fispact-ii applications: materials modelling, scoping and

This work was funded by the RCUK Energy Programme[Grant number EP/P012450/1]

UKAEAFISPACT-II applications:materials modelling, scoping and damage metricsMark GilbertUnited Kingdom Atomic Energy AuthorityFISPACT-II workshop

October 23-25, 2019, Manchester

FISPACT-II workshop October 2019 M. Gilbert2/41

Applications

• Integrated assessment of helium embrittlement

• Material response database

• Primary damage spectra (& emitted particle spectra)


Integrated assessment: Outline

• Neutron transport modellingresults for DEMO (MCNP)

• Neutron-inducedtransmutation (FISPACT-II)

I helium production

• Helium embrittlementmodel and critical lifetimes

DEMO model withdefined 3D plasma

source

-750

-500

-250

0

250

500

750

400 700 1000 1300

0

0.006

0.012

0.018

0.024

0.030

Plas

ma

neut

ron-

sour

cepr

obab

ility

(%

)

First wall & blanket

Shielding & backplates

Vessel Walls

Coils

Divertor

Plasma

(cm)

-750

-500

-250

0

250

500

750

400 700 1000 1300

First wallneutron spectraas a function ofDEMO concept

He productionrates in materials

Gilbert, Dudarev, Nguyen-Manh, Zheng, Packer, SubletJ. Nucl. Mater. 442 (2013) S755Gilbert, Dudarev, Zheng, Packer, SubletNucl. Fus. 52 (2012) 083019





I helium production



source

-750

-500

-250

0

250

500

750

400 700 1000 1300

0

0.006

0.012

0.018

0.024

0.030

Plas

ma

neut

ron-

sour

cepr

obab

ility

(%

)



Vessel Walls

Coils

Divertor

Plasma

(cm)

-750

-500

-250

0

250

500

750

400 700 1000 1300


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

Neutron energy (eV)

hcllhcpbwcll

wccb







I helium production



source

-750

-500

-250

0

250

500

750

400 700 1000 1300

0

0.006

0.012

0.018

0.024

0.030

Plas

ma

neut

ron-

sour

cepr

obab

ility

(%

)



Vessel Walls

Coils

Divertor

Plasma

(cm)

-750

-500

-250

0

250

500

750

400 700 1000 1300


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

Neutron energy (eV)

hcllhcpbwcll

wccb


1

10

100

1000

10000

0 50 100 150 200

He

conc

entr

atio

n (a

ppm

)

Irradiation time (full power years)

FeCr

MoW

VNbTa



Helium production• Helium production is a particular problem for fusion

because of the generally higher neutron energies – manyof the He producing reactions have thresholds

• Material comparison under identical DEMO hcpb conditions

• 3 fpy under outboard equatorial FW armour irradiation:

• FISPACT-II inventorycalculations:

• Helium productionhighest in Be(∼ 710 appm/fpy)

• More than an order ofmagnitude lower in Fe(∼ 120 appm/fpy)

• Only ∼ 2 appm/fpy in W

appm=atomic parts per million; fpy - full power years


Helium production• Helium production is a particular problem for fusion

because of the generally higher neutron energies – manyof the He producing reactions have thresholds

• Material comparison under identical DEMO hcpb conditions

• 3 fpy under outboard equatorial FW armour irradiation:

• FISPACT-II inventorycalculations:

• Helium productionhighest in Be(∼ 710 appm/fpy)

• More than an order ofmagnitude lower in Fe(∼ 120 appm/fpy)

• Only ∼ 2 appm/fpy in W

appm=atomic parts per million; fpy - full power years

1

10

100

1000

Fe W Ta Zr Be Mo Nb Cu Cr V C

He

conc

entr

atio

n (a

ppm

)

Material

After 3 fpy


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

I traps neglectedI most valid for small

grains

GHe = bulk concentration(time evolution frominventory calcs.)n = atom density




2. All He atoms move to GB: – ∴ surface total ≡ bulk total�� 4πR2νHe = 43πR

3nGHe ⇒�� νHe = R

3 nGHe

R

Assumptions:

• All helium atomsproduced migrate tograin boundary

I traps neglectedI most valid for small

grains

GHe = bulk concentration(time evolution frominventory calcs.)νHe = surface density




3. GB destabilize when E of inserted He equals E of surfaces:�� E insrtHe νcHe ≈ 2εsurf

Material He insert. energy Surf. energy Critical He conc. at(eV)† – E insrt

He (Jm−2)∗ – εsurf GBs (cm−2) – νcHe

Fe 2.77 2.4 1.08× 1015

Cr 2.68 2.3 1.07× 1015

Mo 1.91 3.0 1.96× 1015

Nb 1.60 2.7 2.11× 1015

W 1.61 3.5 2.71× 1015

V 2.30 2.6 1.41× 1015

∗Averages of experimental data reported in: L. Vitos et al., 1998, Surf. Sci., 411 186–202

†DFT values – Gilbert et al. J. Nucl. Mater. 442 (2013) S755




3. GB destabilize when E of inserted He equals E of surfaces:�� E insrtHe νcHe ≈ 2εsurf

• Experimental confirmation:I Helium irradiated W

bicrystalsI Expansion of grain

boundaries at He fluenceof 1014–1015 ions cm−2

I our νcHe value: 2.71× 1015

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




4. Critical bulk He concentration:�� G cHe = 3

RnνcHe

Material νcHe n G cHe

(cm−2) (cm−3) (appm)

Fe 1.08× 1015 8.5× 1022 764.6Cr 1.07× 1015 6.4× 1022 771.9Mo 1.96× 1015 5.5× 1022 1833.8Nb 2.11× 1015 6.3× 1022 2275.2W 2.71× 1015 1.2× 1023 2582.1V 1.41× 1015 4.7× 1022 1172.2

• Assumed Grain size of R = 0.5µm

• G cHe varies with 1/R appm – atomic parts per million


appm = atomic parts per million

FISPACT-II results: helium production rates

• standard output during irradiation in FISPACT-II simulation

• Estimated “time to destabilize” tcHe based on inventory calculations

1

10

100

1000

10000

0 50 100 150 200

He

conc

entr

atio

n (a

ppm

)

Irradiation time (full power years)

FeCr

MoW

VNbTa

DEMO hcpb

outboard

equatorial FW

irradiation


He embrittlement: Critical times

appm = atomic parts per million, fpy = full poweryear

• tcHe for irradiations in outboard equatorial DEMO FWarmour position assuming linear grain size of 0.5 µm

ElementνcHe G c

He tcHe (fpy)

(cm−2) (appm) hcll hcpb wcll wccb

Fe 1.08× 1015 764.6 9 6 8 7Cr 1.07× 1015 771.9 7 7 7 7Mo 1.96× 1015 1833.8 58 63 59 62Nb 2.11× 1015 2275.2 45 47 46 46W 2.71× 1015 2582.1 700+ 597 700+ 700+V 1.41× 1015 1172.2 25 25 25 25

• For some elements, such as W, the He production rates are so low,and/or the νcHe is so great that the critical lifetimes are manyhundreds of years

• only for tcHe / 10 is this failure mechanism likely to be of concern


Applications





Application: material response database

CCFE-R(16)36

August 2016

Mark R. Gilbert

Jean-Christophe Sublet

Handbook of activation,transmutation, and radiation damageproperties of the elements simulated

using FISPACT-II & TENDL-2015;Magnetic Fusion Plants

www.ccfe.ac.uk

• Reference document oftypical activity and burn-upresponses of the elements toneutron irradiation is a usefultool during material selectionexercises for nuclearcomponents

• Results for all naturallyoccurring elements from H toBi, with separate reports for:

I predicted DEMO and ITERconditions

I fission conditions (PWR,FBR, HFR)

• Available to download fromhttp://fispact.ukaea.uk

785 pages∼60000 calculations

http://fispact.ukaea.uk


Scoping calculations for each element:

1 Tabulated activation responseI % contributions of important radionuclides to various radiological

quantities as a function of cooling time after irradiation

2 Graphs of activation response after irradiationI decay evolution of total activity, heat, and γ-dose under three

different spectra & compared to Fe + indicative dominant nuclidecontributions

I nuclide contributions as a function of time

3 Importance diagramsI spectrum independent mapping of important radionuclides in the

neutron-energy vs. decay time phase-space

4 Transmutation responseI time evolution under irradiation of initially-pure elemental

compositionI nuclide concentration maps

5 Primary knock-on atom (PKA) distributionsI tirr = 0 spectra plotted as both elemental and isotopic sums

6 Reaction pathwaysI major production pathways for important radionuclides at four

characteristic neutron-energy ranges


Example outputs: W

10-14

10-12

10-10

10-8

10-6

10-4

10-2

10-6 10-4 10-2 100 102 104

Heat Output

Hea

t Out

put (

kW/k

g)

Decay time (years)

FWbackplateVV

Fe results100

102

104

106

108

1010

1012

1014

10-6 10-4 10-2 100 102 104

DEMO-FWSpecific ActivityMin

HourDay

Spe

cific

Act

ivity

(B

q/kg

)Decay time (years)

totalRe187Hf178nHf178mRe186mH3Ta179Ta182

Re186Re188W183mW185mW181W185W187

10-2

10-1

100

101

102

103

104

105

106

107

10-7 10-5 10-3 10-1 101 103 105

W 185Re186W 187W 181Ta182Hf178nTa179Re187Re188W 183mH 3

sec hour daymin Heat output

Neu

tron

Ene

rgy

(eV

)

Decay time (years)

10-2

100

102

104

106

0.0 0.5 1.0 1.5 2.0

1 appm He & 6 appm H per year 5.0 dpa/year

Con

cent

ratio

n (a

ppm

)

Irradiation Time (years)

WReTaOsHHf

He

1 atm.%

10 atm.%

Time: 2.00 years

m

0.01

0.1

1

10

100

1000

104

105

106

conc

entr

atio

n (a

ppm

)

Z

N

71

72

73

74

75

76

77

103 104 105 106 107 108 109 110 111 112 113

114 115 116

117

Lu174

Lu175

Lu176

Lu177

Lu178

Lu179

Lu180

Lu181

Lu182

Lu183

Lu184

Hf175

Hf176

Hf177

Hf178

Hf179

Hf180

Hf181

Hf182

Hf183

Hf184

Hf185

Hf186

Hf187

Hf188

Ta176

Ta177

Ta178

Ta179

Ta180

Ta181

Ta182

Ta183

Ta184

Ta185

Ta186

Ta187

Ta188

Ta189

Ta190

W177

W178

W179

W180

✽ W181

W182

✽ W183

✽ W184

✽ W185

W186

✽ W187

W188

W189

W190

W191

Re178

Re179

Re180

Re181

Re182

Re183

Re184

Re185

Re186

Re187

Re188

Re189

Re190

Re191

Re192

Os179

Os180

Os181

Os182

Os183

Os184

Os185

Os186

Os187

Os188

Os189

Os190

Os191

Os192

Os193

Ir180

Ir181

Ir182

Ir183

Ir184

Ir185

Ir186

Ir187

Ir188

Ir189

Ir190

Ir191

Ir192

Ir193

Ir194

1

2

3

0 1 2 3 4

H1

H2

H3

H4

H5

He3

He4

He5

He6

Li4

Li5

Li6

Li7

106

108

1010

1012

100 102 104 106

pα

HfTaW

PK

As

s-1 c

m-3

PKA energy (eV)

Activation

Nuclide contributions

Importance diagrams

Transmutation

Nuclide charts

PKA distributions


Neutron irradiation fields

FBR – superphenix Fast Breeder ReactorHFR – High Flux Reactor, Petten

PWR – Pressurized Water-cooled Reactor

• Monte Carlo simulations of a fusion DEMOnstration power plant& typical fission reactors

108

109

1010

1011

1012

1013

1014

1015

10-3 10-2 10-1 100 101 102 103 104 105 106 107

Neu

tron

flux

(n

cm-2

s-1

)pe

r le

thar

gy in

terv

al

Neutron Energy (eV)

PWRHFRFBR

DEMO-FW

6 8 10 12 14 16 18 20

Neutron Energy (MeV)

• fusion spectrum in first wall (FW) dominated by 14 MeV peak

• well-moderated (averaged) fission spectra don’t have such dominant peaksbut can have tails that explore the 14 MeV region of fusion

total fluxes φ:(×1014 n cm−2 s−1)

DEMO 6FBR 24HFR 5

PWR 3


Activation – fusion vs. fission

§after 2 years of continuous irradiation

• time snapshot of activity during decay cooling§:

1081010101210141016

H He Li Be B C N O F

Ne

Na

Mg Al

Si P S Cl

Ar K

Ca

Sc Ti V Cr

Mn

Fe

Co Ni

Cu

Zn

Ga

Ge

As

Se Br

Kr

Rb Sr Y Zr

Nb

Mo

0 5 10 15 20 25 30 35 40

@ 12 days coolingA

ctiv

ity (

Bq/

kg)

proton number

1081010101210141016

Ru

Rh

Pd

Ag

Cd In Sn

Sb

Te I

Xe

Cs

Ba La Ce Pr

Nd

Sm Eu

Gd

Tb

Dy

Ho Er

Tm Yb Lu Hf

Ta W Re

Os Ir Pt

Au

Hg Tl

Pb Bi

45 50 55 60 65 70 75 80

DEMO FBR HFR PWR

Act

ivity

(B

q/kg

)

Element


Activation summary – periodic table plot• total becquerel/kg activity from each element at 10-years

following a 2-year PWR irradiation:

PWR@ 10 years

HHydrogen

1

2.1E+08HeHelium

2

2.0E+11

LiLithium

3

5.2E+15BeBeryllium

4

8.3E+12B

Boron

5

5.4E+11C

Carbon

6

3.0E+07N

Nitrogen

7

8.4E+11O

Oxygen

8

6.9E+07F

Fluorine

9

2.0E+08Ne

Neon

10

2.4E+07

NaSodium

11

2.7E+03Mg

Magnesium

12

49Al

Aluminium

13

1.3E+03SiSilicon

14

1.2E+03P

Phosphorus

15

2.0E+07S

Sulphur

16

3.3E+07Cl

Chlorine

17

6.4E+10ArArgon

18

8.9E+08

KPotassium

19

5.1E+11CaCalcium

20

2.2E+09Sc

Scandium

21

2.6E+06Ti

Titanium

22

6.5E+03V

Vanadium

23

2.0E+04Cr

Chromium

24

1.6E+03Mn

Manganese

25

9.7E+03Fe

Iron

26

1.2E+12CoCobalt

27

8.7E+14NiNickel

28

2.1E+12CuCopper

29

2.2E+11Zn

Zinc

30

8.3E+09GaGallium

31

9.7E+03Ge

Germanium

32

1.1E+03AsArsenic

33

1.5E+04SeSelenium

34

1.6E+08Br

Bromine

35

4.7E+08KrKrypton

36

8.8E+11

RbRubidium

37

9.3E+09Sr

Strontium

38

6.6E+07Y

Yttrium

39

1.8E+06Zr

Zirconium

40

1.6E+07NbNiobium

41

5.3E+12Mo

Molybdenum

42

5.2E+09Ru

Ruthenium

44

3.9E+07RhRhodium

45

1.2E+09Pd

Palladium

46

7.5E+08Ag

Silver

47

1.2E+11CdCadmium

48

2.3E+11InIndium

49

9.9E+07Sn

Tin

50

4.8E+11SbAntimony

51

2.9E+11TeTellurium

52

4.6E+07I

Iodine

53

3.8E+05XeXenon

54

2.8E+11

CsCaesium

55

1.4E+14BaBarium

56

1.5E+11

LaLanthanum

57

1.5E+06CeCerium

58

4.7E+07Pr

Praseodymium

59

5.8E+03Nd

Neodymium

60

9.1E+11SmSamarium

62

1.3E+14EuEuropium

63

4.2E+14Gd

Gadolinium

64

1.0E+11TbTerbium

65

2.1E+08Dy

Dysprosium

66

2.4E+11HoHolmium

67

1.1E+11ErErbium

68

1.9E+12TmThulium

69

5.4E+13YbYtterbium

70

5.7E+10LuLutetium

71

4.7E+10

HfHafnium

72

4.6E+07TaTantalum

73

5.0E+05W

Tungsten

74

4.2E+06ReRhenium

75

1.7E+08OsOsmium

76

3.7E+10Ir

Iridium

77

2.7E+12Pt

Platinum

78

1.7E+11Au

Gold

79

2.9E+05HgMercury

80

9.1E+10Tl

Thallium

81

2.0E+13Pb

Lead

82

5.4E+06Bi

Bismuth

83

8.9E+06

TcTechnetium

43

PmPromethium

61

PoPolonium

84

AtAstatine

85

RnRadon

86

FrFrancium

87

RaRadium

88

AcActinium

89

ThThorium

90

PaProtactinium

91

UUranium

92

NpNeptunium

93

PuPlutonium

94

AmAmericium

95

CmCurium

96

BkBerkelium

97

CfCalifonrium

98

EsEinsteinium

99

FmFermium

100

MdMendelevium

101

NoNobelium

102

LrLawrencium

103

RfRutherfordium

104

DbDubnium

105

SgSeaborgium

106

BhBohrium

107

HsHassium

108

MtMeitnerium

109

DsDarmastadtium

110

RgRoentgenium

111

106

107

108

109

1010

1011

1012

1013

1014

Act

ivity

(B

q/kg

)


Activation summary – periodic table

DEMO First Wall@ 10 years

HHydrogen

1

1.1E+07HeHelium

2

4.6E+10

LiLithium

3

3.5E+14BeBeryllium

4

6.6E+12B

Boron

5

1.0E+13C

Carbon

6

8.6E+09N

Nitrogen

7

6.2E+12O

Oxygen

8

8.7E+08F

Fluorine

9

1.8E+12Ne

Neon

10

1.2E+09

NaSodium

11

4.8E+11Mg

Magnesium

12

9.8E+09Al

Aluminium

13

5.7E+10SiSilicon

14

1.3E+09P

Phosphorus

15

6.4E+10S

Sulphur

16

1.9E+09Cl

Chlorine

17

5.4E+10ArArgon

18

3.3E+12

KPotassium

19

1.3E+12CaCalcium

20

1.3E+11Sc

Scandium

21

1.2E+10Ti

Titanium

22

1.2E+08V

Vanadium

23

1.8E+09Cr

Chromium

24

6.2E+09Mn

Manganese

25

1.7E+11Fe

Iron

26

9.0E+12CoCobalt

27

2.8E+14NiNickel

28

4.4E+12CuCopper

29

2.0E+12Zn

Zinc

30

1.2E+11GaGallium

31

1.0E+10Ge

Germanium

32

6.8E+08AsArsenic

33

2.9E+09SeSelenium

34

1.5E+09Br

Bromine

35

3.0E+09KrKrypton

36

6.8E+12

RbRubidium

37

1.1E+12Sr

Strontium

38

7.5E+10Y

Yttrium

39

3.5E+08Zr

Zirconium

40

3.5E+09NbNiobium

41

5.8E+12Mo

Molybdenum

42

1.8E+11Ru

Ruthenium

44

1.3E+10RhRhodium

45

1.0E+13Pd

Palladium

46

3.3E+10Ag

Silver

47

1.8E+11CdCadmium

48

6.9E+12InIndium

49

2.9E+10Sn

Tin

50

1.2E+12SbAntimony

51

1.8E+11TeTellurium

52

2.5E+10I

Iodine

53

1.3E+09XeXenon

54

1.1E+11

CsCaesium

55

1.9E+13BaBarium

56

8.8E+11

LaLanthanum

57

6.6E+08CeCerium

58

5.0E+08Pr

Praseodymium

59

2.4E+09Nd

Neodymium

60

1.8E+12SmSamarium

62

2.1E+13EuEuropium

63

4.9E+14Gd

Gadolinium

64

1.4E+11TbTerbium

65

1.8E+12Dy

Dysprosium

66

8.2E+10HoHolmium

67

2.0E+11ErErbium

68

8.4E+11TmThulium

69

1.7E+12YbYtterbium

70

3.2E+10LuLutetium

71

2.1E+13

HfHafnium

72

4.4E+10TaTantalum

73

2.1E+10W

Tungsten

74

4.0E+09ReRhenium

75

1.4E+09OsOsmium

76

5.9E+09Ir

Iridium

77

5.5E+11Pt

Platinum

78

3.7E+12Au

Gold

79

1.1E+08HgMercury

80

2.8E+10Tl

Thallium

81

2.6E+13Pb

Lead

82

5.4E+09Bi

Bismuth

83

1.0E+11

TcTechnetium

43

PmPromethium

61

PoPolonium

84

AtAstatine

85

RnRadon

86

FrFrancium

87

RaRadium

88

AcActinium

89

ThThorium

90

PaProtactinium

91

UUranium

92

NpNeptunium

93

PuPlutonium

94

AmAmericium

95

CmCurium

96

BkBerkelium

97

CfCalifonrium

98

EsEinsteinium

99

FmFermium

100

MdMendelevium

101

NoNobelium

102

LrLawrencium

103

RfRutherfordium

104

DbDubnium

105

SgSeaborgium

106

BhBohrium

107

HsHassium

108

MtMeitnerium

109

DsDarmastadtium

110

RgRoentgenium

111

106

107

108

109

1010

1011

1012

1013

1014

Act

ivity

(B

q/kg

)

PWR@ 10 years

HHydrogen

1

2.1E+08HeHelium

2

2.0E+11

LiLithium

3

5.2E+15BeBeryllium

4

8.3E+12B

Boron

5

5.4E+11C

Carbon

6

3.0E+07N

Nitrogen

7

8.4E+11O

Oxygen

8

6.9E+07F

Fluorine

9

2.0E+08Ne

Neon

10

2.4E+07

NaSodium

11

2.7E+03Mg

Magnesium

12

49Al

Aluminium

13

1.3E+03SiSilicon

14

1.2E+03P

Phosphorus

15

2.0E+07S

Sulphur

16

3.3E+07Cl

Chlorine

17

6.4E+10ArArgon

18

8.9E+08

KPotassium

19

5.1E+11CaCalcium

20

2.2E+09Sc

Scandium

21

2.6E+06Ti

Titanium

22

6.5E+03V

Vanadium

23

2.0E+04Cr

Chromium

24

1.6E+03Mn

Manganese

25

9.7E+03Fe

Iron

26

1.2E+12CoCobalt

27

8.7E+14NiNickel

28

2.1E+12CuCopper

29

2.2E+11Zn

Zinc

30

8.3E+09GaGallium

31

9.7E+03Ge

Germanium

32

1.1E+03AsArsenic

33

1.5E+04SeSelenium

34

1.6E+08Br

Bromine

35

4.7E+08KrKrypton

36

8.8E+11

RbRubidium

37

9.3E+09Sr

Strontium

38

6.6E+07Y

Yttrium

39

1.8E+06Zr

Zirconium

40

1.6E+07NbNiobium

41

5.3E+12Mo

Molybdenum

42

5.2E+09Ru

Ruthenium

44

3.9E+07RhRhodium

45

1.2E+09Pd

Palladium

46

7.5E+08Ag

Silver

47

1.2E+11CdCadmium

48

2.3E+11InIndium

49

9.9E+07Sn

Tin

50

4.8E+11SbAntimony

51

2.9E+11TeTellurium

52

4.6E+07I

Iodine

53

3.8E+05XeXenon

54

2.8E+11

CsCaesium

55

1.4E+14BaBarium

56

1.5E+11

LaLanthanum

57

1.5E+06CeCerium

58

4.7E+07Pr

Praseodymium

59

5.8E+03Nd

Neodymium

60

9.1E+11SmSamarium

62

1.3E+14EuEuropium

63

4.2E+14Gd

Gadolinium

64

1.0E+11TbTerbium

65

2.1E+08Dy

Dysprosium

66

2.4E+11HoHolmium

67

1.1E+11ErErbium

68

1.9E+12TmThulium

69

5.4E+13YbYtterbium

70

5.7E+10LuLutetium

71

4.7E+10

HfHafnium

72

4.6E+07TaTantalum

73

5.0E+05W

Tungsten

74

4.2E+06ReRhenium

75

1.7E+08OsOsmium

76

3.7E+10Ir

Iridium

77

2.7E+12Pt

Platinum

78

1.7E+11Au

Gold

79

2.9E+05HgMercury

80

9.1E+10Tl

Thallium

81

2.0E+13Pb

Lead

82

5.4E+06Bi

Bismuth

83

8.9E+06

TcTechnetium

43

PmPromethium

61

PoPolonium

84

AtAstatine

85

RnRadon

86

FrFrancium

87

RaRadium

88

AcActinium

89

ThThorium

90

PaProtactinium

91

UUranium

92

NpNeptunium

93

PuPlutonium

94

AmAmericium

95

CmCurium

96

BkBerkelium

97

CfCalifonrium

98

EsEinsteinium

99

FmFermium

100

MdMendelevium

101

NoNobelium

102

LrLawrencium

103

RfRutherfordium

104

DbDubnium

105

SgSeaborgium

106

BhBohrium

107

HsHassium

108

MtMeitnerium

109

DsDarmastadtium

110

RgRoentgenium

111

106

107

108

109

1010

1011

1012

1013

1014

Act

ivity

(B

q/kg

)

DEMO Vacuum Vessel@ 10 years

HHydrogen

1

3.0E+04HeHelium

2

9.2E+08

LiLithium

3

5.2E+12BeBeryllium

4

1.5E+07B

Boron

5

1.3E+08C

Carbon

6

1.4E+04N

Nitrogen

7

3.0E+08O

Oxygen

8

2.3E+04F

Fluorine

9

5.0E+06Ne

Neon

10

993

NaSodium

11

2.2E+06Mg

Magnesium

12

2.0E+04Al

Aluminium

13

1.1E+05SiSilicon

14

2.0E+03P

Phosphorus

15

1.3E+05S

Sulphur

16

1.8E+03Cl

Chlorine

17

3.4E+07ArArgon

18

9.7E+06

KPotassium

19

1.5E+07CaCalcium

20

1.5E+06Sc

Scandium

21

2.0E+04Ti

Titanium

22

146V

Vanadium

23

2.9E+03Cr

Chromium

24

2.2E+04Mn

Manganese

25

1.4E+05Fe

Iron

26

6.7E+08CoCobalt

27

7.1E+11NiNickel

28

1.0E+09CuCopper

29

9.7E+06Zn

Zinc

30

3.9E+06GaGallium

31

1.9E+04Ge

Germanium

32

1.2E+03AsArsenic

33

4.8E+03SeSelenium

34

1.4E+05Br

Bromine

35

5.6E+03KrKrypton

36

6.5E+08

RbRubidium

37

4.4E+06Sr

Strontium

38

1.7E+05Y

Yttrium

39

129Zr

Zirconium

40

1.8E+04NbNiobium

41

2.9E+08Mo

Molybdenum

42

4.3E+06Ru

Ruthenium

44

1.7E+04RhRhodium

45

3.1E+07Pd

Palladium

46

1.0E+05Ag

Silver

47

3.3E+08CdCadmium

48

4.5E+08InIndium

49

8.9E+04Sn

Tin

50

6.1E+08SbAntimony

51

8.5E+05TeTellurium

52

6.6E+04I

Iodine

53

2.0E+03XeXenon

54

1.5E+08

CsCaesium

55

3.0E+11BaBarium

56

1.7E+08

LaLanthanum

57

1.8E+03CeCerium

58

1.1E+05Pr

Praseodymium

59

4.1E+03Nd

Neodymium

60

1.1E+09SmSamarium

62

2.5E+10EuEuropium

63

1.2E+13Gd

Gadolinium

64

3.6E+06TbTerbium

65

1.3E+07Dy

Dysprosium

66

3.6E+08HoHolmium

67

1.9E+09ErErbium

68

2.1E+09TmThulium

69

1.9E+08YbYtterbium

70

2.3E+04LuLutetium

71

8.1E+07

HfHafnium

72

1.5E+05TaTantalum

73

2.5E+04W

Tungsten

74

1.5E+04ReRhenium

75

1.5E+06OsOsmium

76

2.6E+04Ir

Iridium

77

9.5E+06Pt

Platinum

78

1.8E+08Au

Gold

79

164HgMercury

80

6.2E+04Tl

Thallium

81

1.8E+10Pb

Lead

82

1.6E+03Bi

Bismuth

83

1.2E+04

TcTechnetium

43

PmPromethium

61

PoPolonium

84

AtAstatine

85

RnRadon

86

FrFrancium

87

RaRadium

88

AcActinium

89

ThThorium

90

PaProtactinium

91

UUranium

92

NpNeptunium

93

PuPlutonium

94

AmAmericium

95

CmCurium

96

BkBerkelium

97

CfCalifonrium

98

EsEinsteinium

99

FmFermium

100

MdMendelevium

101

NoNobelium

102

LrLawrencium

103

RfRutherfordium

104

DbDubnium

105

SgSeaborgium

106

BhBohrium

107

HsHassium

108

MtMeitnerium

109

DsDarmastadtium

110

RgRoentgenium

111

106

107

108

109

1010

1011

1012

1013

1014

Act

ivity

(B

q/kg

)

HFR@ 10 years

HHydrogen

1

4.5E+09HeHelium

2

2.1E+11

LiLithium

3

6.6E+15BeBeryllium

4

1.6E+13B

Boron

5

1.3E+11C

Carbon

6

9.3E+07N

Nitrogen

7

3.0E+12O

Oxygen

8

1.7E+08F

Fluorine

9

2.7E+09Ne

Neon

10

6.1E+07

NaSodium

11

1.2E+08Mg

Magnesium

12

1.1E+07Al

Aluminium

13

6.8E+07SiSilicon

14

2.3E+06P

Phosphorus

15

4.4E+08S

Sulphur

16

1.3E+08Cl

Chlorine

17

2.9E+11ArArgon

18

1.8E+09

KPotassium

19

1.5E+11CaCalcium

20

1.1E+10Sc

Scandium

21

2.4E+07Ti

Titanium

22

9.4E+05V

Vanadium

23

4.5E+06Cr

Chromium

24

5.7E+06Mn

Manganese

25

6.8E+08Fe

Iron

26

5.9E+12CoCobalt

27

3.1E+15NiNickel

28

9.0E+12CuCopper

29

2.1E+11Zn

Zinc

30

1.5E+10GaGallium

31

1.7E+07Ge

Germanium

32

1.8E+06AsArsenic

33

1.0E+07SeSelenium

34

5.8E+08Br

Bromine

35

5.3E+09KrKrypton

36

2.4E+12

RbRubidium

37

1.0E+10Sr

Strontium

38

4.3E+08Y

Yttrium

39

8.4E+06Zr

Zirconium

40

6.6E+07NbNiobium

41

5.7E+12Mo

Molybdenum

42

1.0E+10Ru

Ruthenium

44

7.1E+07RhRhodium

45

4.7E+09Pd

Palladium

46

2.3E+09Ag

Silver

47

3.4E+11CdCadmium

48

1.6E+11InIndium

49

2.7E+07Sn

Tin

50

8.9E+11SbAntimony

51

1.9E+12TeTellurium

52

2.2E+08I

Iodine

53

5.2E+06XeXenon

54

1.5E+12

CsCaesium

55

2.5E+14BaBarium

56

3.7E+11

LaLanthanum

57

1.8E+07CeCerium

58

7.3E+07Pr

Praseodymium

59

3.1E+07Nd

Neodymium

60

2.5E+12SmSamarium

62

7.1E+13EuEuropium

63

4.6E+13Gd

Gadolinium

64

2.7E+09TbTerbium

65

6.8E+09Dy

Dysprosium

66

3.6E+11HoHolmium

67

3.0E+11ErErbium

68

5.1E+12TmThulium

69

7.4E+13YbYtterbium

70

3.9E+10LuLutetium

71

3.6E+10

HfHafnium

72

1.2E+08TaTantalum

73

2.7E+07W

Tungsten

74

6.5E+07ReRhenium

75

9.1E+08OsOsmium

76

3.8E+11Ir

Iridium

77

4.8E+12Pt

Platinum

78

4.9E+11Au

Gold

79

7.0E+08HgMercury

80

1.1E+12Tl

Thallium

81

7.1E+13Pb

Lead

82

4.5E+07Bi

Bismuth

83

2.4E+08

TcTechnetium

43

PmPromethium

61

PoPolonium

84

AtAstatine

85

RnRadon

86

FrFrancium

87

RaRadium

88

AcActinium

89

ThThorium

90

PaProtactinium

91

UUranium

92

NpNeptunium

93

PuPlutonium

94

AmAmericium

95

CmCurium

96

BkBerkelium

97

CfCalifonrium

98

EsEinsteinium

99

FmFermium

100

MdMendelevium

101

NoNobelium

102

LrLawrencium

103

RfRutherfordium

104

DbDubnium

105

SgSeaborgium

106

BhBohrium

107

HsHassium

108

MtMeitnerium

109

DsDarmastadtium

110

RgRoentgenium

111

106

107

108

109

1010

1011

1012

1013

1014

Act

ivity

(B

q/kg

)


Activation summary – animated• total becquerel/kg activity from each element as a function

of time following 2-year irradiation

DEMO First Wall@ 3.2E-08 years

HHydrogen

1

1.9E+07HeHelium

2

8.2E+10

LiLithium

3

6.5E+14BeBeryllium

4

1.2E+14B

Boron

5

8.3E+13C

Carbon

6

5.0E+10N

Nitrogen

7

3.1E+13O

Oxygen

8

1.1E+14F

Fluorine

9

2.8E+14Ne

Neon

10

1.8E+14

NaSodium

11

3.5E+14Mg

Magnesium

12

3.2E+14Al

Aluminium

13

3.7E+14SiSilicon

14

4.3E+14P

Phosphorus

15

4.2E+14S

Sulphur

16

4.9E+14Cl

Chlorine

17

4.6E+14ArArgon

18

5.2E+13

KPotassium

19

2.0E+13CaCalcium

20

2.3E+14Sc

Scandium

21

9.0E+14Ti

Titanium

22

1.2E+14V

Vanadium

23

2.0E+14Cr

Chromium

24

2.9E+14Mn

Manganese

25

1.4E+15Fe

Iron

26

2.3E+14CoCobalt

27

4.8E+15NiNickel

28

7.5E+14CuCopper

29

6.2E+14Zn

Zinc

30

3.4E+14GaGallium

31

1.2E+15Ge

Germanium

32

3.8E+14AsArsenic

33

1.9E+15SeSelenium

34

5.8E+14Br

Bromine

35

3.4E+15KrKrypton

36

3.8E+14

RbRubidium

37

1.1E+15Sr

Strontium

38

2.0E+14Y

Yttrium

39

9.0E+14Zr

Zirconium

40

4.9E+14NbNiobium

41

5.3E+14Mo

Molybdenum

42

3.2E+14Ru

Ruthenium

44

6.9E+14RhRhodium

45

3.2E+15Pd

Palladium

46

1.1E+15Ag

Silver

47

3.6E+15CdCadmium

48

4.7E+14InIndium

49

7.2E+15Sn

Tin

50

2.8E+14SbAntimony

51

1.7E+15TeTellurium

52

7.3E+14I

Iodine

53

1.7E+15XeXenon

54

4.4E+14

CsCaesium

55

1.1E+15BaBarium

56

2.9E+14

LaLanthanum

57

5.2E+13CeCerium

58

6.9E+14Pr

Praseodymium

59

7.2E+14Nd

Neodymium

60

4.1E+14SmSamarium

62

1.8E+15EuEuropium

63

3.6E+15Gd

Gadolinium

64

3.9E+14TbTerbium

65

2.8E+15Dy

Dysprosium

66

3.2E+14HoHolmium

67

3.6E+15ErErbium

68

8.1E+14TmThulium

69

2.2E+15YbYtterbium

70

2.1E+14LuLutetium

71

2.4E+15

HfHafnium

72

7.4E+14TaTantalum

73

2.0E+15W

Tungsten

74

7.9E+14ReRhenium

75

3.1E+15OsOsmium

76

1.0E+15Ir

Iridium

77

4.1E+15Pt

Platinum

78

3.7E+14Au

Gold

79

2.7E+15HgMercury

80

2.0E+14Tl

Thallium

81

3.2E+14Pb

Lead

82

6.7E+13Bi

Bismuth

83

7.9E+12

TcTechnetium

43

PmPromethium

61

PoPolonium

84

AtAstatine

85

RnRadon

86

FrFrancium

87

RaRadium

88

AcActinium

89

ThThorium

90

PaProtactinium

91

UUranium

92

NpNeptunium

93

PuPlutonium

94

AmAmericium

95

CmCurium

96

BkBerkelium

97

CfCalifonrium

98

EsEinsteinium

99

FmFermium

100

MdMendelevium

101

NoNobelium

102

LrLawrencium

103

RfRutherfordium

104

DbDubnium

105

SgSeaborgium

106

BhBohrium

107

HsHassium

108

MtMeitnerium

109

DsDarmastadtium

110

RgRoentgenium

111

106

107

108

109

1010

1011

1012

1013

1014

Act

ivity

(B

q/kg

)


Activation summary – animated• total becquerel/kg activity from each element as a function

of time following 2-year irradiation


Transmutation – fusion vs. fission

§due to higher neutron capture rates

• % burn-up per full-power year (fpy) for selected elements:

10-3

10-2

10-1

100

101

102

Li Be C Na Al Si Ti V Cr Mn Fe Co Ni Cu Zr Nb Mo Ta W Re Os Pb Bi

3 4 6 11 13 14 22 23 24 25 26 27 28 29 40 41 42 73 74 75 76 82 83

1 %

DEMO FBR HFR PWR

% b

urn-

up/fp

y

Element

proton number

• Fission spectra are more-moderated (“softer”) than fusion & combined with high-fluxin HFR produces greater burn-up rates in many elements§ ⇒ spectrum modification(via shielding) required to match fusion in experimental campaigns


Gas production – fusion vs. fission• Gas appm after 1 fpy in DEMO first wall and PWR:

100101102103104105 10 20 30 40 50 60 70 80

100 appm

1000 appm

FeWCuBeMo

DEMOPWR

He appm

He

appm

in 1

fpy

proton number

100

101

102

103

Hyd

roge

nH

eliu

mLi

thiu

mB

eryl

lium

Bor

onC

arbo

nN

itrog

enO

xyge

nF

luor

ine

Neo

nS

odiu

mM

agne

sium

Alu

min

ium

Sili

con

Pho

spho

rus

Sul

phur

Chl

orin

eA

rgon

Pot

assi

umC

alci

umS

cand

ium

Tita

nium

Van

adiu

mC

hrom

ium

Man

gane

seIr

onC

obal

tN

icke

lC

oppe

rZ

inc

Gal

lium

Ger

man

ium

Ars

enic

Sel

eniu

mB

rom

ine

Kry

pton

Rub

idiu

mS

tron

tium

Yttr

ium

Zirc

oniu

mN

iobi

umM

olyb

denu

m

Rut

heni

umR

hodi

umP

alla

dium

Silv

erC

adm

ium

Indi

um Tin

Ant

imon

yT

ellu

rium

Iodi

neX

enon

Cae

sium

Bar

ium

Lant

hanu

mC

eriu

mP

rase

odym

ium

Neo

dym

ium

Sam

ariu

mE

urop

ium

Gad

olin

ium

Ter

bium

Dys

pros

ium

Hol

miu

mE

rbiu

mT

huliu

mY

tterb

ium

Lute

tium

Haf

nium

Tan

talu

mT

ungs

ten

Rhe

nium

Osm

ium

Irid

ium

Pla

tinum

Gol

dM

ercu

ryT

halli

umLe

adB

ism

uth

100 appm

1000 appmH appm

H a

ppm

in 1

fpy

• gas production is significantly higher under fusion neutronsI with very few exceptions


Applications





Application: PKA distributions

PKA – primary knock-on atom

• Motivation: a full description of the initial damage events(the primary knock-on atoms or PKAs) under irradiation is anecessary input to modelling and simulation of radiation damage

I PKA energy.vs.flux distributions provide more information thansimpler damage-dose measures (e.g. dpa)

• Complete evaluation requiresall possible nuclear reactionchannels to be considered:

I elastic & inelastic scattering,and non-elastic reactions((n, p), (n, 2n), etc.)

I including secondary emitted(light) gas particles - α(4He), protons (1H), etc, asPKAs

(A.E. Sand, Helsinki – 2012 )

150 keV PKA in a perfectbcc W crystal - after

40 ps a large, coherentloop structure has formed


PKA – primary knock-on atom

Additional need• emitted particle spectra for α, protons, neutrons, γ, etc.

• could be used in FISPACT-II to compute transmutation fromsecondary particles


PKA distributions

§the nuclear data processing system developed atLANL

Calculation method (1)

• From raw pointwise nuclear data (TENDL)

• Neutron interaction recoil matrices Mx→y ≡ {mx→yij } calculated

using NJOY§ (via GROUPR)I mx→y

ij is the recoil cross section (in barns) for a recoil energy Ei ofdaughter y resulting from an incident neutron energy Ej on parent x

• for each target (parent) isotope x there will be a set of Mx→y

I (at least) one for each reaction channel

• & each reaction may have more than one associated matrixI for example, (n,α) will produce a heavy recoil and an α-particle

(4He nucleus)

• recoil matrices can also be produced for charged particleinteractions


Mx→y matrices & vectors

100

101

102

103

104

105

106

107

100

101

102

103

104

105

106

107

10-410-310-210-1100

σ (b

arns

)

Incide

nt Neu

tron e

nerg

y (eV

)

Recoil energy (eV)

σ (b

arns

)

5.0

10.0

15.0

20.0

25.0

30.0

104

105

106

107

10-510-410-310-210-1

σ (b

arns

)

Incide

nt Neu

tron e

nerg

y (MeV

)

Recoil energy (eV)

σ (b

arns

)

56Fe(n, n)56Fe27Al(n, α)24Na

• Non-elastic nuclear reactions canproduce two recoiling species

• The main (heavy) residual and ahigher energy light (gas) particle

• On 27Al the threshold (n, α)reaction produces 24Na (grey)recoils and 4He particles (blue)

• The primary reaction channel isnormally simple elastic scattering

• Produces recoils for all incidentneutron energies

• Other channels only becomeimportant at higher energy...

elastic

scattering


Mx→y matrices & vectors – 56Fe

10-6

10-5

10-4

10-3

10-2

10-1

100

100 101 102 103 104 105 106 107

1.02 MeV

cros

s se

ctio

n (b

arns

)

Recoil energy (eV)

10-6

10-5

10-4

10-3

10-2

10-1

100

100 101 102 103 104 105 106 107

102 keV

cros

s se

ctio

n (b

arns

)

Recoil energy (eV)

10-6

10-5

10-4

10-3

10-2

10-1

100

100 101 102 103 104 105 106 107

14.1 MeV

cros

s se

ctio

n (b

arns

)

Recoil energy (eV)

reaction channels

(n,α)53Cr

(n,n)56Fe

(n,2n)55Fe

(n,p)56Mn

(n,nα)52Cr(n,n’1)56Fe

(n,n’c)56Fe

(n,α)4He

(n,nα)4He

(n,p)1H

10-6

10-5

10-4

10-3

10-2

10-1

100

100 101 102 103 104 105 106 107

10.1 MeV

cros

s se

ctio

n (b

arns

)

Recoil energy (eV)

100

101

102

103

104

105

106

107

100101

102103

104105

106107

10-410-310-210-1100

σ (b

arns

)

Incide

nt Neu

tron e

nergy

(eV)

Recoil energy (eV)

σ (b

arns

)

56Fe(n, n)56Fe

• In 56Fe, at low incident energyonly elastic and inelasticchannels are open

• Number of contributingchannels increases at higherenergies (MeV range)


Calculation method (2)

§Gilbert et al., JNM 467 (2015) 121-134

• Collapsing each recoil matrix with a neutron irradiationspectrum {φj} gives the recoil-energy spectrum Rx→y (E ):

≡ Rx→y (E ) ≡ {r x→yi } =

∑j

mx→yij φj

• processing (& summing) done with SPECTRA-PKA§ utility

“PKA-spectrum”under

neutron irradiation

106

108

1010

1012

100 102 104 106

pα

NaMgAl

PK

As

s-1 c

m-3

PKA energy (eV)

106

108

1010

1012

100 102 104 106

PK

As

s-1 c

m-3

PKA energy (eV)He4H1

Al26Na23

Mg26Mg25

Na24Al27

Mg27Al28

Aluminium

Elemental

Aluminium

Isotopic

• PKA spectra of pure Al under DEMO conditions

• many different recoil species (even with just Al27 target)


PKA results – e.g. Fe

∗5.845% 54Fe, 91.754% 56Fe, 2.119% 57Fe,0.282% 58Fe (atomic percentages)

• Isotopic results for each nuclide in the material must be merged:

106

108

1010

1012

100 102 104 106

PK

As

s-1 c

m-3


Fe55Cr52

Mn55Cr53

Fe56Mn56

Fe57

56Fe

106

108

1010

1012

100 102 104 106

PK

As

s-1 c

m-3


Fe53Cr50

Mn53Cr51

Fe54Mn54

Cr53Fe55

54Fe

106

108

1010

1012

100 102 104 106

PK

As

s-1 c

m-3


Fe56Cr53

Mn56Mn55

Cr54Fe57

Mn57Fe58

57Fe

106

108

1010

1012

100 102 104 106

PK

As

s-1 c

m-3


Fe57Cr54

Mn57Cr55

Fe58Mn58

Fe59

58Fe

106

108

1010

1012

100 102 104 106

PK

As

s-1 c

m-3

PKA energy (eV)

He4H1

Fe53Cr50

Mn53Cr51Cr52Fe54Mn54Cr53Fe55

Mn55Cr54Fe56Mn56Cr55Fe57Mn57Fe58Mn58Fe59

Fe∗


PKA results – e.g. Fe• For modelling it is more useful to sum the isotopic spectra:

106

108

1010

1012

100 102 104 106

PK

As

s-1 c

m-3


Fe53Cr50

Mn53

Cr51Cr52Fe54Mn54Cr53

Fe55Mn55Cr54Fe56Mn56

Cr55Fe57Mn57Fe58Mn58

Fe59

Isotopic

106

108

1010

1012

100 102 104 106

pα

CrMnFe

PK

As

s-1 c

m-3

PKA energy (eV)

elemental

• Main constituent usually dominates

• Total PKAs (s−1cm−3) in material can be calculated by summing (& integratingover) all elemental distributions

• here there are 4.33E+14 PKAs s−1cm−3 above 1eV (light particles excluded)

• the average PKA energy above 10 eV for the Fe+Mn+Cr spectrum is 18.8 keV


PKA distributions – elemental

• Under DEMO FW conditions

106

108

1010

1012

100 102 104 106

pα

NaMgAl

PK

As

s-1 c

m-3

PKA energy (eV)

106

108

1010

1012

100 102 104 106

pα

ZrNbMo

PK

As

s-1 c

m-3

PKA energy (eV)

106

108

1010

1012

100 102 104 106

pαYZr

Nb

PK

As

s-1 c

m-3

PKA energy (eV)

106

108

1010

1012

1014

100 102 104 106

pα

HfTaW

PK

As

s-1 c

m-3

PKA energy (eV)

Aluminium Niobium

Molybdenum Tungsten


Total PKA rates – fusion vs. fission• total heavy PKAs (H/He excluded) for selected materials

1013

1014

1015

Na Al Si Ti V Cr Mn Fe Co Ni Cu Zr Nb Mo Ta W Re Os Pb Bi

11 13 14 22 23 24 25 26 27 28 29 40 41 42 73 74 75 76 82 83

DEMO-FW FBR HFR PWR

PK

As

s-1 c

m-3

Element

proton number

• FBR spectrum produces highest rates due to high, fast flux

• PWR the lowest


• FPR missing low and high energy parts due topeaked spectrum

Cumulative (PKA) probability distributions

0.0

0.2

0.4

0.6

0.8

1.0

100 102 104 106

Iron

cum

ul. P

KA

dis

t.

PKA energy (eV)

DEMO

PWR

HFR

FBR

0.0

0.2

0.4

0.6

0.8

1.0

100 102 104 106

Vanadium

cum

ul. P

KA

dis

t.

PKA energy (eV)

DEMO

PWR

HFR

FBR

0.0

0.2

0.4

0.6

0.8

1.0

100 102 104 106

Niobium

cum

ul. P

KA

dis

t.

PKA energy (eV)

DEMO

PWR

HFR

FBR

0.0

0.2

0.4

0.6

0.8

1.0

100 102 104 106

Rhenium

cum

ul. P

KA

dis

t.

PKA energy (eV)

DEMO

PWR

HFR

FBR

pile-up of (n,γ)


(mis)interpretation?

• Typical results from SPECTRA-PKA

• total PKAs in pure elements exposed to DEMO first wallneutrons

107

108

109

1010

1011

1012

1013

101 102 103 104 105 106 107

PKA

s s-1

cm

-3

PKA energy (eV)

FeWCuZrMoBe

• Perhaps gives the impression that there are a relativelyconstant (flat) PKA fluxes at the majority of PKA-energiesin most materials


Scope for misinterpretation• But: these PKA flux spectra are mapped onto the same

energy grid as that used for the neutron transportcalculations (and hence nuclear data libraries)

109

1010

1011

1012

1013

1014

1015

101 102 103 104 105 106 107

n cm

-2 s

-1

neutron energy (eV)

DEMO first wall spectrum 0

100

200

300

400

500

600

700

800

900

1000

10-4 10-2 100 102 104 106 108

grou

p nu

mbe

renergy (eV)

high resolution modern neutronicslow resolution (old) fusion neutronics

• Such grids are designed to give equal representation to low(thermal∼eV) and high (fast∼>MeV) neutron energies

• ⇒ not appropriate for representation of a structuraldamage metric like PKA spectra

equal number of −→groups perdecade


Alternative• For this reason part of the recent developments in

SPECTRA-PKA have included the ability to (user-)definean output energy grid more relevant to damage modelling

0

100

200

300

400

500

600

700

800

900

1000

10-10 10-8 10-6 10-4 10-2 100 102

grou

p nu

mbe

r

log-energy (MeV)

high resolution modern neutronicslow resolution fusion neutronics10 keV linear steps

0

500

1000

1500

2000

0 5 10 15 20gr

oup

num

ber

linear-energy (MeV)

high resolution modern neutronicslow resolution fusion neutronics10 keV linear steps

• E.g. an energy grid with equal bins (groups) of 10 keV inwidth

I this is linear on a linear energy axis(and exponential on a logarithmic one)


Implications for interpretation• Returning to the first wall DEMO example:

I and using a very fine linear grid spacing of 10 eV

108

109

1010

1011

1012

1013

101 102 103 104 105 106

PKA

s s-1

cm

-3

PKA energy (eV)

FeWCuZrMoBe

0

2x108

4x108

6x108

8x108

1x109

1.2x109

1.4x109

0.0 0.5 1.0 1.5PK

As

s-1 c

m-3

PKA energy (MeV)

FeWCuZrMoBe

log-log lin-lin

• on a log-log scale the profiles have a power-law appearanceI the profiles are similar regardless of target mass

• & in linear energy versus PKA-flux there is anexponential decay


Cross-check• No fundamental change in results – just re-binning

• Only the visualization is different

• To check use the standard (neutronics) approach ofdividing by lethargy to smooth variations in grid

108

109

1010

1011

1012

1013

1014

1015

101 102 103 104 105 106

PKA

s s-1

cm

-3 p

er le

thar

gy

PKA energy (eV)

FeWCuZrMoBe

108

109

1010

1011

1012

1013

1014

1015

101 102 103 104 105 106

PKA

s s-1

cm

-3 p

er le

thar

gy

PKA energy (eV)

FeWCuZrMoBe

10 eV grid neutronics grid

• lethargy is natural log of ratio of upper to lower bin energy


§Lindhard, Scharff, Schiøtt, Mat. Fys. Medd.Dan. Vid. Selsk. 33 (1963) 1–42

Damage energy & dpa from SPECTRA-PKA• The displacement energy in the NRT-dpa formula is normally

calculated using the total damage kerma cross section

• However, with SPECTRA-PKA, it is possible to calculate the damagecontribution as a function of reaction channel

– a new & novel capability

• Standard LSS§ formula to account for electronic loss and convert PKAenergy into damage energy – including correct treatment of parent anddaughter mass

• displacement-energy rate accumulated and summed using PKA rate ateach damage energy. NRT formula can be applied to the total

• For a given reaction channel, the total displacement energy is:∑i

T LSS(Epkai )Rpka

i ,

where T LSS(E pka) is the LSS equivalent energy for PKA energy E pka, and Rpkai is

number of PKAs at energy E pkai


dpa evaluations with SPECTRA-PKA

§Lindhard, Scharff, Schiøtt, Mat. Fys. Medd.Dan. Vid. Selsk. 33 (1963) 1–42

The per-reaction-channel approachof SPECTRA-PKA

can also be appliedto displacementsper atom (dpa)evaluations toproduce new

insight

0

1

2

3

4

5

6

7

8

9

10

tota

l

Fe

56

(n,a

)

Fe

56

(n,2

n)

Fe

56

(n,p

)

Fe

56

ela

stic

Fe

56

ine

lastic

Fe

54

sca

tte

r

oth

er

NR

T d

pa/y

ear

±0.6%

±190.0%

±14.0%

±6.0%

±0.6%

±3.8%

±0.8%2.2%

12.9%

4.3%

40.9%

28.1%

4.5% 7.0%

0

1

2

3

4

5

NR

T D

PA

/ye

ar

total scatter (n,2n) other

54.1%

44.7%

1.2%

0

0.5

1

1.5

2

2.5

3

3.5

4

tota

l

Fe

56

(n,a

)

Fe

56

(n,2

n)

Fe

56

(n,p

)

Fe

56

ela

stic

Fe

56

ine

lastic

Fe

54

sca

tte

r

oth

er

NR

T D

PA

/year

63.6%

26.5%

6.7%2.9%

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

NR

T D

PA

/year

total scatter (n,2n) other

0.7% 0.6%

J. Nucl. Mater. 504 (2018) 101-108

iron in fusion iron in fission

tungsten in fusion tungsten

in fission


Running SPECTRA-PKA

• SPECTRA-PKA is now open-source and downloadable from:https://github.com/fispact/SPECTRA-PKA

• code is command-line driven

• execution controlled by an input file of code words and values(similar to FISPACT-II, but order does not matter)

<location of SPECTRA-PKA>SPECTRA-PKA input.in

• manual on github repository explains use of all code-words & thereis an example provided. . .

I including example plotting script to visualize results (with gnuplot)

• . . . this is a good place to startI & example input can be easily modified to a specific

material/spectrum of interestI if not already compiled on your system, the executable for

SPECTRA-PKA can be easily created

navigate to fispact/source/spectra-pka and type make

Gilbert and Sublet, JNM 504 (2018) 101-108

https://github.com/fispact/SPECTRA-PKA


Further input to damage modelling

• Stochastic sampling of PKAdistributions to defineseparation in time and spaceof PKA events in a givenvolume

I prototyping for futureSPECTRA-PKA development

• Example:I lattice of Fe-25%Cr-25%W

(randomly distributed)I fusion first-wall neutron fluxI PKAs introduced in 1

second timesteps in asquare box of size ∼140nm3 (equivalent to 250Matoms)

0 40

80 120 0

40 80

120 0

20

40

60

80

100

120

140

1000.0 seconds

(nm)

1 MeV

100 keV

10 keV

1 keV

100 eV

0 40

80 120 0

40 80

120 0

20

40

60

80

100

120

140

1000.0 seconds

(nm)

FeWCr


Statistics

• Fe+Cr majority of higher energyPKAs, W predominant at energiesbelow displacement thresholds

• Future: compare to cascade sizesto understand overlap thresholds,etc.

I integrated modelling

0 40

80 120 0

40 80

120 0

20

40

60

80

100

120

140

1000.0 seconds

(nm)

1 MeV

100 keV

10 keV

1 keV

100 eV

0 40

80 120 0

40 80

120 0

20

40

60

80

100

120

140

1000.0 seconds

(nm)

FeWCr

1

10

100

0 200 400 600 800 1000 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

dist

ance

(nm

)

x10-3

NR

T-d

pa

time (seconds)

1000.0 seconds

average distance between PKAs>0eVPKAs>100eV

PKAs>1keVPKAs>100keVPKAs>0.5MeV

milli-dpa

0

50

100

150

200

250

300

<1eV <10eV <100eV <1keV <10keV<100keV <1MeV

num

ber

PK

As

PKA energy bin

1000.0 seconds

WFeCr


Prototype integration

• e.g. using a binarycollisionapproximation (BCA)code to define thePKA trajectories andrecoils

I same FeCrWsystem

I each PKA givenrandom initialdirection

0 40

80 120 0

40 80

120 0

20

40

60

80

100

120

140

(nm)

200.0 secondspka path

recoilssecondary recoils

fispact-ii applications: materials modelling, scoping and

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