Properties of vacancy clusters in FeMnNi alloys for the parameterization of OKMC models

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Properties of vacancy clusters in FeMnNi alloys for the parameterization of OKMC models

L. Messina, M. Chiapetto, C. Becquart, C. Domain, P. Olsson, P. Efsing, L. Malerba

To cite this version:

L. Messina, M. Chiapetto, C. Becquart, C. Domain, P. Olsson, et al.. Properties of vacancy clusters in FeMnNi alloys for the parameterization of OKMC models. International Group for Radiation Damage in Materials (IGRDM-19), Apr 2016, Asheville NC, United States. �cea-02435105�

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Properties of vacancy clusters in FeMnNi alloys for

the parameterization of OKMC models

L. Messina

a,b

_{, M. Chiapetto}

c

_{, C. Becquart}

d

_{, C. Domain}

e

_,

P. Olsson

b

_{, P. Efsing}

b,f

_{, L. Malerba}

c

IGRDM-19, Asheville NC April 11th_-15th ₂₀₁₆ a _{CEA Saclay, Service de Recherches de Métallurgie Physique (France)} b _{KTH Royal Institute of Technology, Reactor Physics (Sweden)} c _{SCKCEN, Nuclear Materials Science Institute (Belgium)} d _{Université de Lille 1, Unité Matérieux et Transformations (France)} e _{EDF-R&D, Département Matérieux et Mécanique des Composants (France)} f _{Vattenfall AB, Sweden} Asheville, April 12th₂₀₁₆ _{Contact: messina@kth.se} !!! PhD thesis on modeling of Mn-Ni-Si clusters in RPV steels !!! “Multiscale modeling of atomic transport phenomena in ferritic steels” L. Messina, KTH Royal Institute of Technology (December 2015)

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PhD thesis summary

2 corporate.vattenfall.se L. Messina et al., IGRDM-19 Asheville, April 10-15th 2016 400 800 1200 1600 –1.0 –0.5 0.0 0.5 1.0 Cr Cu Mn Ni P Si Temperature [K] Wind factor drag no drag 300°C 10–6 ₁₀–5 ₁₀–4 ₁₀–3 ₁₀–2 ₁₀–1 1020 1021 1022 1023 1024 1025 1026 1027 1028 FeMnNi (APT) FeMnNi (TEM) Ringhals (APT) Exp. FeMnNi (APT) Exp. FeMnNi (TEM) Exp. Ringhals (APT)

Cluster density [m −3] Dose [dpa] Interstitial clusters Systematic vacancy drag at 300°C Interstitial loops ó MNSPs

Solute-defect flux coupling in dilute alloys

Fe(X), X = Cr, Cu, Mn, Ni, P, Si (and many more)

Modeling of solute transport in kinetic Monte

Carlo (KMC) simulations

1. Solute transport by vacancy drag (Cu, Mn, Ni, P, Si) and single dumbbells (Cr, Mn). 2. Predicition of radiation-induced segregation profiles. 3. Effect of strain fields on solute transport next to dislocation lines. 1. Properties of vacancy-solute clusters in FeMnNi alloys. 2. Prediction of energy barriers by DFT-aided artificial neural networks. 3. Microstructure evolution simulation of high-Mn, high-Ni RPV steels (Ringhals).

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PhD thesis summary

3 corporate.vattenfall.se L. Messina et al., IGRDM-19 Asheville, April 10-15th 2016 400 800 1200 1600 –1.0 –0.5 0.0 0.5 1.0 Cr Cu Mn Ni P Si Temperature [K] Wind factor drag no drag 300°C 10–6 ₁₀–5 ₁₀–4 ₁₀–3 ₁₀–2 ₁₀–1 1020 1021 1022 1023 1024 1025 1026 1027 1028 FeMnNi (APT) FeMnNi (TEM) Ringhals (APT) Exp. FeMnNi (APT) Exp. FeMnNi (TEM) Exp. Ringhals (APT)

Cluster density [m −3] Dose [dpa] Interstitial clusters Systematic vacancy drag at 300°C Interstitial loops ó MNSPs

Solute-defect flux coupling in dilute alloys

Fe(X), X = Cr, Cu, Mn, Ni, P, Si (and many more)

Modeling of solute transport in kinetic Monte

Carlo (KMC) simulations

1. Solute transport by vacancy drag (Cu, Mn, Ni, P, Si) and single dumbbells (Cr, Mn). 2. Predicition of radiation-induced segregation profiles. 3. Effect of strain fields on solute transport next to dislocation lines. 1. Properties of vacancy-solute clusters in FeMnNi alloys. 2. Prediction of energy barriers by DFT-aided artificial neural networks. 3. Microstructure evolution simulation of high-Mn, high-Ni RPV steels (Ringhals).

PRESENTED AT IGRDM-18

Lorenzo’s presentation

This presentation

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• Objective: parameterization of object KMC simulations of RPV

microstructure evolution.

• Two alloys: model Fe-C-MnNi alloy

[1]

_{and Ringhals RPV steel}

[2]

_.

• Parameterization of all objects.

• Solutes can be introduced

explicitly

or with a

“gray-alloy”

approach.

• Usual techniques: kinetic Monte Carlo, molecular dynamics, ab initio

with mean-field treatment.

Introduction

4

L. Messina et al., IGRDM-19 Asheville, April 10-15th 2016

Size Prefmig _Emig _Prefdiss _Ediss

1 8.1e13 0.31 eV -

-2 3.4e14 0.42 eV 6e12 0.30 eV 3 1.2e13 0.42 eV 6e12 0.30 eV 4 1.2e13 0.80 eV 6e12 0.30 eV 5 1.6e12 0.10 eV 6e12 0.30 eV

… … … … …

MOBILITY

Probability of migration*

STABILITY

Probability of dissociation [1] M. Hernández-Mayoral et al., J. Nucl. Mat. 399 (2010). [2] P. Efsing et al., J. ASTM Int. 4 (2007).

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Defect clusters in FeC

5 RINGHALS us.arevablog.com declanbutler.info/Fukushima/Fukushima.kmz L. Messina et al., IGRDM-19 Asheville, April 10-15th 2016 1 10 100 1000 10000 10–4 10–1 102 105 108 1011 1014

Cluster size [N. defects]

Migration frequency at 573 K [s −1 ] VACANCIES no solutes 1 10 100 1000 10000 10–4 10–1 102 105 108 1011 1014

Migration frequency at 573 K [s −1 ] INTERSTITIALS no solutes • Atomistic KMC simulations with neural network prediction of migration barriers, based on molecular dynamics database. N. Castin et al., J. Nucl. Mat. 429 (2012). corporate.vattenfall.se • Molecular dynamics simulations. • Postulated substantial slowdown for n > 90. D. Terentyev et al., Phys. Rev. B 75 (2007) N. Anento et al., Mod. Sim. Mat. Sci. Eng. 18 (2010) V. Jansson et al., J. Nucl. Mat. 443 (2013)

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Interstitial clusters in FeC-MnNi

6 RINGHALS corporate.vattenfall.se declanbutler.info/Fukushima/Fukushima.kmz L. Messina et al., IGRDM-19 Asheville, April 10-15th 2016

1

10

100 1000

10000

10

–10

10

–6

10

–2

10

2

10

6

10

14

Cluster size [N. defects]

Migration frequency at 573 K [s

−1

]

INTERSTITIALS

no solutes with Mn&Ni Cluster-solute binding energy (DFT calculations by C. Domain):

• Mobility reduction due to

strong attractive interaction

between interstitial clusters

and Mn, Ni.

• In analogy to effect of Cr

on interstitial clusters in Fe

[1]

_.

[1] _{D. Terentyev et al., Philos. Mag. Lett. 85 (2005)}

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Vacancy clusters in FeC-MnNi

7 RINGHALS us.arevablog.com corporate.vattenfall.se declanbutler.info/Fukushima/Fukushima.kmz L. Messina et al., IGRDM-19 Asheville, April 10-15th 2016 100 101 102 103 104 0.4 0.8 1.2 1.6

Migration Energy [eV]

VACANCIES no solutes with Mn&Ni 1 10 100 1000 10000 10–4 10–1 102 105 108

Migration frequency at 573 K [s

−1 ] _{no solutes}

with Mn&Ni

Migration barriers Migration frequency

??

• “Arbitrary” reduction of vacancy cluster mobility (and immobilization for n > 10) to match experimental characterization of FeMnNi alloy.

• Same assumption works also for Ringhals steels (Lorenzo’s previous presentation).

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Atomistic KMC method

RINGHALS

us.arevablog.com

corporate.vattenfall.se declanbutler.info/Fukushima/Fukushima.kmz

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Vacancy-solute pairs

9

V-Cr

V-Cu

V-Mn

V-Ni

V-P

V-Si

MEAN FREE PATH BEFORE DISSOCIATION (550 K)

0.24 nm

0.86 nm

0.68 nm

0.42 nm

3.51 nm

1.00 nm

FROM AB INITIO DATA!!

0.6 0.65 0.7 0.75 0.8 Cr Cu Mn Ni P Si

Migration barrier [eV]

0.7 0.8 0.9 1 1.1 1.2 Cr Cu Mn Ni P Si

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Mobility of V

_x

Mn

_y

Ni

_z

clusters

RINGHALS us.arevablog.com corporate.vattenfall.se declanbutler.info/Fukushima/Fukushima.kmz

IMMOBILITY

0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

Dissociation energy [eV]

V₁ 1−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₂ 2−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₃ 3−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₄

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Mobility of V

_x

Mn

_y

Ni

_z

clusters

IMMOBILITY

0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₁ Mn 2 Mn 1 1−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₂ Mn 2 _Mn 1 2−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₃ Mn 2 Mn 1 3−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₄

Mn

1

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Mobility of V

_x

Mn

_y

Ni

_z

clusters

IMMOBILITY

0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₁ Ni₂ Mn 2 Mn 1 Ni 1 1−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₂ Ni 2 Mn 2 _Mn 1 Ni 1 2−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₃ Ni 2 Mn 2 Mn 1 Ni1 3−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₄ Ni 2 Mn 1 Ni 1 4−vacancy clusters

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Mobility of V

_x

Mn

_y

Ni

_z

clusters

IMMOBILITY

0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₁ Mn 2Ni2 Mn 1Ni1 Ni₂ Mn 2 Mn 1 Ni 1 1−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₂ Mn 2Ni2 Mn 1Ni1 Ni 2 Mn 2 _Mn 1 Ni 1 2−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₃ Mn 2Ni2 Mn 1Ni1 Ni 2 Mn 2 Mn 1 Ni1 3−vacancy clusters 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

V₄ Mn 2Ni2 Mn 1Ni1 Ni 2 Mn 1 Ni 1 4−vacancy clusters

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Mobility of V

_x

Mn

_y

Ni

_z

clusters

IMMOBILITY

+Mn&Ni +Ni +Mn Partial immobilization observed (Emig < 1.20 eV) 0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

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Mobility of V

_x

Mn

_y

Ni

_z

clusters

RINGHALS us.arevablog.com corporate.vattenfall.se declanbutler.info/Fukushima/Fukushima.kmz 0.4 0.8 1.2 1.6 2.0 V 2 V 3 V 4

Mean free path [nm] V 1Mn1 V 1Mn2 V 2Mn1 V 2Mn2 V 3Mn1 V 3Mn2 V 4Mn1 V 1Ni1 V 1Ni2 V 2Ni1 V 2Ni2 V 3Ni1 V 3Ni2 V 4Ni1 V 4Ni2 0.4 0.8 1.2 1.6 2.0 V 1Mn1Ni1 V 1Mn2Ni2 V 2Mn1Ni1 V 2Mn2Ni2 V 3Mn1Ni1 V 3Mn2Ni2 V 4Mn1Ni1 V 4Mn2Ni2

Mean free path [nm]

0.70 0.80 0.90 1.00 0.60 0.80 1.00 1.20 1.40

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Gray-alloy perspective

16 RINGHALS us.arevablog.com declanbutler.info/Fukushima/Fukushima.kmz L. Messina et al., IGRDM-19 Asheville, April 10-15th 2016 0.0 0.4 0.8 1.2 1.6 2.0 0.80 0.90 1.00 1.10 1.20 1.30 1.40

Dissociation energy [eV]

x_Mn [at.%] 0.0 0.4 0.8 1.2 1.6 2.0 0.70 0.80 0.90 1.00 1.10 1.20 1.30

Migration energy [eV]

x_Mn [at.%] 1.6% Ni 0.0% Ni 0.0% Ni 1.6% Ni

a)

_b)

Stability and mobility of a di-vacancy in a random Fe-MnNi alloy

• Presence of Ni atoms has strong immobilizing effect.

• Presence of Mn atoms increases the probability of dissociation

(because of strong V-Mn binding).

• Functions E

m/d

_= f(x

Mn

, x

Ni

) to be directly implemented in OKMC code.

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Gray-alloy perspective

17 RINGHALS us.arevablog.com corporate.vattenfall.se declanbutler.info/Fukushima/Fukushima.kmz L. Messina et al., IGRDM-19 Asheville, April 10-15th 2016 VACANCY CLUSTERS 1 10 100 10–4 10–1 102 105 108

−1 ] FeC (previous AKMC)

FeCMnNi (postulated)

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Gray-alloy perspective

18 RINGHALS us.arevablog.com corporate.vattenfall.se declanbutler.info/Fukushima/Fukushima.kmz L. Messina et al., IGRDM-19 Asheville, April 10-15th 2016 1 10 100 10–4 10–1 102 105 108

−1 ] FeC (previous AKMC)

FeCMnNi (postulated) FeC (this AKMC) FeCMnNi (this AKMC)

VACANCY CLUSTERS Migration frequency 1.6%Mn, 1.6%Ni 0%Mn, 0%Ni

• Estimated slowdown at 573 K

is only 1 order of magnitude.

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Conclusions

• _{The properties of vacancy clusters in FeMnNi were calculated}

by means of atomistic kinetic Monte Carlo simulations.

• Mn transport in Fe alloys is more efficient than Ni and Si.

• _{Mn seems to have a stabilyzing effect on vacancy clusters,}

whereas Ni contributes more to the slowdown.

• The current calculations do not confirm a slowdown of vacancy

clusters as strong as assumed by Lorenzo’s OKMC model. Effect of

vacancy-carbon(-solute) complexes?

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• L. Messina, M. Nastar, T. Garnier, C. Domain, P. Olsson, Exact ab initio transport coefficients in bcc Fe-X dilute alloys, Physical Review B 90, 104203 (2014). • L. Messina, L. Malerba, P. Olsson, Stability and mobility of small vacancy-solute complexes in Fe-MnNi and dilute Fe-X alloys: A kinetic Monte Carlo study, Nuclear Instruments and Methods in Physics Research B 352, 61-66 (2015). • L. Messina, Multiscale modeling of atomic transport phenomena in ferritic steels, PhD Thesis, KTH Royal Institute of Technology (2015). • L. Messina, M. Nastar, N. Sandberg, P. Olsson, Systematic electronic-structure investigation of substitutional impurity diffusion and flux coupling in bcc iron, accepted for publication in Physical Review B (2016). • L. Messina, M. Chiapetto, P. Olsson, C. Becquart, L. Malerba, An object kinetic Monte Carlo model for the microstructure evolution of neutron-irradiated reactor pressure vessel steels, accepted for publication in Nuclear Instruments and Methods in Physics Research B (2016).

THANKS FOR YOUR ATTENTION!

Publications

Acknowledgments

• Financial support from Vattenfall AB, Göran Gustafsson Stiftelse, MatISSE and SOTERIA FP7 European projects. • Computational power from SNIC, CSCS, EDF. • Host institutions: KTH, CEA, EDF, SCK-CEN. • Collaborators: - M. Nastar, T. Garnier, F. Soisson, T. Schuler (CEA) - C. Domain (EDF) - N. Castin, L. Malerba, M. Chiapetto (SCK-CEN) - C. Becquart (Université de Lille)

Financial support from: Vattenfall AB, Göran Gustafsson Stiftelse, MatISSE and SOTERIA FP7 EU projects