Kinetic Monte Carlo simulation of irradiation effects in bcc Fe-Cu alloys

L. Malerba1, C. Domain2,

C. S. Becquart3 and D. Kulikov1,4,5

COSIRES-7, Helsinki, 28 June – 2 July 2004

1SCK-CEN, 2EDF, 3U. Lille4UL Bruxelles, 5Ioffe Institute S. Petersburg

Work performed in the framework of

2

Motivation

Reactor pressure vessel (RPV) steels harden and embrittle under irradiation during operation mainly as a consequence of Cu precipitation

Fe-Cu is the model alloy typically used to study the basic mechanisms of RPV steel embrittlement, both in modelling-oriented experiments and multiscale models

Object KMC methods are promising tools to simulate the long-term effects of irradiation, taking into account the inherent inhomogeneity of neutron radiation damage

3

Problem

The open question concerning OKMC methods is the elaboration of the parameter set describing interactions between radiation-produced defects

The elaboration of an adequate parameter set requires a delicate work of:

identification of key physical mechanisms

calculation of basic magnitudes, such as cluster binding and migration energies

feedback from experimental observations

4

Method: Object Kinetic Monte Carlo

Solute-vacancy complex

Solute atom

Annihilation

Interstitial loop

Emission

Interstitial clusterVacancy cluster

Traps

Vacancyloop

Electrons

Neutrons

Frenkelpairs

cascade

+

Emission

Migration

++

Recombination

200nm

PBCor surface

P1P1 P2P2 PiPi PNPN

00 11

Random number extraction, Rn [0,1]

Random number extraction, Rn [0,1]

ekek

kT

E iaii

,exp

eN

ii

1

1

Each object defined by: type centre-of-mass position reaction radius possible reactions

probabilities = frequencies

residence time algorithm

5

Calculation of Cu-VC binding energies(see poster by D. Kulikov)

MetropolisMC on

rigid lattice

NCu

NVLo

west energ

y

configura

tion

MD relaxationat 0 K

Ef(NV)=(N0-NV)[Ecoh(NV inFe)-Ecoh(bccFe)]

Ef(NCu)=N0Ecoh(NCu inFe)-[(N0-NCu)Ecoh(bccFe)+NCuEcoh(fccCu)]

Ef(NV+NCu)=(N0-NV)Ecoh(NV+NCu inFe)-[(N0-NCu-NV)Ecoh(bccFe)+NCuEcoh(fccCu)]

Eb(V) = Ef(cluster) + Ef(V) – Ef(cluster+V)

Eb(Cu-Vpair) = Ef(cluster) + Ef(CuVpair) – Ef(cluster+CuVpair)

Eb(Cu) = Ef(cluster) + Ef(Cu) – Ef(cluster+Cu)

6

What do experiments say on Cu-VC ?

Main reference:Nagai et al. Phys. Rev. B 63 (2001) 134110Positron annihilation work on Fe-0.3%Cu, -0.15%Cu & -

0.05%CuNeutron irradiated at 100 & 300°C in JMTR8.3e18 n/cm2 (~0.012 dpa), ~10-8 dpa/sSpecimens irradiated at 100°C annealed up to 700°C

0 10 20 30 400.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Rat

io to

pur

e F

e

PL [10-3m0c]

Fe-0.3wt%Cu

pure Cu

As irradiated

100 °C Fe-0.3%Cu

1=165 ps ~Cu-V1

2=405 ps ~V30/25

I2>50%

300 °C Fe-0.3%Cu

2=300 ps V10

I2~30%

Cu-coated voids

Ncu < 50 (?)

7

0 5 10 15 20 25 30 35

100

200

300

400

500

600

700

What do experiments say on Cu-VC ?

0 5 10 15 20 25 30 35

100

200

300

400

500

600

700

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Isochronal annealing

From 100°C to 700°C, steps of 50°C

30 min at each temperature:

Results:

- Nanovoids anneal out at 300-350°C

- Cu ppts anneal out at T > 650°C

Fe-0.3%Cu

Fe-0.05%Cu

Nanovoids

Nanovoids

Cu ppts

Cu ppts

Pictures from:Nagai et al. Phys. Rev. B 63 (2001) 134110

8

What experiments do NOT say

No measurements on reference pure Fe

No Cu-V cluster size distribution or number density

The positron signal is a function of cluster size, volume concentration AND specific trapping rate

The specific trapping rate of Cu-V clusters is not known

Only a complementary atom probe study could (partially) provide this information (but atom probe alone does not see vacancies …)

No information on pure Cu ppts size (not even indicative value)

Only information from positrons concerns saturation to pure Cu

No information on interstitial loops in these conditions

Even TEM study would not provide anything, because most likely loops would be too small in the considered irradiation conditions to be seen

9

Choice of the OKMC parameters

General (as in the past)

Dose-rate from 5, 10 and 20 keV MD cascades

All clusters mobile, but prefactors decrease with size

3nn distance reaction radius

SIA traps, V traps (impurities, elastic interactions, …)

Sinks: points (GB) & dislocation segments

10

Choice of the OKMC parameters

SIA cluster size (nI)

(s-1) Em (eV) Direction of motion

1 0 = 6·1012 0.3 3D

2-100/nI

s s=100.4 3D

10 0.04 1D

Interstitial cluster mobility: recent picture

Emission of vacancies and Cu-V pairs: Cu-coating effectCluster size (nV, nCu)

(s-1) Ea = Em+ Eb (eV)

nV2/3-nCu > 0 0x(nV

2/3-nCu) Em=0.7 ; Eb=formulae

(see D. Kulikov)nV2/3-nCu < 0 0x(nV

2/3/nCu)

11

Choice of the parameters

Comparison with experiment of resistivity recovery during low temperature isochronal annealing for pure Fe using proposed parameters (Abe & Kuramoto, JNM 283-287,

2002, 174):Defect

Experiment

Simulation

Single SIA

77-150 K 88 K

Di-SIA 150-200 K 148 K

Single vacancy

180-240 K 188 K

This is necessary condition for the acceptability of the parameter set (but not sufficient )

Temperature (K)

0

500

1000

1500

2000

2500

3000

0 100 200 300 400 500

mono vacancies

di - vacancies

SIAs

di - SIAs

88 K148 K 188 K

Num

b er

o f d

e fe c

ts

12

Results: Irradiation1 4 7

10 13 17 20 27

14

10

62

0

10

20

30

40

50

60

number of clusters

number of vacancies

number of Cu atoms

Fe-0.3%Cu - 100°C

0.012 dpa, 10-8 dpa/s

100a0 side simulation box

1 4 7

10 13 16 20 26

10

62

0

5

10

15

20

25

30

35

number of clusters

number of vacancies

number of Cu atoms

Fe-0.05%Cu - 100°C

Mixed Cu-V complexes form, in larger number for larger Cu concentrations

Ncu << 50 (not in disagreement with PAS)

Size is fairly small (~1 nm maximum)

13

Results: Irradiation

1,0E+16

1,0E+17

1,0E+18

1,0E+19

0 10 20 30 40 50

vacancy cluster size

num

ber

de

nsity

(cm

-3)

323 K 373 K 400 K 523 K 573 K

126 vacancy cluster ...

1,0E+16

1,0E+17

1,0E+18

1,0E+19

0 10 20 30 40 50

vacancy cluster size

num

ber

de

nsity

(cm

-3)

323 K 373 K 400 K 523 & 573 K

up to 60

T (K) n (cm-3)sim

(ps)exp

(ps)

3232.1·101

9 315

3735.5·101

8 343~40

0

4005.7·101

8 377

5232.4·101

7 356

5734.0·101

6 //~30

0

Pure Fe

0.012 dpa, 10-8 dpa/s

100a0 side simulation box

Fe-0.3%Cu

diameterD

fractionvolumeC

nDnC

nnDnC

)()(

)()()( Density

decreases with T

14

1,0E+15

1,0E+16

1,0E+17

1,0E+18

1,0E+19

0 10 20 30 40 50

vacancy cluster size

num

ber

dens

ity (

cm-3

)

323 K 373 K 400 K 523 K 573 K

1,0E+15

1,0E+16

1,0E+17

1,0E+18

1,0E+19

0 10 20 30 40 50

vacancy cluster size

num

ber

de

nsity

(cm

-3) 323 K 373 K 400 K 523 K 573 K

up to 68

Results: Irradiation

T (K) n (cm-3)sim

(ps)exp

(ps)

3231.3·101

9 316

3735.1·101

8 346~40

0

4002.8·101

8 374

5231.1·101

7 416

5731.5·101

6 351~30

0

Pure Fe

0.012 dpa, 10-8 dpa/s

200a0 side simulation boxFe-0.3%Cu

diameterD

fractionvolumeC

nDnC

nnDnC

)()(

)()()(

15

Results: Irradiation

In Fe slightly larger sizes than in Fe-0.3Cu around 100°C

In Fe-0.3Cu voids form up to 573 K - in Fe they start not to form earlier (right above stage V)

Calculated positron lifetime varies with temperature less or in a different way than in experiments

Better temperature regime reproduction with larger box

Considering the many approximations and unknowns, the model is at least reasonable in the irradiation description

16

Results: Annealing

0

20

40

60

80

100

120

140

300 400 500 600 700 800 900 1000 1100

annealing T (K)

nu

mb

er o

f vo

ids

Fe - 30 min

Fe-0.3Cu - 30 min

Fe - 300 min

Fe-0.3Cu - 300 min

Fe - 3000 min

Fe-0.3Cu - 3000 min

0

5

10

15

20

25

30

35

40

45

50

300 400 500 600 700 800 900 1000 1100

annealing T (K)

% C

u i

n s

olu

tio

n30 min

300 min

3000 min

←Voids disappear during 30 min annealing at increasing T, but they do so ~50-100 K above experiments

←Temperature is ~correct for much longer annealing than in experiment

←Little difference Fe-Cu/Fe

Expected annealing Fe-CuExpected annealing Fe

Cu precipitate dissolution during thermal ageing according to the

model takes too high temperatures or too long times

compared to experiments

Overall, the annealing description is not fully satisfactory

17

Summary

Positron annihilation experiments on Fe-Cu alloys provide useful information concerning features and (partially) size of Cu-V complexes formed in Fe-Cu under irradiation and their stability during annealing

A first attempt OKMC parameter set for the description of Fe-Cu alloys has been elaborated, based on:

Latest qualitative guess concerning SIA and SIA cluster mobility in Fe

Extensive MC/MD calculation of Cu-V cluster binding energies as a function of size

Biased prefactor for V and Cu-V pair emission from Cu-VC to account for effect of Cu-coating of voids

The application of this first attempt parameter set gives reasonable results for the reproduction of realistic irradiation conditions, but does not fully reproduce the correct temperature/time behaviour during annealing

18

Missing ingredients and open problems

Detailed mobility description of SIA clusters according to recent picture (migration energies, directionality, nature of clusters, …)

Actual law of pre-factor decrease for diffusivity of all clusters

Complex defect-defect interactions (trapping of SIA clusters by vacancies before recombination, …)

Detailed trap description (different behaviour for different impurities, mobile traps, elastic interactions, …)

Detailed description of migration and emission for V clusters and Cu-V clusters (energy barriers, size effect, effect of Cu coating, …)

Interaction between solute atoms and SIA clusters

Sink evolution (dislocation density) under irradiation

…

Importance of box size effect?

Acknowledgements

This work was financed by the PERFECT IP, 6th FP, Euratom,

Contract no. F160-CT-2003-508840

Special thanks to Jan Kuriplach (C. U. Prague) for his assistance in understanding positron

results