FISPACT-II applications: materials modelling, scoping and ...
Transcript of 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)
FISPACT-II workshop October 2019 M. Gilbert2/41
Applications
• Integrated assessment of helium embrittlement
• Material response database
• Primary damage spectra (& emitted particle spectra)
FISPACT-II workshop October 2019 M. Gilbert3/41
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
FISPACT-II workshop October 2019 M. Gilbert3/41
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
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
He productionrates in materials
Gilbert, Dudarev, Nguyen-Manh, Zheng, Packer, SubletJ. Nucl. Mater. 442 (2013) S755Gilbert, Dudarev, Zheng, Packer, SubletNucl. Fus. 52 (2012) 083019
FISPACT-II workshop October 2019 M. Gilbert3/41
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
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
He productionrates in materials
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
Gilbert, Dudarev, Nguyen-Manh, Zheng, Packer, SubletJ. Nucl. Mater. 442 (2013) S755Gilbert, Dudarev, Zheng, Packer, SubletNucl. Fus. 52 (2012) 083019
FISPACT-II workshop October 2019 M. Gilbert3/41
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
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
He productionrates in materials
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
Gilbert, Dudarev, Nguyen-Manh, Zheng, Packer, SubletJ. Nucl. Mater. 442 (2013) S755Gilbert, Dudarev, Zheng, Packer, SubletNucl. Fus. 52 (2012) 083019
FISPACT-II workshop October 2019 M. Gilbert4/41
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
FISPACT-II workshop October 2019 M. Gilbert4/41
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
FISPACT-II workshop October 2019 M. Gilbert5/41
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
FISPACT-II workshop October 2019 M. Gilbert5/41
Modelling: He embrittlement of GBs
Simple modelling of grain boundary (GB) failure
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
FISPACT-II workshop October 2019 M. Gilbert5/41
Modelling: He embrittlement of GBs
Simple modelling of grain boundary (GB) failure
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
FISPACT-II workshop October 2019 M. Gilbert5/41
Modelling: He embrittlement of GBs
Simple modelling of grain boundary (GB) failure
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
FISPACT-II workshop October 2019 M. Gilbert5/41
Modelling: He embrittlement of GBs
Simple modelling of grain boundary (GB) failure
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
FISPACT-II workshop October 2019 M. Gilbert6/41
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
FISPACT-II workshop October 2019 M. Gilbert7/41
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
FISPACT-II workshop October 2019 M. Gilbert8/41
Applications
• Integrated assessment of helium embrittlement
• Material response database
• Primary damage spectra (& emitted particle spectra)
FISPACT-II workshop October 2019 M. Gilbert9/41
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
FISPACT-II workshop October 2019 M. Gilbert10/41
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
FISPACT-II workshop October 2019 M. Gilbert11/41
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
FISPACT-II workshop October 2019 M. Gilbert12/41
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
FISPACT-II workshop October 2019 M. Gilbert13/41
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
FISPACT-II workshop October 2019 M. Gilbert14/41
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
)
FISPACT-II workshop October 2019 M. Gilbert15/41
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
)
FISPACT-II workshop October 2019 M. Gilbert16/41
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
)
FISPACT-II workshop October 2019 M. Gilbert16/41
Activation summary – animated• total becquerel/kg activity from each element as a function
of time following 2-year irradiation
FISPACT-II workshop October 2019 M. Gilbert17/41
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
FISPACT-II workshop October 2019 M. Gilbert18/41
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
FISPACT-II workshop October 2019 M. Gilbert19/41
Applications
• Integrated assessment of helium embrittlement
• Material response database
• Primary damage spectra (& emitted particle spectra)
FISPACT-II workshop October 2019 M. Gilbert20/41
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
FISPACT-II workshop October 2019 M. Gilbert21/41
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
FISPACT-II workshop October 2019 M. Gilbert22/41
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
FISPACT-II workshop October 2019 M. Gilbert23/41
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
FISPACT-II workshop October 2019 M. Gilbert24/41
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)
FISPACT-II workshop October 2019 M. Gilbert25/41
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)
FISPACT-II workshop October 2019 M. Gilbert26/41
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
PKA energy (eV)He4H1
Fe55Cr52
Mn55Cr53
Fe56Mn56
Fe57
56Fe
106
108
1010
1012
100 102 104 106
PK
As
s-1 c
m-3
PKA energy (eV)He4H1
Fe53Cr50
Mn53Cr51
Fe54Mn54
Cr53Fe55
54Fe
106
108
1010
1012
100 102 104 106
PK
As
s-1 c
m-3
PKA energy (eV)He4H1
Fe56Cr53
Mn56Mn55
Cr54Fe57
Mn57Fe58
57Fe
106
108
1010
1012
100 102 104 106
PK
As
s-1 c
m-3
PKA energy (eV)He4H1
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∗
FISPACT-II workshop October 2019 M. Gilbert27/41
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
PKA energy (eV)He4H1
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
FISPACT-II workshop October 2019 M. Gilbert28/41
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
FISPACT-II workshop October 2019 M. Gilbert29/41
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
FISPACT-II workshop October 2019 M. Gilbert30/41
• 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)
FISPACT-II workshop October 2019 M. Gilbert31/41
(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
FISPACT-II workshop October 2019 M. Gilbert32/41
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
FISPACT-II workshop October 2019 M. Gilbert33/41
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)
FISPACT-II workshop October 2019 M. Gilbert34/41
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
FISPACT-II workshop October 2019 M. Gilbert35/41
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
FISPACT-II workshop October 2019 M. Gilbert36/41
§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
FISPACT-II workshop October 2019 M. Gilbert37/41
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
FISPACT-II workshop October 2019 M. Gilbert38/41
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
FISPACT-II workshop October 2019 M. Gilbert39/41
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
FISPACT-II workshop October 2019 M. Gilbert40/41
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
FISPACT-II workshop October 2019 M. Gilbert41/41
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