RPV steels microstructure evolution under irradiation: a multiscale approach

Cosires 2004 C.S. Becquart

RPV steels microstructure evolution under irradiation: a multiscale approach

Charlotte Becquart and...

EDFElectricitéde France

A. Barbu: CEA, C. Domain: EDF, S. Jumel: EDF, M. Hou: U.L.B, A. Legris: LMPGM, L. Malerba: SCK-CEN,J-M. Raulot, J-C. Van Duysen: EDF, A. Souidi: U. Saida, D. Bacon: U. Liverpool, M. Perlado: Polytech., M. Hernández-mayoral, CIEMAT, R. Stoller: ORNL, B. Wirth: LLNL, B. Odette: UCSB...

PhD and Master of Science students : P. Renuit, E. Vincent, S. Jumel, A. Marteel, P. Herrier, J-C. Turbatte, J-M Raulot, S. Pourchet, A. Tigeras, Z. Zhao


Vessel

12 m

4.4 m

22 cm


0

50

100

150

200

250

-200 -100 0 100 200 300

Temperature (°C)

En

erg

y (J

) baselineirradiated

DBTT shift (41 J level)

USE drop

Displacement

Lo

ad

Baseline

Irradiated

04 Oct 2001 29 Nov 2001

yield increase

DD

00

ll

00

Displacement

------ Baseline

------ Irradiated

Under irradiation: modification of the mechanical properties

===> hardening and embrittlementTDoseFluxComposition

C S P Si Cr Mo Mn Ni Al Co Cu

0.16 0.008 0.008 0.19 0.24 0.55 1.25 0.74 0.009 0.01 0.07

Chemical composition (wt.%) of DAMPIERRE 2


SIA-Loop

NanovoidCu-rich ppt or atmospheres

P-segregation

Matrix

Damage

Precipitation

Segregatio

n

at GBs

Microstructural changes

Tomographic atom probe

Université de Rouen

V = 4 x 4 x 4 nm3

Fe-0.1%Cu , dose 5.5 1019n/cm2


1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E-08 1.E-06 1.E-04 1.E-02 1.E+00 1.E+02

Eneutron (MeV)

Flux

(n/c

m2/

s)

SIA-Loops

NanovoidCu-rich ppt

P-segregation

Matrix

Damage

Precipitation

Segregatio

n

at GBs

?

0

50

100

150

200

250

-200 -100 0 100 200 300temperature (°C)

ener

gy (

J)

?

Necessary balance between simplifications and

approximations versus completeness and physical

detail


Rapid overview of the REVE ’s VTR

The primary damage : role of the cohesive model

The evolution of the primary damage : parameterisation of the Object Kinetic Monte Carlo

Outline of the talk


A. Seeger, Proc. 2nd UN Int. Conf. on Peaceful Usess of Atomic Energy, Geneva, 1958, vol.6 (United Nations, New York, 1958) p 250.


- defect - dislocation interaction :

Screw DislocationDefect

Hardening

V-Cu clusters (s to h)

- Evolution - Primary damage

vacancies & interstitials (15 ps)

Microstructure

Clusters and loops

- PKA spectrum

Spectre de neutron

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E-08 1.E-06 1.E-04 1.E-02 1.E+00

1.E+02

Flu

x (n

/cm

2/s)

1.E-08

1.E-05

1.E-02

1.E+01

1.E+04

1E-05 1E-04 1E-03 1E-02 1E-01 1E+00 1E+01

EPKA (MeV)

PK

A F

lux

(PK

A/µ

m3/M

eV/s

)

PWR

- neutron spectrum

Simplified overview of the REVE ’s VTR

Specter

Incas

Dymoka Lakimoca

Dupair


VASP (Vienna Ab initio Simulation Package)

Density Functional Theory

Plane wave & ultra soft pseudo potentials (Vanderbilt type pseudo potentials)

Exchange and correlation: LDA and GGA (PW91)

Spin polarised

54 atoms (555 k points) – 128 atoms (333 k points)

all atomic positions for defects calculation are relaxed

Methods and cohesive models

Ab initio

Semi-empirical potentials (FeCu)

M. Ludwig, D. Farkas, D. Pedraza and S. Schmauder, Modelling Simul. Mater. Sci. Eng, 6 (1998) 19

G.J. Ackland, D.J. Bacon, A.F. Calder and T. Harry Phil. Mag. A, vol.75 (1997) 713

VASP:

G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993); ibid. 49, 14 251 (1994)G. Kresse and J. Furthmüller, Comput. Mat. Sci. 6, 15 (1996)G. Kresse and J. Furthmüller, Phys. Rev. B 55, 11 169 (1996)

Static calculations, molecular dynamics, atomic Kinetic Monte Carlo


The primary damage : MD simulations


The primary damage

MD simulations 2i

2

ii t

rmf

Large systems ===> empirical potentials

Embedded Atom Method

Finnis Sinclair...

i

ii r

rf

V

M.W. Finnis and J.E. Sinclair, Phil. Mag. A 50 (1984) 45

R.J. Harrison, A.F. Voter and S.P. Chen, "Embedded Atom Potential for BCC Iron", Atomistic simulation

of Materials- Beyond Pair Potentials, V. Vitek and D.J. Srolovitz (editors), 219, Plenum New York (1989)

M.I. Haftel, T.D. Andreadis, J.V. Lill and J.M. Heridon, Phys. Rev. B 42 (1990) 11540

G. Simonelli, R. Pasianot and E.J. Savino, Mat. Res. Soc. Symp. Proc. 291 (1993) 567

R.A. Johnson and D.J. Oh. J. Mater. Res. 4 (1989)1195

Yu. N Osetsky and A. Serra, Phys. Rev. B 57 (1998) 755


Fe I

•Not a T effect

•role of short range interaction of the potential

F

Fe II

RCS

Role of the cohesive model (interatomic potential)


Use BCA adjusted on MD results

121212

62.13.022

1.055.035.0 a

r

a

r

a

r

eeer

eZrV 12a

r

eArV

Molière potential Born Mayer potential

range = distance between atoms for which V(r ) = 30 eV

)(rVh rstifness

Statistics needed:



0

50

100

150

200

0.1 0.6 1.1 1.6

Molière IIIBorn Mayer III

Distance (Å)

Pot

entia

l Ene

r gy

(eV

)

0-200 eV : formation range of RCS


0 200 400 600 800 1000 1200 1400 16000

100

200

300

400

500

Effet du potentiel sur les LCSComparaison entre Molière et Born-Mayerajustés aux FeIII (Farkas)Sans DBND

Sans DBNDE=20 keV

Molière (a12

=0.0781) Born-Mayer (a

12=0.2180)

Mean n

um

ber

of

LC

S

Temperature (K)

No

mb

re m

oye

n d

e R

CS

Température (K)

Molière III

BM III

Mea

n nu

mbe

r of

RC

S

Temperature (K)


Kin

etic

ene

rgy

(eV

)Role of the cohesive model

(interatomic potential)

0

10

20

30

40

50

0 1000 2000 3000 4000 5000 6000

Time (s)

Kin

eti

c e

ne

rgy

(e

V)

Time (x10-16s)

0

5

10

15

20

25

30

35

40

45

50

0 500 1000 1500 2000 2500 3000 3500

Time (s)

Kin

eti

c e

ne

rgy

(e

V)

Time (x10-16s)

Kin

etic

ene

rgy

(eV

)

MD Fe III potential. The sequence is defocusing, then focusing

MD Fe I potential. The sequence is defocusing

50 eV PKA initiated at 0.3 deg. from <111>

Influence of potential on focusing


The stiffer the BCA potential (the shorter ranged)

•the lower the focalisation threshold•the less kinetic energy losses between successive collisions•the more numerous the RCS and the longer.

0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.11510

20

30

40

50

60

70

80

90

100

AMLJ

Initial directions: <15, 15, 16> <15, 1, 1>

Seuil111 Seuil100

Focu

sin

g t

hre

sh

old

(e

V)

Screening length (Å)rayon d’écrantage (Å)

Seu

il de

foca

l isat

ion

(eV

)

Molière I

Molière III

Influence of potential on focusing



The shorter the range for very high energies, the larger the cascade volume

Molière IIIBM III

Volume ao3

Fré

quen

cy

0

1000

2000

3000

4000

5000

0.1 0.6 1.1 1.6

Molière IIIBorn Mayer III

Distance (Å)

Pot

entia

l ene

rgy

(eV

)

The more diluted the cascade

Influence of potential on cascade expansion



• Short potential range favours focusing in RCS

• Large potential range favours focusons on the expense of RCS

One third of the energy given by

PKA partitioned between replacement

sequences and focusons.



• During the cascade development, one third of the energy given by the PKA to the lattice is partitioned between replacement sequences and focusons.

• Short potential range favours focusing and energy transport in RCS on the expense of focusons.

• The shorter the range for very high energies, the larger the cascade volume, the more “diluted” the cascade.

Main conclusions on the cohesive model

Quantitative results have to be taken with care

Better model for atomic interactions at small separations : ab initio calculations

M. I. Mendelev, S. Han, D. J. Srolovitz, G. J. Ackland, D. Y. Sun and M. Asta, Phil. Mag. A 83 (2004) 3977.

Threshold displacement energies not enough


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 2 3 4 5 6 7 8 9

cluster size (number of interstitials)

10 keV Fe III

10 keV Finnis type Fe [16]

5 keV Fe III

5 keV Finnis type Fe [16]

Cluster size (number of interstitials)


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 500 1000 1500 2000 2500

Fe I

Fe II

Fe III

Experimental

Temperature (K)

MS

D (

Å3 )

Temperature (K)

Latt

ice

para

met

er

(Å)

2.86

2.88

2.9

2.92

2.94

2.96

2.98

0 400 800 1200 1600 2000

Fe I

Fe II

Fe III

Experimental

Let’s not forget the thermal properties


Evolution of the primary damage

Object Kinetic Monte Carlo


Annihilation

Interstitial loop

Emission

Interstitial cluster

Vacancy cluster

traps

Vacancyloop

Electrons

Neutrons

Frenkel pairs

cascade

Object KMC: the events

+

Emission

Migration

Parameterisation

+

+

Recombination

•Gi =Gi0 exp( -Ea / kT)

>300nm

PBCor surface

sinks


0

10

20

30

40

50

1E-12 1E-10 1E-08 1E-06 0.0001 0.01 1 100

Time (s)

Num

ber of

def

ects

All vacancies

Vacancy clusters

All interstitials

Interstitial clusters

OKMC ageing of 20 keV cascade in Fe 0.2%Cu

Absorbing boundary conditions


Parameterisation : interaction with solute

atomsInterstitials

– No interaction with solute atoms

Vacancies

– V-Cu clusters: mobility decreases with size (# solute atoms and # V)

– V and (V-Cu) emission depends on binding and formation energies

diffusion / migration

V emission

V-Cu emission


BABA rrd

loops

Reaction radii

V-I recombination distance

Exp 2.2 a0 - 3.3a0

MD 1.7 a0 - 1.9 a0

J. Dural, J. Ardonceau and J. C. Roussett, Le Journal de Physique 38 (1977) 1007‑1011.

M. Biget, R. Rizk, P. Vajda and A. Bessis, Solid state comm. 16 (1975) 949-952.

F. Gao, D. J. Bacon, A. V. Barashev and H. L. Heinisch, Mater. Res. Soc. Symp. Proc. 540 (1999) 703-708.


Ab initio

EAM Ludwig et al.

4.05 Å

No recombination

FS Ackland et al.

Reaction radii


Reaction radii

Highly anisotropic


Reaction radii

Ageing of a 20 keV cascade

0

10

20

30

40

50

60

70

80

-14 -12 -10 -8 -6 -4 -2

r = 1 nn

r = 1.9 a0

r = 2.2 a0

r = 3.3 a0

Log(t) (s)

Me

an

nu

mb

er o

f de

f ect in

cluste

rs

1 st nn/2

1.9 a0/2

2.2a0/2

3.3a0/2


0

1

2

3

4

5

-16 -12 -8 -4

Log(t) (s)

Me

an

nu

mb

er o

f V m

ixed

Cu

- V c lu

s ter s

0

0.5

1

1.5

2

2.5

3

-16 -11 -6

r = 1.25

r = 2.7

r = 3.2

r = 4.7

Log(t) (s)M

ea

n n

um

be

r of C

u in

mix e

d C

u-V

cluste

rs

Å

Å

Å

Å

Ageing of a 20 keV cascade containing 0.2 at.%Cu

Reaction radii

1 st nn/2

1.9 a0/2

2.2a0/2

3.3a0/2


M. Eldrup, B.N. Singh, S.J. Zinkle, T.S. Byun and K. Farrell, Journ. Nucl. Mater. 307-311 (2002) 912-917] .

Neutron irradiation (HFIR flux)Density of vacancy clusters

Reaction radii

HFIR : dose-rate 10-6 dpa/s

dpa

Den

sity

(m

-3)

1E+23

1E+24

1E+25

0.0001 0.001 0.01 0.1 1

r = 1 nn/2

r = 1.9 a0/2

r = 3.3 a0/2

experimental

*

70°C

31016 FPcm‑3s‑1

41014 10 keV and 21014 20 keV cascade-debriscm‑3s‑1


0

20

40

60

80

100

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

dpa

% C

u i

n p

rec

ipit

ate

s

Fe0.2at.%Cu, r = 1nn Fe0.1at.%Cu r = 1nn Fe0.2at.%Cu r = 1.9a0 Fe0.1at.%Cu 1.9a0 Fe0.2at.%Cu r = 3.3a0 Fe0.1at.%Cu r = 3.3a0 Experimental results

P. Auger, P. Pareige, S. Welzel, and J‑C. Van Duysen, J. Nucl. Mater. 280 (2000) 331.

% o

f C

u pr

ecip

itate

d

dpa

Neutron irradiation (HFIR flux)

% of Cu precipitated

Reaction radii

Fe0.2at.%Cu r = 1nn/2

Fe0.1at.%Cu r = 1nn/2

Fe0.2at.%Cu r = 1.9 a0/2

Fe0.1at.%Cu r = 1.9 a0/2

Fe0.2at.%Cu r = 3.3 a0/2

Fe0.1at.%Cu r = 3.3 a0/2

Experimental


1E+22

1E+23

1E+24

1E+25

1E+26

1E+27

0.0001 0.001 0.01 0.1 1

Set A

set B, s = 0.51

set B, s = 10

set C

experimental

min

max

dpa

Den

sity

(m

-3)

M. Eldrup, B.N. Singh, S.J. Zinkle, T.S. Byun and K. Farrell, Journ. Nucl. Mater. 307-311 (2002) 912-917] .


Density of vacancy clusters

Mobilities

dose-rate 10-6 dpa/s31016 FPcm‑3s‑1

41014 10 keV and 21014 20 keV cascade-debriscm‑3s‑1


Mobilities

• INTERSTITIALS– mono–interstitials: 3D random walk– clusters: 3D random walk or 1D

along <111> direction (cf. MD)

I à 1000K

I à 600K 2 I à 600K

MD simulations

sm0clusters (size m >=2): attempt frequency

Em = 0.04 eV, s = 0.51

Yu. N. Osetsky, D. J. Bacon, A. Serra, B. N. Singh and S. I. Golubov, J. Nucl. Mater. 276 (2000) 65.

C.-C. Fu, F. Willaime, and P. Ordejón, Phys. Rev. Lett. 92, 175503 (2004)

Exp and Ab initio Em = 0.3 eV for SIA


A. Hardouin du parc, Ph. D. Thesis, Paris XI-Orsay University (1997), ISSN 0429‑3460, CEA report R‑5791

Model experiment (A. Hardouin du parc, A. Barbu, CEA France)

1400 nm

1.5 10-4 dpa/s

900 s

TEM : interstitial dislocation loop density

Mobilities


Mobilities

Set B, s = 10, large clusters almost immobile

Loop density after 1200 s

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

0.0015 0.0019 0.0023 0.0027 0.0031

1/T (K-1)

Loop

den

sity

(cm

-3)

*

set A

set B, r = 1nn/2

set B, r = 3.3 a0/2

experimental

s0 mclusters (size m >=2): attempt frequency

Em = 0.04 eV


0.28 eV 0.36 eV 0.70 eV

Binding energies V-clusters 128 atoms,

3x3x3 kpoints

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

V cluster size (n)

Eb

(V(n

)-V

) (

eV

)

Ludwig et al.

Johnson & Oh

FS

ab initio (128 at.)

0.26 eV

0.36 eV


Binding energies: larger clusters

Turn to empirical potentials

Need a clever way to find the most stable configuration

See D. Kulivov poster

050

100150

200250

300

50

100

150

200

0

20

40

60

80

100

120

140

Ef = 0.9 - 1.72*N

V

1/3 + 2.69*N

V

2/3 + 0.215*N

Cu

0.85 - N

Cu*0.0004*(N

V

1/3 + N

V

2/3)

Ef

N V

NCu

140120

10080

6040

20

0

10

20

30

40

50

0

10

20

3040

50

Ef (

eV

)

N V

NCu


Main conclusions on the OKMC

•Very powerful technique to simulate many experimental situations:

•electron irradiation, neutron irradiation, annealing, isochronal annealing ...

•Combination of simulation techniques (AKMC, MD, MC, AB initio…) necessary

•Simple experiments necessary also

•Many unresolved questions, do we know enough physics?


REVE VTR : a multiscale modelling of RPV vessel.

Very simple models, lots of parameters : need to use combined techniques, simpler as well as more

complicated ones.

Simple modelling oriented experiments very useful.

Need more physical insight (SIA loops).

REVE continues in the PERFECT project (6th FP Euratom).

CONCLUSIONS


0

1

2

3

4

5

-16 -12 -8 -4

Log(t) (s)

Mean num

b er o f V m

i xe d Cu -V

clu st er s


VIVVVVV cccDkKdt

dc 2

Vacancy production rate

Vacancy production rate

Vacancy-SIA recombination rate

Vacancy-SIA recombination rate

Disappearance of vacancies at sinksDisappearance of vacancies at sinks

Coupling with SIA concentration equation !

Coupling with SIA concentration equation !


0

20

40

60

80

100

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

dpa

% C

u i

n p

rec

ipit

ate

s

Fe0.2at.%Cu, r = 1nn Fe0.1at.%Cu r = 1nn Fe0.2at.%Cu r = 1.9a0 Fe0.1at.%Cu 1.9a0 Fe0.2at.%Cu r = 3.3a0 Fe0.1at.%Cu r = 3.3a0 Experimental results

P. Auger, P. Pareige, S. Welzel, and J‑C. Van Duysen, J. Nucl. Mater. 280 (2000) 331.

% o

f Cu

pre

cip

i tate

d

dpa


% of Cu precipitated

Reaction radii

Fe0.2at.%Cu r = 1nn

Fe0.1at.%Cu r = 1nn

Fe0.2at.%Cu r = 1.9 a0/2

Fe0.1at.%Cu r = 1.9 a0/2

Fe0.2at.%Cu r = 3.3 a0/2

Fe0.1at.%Cu r = 3.3 a0/2

Experimental


Ab initio(pure Fe: 0.64 eV)

FS Ackland et al. (pure Fe: 0.77 eV)

EAM Ludwig et al.(pure Fe: 0.69 eV)

Mobilities

And what about clusters ?

J.R. Beeler Jr and R.A Johnson, Phys. Rev. 156 (1967) 677-684.

Mobility decreases with vacancy cluster size (size > 2)

Attempt frequency

Migration energy constant

1n112 )q(10.6


Binding energies: Cun clusters

0.26 eV (128 at. 2x2x2 kpts2)

Most stable configurations 0.15 eV (128 at. 3x3x3 kpts)

-0.23 eV

-0.500.5

.

Eb (

eV

)

ab initio (54 at.)

ab initio (128 at.)

Eval (1nn & 2nn - ab initio 128 at.)

EAM (54 at.)

EAM (128 at.)

EAM (2000 at.)

Cu(n) clusters

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Cu–Cu (1nn) Cu–Cu (2nn) Cu–Cu (3nn) Cu2–Cu Cu3–Cu

Eb

(e

V)


0.26 eV 0.17 eV0.28 eV

0.21 eV -0.03 eV 0.36 eV

Cu-Cu 1st nn - V 1nn

V 1st nn to both Cu atoms (no Cu interaction in 2nd nn)

128 atom cells calculations

Binding energies


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6

V cluster size (n)

Eb

(V(n

)-V

) (

eV

)EAM Ludwig et al.

Johnson & Oh,Soneda

FS Ackland, Bacon

Object KMC param,Wirth

ab initio (128 at.)


w’3w2

w6

w

5

w4

w3

w’’3w’’4

w’4

)/66.2exp(2.2 kTeVDFeFe

)/44.2exp(2.2 kTeVDCuFe

cm2 s – 1

cm2 s – 1

9-frequency model (Le Claire)

nFe = nCu = 3.65 10 15s-1

Hypothesis

[1] A.D. Le Claire, in Physical Chemistry: an advanced treatise, edited by H. Eyring, Academic Press, New York, 1970), vol. 10, chap. 5.

[1]

[2]

CuFe

FeFe DD

[2] F. Soisson, G. Martin and A. Barbu, Annales de Physique, vol.20 (1995) C3-13.


Influence of potential on vacancy-interstitial separation distances

Frenkel Pair separation distancedistributions.

The frequencies are the largestwhen the energy carried by RCS is the largest and energy carried byfocusons is the smallest

0 1 2 3 4 5 6 7 8

0

100

200

300

400

500

600Statistics over 1000 cascadesE

PKA = 20 keV

T = 0 K

Freq

uenc

y

Vacancy-Intersitial Pair separation distance (lu)

MolièreI MoliereII MolièreIII

freq

uenc

y

Vacancy-interstitial pair separation distance (a0)



Fuel. Usually pellets of uranium oxide (UO2) arranged in tubes to form fuel rods. The rods are arranged into fuel assemblies in the reactor core.

Moderator. This is material which slows down the neutrons released from fission so that they cause more fission. It may be water, heavy water, or graphite.

Control rods. These are made with neutron-absorbing material such as cadmium, hafnium or boron, and are inserted or withdrawn from the core to control the rate of reaction, or to halt it. (Secondary shutdown systems involve adding other neutron absorbers, usually as a fluid, to the system.)

Coolant. A liquid or gas circulating through the core so as to transfer the heat from it.

Pressure vessel or pressure tubes. Either a robust steel vessel containing the reactor core and moderator, or a series of tubes holding the fuel and conveying the coolant through the moderator.

Steam generator. Part of the cooling system where the heat from the reactor is used to make steam for the turbine.

Containment. The structure around the reactor core which is designed to protect it from outside intrusion and to protect those outside from the effects of radiation or any malfunction inside.Ý It is typically a metre-thick concrete and steel structure.

There are several different types of reactors as indicated in the following table.


guide design and analysis of experimental irradiation programs

explore conditions outside existing databases (very long time and high fluences), important to lifetime extension

systematically evaluate individual and combined influence of multitude of material variables (composition and microstructure) and the irradiation service conditions (T, flux, spectrum, ...)

help design advanced materials for future fission and fusion reactors.

Virtual Test Reactors (VTRs)


Reconstruction 3D acier VVER 440 irradié neutrons (20 ans)

Volume de 1515 50 nm3 (serie1)Cu

PSi

FeNiNi

Mn

Courtesy: Philippe Pareige


Volume de 1515 50 nm3 (série 2) Cu

+

P Si

FeNi Ni

Mn


Zoom sur un des amas 555 nm3Cu

+

P Si

FeNi Ni Mn

RPV steels microstructure evolution under irradiation: a multiscale approach

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