV

than that of <110> loops for tetra-interstitials and

by 4 eV than that of <111> loops for octa-

interstitials [2, 3]. This characteristic is very well

reproduced by the M07 EAM potential for iron but

not by the Ackland-Mendelev potential. The

systematic exploration of the energy landscape

performed using the Activation Relaxation

Technique (ART) and the M07 potential confirms

the exceptional stability of these clusters and

shows how they can grow by capturing self-

interstitials. These clusters are predicted to be the

lowest energy structures up to sizes of about 40

SIAs. According to DFT calculations this behavior

does not occur in other bcc metals, except for Ta

but in a smaller range of sizes. This new morphology of self-interstitial clusters thus

constitutes an important element to account for when predicting the microstructural

evolution of iron base materials under irradiation.

[1] D. J. Bacon, F. Gao, and Y. Osetsky, J. Nucl. Mater. 276, 1 (2000)

[2] M.-C. Marinica, F. Willaime, and J.-P. Crocombette, Phys. Rev. Lett. 108 (2012)

025501.

[3] L. Dézerald, M.-C. Marinica, L. Ventelon, D. Rodney, F. Willaime, J. Nucl. Mater.

(in press)

Figure 1: Tetra-interstitial cluster with C15 structure in a bcc lattice. Blue cubes: vacancies, orange atoms: self-interstitials, grey atoms: bcc lattice.

The thermal stability and structure of neutron irradiation induced vacancy-solute

clusters in iron alloys

M. Konstantinović, G. Bonny, Monica Chiapetta

SCK•CEN, Nuclear Materials Science Institute, Boeretang 200, B-2400 Mol, Belgium

The structural properties of nanoclusters formed under neutron irradiation in iron-based

alloys are essential for understanding embrittlement and hardening of reactor pressure

vessel (RPV) steels. Even at nanometric sizes, the variety of solute, vacancy, interstitial

clusters, and their mutual complexes strongly affects the dislocation motion, causing

macroscopic changes in the mechanical properties. These changes, occurring in the RPV

during service of a nuclear power plant (NPP), are of considerable importance for the safe

operation and play a major role in the NPP life extension analyzes.

In this work the thermal stability and structure of clusters formed by neutron irradiation

are studied by means of positron annihilation spectroscopy of postirradiation annealed

FeCu, FeCuMnNi and FeMnNi alloys and rigid lattice calculations. While most of the

vacancy-solute clusters dissolve in the temperature range between 650 K and 700 K, the

presence of Ni and Mn solutes in vacancy-MnNi clusters provides an additional thermal

stability and shifts the annealing stage corresponding to the dissociation of these clusters

to higher temperature. Very good agreement between the measurements and calculations

is obtained for vacancy-MnNi clusters of nanometric size, containing of about 25-50 % of

vacancies.

Flux coupling between vacancies and interstitial solutes (C, N and O) in α-Fe solid

solution

Thomas Schuler, Maylise Nastar

CEA, DEN, Service de Recherches de Métallurgie Physique, F-91191 Gif-sur-Yvette,

France

We show that even at very low concentrations of carbon, nitrogen and oxygen in α-iron

(Fe), non-negligible concentrations of vacancy-solute clusters form under equilibrium or

irradiated conditions. The net flux of vacancies towards point defect sinks is thus likely to

induce an interstitial solute net flux, which can result in radiation induced segregation

phenomena.

For each solute, a generalized Hamiltonian is derived on the perfect body-centered cubic

lattice including substitutional and octahedral interstitial sites. Interactions are fitted to a

whole set of DFT calculations of small vacancy-solute clusters binding energies. Other

interactions are then added to the Hamiltonian, corresponding to interactions of Fe or

solute atom at the saddle point with the surrounding atoms. The latter are fitted so as to

reproduce DFT calculations of migration energies of solutes and vacancies in various

environments.

We extend the Self-Consistent Mean Field (SCMF) formalism to systems containing two

migrating species (interstitial solutes and vacancies) located on two different sublattices.

This extension is validated against Atomic Monte Carlo simulations which are perfomed

at high vacancy and solute concentrations. The atomic diffusion model is inserted into the

SCMF formalism and Low Temperature Expansions are used to calculate the ensemble

averages and the resulting full Onsager matrix of the system. For the first time, the

contribution of multiple vacancies is considered. The amplitude and the sign of flux

coupling is observed to strongly depend on the clustering tendency of vacancies and

interstitial solutes. Mobilities of vacancy-solute clusters are calculated as well.

This work was supported by the joint program "CPR ODISSEE" funded by AREVA,

CEA, CNRS, EDF and Mécachrome under contract n°070551.

Atomic Scale Strengthening Mechanisms due to Hard Obstacles in Fe

Yury Osetskiy, Roger Stoller

Materials Science and Technology Division, ORNL, Oak Ridge, TN 37831- 6138, USA

In this research we have studied dislocation – obstacle interactions over a wide range of

environmental and microstructural parameters with the main objectives focused on the

direct comparison with available and future experiments. Conventional range of

parameters such as obstacle size, temperature range and dislocation speed effects was

considered together with the specific output from “computer modeling experiment”. This

includes stress-strain behavior, critical resolved shear stress (CRSS) temperature

dependence and a complete analysis of the interaction mechanisms and their temperature

behavior. For the mechanism analysis we used a recently developed new dislocation

characterization and visualization technique that allowed us to define the dislocation line

direction and the local Burgers vector with an unachievable so far accuracy. This new

technique allows us to have a direct comparison with in situ deformation TEM

experiments and especially with the recently developed 3D TEM tomography.

This work was supported by the US Department of Energy Office of Fusion Energy

Sciences.

Effect of impurities on the mobility of self-interstitial clusters in α-Fe

Anna Serra

1, Napoleon Anento

1, Dmitry Terentyev

2, Yuri Osetsky

3

1Dept. Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain

2SCK•CEN, Boeretang 200, Mol, Belgium

3Materials Science and Technology Division, ORNL, Oak Ridge, TN 37831, USA

Self-interstitial atom (SIA) clusters formed by <111> crowdions are highly mobile

in pure iron. MD simulations have shown that cluster trajectories are one dimensional

(1D) with an almost continuous motion and activation energy of the order of 0.05eV [1,

2]. However, there is an essential discrepancy between simulations and experiment in

terms of the type of movement. Experimentally, 1D migration has been observed as

discrete 1D jumps interrupted from time to time due to some invisible obstacles or traps

at room temperature [3,4]. In this work, we address the problem of the SIA cluster’s

trapping mechanism that may lead to the slowing down or complete blockage of

highly mobile small (tens of defects) <1 1 1> SIA clusters in bcc Fe due to impurity

atoms in solid solution. Thus, we present the interaction of clusters with solute atoms

such as C, Ni, Cu, and Cr as well as with the stable solute-vacancy complexes.

Whereas the activation energy for the diffusion of clusters in pure iron is independent on

the cluster size, for clusters with diameters under 3nm, the presence of impurities

introduces a dependence of the activation energy on the impurity type and concentration,

cluster size and temperature.

This work was performed under the auspices of The Spanish ‘Ministerio de Economia y

Competitividad’ (FIS2012-39443-C02-02) and the Catalan Government (AGAUR

2009SGR 1003). The computing was partly carried out in CSUC (www.CESUC.CAT).

This work was partly supported by the CDP, an Energy Frontier Research Center at

ORNL funded by US DOE. The authors acknowledge useful discussions with Dr.

Lorenzo Malerba

[1] N. Anento, A. Serra, Y.N. Osetsky, Modell. Simul. Mater. Sci. Eng. 18, 025008

(2010)

[2] D. Terentyev, L. Malerba, M. Hou, Phys. Rev. B 74, 104108 (2007)

[3] Y. Satoh, H. Matsui, T. Hamaoka, Phys. Rev. B 77, 094135 (2008) [4] T. Hamaoka,

Y. Satoh, H. Matsui, J. Nuc. Mater. 433, 180 (2013)

Combined Molecular Dynamics and Object Kinetic Monte Carlo simulations of ion

implantation in Fe thin films

M. Aliaga1, I. Martin-Bragado

2 and M. J. Caturla

1

1

Dept. Física Aplicada, Facultad de Ciencias, Fase II, Universidad de Alicante, Alicante,

E-03690, Spain 2 IMDEA Materials Institute, C/ Eric Kandel, 2, Tecnogetafe, 28906 Getafe, Madrid,

Spain

Ion implantation experiments are being used extensively to validate multiscale models of

damage production in metals for fusion applications. In particular, in-situ TEM

measurements can be taken during implantation providing detailed information about the

process of defect production and evolution.

In this work we present a combined study using Molecular Dynamics (MD) and Object

Kinetic Monte Carlo (OKMC) to reproduce the ion implantation experiments in Fe of

Yao et al. [1]. Our objectives are, on the one hand, to study the effects of the surface on

the distribution of damage and, on the other hand, to follow the evolution of the

microstructure of the irradiated material.

These in-situ TEM irradiation experiments require of special conditions of the sample, in

particular the use of thin films, with thicknesses that can be as small as 50nm. We prove,

using Molecular Dynamics calculations with recent interatomic potentials developed for

Fe, that the primary damage in thin films is very different from the primary damage in the

bulk material. For example, large vacancy clusters are produced under ion implantation

more frequently than in the bulk. They occur near the surfaces. In addition it seems that

the largest defect clusters close to surfaces are vacancy in nature and have a Burgers

vector <100>. We have used the cascade database obtained with MD for thin films and

bulk samples as input for the OKMC code MMonCa [2] in order to compare directly to

the experiments. In these type of experiments, <100> and 1/2 <111> loops are always

observed, but the way they evolve from smaller clusters is not clear. We test two different

models for the evolution of these clusters. Comparing our simulation results with the

experimental ones we are able to assess which of the models is the most accurate.

[1] Z. Yao, M. Hernández Mayoral, M. L. Jenkins, M. A. Kirk, Phil. Mag. 88 (2008)

2851.

[2] I. Martin-Bragado, et. al., MMonCa: An Object Kinetic Monte Carlo simulator for

damage irradiation evolution and defect diffusion. Computer Physics Communications

(2013).

Development of object kinetic Monte Carlo models for nanostructural evolution

under irradiation in Fe-Cr alloys

Monica Chiapetto1,2

, Lorenzo Malerba1, Charlotte S. Becquart

2, Giovanni U. Bonny

1

1

SCK•CEN, Nuclear Materials Science Institute, Boeretang 200, B-2400 Mol, Belgium 2

Unité Matériaux Et Transformations, UMET, UMR 8207, USTL, 59600 Villeneuve d’Ascq,

France

High-chromium ferritic-martensitic steels are candidate structural materials for future

fusion reactors, accelerator driven systems (ADS) and core components in Gen-IV

reactors, thanks to their good resistence to irradiation-induced swelling and

embrittlement. Starting from the already existing object kinetic Monte Carlo (OKMC)

model for neutron irradiated Fe-C binary alloys [1], we developed physically-based sets

of parameters able to consider the effects of Cr substitutional solutes and simulate the

irradiation-induced nanostructural evolution and defect formation in Fe-Cr alloys. Our

models proved to be able to describe the buildup of irradiation defect populations at the

operational temperature of light water reactors (~300 °C), in terms of both density and

size distribution of the defect cluster populations. Four Cr concentrations (2.5, 5, 9 and 12

wt.%Cr) were investigated up to ~0.6 dpa under both neutron and ion irradiation and

specific reference irradiation experiments were simulated [2,3]. Different dose-rate and

irradiation temperature ranges were also investigated.

Cr content has been shown to be

a key parameter to determine the

self-interstitial clusters

diffusivity in Fe-Cr alloys, which

proved to be strongly reduced in

a non-monotonic way depending

on both Cr content and cluster

size when compared to "pure"

Fe. This mobility reduction is the

consequence of a relatively long-

ranged, ~1 nm, attractive

interaction between Cr atoms

and SIA in the crowdion

configuration [4] and exhibits the

same non-monotonic dependence

on Cr content of empirically

observed void swelling suppression. The clustering of the vacancy population, when

compared to Fe-C alloys, also appears to be significantly reduced already in the presence

of limited Cr concentrations [Fig.1] and increases only slightly with Cr content. [1] V. Jansson, M. Chiapetto, L. Malerba, J. Nucl. Mater. 442 (2013) 341-349.

[2] C.D.Hardie, C.A.Williams, S. Xu, S.G.Roberts, J. Nucl. Mater. 439 (2013) 33-40. [3] M.

Mayoral et al, DELIVERABLES D4.7-D4.9, FP7/GetMat project (2013).

[4] D. Terentyev, L. Malerba, A.V. Barashev, Philos. Mag. Lett. 85 (2005) 587-594.

PERFORM 60 - Prediction of the Effects of Radiation FOr Reactor pressure vessel

and in-vessel Materials using multi-scale modelling – 60 years foreseen plant lifetime

A. Al Mazouzi1, J. Sharples

2, M. Konstantinovic

3, D. Moinereau

1, D. Feron

4, C Domain

1

1EDF R&D, Avenue les Renardières, Ecuelles, 77818 Moret sur Loing Cedex, France

2SERCO assurance, Walton House, Warrington Cheshire WA3 6GA, UK

3SCK.CEN, Boeretang 200, 2400 Mol, Belgium

4CEA, Saclay 91 191 Gif-sur-Yvette cedex, France

In nuclear power plants, materials may undergo degradation due to severe irradiation

conditions that may limit their operational life. Utilities that operate these reactors need to

quantify the ageing and the potential degradations of some essential structures of the

plant to ensure its safe and reliable operation. So far, to take into account these

degradations in the design and safe operation of the installations, the utilities and

consequently the safety authorities rely mainly on in-field experience and on the

experimental testing of surveillance materials in specialized hot cells.

Continuous progress in the physical understanding of the phenomena involved in

irradiation damage and environmental effects, and in computer sciences encouraged the

development of multi-scale numerical tools able to simulate the material behavior in

nuclear field. Thus, recently, the FP7 Collaborative Project PERFORM 60 [1], has been

launched to pursue the improvement of the developed tools under the previous FP6

PERFECT project [2], for reactor pressure vessel (RPV) steels and to initiate the

development of similar multi-scale modeling tools to simulate the combined effects of

irradiation and corrosion on the RPV internals.

To reach these objectives, twenty European organizations involved in the nuclear field

are engaged to develop the necessary computer tools and their integration in a user

friendly platform with the main concern to produce experimentally validated physical

models to predict the lifetime of these components.

In this lecture, in addition to an overview of the project, the work that is being performed

will be illustrated by examples to demonstrate the robustness and the complexity of the

multi-scale modeling approach when applied to nuclear materials.

[1] www.perform60.net

[2] www.fp6-perfect.net