Kinetic Monte Carlo simulation of irradiation effects in bcc Fe-Cu alloys
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Transcript of Kinetic Monte Carlo simulation of irradiation effects in bcc Fe-Cu alloys
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
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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
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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
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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
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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)
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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 (?)
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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
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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
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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
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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)
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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
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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)
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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
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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
)()(
)()()(
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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
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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
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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
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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