Multiscale Computer Simulations and Predictive Modeling of RPV Embrittlement

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




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


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


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


242007/09/29

Large SIA & large vacancy cluster (3)


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


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


272007/09/29

Summary of Cascade Database


53% 17% 10%15%5%

50keV(100runs)

20keV(50runs) 80% 8%10%

2%


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


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




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


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



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


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




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


Co

un

ts


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




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


Co

un

ts


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


6.6M atoms

400oC 450oC 500oC 600oC

31x42x299 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


radius / nm

DW2-40_01261

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5


radius / nm

DW2-45_01236

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5


radius / nm

DW2-50_01265

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5


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




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




762007/09/29




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




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


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


Co

un

ts

Nd 2.94 x 1023 m-3

Vf 1.25 x 10-3

dG 1.96 nm



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.%

)


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



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.%

)


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


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.

Multiscale Computer Simulations and Predictive Modeling of RPV Embrittlement

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Transcript of Multiscale Computer Simulations and Predictive Modeling of RPV Embrittlement