multiscale computer simulations and predictive modeling of rpv embrittlement
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Multiscale Computer Simulations and Predictive Modeling of RP
V Embrittlement
Naoki SonedaCentral Research Institute of Electric Power Industry (CRIEPI), Japan
MATGEN-IVCargese, CorsicaSeptember 29, 2007
Multiscale Modeling of RPV Embrittlement
Naoki SonedaCentral Research Institute of Electric Power Industry (CRIEPI), Japan
MATGEN-IVCargese, CorsicaSeptember 29, 2007
32007/09/29
Irradiation Embrittlement of LWR RPV Steels
The accurate prediction of the transition temperature shift is very important in ensuring the structural integrity of reactor pressure vessels.
PWR RPV
Fra
ctur
e T
ough
ness
Temperature
Increase in transition temperature
Decrease in USE
Before irradiation
After irradiation
Goal:Development of an accurate embrittlement correlation method to predict the transition temperature shifts
42007/09/29
Current Embrittlement Correlation Equation– Prediction of Transition Temperature Shift –
US NRC Regulatory Guide 1.99 Rev.2
JEAC4201-1991, Japan
Statistical analysis was performed to identify chemical elements (Cu, Ni, Si and P) to be used in the equations.
Both the surveillance data of commercial reactors and test reactor irradiation data were used.
The equations were developed based on the knowledge in the 80’s.
fNDT fNiCuCuPRT log04.029.077215121016
fNDT fNiCuNiSiRT log1.025.03016124026
Base Metal
Weld Metal
52007/09/29
Activities in the 90’s and 00’s
New information and new findings Surveillance data at higher fluences became available. New understandings on the embrittlement mechanisms have been
obtained by state-of-the-art experiments and simulations. New projects have started in the US
Development of mechanism guided correlation US NRC, NUREG/CR-6551 (1998) & revised version (2000) ASTM, ASTM Standard E 900–02 (2002) US NRC, Regulatory Guide 1.99 Rev.3 (2007?)
Plant Life Management for 60-years operation is necessary 2 plants will be 40 years old in 2010, and more than 10 plants are
now older than 30 years in Japan Accurate prediction of embrittlement is very important for safe and
economical operation of the plants
62007/09/29
Surveillance Data
In the commercial light water reactors, some surveillance capsules containing surveillance specimens are installed at the vessel inner wall to irradiate the same RPV material at a very similar irradiation condition to the vessel.
Surveillance capsules are retrieved according to the schedule of the surveillance program. The surveillance specimens irradiated in the capsule are tested to measure the transition temperature shift. This data is called surveillance data.
72007/09/29
Activities in the 90’s and 00’s
New information and new findings Surveillance data at higher fluences became available. New understandings on the embrittlement mechanisms have been
obtained by state-of-the-art experiments and simulations. New projects have started in the US
Development of mechanism guided correlation US NRC, NUREG/CR-6551 (1998) & revised version (2000) ASTM, ASTM Standard E 900–02 (2002) US NRC, Regulatory Guide 1.99 Rev.3 (2007?)
Plant Life Management for 60-years operation is necessary 2 plants will be 40 years old in 2010, and more than 10 plants are
now older than 30 years in Japan Accurate prediction of embrittlement is very important for safe and
economic operation of the plants
82007/09/29
Analysis of the Recent Surveillance DataT
rans
ition
Tem
pera
ture
Shi
ft
Neutron Fluence (n/cm2, E>1MeV)
6x1019n/cm2
(40years, PWR)1x1020n/cm2
(60years, PWR)
High Cu materialHigh Cu materialIrradiated at low flux
Low Cu material
Low Cu materialIrradiated to high fluences
Current predictionSurveillance data
<3x1018n/cm2
(60years, BWR)
fNDT fNiCuCuPRT log04.029.077215121016
92007/09/29
Embrittlement Mechanism– General Consensus –
Formation of Cu-enriched clusters (CEC) in high Cu materials CEC is associated with Ni, Mn and Si 2~3 nm in diameter obstacle to dislocation motion dose rate effect exists
Formation of matrix damage (MD) point defect clusters such as dislocation loops or vacancy cl
usters, or point defect – solute atom complexes. main contributor to the embrittlement in low Cu materials
Phosphorus segregation on grain boundary P segregation weakens grain boundaries. not very important for relatively low P materials
P
MD
CECG.B.
Dislocation
Cu
102007/09/29
ASTM E 900-02
5076.018
460
370,20exp1070.6 f
TSMD
c
CRPSMDRTNDT
052.1
24.18logtanh
2
1
2
1106.21 173.1 f
CuFNiBCRP
Are the formation of SMD(MD) and CRP(CEC) independent?
No effect of chemical composition?
Is an exponential function appropriate?
Is it product-form dependent?
sother weldfor .%,305.0
0091flux; Lindeor 80 Linde with for welds .%,25.0
,
wt%072.0,0.072-Cu
wt%072.0,0
,
platesother ,156
plates CE ,208
forgings ,128
welds,234
max
maxmax
577.0
wt
wtCu
CuCuCu
Cu
Cu
CuFB
Is the threshold value appropriate
Is there any other effect such as dose rate and other elements?
Is the linear sum approximation appropriate?
Dose it saturate at high fluences?
T
f1/2
SMD
CRP
Total
112007/09/29
Issues to be studied
Do CEC and MD cause embrittlement? What is the nature of MD? What is the nature of CEC?
Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?
122007/09/29
Approach
Mechanical property tests of neutron irradiated RPV steels
Nano-structural characterization
Multi-scale computer simulation
132007/09/29
Nano-structural Characterization
3-Dimensional Atom Probe
Positron Annihilation(Coincidence Doppler Broadening) Cu-enriched clusters formed
by neutron irradiation
~4
0 n
m
~300 nm
LEAP(Local Electrode Atom Probe)
1.4
1.2
1.0
0.8
0.6
Rat
io t
o F
e
50403020100
PL (x10-3
m0c)
Unirrad. As-irrad. 500°C
規格
化さ
れた
強度
電子の運動量
未照射材照射材
熱時効材
Nor
mal
ized
cou
nts
of
gam
ma
ray
s
Electron momentum
Irradiated unirradiated
thermallyaged
50nm
Transmission Electron Microscope(TEM)
142007/09/29
Multi-scale Computer SimulationMolecular DynamicsDislplacement cascade
Kinetic Monte CarloMicrostructural evolution during irradiation
Dislocation DynamicsDislocation behavior during deformation
Detailed analysis of microstructure
Point defect production
Cu atoms
Vacancies
Dislocationloop
Dislocation
Radiation damage
Molecular Dynamics
Molecular Dynamics
Str
ess
(M
Pa
)Strain (%)
~10-11sec~10-8m
~109sec~10-7m
~100sec~10-4m
Dislocation DynamicsPrediction of mechanical property ~100m
Unirradiated
Irradiated
Interaction between dislocation and damage
152007/09/29
Issues to be studied
Do CEC and MD cause embrittlement? What is the nature of MD? What is the nature of CEC?
Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?
162007/09/29
Damage accumulation in bcc-Fe– Kinetic Monte Carlo (KMC) simulation –
• Database of displacement cascades for a wide range of PKA energies
• Diffusion kinetics such as diffusivities and diffusion modes (1D, 3D…) of point defects and clusters
• Thermal stabilities (binding energies) of point defect clusters
Defect production
Clustering
Formation and growth of loops
Microstructure evolution
10-9-10-8m
~ 10-11s
~ 10-5m
10-6-10-3m
Diffusion
Cluster diffusion
10-9-10-7m
10-12-10-8s
Dissociation
KMC tracks all the events.
Most of the data can be obtained from molecular dynamics simulations.
Input Data
172007/09/29
Primary Knock-on Atom (PKA) Energy Spectrum
• Displacement cascade simulation results are necessary for different PKA energies to simulate the PKA energy spectrum.
• Molecular dynamics simulations have done for the PKA energies of 100eV, 200eV, 500eV, 1keV, 2keV, 5keV, 10keV, 20keV and 50keV.
L.R. Greenwood, JNM 216 (1994) 29.
182007/09/29
Displacement Cascade Simulation
Molecular Dynamics Inter-atomic potential
Ackland Potential ZBL pair potential is used for the short distance interaction
Constant volume at a temperature of 600K Thermal bath at the periphery of the computation box
Periodic boundary condition Automatic time step control Number of atoms :
12,000 atoms for 100eV PKA cascade~4,000,000 atoms for 50keV PKA cascade
192007/09/29
MD Simulation of Displacement CascadeVolume : (28.6nm)3
2,000,000 atomsPKA energy: 50keV
Wide variety of defect production is observed in high energy cascades of 50keV, which is not be observed in lower energy cascades.
SIA Vacancy
202007/09/29
Small SIA & Small Vacancy Cluster
Black dots : vacanciesWhite circles : SIAs
Case 45
Isolated subcascade formation
@3.2ps @10.0ps
212007/09/29
Large SIA & Small Vacancy Cluster
Black dots : vacanciesWhite circles : SIAs
Case 09
Overlapped subcascade formation(similar size subcascades)
@0.1ps @11.0ps
222007/09/29
Large SIA & Large Vacancy Cluster (1)Case 28
Overlapped subcascade formation(large & small subcascades)
@3.2ps @10.2ps
Black dots : vacanciesWhite circles : SIAs
232007/09/29
Large SIA & Large Vacancy Cluster (2)Case 39
One large cascade is formed, and then …
234 vacancies
70 SIAs93 SIAs
@1.9ps @12.1ps
Black dots : vacanciesWhite circles : SIAs
242007/09/29
Large SIA & large vacancy cluster (3)
Black dots : vacanciesWhite circles : SIAs
Case 39
Large SIA loopb = a0/2 <111>
Large vacancy loopb = a0 <100>
Cascade collapse occurred in -Fe
[110]
[001]
[010]
[001]
@40.0ps
252007/09/29
Channelling
Black dots : vacanciesWhite circles : SIAs
Case 31
<112> direction
Direction 50keV 20keV
011 2 0
133 1 0
233 2 0
111 0 1
112 1 1
337 1 0
113 1 0
114 1 0
115 0 1
116 1 2
001 7 0
• All the events occur on (110) plane.
• PKA is always the channeling particle in 20keV cascades.
Periodic boundary condition
262007/09/29
Dispersed defect production
Black dots : vacanciesWhite circles : SIAsGray : replaced atomsCase 42
Direction 50keV 20keV
011 1 0
111 1 0
113 2 0
001 1 0
• Similar direction to channeling, but associated with many interactions
• Did not occur in 20keV cascades
Periodic boundary condition
272007/09/29
Summary of Cascade Database
Periodic boundary condition
53% 17% 10%15%5%
50keV(100runs)
20keV(50runs) 80% 8%10%
2%
Periodic boundary condition
Small clusters
Channeling
Dispersed defect formation
Large SIA clusters
Large SIA & V clusters
100eV, 200eV, 500eV, 1keV, 2keV, 5keV, 10keV, 20keV, 50keV
282007/09/29
Diffusivity
Diffusion simulation of a point defect by MD Calculate Do and Em by MD
kT
EDD mexp0
U
x
292007/09/29
Diffusion Kinetics – Molecular Dynamics –
1D motion of SIA clusters
Diffusivity
Rotation frequency
Migration energy, Em
N. Soneda, T. Diaz de la Rubia, Phil. Mag. A, 81 (2001), 331.
kT
EDD mexp0
kT
Eaexp0
302007/09/29
MD Simulation of SIA Cluster (I3)
1D motion + rotation1D motion(lattice unit)
1.6ns @ 500K 1.6ns @ 1000K
312007/09/29
Diffusivities of SIA Clusters – I1 ~ I20 –
• 1D motion is a common feature for the SIA cluster migration• Migration energies of large SIA clusters are as low as 0.06eV, which
means that SIA clusters are highly mobile.
1/T (K-1)1/T (K-1)
Diff
usiv
ity (
cm2 /
s)
Diff
usiv
ity (
cm2 /
s)
322007/09/29
Migration Energies of SIA Clusters
6.1
11.006.0
nEm
332007/09/29
Rotation Frequency of Small Clusters
Activation energy of rotation for the I3 cluster is high.
342007/09/29
Binding Energies of Point Defect Clusters
N. Soneda, T. Diaz de la Rubia, Phil. Mag. A, 78 (1998), 995.
nEEnEnE fffb 11
352007/09/29
Algorithm of KMC Simulation
Set all the possible events
Calculate event frequency
Choose one event
Update time
Do event
Diffusion Em
Dissociation Eb+Em
Disp. cascade dose rate
P = Ni Pi
i
R = Random()*P
t = -log(R) / P
Calculate interaction between the neighboring particles (clustering, annihilation, etc.)
Rep
eat
until
tar
get
dose
or
time
is r
each
ed
Bigmac (LLNL) KineMon (CRIEPI / Univ. Tokyo)
362007/09/29
Accumulation of Point Defect Clusters in Neutron Irradiated bcc-Fe
350K 600K
1021
1022
1023
10-4
10-3
10-2
10-1
SIA cluster (>37)SIA cluster (>100)SIA loop (Nicol et al., 2000)SIA loop (Victoria et al., 2000)
Nu
mb
er
den
sity
(m
-3)
Dose (dpa)
Dose rate: 10-8
dpa/sTemperature: 600Kn-spectrum: FissionGrain size: 10m
No stable vacancy cluster
372007/09/29
Microstructural evolution at different dose rates
1021
1022
1023
1024
1025
10-5
10-4
10-3
10-2
10-1
Nu
mbe
r de
nsi
ty (
m-3
)
Dose (dpa)
Temperature: 600Kn-spectrum: FissionGrain size: 10m
No stable vacancy cluster
at 10-8
dpa/s and 10-10
dpa/s
10-4dpa/s
10-6dpa/s
1021
1022
1023
1024
1025
10-5
10-4
10-3
10-2
10-1
Nu
mbe
r de
nsi
ty (
m-3
)Dose (dpa)
SIA cluster > 37
(Smoothed data)Temperature: 600Kn-spectrum: FissionGrain size: 10m
10-4 dpa/s
10-6 dpa/s
10-10 dpa/s
10-8 dpa/s
• Stable SIA clusters are always produced, but the stability of vacancy clusters depends on the dose rate.
• Threshold dose rate exists between 10-6dpa/s and 10-8dpa/s, below which no dose rate effect is observed in defect cluster formation.
Vacancy SIA
10-4dpa/s
10-6dpa/s
No stable vacancy cluster is formed below 10-8dpa/s
10-4dpa/s
10-6dpa/s
10-8dpa/s
10-10dpa/s
382007/09/29
Experimental observation of SIA loops– TEM observation –
50nm50nmB=[011] 、 3g (g=21-1)
B=[133] 、 3g (g=-110)
0.12Cu/0.58Ni4x1019n/cm2
0.68Cu/0.59Ni6x1019n/cm2
• Dislocation loops are observed in the RPV materials irradiated in commercial reactors.
• Number densities of the loops are relatively low.
Mean size: 2.6 nmNumber density: 1.8x1022 m-3
Mean size: 2.3 nmNumber density: 1.9x1022 m-3
392007/09/29
• Box size : 37×16×35nm (~1.7million atoms)• Potential : EAM potential (Ackland et.al.) • Burgers vector: Edge dislocation [111]
SIA loop [111]• SIA loop size : ~2nm• Applied shear stress : 50MPa ~ 650MPa• Temperature : 300K
011
211
111
b=[111]
b=[111]
Dislocation – Loop interaction
402007/09/29
Dislocation Loop – Edge Dislocation InteractionMolecular Dynamics Simulation
I
II III II’
IV
= 150MPa = 250MPa = 300,350,500MPa
= 650MPa = 50MPa
Repulsion
PinningSuperjog (I) Superjog (I’)
Superjog (II)
412007/09/29
Dislocation reacts with SIA loop
Superjog formation Vacancies are left behind.
150MPa
Dislocation is pinned. No bowing-out of the dislocation is observed at this applied stress.
1 2 3
4 5 6
Type II Interaction
422007/09/29
Details of Loop – Dislocation Interaction
b=1/2[1 -1 1]
b=1/2[-1 1 1] Formation of Bridge Dislocationb= [0 0 1] (=1/2[-1 1 1]+1/2[1 –1 1])
Trailing Bridge Dislocationb=1/2[-1 -1 1]
Leading Bridge Dislocationb=1/2[1 1 1]
b= [0 0 1]
Pinning occurs at this stage.
432007/09/29
Contribution of vacancy-type defects to embrittlement
-10
-5
0
5
10
15
20
25
-100 0 100 200 300 400 500 600
EP2 BWR4AEP2 BWR4C
VH
N
Annealing Temperature (oC)A/R
0
0.0005
0.001
0.0015
0.002
-100 0 100 200 300 400 500 600
EP2, BWR4AEP2, BWR4D
S
Temperature (oC)A/R
Low Cu, BWR Irradiation
Low Cu, BWR Irradiation
Recoveries of Hv and S occur at different temperatures indicating that the vacancy type defect is not responsible for the Hv.
Recovery of Hardness during PIA Recovery of S during PIA
S is a measure of total amount of open volume.
EPRI/CRIEPI Joint Program
442007/09/29
Summary of matrix damage
Candidates Answer
Dislocation loop of interstitial type Yes
Vacancy cluster No
Point defect – solute atom complex See the followings
452007/09/29
Issues to be studied
Do CEC and MD cause embrittlement? What is the nature of MD? What is the nature of CEC?
Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?
462007/09/29
3D Atom Probe
Time of flight
Y
X
Z
Fast = light
Needle tip
Pulse voltage
Detection positionElement
3D position
Slow = heavy
Detector
500m
Optical Microscope
TEM
50nm
0.3x0.3x10mm
Electro-polish
472007/09/29
Formation of Cu-enriched Clusters
~20
0nm
~40nm
• High Cu (0.25wt.%) RPV steel irradiated in a test reactor was examined.
• Cu-enriched clusters are formed with very high density, and they are associated with Ni, Mn, Si and, sometimes, P.
• The primary mechanism in high Cu content materials is the precipitation of Cu atoms beyond the solubility limit.
CuSi
• What is the formation process?• What happens in medium – low Cu materials?
482007/09/29
Thermal ageing of Fe-Cu-Ni-Mn-Si alloys40
30
20
10
0
(Δ
Hv)
ビッ
カー
ス硬
さ上
昇量
1000080006000400020000
(Hour)熱時効時間
HL HM HH HHC
Cu高 材350℃熱時効温度:
Clusters consist of Cu, Ni, Mn and Si. Amount of Si is very small.
Ageing time (hour)
Incr
ease
in V
icke
rs H
ardn
ess
(H
v)
Cu Ni Mn Si CHL 0.3 0.6 1.4 0.2 –HM 0.3 1.0 1.4 0.2 –HH 0.3 1.8 1.4 0.2 –HHC 0.3 1.8 1.4 0.2 0.1
aged at 350oC
0%
20%
40%
60%
80%
100%
1 10 19 28 37 46 55 64 73 82 91 100 109 118
Cluster number
Com
posi
tion
SiCuNiFeNi58MnFe
Cluster SizeSmall Large
Distribution of Cu atoms
49 x 65 x 270 nm3
17.5M atoms
LEAP measurement
492007/09/29
Computer simulation of the thermal ageing– Kinetic Lattice Monte Carlo (KLMC) simulation –
Consider all the atoms in the crystal Diffusion by vacancy mechanism + regular solution approximation
for complex alloys
1
z
iji j
E
exp aw v E kT
02aE E e
0m bv i ve E E
2ij ij ii jjV
ln 1 ln 1 2ij ij ij ijV kT C C z C
1
z
i i jj
w w
Jump probability
Activation energy
Total energy of the crystal
Vacancy migration energy & vacancy binding energy
Choose one of the possible sites
Energy change by vacancy jump
Migration energy
Pair interaction energy
Ordering parameter
Solubility
502007/09/29
Determination of KLMC parameters
Binding energies between a vacancy and a solute atom in pure iron are obtained from first principles calculations
using the VASP code.
0m bv i ve E E
Fe
Co
Cu
MnNi
VCr
Zn
Ti
Sc
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Vacancy - solute atom binding volume (Å3)
Vac
ancy
- s
olut
e at
om bi
ndin
g en
ergy
(eV
)V
aca
ncy
– S
olu
te A
tom
Bin
din
g E
ne
rgy
(eV
)
Vacancy – Solute Atom Binding Volume (A3)
512007/09/29
Process of precipitation : KLMC result
~40nm
673K 573K
522007/09/29
(a) 1.6x107sec (b) 3.2x107sec (c) 7.9x107sec (d) 7.9x108sec
CuNiMnSi
::::
0.31.0 or 1.81.40.9 (at.%)
Effect of Ni on cluster formation8760hrs = 3.15x107sec
Nd ~ 6.8x1023 m-3
(a) 1.6x107sec (b) 3.2x107sec (c) 7.9x107sec (d) 7.9x108sec
1.8at.% Ni
1.0at.% Ni
Cu : 0.3, Mn 1.4, Si 0.9 (at.%)
Ni enhances the nucleation of clusters.
532007/09/29
Comparison between simulations and experiments
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
1.E+06 1.E+07 1.E+08 1.E+09
時効時間 (sec)
体積
分率
(at
.%)
Ni: 0.6at.%Ni: 1.0at.%Ni: 1.8at.%
Cu: 0.3at.%
Vol
um
e fr
actio
n (a
t.%
)
Ageing time (sec)
Simulation Experiment
0.3Cu, 1.8Ni
Direct and quantitative comparison of the microstructural changes with experiments can be made.
542007/09/29
Calculation Conditions
Potential : Ackland potential Edge dislocation : b=a/2[111] Cu precipitate size : 1.5 ~ 5nm Box size :
50×24×56nm( ~ 6.0x106 atoms) for small Cu 50×36×56nm( ~ 8.5x106 atoms) for large Cu
Applied shear stress : 350MPa Temperature : 300K
011
211
111
b=a/2[111]Edge dislocation
Cu precipitate
τ
τ
x
y
z
552007/09/29
Hardening due to Cu precipitates– Molecular Dynamics –
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6
Maximum bowing distance (nm)
Cu precipitate size (nm)Diameter of Cu ppt (nm)
Max
imum
bow
-out
dis
tanc
e (n
m)
4nm Cu ppt350MPa shear stress
bow-outdistance
562007/09/29
Interaction Process (Small Precipitate)
Simple Shear
011
111
572007/09/29
Atom stacking below/on/above the slip plane changes from bcc to fcc-like structure.
(011)
211
111
Interaction Process (Large Precipitate)
582007/09/29
Dislocation Motion at Break-out
Original slip plane
Motion of screw dislocation
Super jog formation
Pure edge
Pure screw
Top view
592007/09/29
0%
20%
40%
60%
80%
100%
1 10 19 28 37 46 55 64 73 82 91 100 109 118
Cluster number
Com
posi
tion
SiCuNiFeNi58MnFe
What is the difference between the thermal ageing and irradiation?
Si content is much larger in the irradiated material than in the thermally aged materials.
Low Si content in thermally aged materials is also seen by simulations aged for much longer time.
0%
20%
40%
60%
80%
100%
251
262
273
284
295
306
317
328
339
350
361
372
383
394
405
416
427
438
449
460
471
482
493
504
Cluster #
Com
pos
itio
n
Com
pos
itio
n
Cluster number Cluster number
Neutron irradiation Thermal ageing
602007/09/29
0%
20%
40%
60%
80%
100%
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201 211 221 231 241 251 261 271 281 291 301 311 321 331 341 351 361
0
10
20
30
40
50
60
70
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0
Cluster diameter (nm)
Cou
nts
Cluster diameter (nm)
Cou
nts
0.12Cu4x1019n/cm2
RG Guinier D Composition (at.%)
(nm) (nm) Fe Mn FeNi58 Ni Cu Si P
V-weighted average 1.40 3.62 61.9 5.6 6.8 3.3 4.3 6.7 1.0Simple average 1.19 3.07 60.3 5.7 7.2 3.3 3.9 7.1 1.1
35 x 41 x 491 nm3
13.7M atomsCuP
Nd 2.24 x 1023 m-3
Vf 4.16 x 10-3
dG 3.07 nm
Cluster ID
Com
posi
tion
(at.
%)
Fe
Mn
NiNi
Cu
Si
612007/09/29
0%
20%
40%
60%
80%
100%
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125 129 133
Cluster ID
RG Guinier D Composition (at.%)
(nm) (nm) Fe Mn FeNi58 Ni Cu Si P
V-weighted average 1.48 3.83 61.7 5.3 7.5 3.1 1.9 8.7 0.7
Simple average 1.32 3.40 59.8 5.5 7.7 3.2 1.8 8.9 0.7
33 x 38 x 284 nm3
8.1M atoms
CuPSi
Cluster ID
Com
posi
tion
(at.
%)
0
5
10
15
20
25
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0
Cluster diameter (nm)
Co
un
tsC
ount
s
Guinier diameter (nm)
Nd 1.21 x 1023 m-3
Vf 2.87 x 10-3
dG 3.40 nm
Fe
Mn
NiNi
Cu
Si
0.07Cu6x1019n/cm2
622007/09/29
0%
20%
40%
60%
80%
100%
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126 131 136 141
RG Guinier D Composition (at.%)
(nm) (nm) Fe Mn FeNi58 Ni Cu Si P
V-weighted average 1.48 3.80 62.5 5.7 8.3 3.4 0.3 11.8 1.1
Simple average 1.22 3.14 60.9 6.2 8.2 3.4 0.3 11.6 1.0
Cluster ID
Com
posi
tion
(at.
%)
41 x 49 x 264 nm3
11.2M atoms
0
5
10
15
20
25
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0
Cluster diameter (nm)
Co
un
ts
Cluster diameter (nm)
Cou
nts
Nd 5.61 x 1022 m-3
Vf 1.13 x 10-3
dG 3.14 nm
Fe
Mn
NiNi
Cu
Si
0.03Cu6x1019n/cm2
CuPSi
632007/09/29
0%
20%
40%
60%
80%
100%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73
Cluster ID
0.04Cu3x1019n/cm2
RG Guinier D Composition (at.%)
(nm) (nm) Fe Mn FeNi58 Ni Cu Si P
V-weighted average 1.46 3.78 60.8 6.2 9.1 3.7 0.3 11.5 0.7
Simple average 1.20 3.10 59.2 6.7 8.8 3.9 0.3 11.6 0.7
Cluster ID
Com
posi
tion
(at.
%)
43 x 52 x 194 nm3
9.6M atoms
0
1
2
3
4
5
6
7
8
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0
Cluster diameter (nm)
Co
un
ts
Cluster diameter (nm)
Cou
nts
Nd 2.31 x 1022 m-3
Vf 4.51 x 10-4
dG 3.10 nm
Fe
Mn
NiNi
CuSi
CuPSi
642007/09/29
Are the Ni-Si-Mn clusters responsible for embrittlement (hardening)?
35x45x300 nm3
10.4M atoms50x60x158 nm3
10.0M atoms31x39x238 nm3
6.6M atoms
400oC 450oC 500oC 600oC
31x42x299 nm3
8.6M atoms24x33x272 nm3
5.1M atoms
As irrad.
180
200
220
240
260
280
0 50 100 150 200 250 300 350 400 450 500 550 600 650
温度 (℃)
ビッ
カー
ス硬
さ
(Hv
(1.0
))
DW0DW2
等時焼鈍時間:30分
Temperature (oC)
Hv
Holding time: 30min
• Recovery of hardness occurs at 500 .℃
• Clusters becomes very diffuse at the same temperature.
652007/09/29
N
kk rn
Nrn
1
1
rnrr
rSDF
24
1
rr
r : <5nm r : 0.1nm
Spacial Distribution Function, SDF(r)
Mean concentration of the element of interest as a function of the distance from an atom of the element.
SD
F
SD
F
r r
Uniform distribution clustering
662007/09/29
Analysis of clustering using SDF
Slope becomes very weak at 500oC in good correspondence with the diffuse clustering.
Ni-Si-Mn clusters cause hardening.
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5
Cu_aRDFNi_aRDFFeNi58_aRDFMn_aRDFSi_aRDFP_aRDFC_aRDF
radius / nm
DW2_00693
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5
Cu_aRDFNi_aRDFFeNi58_aRDFMn_aRDFSi_aRDFP_aRDFC_aRDF
radius / nm
DW2-40_01261
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5
Cu_aRDFNi_aRDFFeNi58_aRDFMn_aRDFSi_aRDFP_aRDFC_aRDF
radius / nm
DW2-45_01236
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5
Cu_aRDFNi_aRDFFeNi58_aRDFMn_aRDFSi_aRDFP_aRDFC_aRDF
radius / nm
DW2-50_01265
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5
Cu_aRDFNi_aRDFFeNi58_aRDFMn_aRDFSi_aRDFP_aRDFC_aRDF
radius / nm
DW2-60_01219
As Irrad. 400℃ 450℃
500℃ 550℃
SD
F (
atom
s/nm
3)
SD
F (
atom
s/nm
3)
SD
F (
atom
s/nm
3)
SD
F (
atom
s/nm
3)
SD
F (
atom
s/nm
3)
Distance (nm) Distance (nm) Distance (nm)
Distance (nm) Distance (nm)
672007/09/29
Answer to “What is the nature of CEC?” CEC is a Cu-Ni-Si-Mn cluster. The Cu content in the clus
ter is affected very much by the bulk Cu content, while Ni, Si and Mn contents are not affected by their bulk contents and it can be a Ni-Si-Mn cluster without Cu at very low Cu material. Thus it will be more appropriate to call such clusters as “Solute-atom Clusters (SC)”.
The number density of SC becomes larger when Cu content is high.
SC causes hardening, and thus embrittlement. Further question: Why do Ni, Si and Mn form clusters ev
en though their solubility is very high in Fe-matrix? (cf: Cu form clusters because of its low solubility.) One possible answer: It is the irradiation induced segregation of
Ni, Si and Mn atoms on point defect clusters. (heterogeneous nucleation)
Interaction between SC (CEC) and MD
682007/09/29
Issues to be studied
Do CEC and MD cause embrittlement? What is the nature of MD? What is the nature of CEC?
Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?
692007/09/29
Are SC (CEC) and MD formed independently?
Cu atoms beyond the solubility limit form precipitates in high Cu materials. This mechanism is independent of the MD formation.
Formation of Ni-Si-Mn clusters may be caused by solute-atom segregation to point-defect clusters
What is the interaction between Cu and point defect clusters?
702007/09/29
Precipitation of Cu on dislocations in FeLEAP analysis of irradiated RPV steel
Clustering of Cu atoms on dislocations is evident.
KLMC results of thermal ageing of Fe-Cu crystal at 823K using the lattice sites including two edge dislocations.
KLMC
712007/09/29
Interaction between Cu atoms and point defect clusters
Computer simulations show strong binding between the Cu atoms and point defect clusters of both vacancy and SIA.
100 Vac & 100 Cu
vacancy
Cu atom
20 SIA &20 Cu
SIA
Cu atom
KLMC, with Metropolis algorithm, + MD results of the lowest energy configuration of point defect – Cu atom clusters.
722007/09/29
Cu-vacancy clusters
100 Vac. & 10 Cu atoms 100 Vac. & 100 Cu atoms
10 Vac. & 10 Cu atoms 10 Vac. & 100 Cu atoms
VacancyCu atom
• Cu atoms and vacancies form stable clusters.
• Central vacancy cluster + Cu shell
732007/09/29
Cu-SIA clusters
4 SIAs & 1 Cu atoms 4 SIAs & 8 Cu atoms
4 SIAs & 16 Cu atoms 20 SIAs & 20 Cu atoms
Fe atom
Cu atom
Lattice site
A row of four Cu atoms is a stable configuration.
742007/09/29
Mechanism Cu-SIA cluster formation
Binding energy of the Cu precipitate and the SIA loop ~1.7eV
Fe atomCu atomLattice site
752007/09/29
Issues to be studied
Do CEC and MD cause embrittlement? What is the nature of MD? What is the nature of CEC?
Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?
762007/09/29
Issues to be studied
Do CEC and MD cause embrittlement? What is the nature of MD? What is the nature of CEC?
Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?
772007/09/29
Temperature effect on MD
R.B. Jones, T.J. Williams, Effects of Radiation on Materials: 17th International Symposium, ASTM STP 1270, American Society for Testing and Mateirals, 1996, 569.
0.5
31.869 4.57 10
T
T
SMD A F t
F T
(T : 100 ~ 350oC)
Kinetic Monte Carlo SimulationExperimental correlation
227℃ 307℃
ASTM E 900-02
0.0 100
2.0 1012
4.0 1012
6.0 1012
8.0 1012
1.0 1013
1.2 1013
480 500 520 540 560 580 600 620
Nd1/
2 / (
t)1/
2 (m
-3/2dp
a1/
2 )
T (K)
Nd
1/2 = B(2.6 - 4.6x10 -3T)(t)1/2
Nd
1/2 = A(2.9 - 4.6x10 -3T)(t)1/2
Vacancy clusterSIA cluster5076.0
460
370,20exp f
TASMD
c
Jones & Williams(T in oF)
782007/09/29
Issues to be studied
Do CEC and MD cause embrittlement? What is the nature of MD? What is the nature of CEC?
Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?
792007/09/29
Dose Rate Effect in Low Cu Material
60
50
40
30
20
10
0MPa
硬化
量(
)5 6 7 8 9
1011
2 3 4 5 6 7 8 9
1012
n/ cm中性子照射速度( 2- s)
中性子照射量 (~10低 18n/ cm2) (~10高 19n/ cm2)
高照射量
低照射量
Incr
ease
in y
ield
str
ess
(M
Pa)
Dose rate (n/cm2-s)
Tra
nsiti
on t
em
pera
ture
sh
ift (
oC
)
Fluence (x1019n/cm2)
Comparison of French surveillance data and test reactor irradiation data
Comparison of test reactor data irradiated at different fluxes
No clear dose rate effect is observed in low Cu materials.
P. Petrequin, ASMES:1996. Report Number 6 EUR 16455 EN 1996.
CRIEPI/UCSB Joint Program
FluenceLowHigh
802007/09/29
Dose Rate Effect in High Cu MaterialLow Dose Region High Dose Region
Dose rate effect is evident in high Cu materials
T.J. Williams, P.R. Burch, C.A. English, and P.H.N. Ray, 3rd Int. Symp. on Environmental Degradation of Materials in Nuclear Power Systems – Water Reactors (1988), 121.
0.001 0.010 0.100
0.001 0.010 0.100
High Cu
Low Cu
G.R. Odette, E.V. Mader, G.E. Lucas, W.J. Phythian, C.A. English, ASTM STP 1175 (1994), 373.
812007/09/29
0
10
20
30
40
50
60
70
80
0.0E+00 5.0E+17 1.0E+18 1.5E+18 2.0E+18 2.5E+18 3.0E+18
Fluence (n/cm2)
De
lta T
r30
(o C)
Surveillance (A)
Surveillance (W)
MTR
SPT1
SPT2
SP1
Detailed Comparison of Surveillance Data and Test Reactor Irradiation Data of High Cu Material
0.24 wt.%Cu
Very clear dose rate effect is observed in the material irradiated at very low dose rates.
Dose Rate (n/cm2-s)~1x109
~2x1010
7x1011
822007/09/29
0%
20%
40%
60%
80%
100%
1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 229 241 253 265 277 289 301 313 325 337 349 361 373 385 397 409
SP1
Com
pos
itio
n (a
t.%
)
Cluster ID
41 x 48 x 149 nm3
6.3M atoms
Fe Mn FeNi58 Ni Cu Si P
Size-weighted average 3.0 62.4 6.5 6.5 3.2 11.0 3.3 0.3
Simple average 2.6 61.6 6.5 5.9 3.2 11.2 3.7 0.2
(at.%)Method
Guinier(nm)
SP1
0
10
20
30
40
50
60
70
80
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0
Cluster diameter (nm)
Counts
Cou
nts
Guinier diamter (nm)
CuP
Nd 4.32 x 1023 m-3
Vf 4.39 x 10-3
dG 2.58 nm
Fe
Mn
NiNi
Si
Cu
Cu contentBulk: 0.18at.%Matrix: 0.11at.%
832007/09/29
SPT1
0%
20%
40%
60%
80%
100%
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111
Cluster ID
Co
mp
osi
tion
(a
t.%)
0
5
10
15
20
25
30
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0
Cluster diameter (nm)
Co
un
ts
Nd 2.94 x 1023 m-3
Vf 1.25 x 10-3
dG 1.96 nm
Fe Mn FeNi58 Ni Cu Si P
Size-weighted average 2.1 58.4 6.6 5.8 2.7 11.1 3.5 0.2
Simple average 2.0 56.8 6.8 6.0 2.7 11.7 3.7 0.2
(at.%)Method
Guinier(nm)
Cluster ID
Com
posi
tion
(at.%
)
Guinier diameter (nm)
Cou
nt
Fe
Mn
NiNi
Si
Cu
TG1-L1 01865: 24.1x28.6x175nm3 2.7M atoms
CuP
842007/09/29
0
5
10
15
20
25
30
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0
SPT2
0%
20%
40%
60%
80%
100%
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117
Nd 6.37 x 1023 m-3
Vf 2.94 x 10-3
dG 2.01 nm
Fe Mn FeNi58 Ni Cu Si P
Size-weighted average 2.2 57.1 5.6 6.6 2.9 11.1 4.2 0.2
Simple average 2.0 55.0 5.8 6.9 3.1 11.7 4.3 0.3
(at.%)Method
Guinier(nm)
Cluster ID
Com
posi
tion
(at.%
)
Guinier diameter (nm)
Cou
nt
Fe
Mn
NiNi
Si
Cu
TG1-L2 01849: 27.7x32.1x259nm3, 5.1M atoms
CuP
852007/09/29
Estimation of the Number of Vacancy Jumps
3
020
6exp 2 exp exp
vvfm k
th
EE Sn t D
kT a k kT
Diffusion of vacancies leads to the diffusion of solute atoms such as copper. We have two types of vacancies in the irradiated metals: Irradiation-induced vacancy Thermal vacancy
Effect of dose rate on the number of vacancy jumps can be a measure of the dose rate effect on the solute diffusion (and clustering). In KMC, we can count the number of vacancy jumps.
The number of thermal vacancy jumps can be estimated as:
862007/09/29
Dose rate effect on the number of vacancy jumps- KMC study -
0
10
20
30
40
50
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
Nu
mbe
r of
va
can
cy ju
mp
s (x
10
8 )
Dose rate (dpa/s)
Total vacancy jumps
Irradiation-induced vacancy jumps
Thermal vacancy jumps
Dose: 0.01 dpan-spectrum: fissionTemperature: 600K
1010
109
108
107
106
105
104
103
102
Irradiation time (s)
At low dose rates, it is likely that the diffusion due to thermal vacancy may contribute to solute atom clustering.
BWR PWR
872007/09/29
Dose rate effect at high dose region
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6Diameter (nm)
Critic
al a
ngle
(de
g.)
V (Osetsky, Bacon, Mohles, 2003)I (b[-111])I (b[1-11])I (b[11-1])I (b[111])
Dislocation DynamicsSimulations
Obstacle strength of SIA loops (MD)
1021
1022
1023
1024
1025
10-5
10-4
10-3
10-2
10-1
Nu
mbe
r de
nsi
ty (
m-3
)
Dose (dpa)
Temperature: 600Kn-spectrum: FissionGrain size: 10m
No stable vacancy cluster
at 10-8
dpa/s and 10-10
dpa/s
10-4dpa/s
10-6dpa/s
Vacancy
10-4dpa/s
10-6dpa/s
No stable vacancy cluster is formed below 10-8dpa/s
1021
1022
1023
1024
1025
10-5
10-4
10-3
10-2
10-1
Nu
mbe
r de
nsi
ty (
m-3
)
Dose (dpa)
SIA cluster > 37
(Smoothed data)Temperature: 600Kn-spectrum: FissionGrain size: 10m
10-4 dpa/s
10-6 dpa/s
10-10 dpa/s
10-8 dpa/s
SIA
10-4dpa/s
10-6dpa/s
10-8dpa/s
10-10dpa/s
882007/09/29
DD simulations of flux effect in Fe
0.0E+00
5.0E+07
1.0E+08
1.5E+08
2.0E+08
2.5E+08
3.0E+08
3.5E+08
0 0.0005 0.001 0.0015 0.002 0.0025
Strain
Stre
ss (
Mpa
)
1e-9dpa/s1e-7dpa/s1e-5dpa/s
892007/09/29
Summary of Understanding on Embrittlement Mechanism
Hardening due to the formation of solute atom clusters (SCs) and dislocation loops (MD) is the primary mechanism of embrittlement.
Formation of SC depends on the formation of MD. Irradiation induced solute clustering model
Formation of MD is temperature dependent. Dose rate effect exists in high Cu materials especially at
very low dose rates.
902007/09/29
Development of Embrittlement Correlation Method
Two step modeling Step 1: modeling of microstructural changes Step 2: modeling of mechanical property change
Approach To formulate the microstructural changes by rate
equations. To optimize the coefficients of the equations using
surveillance data.
912007/09/29
Modeling of Microstructural Changes
2089214 1 NiCu
availCuMDCu
matCu
enhSC
indSCSC
CDCCDC
t
C
t
C
t
C
t
CCF
t
C SCNit
MD
276
25
rCuavailCuSC tDCv
2
2
SCSC
enhSc
SC
matCu Cv
t
Cv
t
C
solCu
matCu
solCu
matCu
solCu
matCuavail
CuCCCC
CCC
0
21
thermalCu
irradCu
thermalCuCu DDDD
CuavailCuSC DCv 1
Irradiation induced SC Irradiation enhanced SC
Effect of NiEffect of Tirrad
Cu available to form clusters decreases.
Thermal vacancy plays a role.
matCuC : amount of Cu in the matrix
availCuC : amount of Cu beyond the
solubility in the matrix
SC depends on MD
922007/09/29
0
20
40
60
80
100
0 0.02 0.04 0.06 0.08
Vf1/2
T41
J
Transition temperature shift is almost proportional to Vf1/2 of
solute atom clusters.
Correlation between microstructure and mechanical property
932007/09/29
Modeling of Mechanical Property Change
13
0
12,
SC
matCuCu
SCmatCu C
CCCCf
MDMD CT 18
22MDSC TTT
SCNiSCmatCufSC CthCgCCfVT 0
161717 ,
2014
0 151 NiNi CCg
CuSC
SC
DD
tDth
1110 1
Model of cluster size
Cu effect
Ni effect
Total shift is NOT a simple sum of the two contributions.
SC contribution does not saturate at least under test reactor irradiation
one set of coefficients is determined.
942007/09/29
Comparison between the measured value and the prediction
プラント補正なしプラント補正あり
-20
0
20
40
60
80
100
120
140
-20 0 20 40 60 80 100 120 140
監視試験測定値(℃)
予測
値(℃
)
補正なし補正あり1:1- 2σ+2σ
Method Std. Dev. Mean Error
JEAC4201 11.9 -1.3
RG1.99 r2
15.4 -1.9
EWO 10.4 2.8
E900-02 11.7 2.3
CRIEPI 9.4 0.7
CRIEPI adj 5.4 0.1
Pre
dict
ion
(o C)
Measured value (oC)
w/o adjustmentw adjustment
T
t
Offset
T
t
Offset
952007/09/29
Summary
The mechanisms of neutron irradiation embrittlement of RPVs are studies using multi-scale computer simulations and experiments.
A new embrittlement correlation method to predict transition temperature shifts is developed, in which the understandings of the mechanisms were formulated using the rate equations.
The above approach will be adopted in the revision of JEAC4201 this year.
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