Integratedcomputationalstudyofmateriallifetime ... · Integratedstudies(talkoutline) • 1. Neutron transport calculations (neutronics) with MCNP predicts the irradiation environment

Integrated computational study of material lifetime

in a fusion reactor environment

M. R. Gilbert, S. L. Dudarev, S. Zheng,L. W. Packer, and J.-Ch. Sublet

EURATOM/CCFE Fusion Association, UK

October 12, 2012

24th IAEA Fusion Energy Conference, San Diego

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Introduction

• The neutrons generated in fusion plasmas bombard thesurrounding materials. . .

◮ ∼ 1015 neutrons cm−2 s−1 expected on plasma-facing first wall(FW) in DEMO

• . . . and induce nuclear reactions◮ e.g. 56Fe(n, γ)57Fe, 12C(n, α)9Be, 64Cu(n, p)63Ni

• During reactor operation these transmutations will producenew elements, including gases (helium and hydrogen)

• Accumulation of these impurities could significantly alter thestructural and mechanical properties of materials

◮ Hardening, swelling, gas-induced embrittlement,etc.

• A full picture of the transmutation response and consequencesrequires:

◮ knowledge of the irradiation conditions◮ calculation of the burn-up of materials◮ modelling the effect of impurities

2/20

Integrated studies (talk outline)

• 1. Neutron transport calculations (neutronics) with MCNP◮ predicts the irradiation environment for components within a

given reactor design◮ delivers neutron fluxes and energy spectra

• 2. Inventory calculations with FISPACT◮ neutron spectrum and flux as input◮ calculates the activation and burn-up (transmutation) of

materials◮ quantifies the changes to material composition in time

• But the absolute transmutation numbers do not informwithout models to predict consequences

• 3. Modelling of material properties (atomistic or otherwise)◮ First attempt:

Helium embrittlement of grain boundaries in differentmaterials using production rates from FISPACT

3/20









3/20

1. Neutronics: DEMO model for MCNP

• 2009 model designed usingHERCULES1

• 2.7 GW fusion power output

• Cell-based geometry

• Solid Be+Li tritium breedingblanket + W divertor + Hecooling

• Neutrons transportedthrough model from acorrectly definedfusion-plasma source

• Simulation of sufficientneutrons to provide goodstatistics

First wall & blanketShielding & backplatesVessel WallsCoilsDivertor armourDivertor structure

Plasma

(cm)-1000

-750

-500

-250

0

250

500

750

1000

0 300 600 900 1200 1500-1000

-750

-500

-250

0

250

500

750

1000

0 300 600 900 1200 1500

4/20

0

0.01

0.02

0.03

0.04

0.05

Prob

abili

ty o

f so

urce

neu

tron

1Pampin and Karditsas, 2006 Fusion Eng. Des., 81 1231-7

1. Neutronics: example spectra

• Neutron spectra as a function of depth into outboardequatorial First Wall (FW):

1e+06

1e+07

1e+08

1e+09

1e+10

1e+11

1e+12

1e+13

1e+14

1e+15

1e-01 1e+01 1e+03 1e+05 1e+07

Neu

tron

Flu

x (n

cm

-2s-1

)pe

r le

thar

gy in

terv

al

Energy (eV)

0-0.5 cm (FW)1.5-2 cm (FW)

2-3 cm (Blanket)27-32 cm (Blanket)57-62 cm (Blanket)

62-82 cm (Backplate)92-122 cm (Shield)

152-122 cm(Vacuum Vessel)

(a)

Plasma

(cm)-1000

-750

-500

-250

0

250

500

750

1000

0 300 600 900 1200 1500

• Energy spectrum softens with depth• Total flux also falls:

◮ Total in 2 cm FW is 8.25× 1014 n cm−2 s−1

◮ In final 5 cm of blanket drops to 3.90× 1013 n cm−2 s−1

◮ In vessel walls it is only 1.38× 1012 n cm−2 s−1

• Variation is complex, so standard practice is to calculateintegrated quantity −→ e.g. dpa

5/20

1. Integrated results: dpa

-600

-400

-200

0

200

400

600

500 700 900 1100 1300(cm) 0

2

4

6

8

10

12

14

dpa/

fpy

in F

e

• Displacements per atom(dpa): Integrated measureof total exposure

◮ Spectra and fluxes mergedwith Material dependentnuclear data (EFF 1.1)

dpa per second =

Ng∑

i

φiσdpai

• shows the variation in“exposure” with position

• dpa/fpy in Fe in FW armouris ∼ 3 times higher than inblanket

• Note: dpa estimates do not take into account the time evolution of

radiation damage and give no direct information about changes to

microstructure or properties

6/20 fpy=full power year

Globalvariation indpa/fpy inFe

Caution with dpa interpretation

7/20

X. Yi1, M.L. Jenkins1, M.A. Kirk2, S.G. Roberts1 – 20121Department of Materials, University of Oxford; 2Argonne National Laboratory

• self-ion irradiation of pure W to 0.01 dpa at a range of temperatures

Damage varieswith temperature

for same dpa

• However, dpa is a convenient atom-based measure of irradiation exposure

1. dpa: variation with poloidal angle in FW armour

• Exposure measured as dpa/fpy in Fe for the 2 cm FW armour

• poloidal variation in dpa/fpy follows variation in total flux. . .


0

2

4

6

8

10

12

14

16

A B C D E F G H I J K L M 0

1.2

2.4

3.6

4.8

6

7.2

8.4

9.6dp

a/fp

y in

Fe

x 10

14 e

quiv

alen

t flu

x (n

cm

-2 s

-1)

Position

dpa/fpyflux

-600

-400

-200

0

200

400

600

500 700 900 1100 1300

A

B

CDE

FG

H

I

J

K L

M

(cm)

Plasma

1. dpa: variation with depth


• . . . but dpa variation does not always follow change intotal flux

• dpa/fpy in Fe and totalflux as a function ofdepth into outboardequatorial FW

• total flux initiallyincreases due to neutronmultiplication

• but equivalent dpa/fpy isalways decreasing 0

2

4

6

8

10

12

14

16

18

0 5 10 15 20 25 30 35 40 0

1e+14

2e+14

3e+14

4e+14

5e+14

6e+14

7e+14

8e+14

9e+14

dpa/

fpy

in p

ure

Fe

Tot

al n

eutr

on f

lux

(n c

m-2

s-1)

distance from plasma facing wall (cm)

arm

our

blanketinboard dpa/fpy

outboard dpa/fpyinboard flux

outboard flux

1. dpa: variation with material


• Comparison between W and Fe in FW armour regions

• dpa/fpy in W is ∼1/3 of that in Fe (Nuclear data dependent. . . )

0

2

4

6

8

10

12

14

16

A C G I K L

dpa/

fpy

Position

in Fe

0

2

4

6

8

10

12

14

16

A C G I K LPosition

in W

-600

-400

-200

0

200

400

600

500 700 900 1100 1300

A

CG

I

K L

(cm)

Plasma

Final caution with dpa: Nuclear-data dependence

• . . . results from dpacalculations are verysensitive to inputreaction-cross-section data

• The newly developed inventorycode FISPACT-II can calculatedpa values directly fromneutron spectra

• Calculations using the latestnuclear data libraries(TENDL-2011) revealsignificantly different dpavalues to previous resultsobtained from NJOY using theEFF 1.1 library

• For example, the exposuremeasured as dpa/fpy in pure Whas risen by a factor of 3 in the2 cm FW armour

11/20

0 2 4 6 8

10 12 14 16 18 20

0 10 20 30 40 50 60

dpa/

fpy

Depth from plasma-facing wall (cm)

Fe - EFF 1.1Fe - TENDL 2011

W - EFF 1.1W - TENDL 2011

(dpa/fpy as a function of depthinto outboard equatorial FW)









12/20

2. Inventory calculations

FISPACT:

• calculates the time-evolution of composition by solving a setof coupled differential equations ∀ possible nuclides Ni :

The Bateman equations

dNi

dt= −Ni(λi + σiφ)

︸︷︷︸

loss

+∑

j 6=i

Nj(λji + σjiφ)︸︷︷︸

creation

• a database of reaction cross sections (‘European Activation File’ –EAF) is collapsed with the neutron energy spectra → σi , σij

• EAF also provides decay constants λi , λij

• fluxes φ from neutronics (MCNP)

13/20

2. Transmutation example

14/20 appm=atomic parts per million

• Pure W and Fe under outboard equatorial FW armour flux for 5 fpy

• Metal impurities build-up over time◮ primarily Re, Os, Ta in W◮ Mn and Cr from Fe

• Helium and hydrogen are also produced◮ gas production is very low in W (∼ ×10 less than in Fe)

10-2

100

102

104

106

0 1 2 3 4 5

Con

cent

ratio

n (a

ppm

)

Irradiation Time (years)

10-2

100

102

104

106

0 1 2 3 4 5

Con

cent

ratio

n (a

ppm

)

Irradiation Time (years)

WReOsTaHfHHeIrPt

0 1 2 3 4 5Irradiation Time (years)

FeMnHCrHeVCoNiTi

0 1 2 3 4 5Irradiation Time (years)

FeMnHCrHeVCoNiTi

M.R. Gilbert and J.-Ch. Sublet, Nuclear Fusion 51 (2011) 043005

from W from Fe

2. W transmutation: 5 fpy FW armour


Time: 0.000 seconds

0.01

0.1

1

10

100

1000

104

105

106

conc

entr

atio

n (a

ppm

)

Pure W irradiated in aDEMO FW armour spectrum

Total flux: 8.25 x 10 14 n cm-2 s-1

ZN

Lu176

Lu177

Lu178

Lu179

Lu180

Lu181

Lu182

Lu183

Lu184

Hf177

Hf178

Hf179

Hf180

Hf181

Hf182

Hf183

Hf184

Hf185

Hf186

Hf187

Ta178

Ta179

Ta180

Ta181

Ta182

Ta183

Ta184

Ta185

Ta186

Ta187

Ta188

Ta189

Ta190

W179

W180

W181

W182

W183

W184

W185

W186

W187

W188

W189

W190

W191

Re180

Re181

Re182

Re183

Re184

Re185

Re186

Re187

Re188

Re189

Re190

Re191

Re192

Os181

Os182

Os183

Os184

Os185

Os186

Os187

Os188

Os189

Os190

Os191

Os192

Os193

Ir182

Ir183

Ir184

Ir185

Ir186

Ir187

Ir188

Ir189

Ir190

Ir191

Ir192

Ir193

Ir194

Pt183

Pt184

Pt185

Pt186

Pt187

Pt188

Pt189

Pt190

Pt191

Pt192

Pt193

Pt194

Pt195

Au185

Au186

Au187

Au188

Au189

Au190

Au191

Au192

Au193

Au194

Au195

Au196

71

72

73

74

75

76

77

78

79

105 106 107 108 109 110 111 112 113

114 115

116 117

H1

H2

H3

He3

He4

He6

Li5

Li6

Li7

1

2

3

0 1 2

3

4



Time: 1.000 day

0.01

0.1

1

10

100

1000

104

105

106

conc

entr

atio

n (a

ppm

)



ZN

Lu176

Lu177

Lu178

Lu179

Lu180

Lu181

Lu182

Lu183

Lu184

Hf177

Hf178

Hf179

Hf180

Hf181

Hf182

Hf183

Hf184

Hf185

Hf186

Hf187

Ta178

Ta179

Ta180

Ta181

Ta182

Ta183

Ta184

Ta185

Ta186

Ta187

Ta188

Ta189

Ta190

W179

W180

W181

W182

W183

W184

W185

W186

W187

W188

W189

W190

W191

Re180

Re181

Re182

Re183

Re184

Re185

Re186

Re187

Re188

Re189

Re190

Re191

Re192

Os181

Os182

Os183

Os184

Os185

Os186

Os187

Os188

Os189

Os190

Os191

Os192

Os193

Ir182

Ir183

Ir184

Ir185

Ir186

Ir187

Ir188

Ir189

Ir190

Ir191

Ir192

Ir193

Ir194

Pt183

Pt184

Pt185

Pt186

Pt187

Pt188

Pt189

Pt190

Pt191

Pt192

Pt193

Pt194

Pt195

Au185

Au186

Au187

Au188

Au189

Au190

Au191

Au192

Au193

Au194

Au195

Au196

71

72

73

74

75

76

77

78

79

105 106 107 108 109 110 111 112 113

114 115

116 117

H1

H2

H3

He3

He4

He6

Li5

Li6

Li7

1

2

3

0 1 2

3

4



Time: 1.016 years

m

0.01

0.1

1

10

100

1000

104

105

106

conc

entr

atio

n (a

ppm

)



ZN

Lu176

Lu177

Lu178

Lu179

Lu180

Lu181

Lu182

Lu183

Lu184

Hf177

Hf178

Hf179

Hf180

Hf181

Hf182

Hf183

Hf184

Hf185

Hf186

Hf187

Ta178

Ta179

Ta180

Ta181

Ta182

Ta183

Ta184

Ta185

Ta186

Ta187

Ta188

Ta189

Ta190

W179

W180

W181

W182

W183

W184

W185

W186

W187

W188

W189

W190

W191

Re180

Re181

Re182

Re183

Re184

Re185

Re186

Re187

Re188

Re189

Re190

Re191

Re192

Os181

Os182

Os183

Os184

Os185

Os186

Os187

Os188

Os189

Os190

Os191

Os192

Os193

Ir182

Ir183

Ir184

Ir185

Ir186

Ir187

Ir188

Ir189

Ir190

Ir191

Ir192

Ir193

Ir194

Pt183

Pt184

Pt185

Pt186

Pt187

Pt188

Pt189

Pt190

Pt191

Pt192

Pt193

Pt194

Pt195

Au185

Au186

Au187

Au188

Au189

Au190

Au191

Au192

Au193

Au194

Au195

Au196

71

72

73

74

75

76

77

78

79

105 106 107 108 109 110 111 112 113

114 115

116 117

H1

H2

H3

He3

He4

He6

Li5

Li6

Li7

1

2

3

0 1 2

3

4



Time: 5.000 years

m

m

0.01

0.1

1

10

100

1000

104

105

106

conc

entr

atio

n (a

ppm

)



ZN

Lu176

Lu177

Lu178

Lu179

Lu180

Lu181

Lu182

Lu183

Lu184

Hf177

Hf178

Hf179

Hf180

Hf181

Hf182

Hf183

Hf184

Hf185

Hf186

Hf187

Ta178

Ta179

Ta180

Ta181

Ta182

Ta183

Ta184

Ta185

Ta186

Ta187

Ta188

Ta189

Ta190

W179

W180

W181

W182

W183

W184

W185

W186

W187

W188

W189

W190

W191

Re180

Re181

Re182

Re183

Re184

Re185

Re186

Re187

Re188

Re189

Re190

Re191

Re192

Os181

Os182

Os183

Os184

Os185

Os186

Os187

Os188

Os189

Os190

Os191

Os192

Os193

Ir182

Ir183

Ir184

Ir185

Ir186

Ir187

Ir188

Ir189

Ir190

Ir191

Ir192

Ir193

Ir194

Pt183

Pt184

Pt185

Pt186

Pt187

Pt188

Pt189

Pt190

Pt191

Pt192

Pt193

Pt194

Pt195

Au185

Au186

Au187

Au188

Au189

Au190

Au191

Au192

Au193

Au194

Au195

Au196

71

72

73

74

75

76

77

78

79

105 106 107 108 109 110 111 112 113

114 115

116 117

H1

H2

H3

He3

He4

He6

Li5

Li6

Li7

1

2

3

0 1 2

3

4

Aside: Motivation for quantifying He production

• Transmutant helium can accumulate in pre-existing cracksand voids – swelling

• Helium can also migrate to grain boundaries (GBs) leading toembrittlement

• Particular problem for fusion because of the generally higherneutron energies – many of the helium-producing reactionshave thresholds

16/20


V.P. Chakin, Z. Ye OstrovskyJ. Nucl. Mater. 307-311

(2002) 657




16/20





16/20

5 10 15 20Incident Neutron energy (MeV)

0

0.1

0.2

0.3

0.4

0.5

Cro

ss s

ectio

n (b

arns

)

12C(n,n′2α)

4He

12C(n,α)

9Be

0 5 10 15 20Incident Neutron energy (MeV)

0.00

0.01

0.02

0.03

0.04

0.05

Cro

ss s

ectio

n (b

arns

)

56Fe(n,α)

53Cr

0 5 10 15 20Incident Neutron energy (MeV)

0

0.05

0.1

0.15

0.2

0.25

Cro

ss s

ectio

n (b

arns

)

28Si(n,α)

25Mg

28Si(n,nα)

24Mg

1barn = 10−24 cm2

2. He production

• Material comparison under identical conditions

• 3 fpy under outboard equatorial FW armour irradiation:

• He production highest inBe (∼ 4300 appm/fpy)

• More than an order ofmagnitude lower in Fe(∼ 140 appm/fpy)

• Only ∼ 4 appm/fpy in W


1

10

100

1000

10000

Fe W Ta Zr Be Mo Nb Cu Cr V SiC C

He

conc

entr

atio

n (a

ppm

)

Material

DEMO - 3 fpy

2. He production

• Material comparison under identical conditions

• 3 fpy under outboard equatorial FW armour irradiation:

• He production highest inBe (∼ 4300 appm/fpy)

• More than an order ofmagnitude lower in Fe(∼ 140 appm/fpy)

• Only ∼ 4 appm/fpy in W

• concentrationssignificantly higher thanpredicted for full-lifetimeof ITER FW (withapproximate campaigntiming)


1

10

100

1000

10000

Fe W Ta Zr Be Mo Nb Cu Cr V SiC C

He

conc

entr

atio

n (a

ppm

)

Material

DEMO - 3 fpy

ITER - 14 years










3. Modelling: He embrittlement of GBs

Simple modelling of grain boundary (GB) failure

1. Number of He atoms in spherical grain:✞

✝

☎

✆NHe ≈

43πR

3nGHe

R

Assumptions:

• All helium atomsproduced migrate tograin boundary

◮ traps and obstaclesneglected

◮ most valid for smallgrains

GHe = bulk concentration(from inventory calcs.)n = atom density

19/20



2. All He atoms move to GB: – ∴ surface total ≡ bulk total✞

✝

☎

✆4πR2νHe =

43πR

3nGHe ⇒

✞

✝

☎

✆νHe =

R3 nGHe

R

Assumptions:

• All helium atomsproduced migrate tograin boundary

◮ traps and obstaclesneglected

◮ most valid for smallgrains

GHe = bulk concentration(from inventory calcs.)νHe = surface density

19/20



3. Assume GBs destabilized when E of solute He equals E of surface:✞

✝

☎

✆E solHe ν

cHe ≈ 2εsurf

Material He solution energy Surface energy Critical He conc. at(eV)∗ – E sol

He (Jm−2)∗ – εsurf GBs (cm−2) – νcHe

Fe 4.34 2.4 6.90× 1014

Mo 4.65 3.0 8.05× 1014

Ta 4.82 3.0 7.77× 1014

W 4.77 3.5 9.16× 1014

Be 3.46 2.2 7.94× 1014

SiC 1.50† 2.5 2.08× 1015

∗Estimates taken from: F. Willaime and C. C. Fu, 2006, Mater. Res. Soc. Symp., 981 0981–JJ05–04, M. G.Ganchenkova et al., 2009, J. Nucl. Mater., 386–388 79–81, L. Vitos et al., 1998, Surf. Sci., 411 186–202, Yu M.Koroteev et al., 2009, Phys. Solid State, 51 1600–1607, and S. C. Middleburgh and R. W. Grimes, 2011, ActaMater., 59 7095–7103

†Energy for He interstitial surrounded by Si atoms – R. M. Van Ginhoven et al., 2006, J. Nucl. Mater., 51 348

19/20



3. Assume GBs destabilized when E of solute He equals E of surface:✞

✝

☎

✆E solHe ν

cHe ≈ 2εsurf

• Experimental confirmation:◮ Helium irradiated W

bicrystals◮ Expansion of grain

boundaries at He fluenceof 1014–1015 ions cm−2

◮ our νcHe value: 7.51× 1014

19/20

Gerasimenko, Mikhaılovskiı,Neklyudov, Parkhomenko, andVelikodnayaTech. Phys. 43 (1998) 803



4. Critical bulk He concentration:✞

✝

☎

✆G cHe =

3Rn

νcHe

Material νcHe n G cHe

(cm−2) (cm−3) (appm)

Fe 6.90× 1014 8.5× 1022 488.0Mo 8.05× 1014 6.4× 1022 753.2Ta 7.77× 1014 5.5× 1022 841.3W 9.16× 1014 6.3× 1022 871.5Be 7.94× 1014 1.2× 1023 385.2SiC 2.08× 1015 4.7× 1022 2645.6

• Assumed Grain size of R = 0.5µm

• G cHe varies linearly with 1/R

19/20

3. Critical lifetimes for GB embrittlement by He

• Critical embrittlement lifetimes estimated using FISPACT

Material G cHe Critical GB embrittlement lifetimes tcHe for DEMO

(appm) Outboard Polar Equatorial Shielded

Equatorial FW blanket divertor

FW 17-19 cm armourFe 488.0 4 years 7 years 18 years 78 yearsMo 753.2 18 years 36 years 114 years 420 yearsTa 841.3 216 years 300+ years 300+ years 300+ yearsW 871.5 300+ years 300+ years 300+ years 300+ yearsBe 385.2 1 month 2 months 4 months 1.5 yearsSiC∗ 2645.6 1.8 years 3.5 years 9.5 years 41 years

• Wide variation in lifetimes between different materials and for thesame material as a function of position

• Be has very short expected lifetimes• This type of failure probably won’t occur in W (or Ta)

20/20 ∗modelling less valid for non-metallic SiC because of structure and He migration E

Summary

• An integrated model of neutron-irradiation-induced changes inmaterial properties for DEMO:

• 1. Neutron-transport simulations of a fusionreactor model:

◮ wide variation in exposure with depth and position - evenwithin the same components

• 2. Inventory calculations:◮ the variation in irradiation environment creates large

differences in the transmutation or burn-up rates of materials◮ He production rates are strongly dependent on material

• 3. Simple modelling of He-induced grain-boundaryembrittlement suggests that some materials could fail onrelatively short timescales (Be in particular)

21/20

Gilbert M R et al., 2012, Nucl. Fus., 52 083019

Summary

Future

• Fully heterogenous reactor models could predict very differentirradiation conditions

• The GB failure model needs to fully account for the traps andmigration barriers for He

◮ lifetimes could be increased in a more complete model

• Integration of other predictive techniques:◮ e.g. swelling-induced stresses leading to fracture, changes in

strength due to transmutation impurities,etc.

21/20

Documents

Integratedcomputationalstudyofmateriallifetime ... · Integratedstudies(talkoutline) • 1. Neutron transport calculations (neutronics) with MCNP predicts the irradiation environment