Helium Accumulation and Retention in He-irradiated and Annealed Tungsten

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Helium Accumulation and Retention in
He-irradiated and Annealed Tungsten
S.I. Golubov, S.J. Zinkle and R.E.
Stoller Metals and Ceramics Division, Oak Ridge
National Laboratory,
High Average Power Laser Workshop University of
Rochester, Rochester, New York November 8-9, 2005
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1.3 MeV He implanted annealed tungsten
Critical incremental He fluence for nearly
complete annealing is 1016/m2
Tirr850 C Ramp anneal to 2000 C
Fusion Science and Technology 47 (2005) 881
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Flash annealing regime used in the calculations
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Model Description

• It is assumed that the problem may be simulated
  by considering a foil with thickness of about
  0.7µm uniformly irradiated with He ions
• Sink in the form of foil boundaries is treated by
  using continuum approach
• Point defect generation and He generation rates
  in the foil are equal to Gpd 2.510-7 dpa/s and
  GHe 2.510-9 1/s, respectively
• Total flux of He ions of 1019 ions/m2
  corresponds to accumulation of about 250 appm He
• Duration of 1 step of irradiation is 102s in the
  case of 103 cycles, 103s in the case of 102
  cycles and so on total time of irradiations is
  equal to 105 s
• Duration of one step of flash annealing is equal
  10 s (5 s heating, 5 s cooling)
• He atoms diffuse interstitially and are captured
  by vacancies, He-vacancy clusters and foil
  boundaries

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Sink strength of foil boundaries
where
is sink strength of foil interior defects
is a good approximation in the case
At l0.7 µm
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Mechanisms providing He-vacancy cluster evolution
under irradiation or annealing

• Absorption of newly created, injected or
  re-dissolved He atoms
• Absorption of point defects
• Thermal evaporation of He atoms and vacancies
• Radiation He resolution
• Coalescence of the clusters

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Transitions of x, m cluster via point defect
reaction kinetics
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Two dimensional Master Equation
(x- number of vacancies and m- number of He atoms
in a cluster)
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Scheme of new Grouping Method(S.I. Golubov et
al.)
mean x,m fluxes
10 fluxes for each group are required only
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Parameters used in the W-He calculations

• He-vacancy dissociation energies, Edis,
• for mHe1V clusters

mHe Edis (eV)
1 4.5
2 3.75
3 3.46
4 3.11
5 2.89
Parameters used in the calculation Evf 4.13
eV, Evm 1.95 eV, EHem Evm 0.24 eV
, O1.58510-29 m-3 , ?2.8 J/m2, Dislocation
capture efficiencies Zv1.00, Zi 1.25
He2Vm
HeVm
Edis are taken to be equal to 4.5 eV at xgt1
Calculated dissociation energies Vs size of He-V
clusters (Van Veen)
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Evolution of calculated 1-D cluster size
distribution function, f(x), during 1 step
irradiation of He
0.25 appm 1x1016/m2 He
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Evolution of 2-D cluster size distribution
function, f(x), during 1 step irradiation of W at
850oC
Red curve on right bottom plot corresponds to the
equilibrium He bubbles
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He accumulation during the implantation of W at
850oC, I
1 step equals 1016 He/m2
Dose dependence of He accumulation in the
He-vacancy clusters
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He accumulation during the implantation at 850oC,
II
1 cycle equals 1016 He/m2
Dose dependence of He accumulation and sink
strength of the He-vacancy clusters at different
foil thickness
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He release during the flash annealing
Calculations have been done by using stepwise
approach, namely five steps of 2 second each at
temperatures 1080oC 1540oC, 1885oC, 1540oC and
1080oC. Calculations show that He release from
bubbles during annealing at 1080oC and 1540oC is
negligible small. Main effect occurs during 2
seconds annealing at 1885oC thus for evaluating
irradiation/annealing cycles only the high
temperature part of annealing has been used.
It is found that He accumulation does not occur
during irradiation/flash annealing in 1000 steps
cycle (1016/m2 for each cycle) all He release
from the crystal occurs during 0.5 second
annealing at 1885oC
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He accumulation during irradiation/flash
annealing in 100 steps cycle (1017/m2 He for each
cycle)
Although significant He release occurs during
each anneal cycle, there is steady He
accumulation with increasing number of cycles
He releases from crystal during each annealing
step however the total amount of He accumulated
in the clusters continuously increases- during
1st 5 cycles of 100 30 of He implanted are
already stored in the clusters. He release is
decreased with increasing number of cycles. This
effect is related to increase of cluster sink
strength
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He accumulation during irradiation/flash
annealing in 10 steps cycle (1018 He/m2 each
cycle)
He practically does not release from crystal
during an annealing step
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He content evolution in tungsten for the case of
1000-step irradiation/anneal (1016/m2 He for each
cycle)
Evolution of helium clusters during annealing at
1885oC
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Temperature dependence of He emission from VnHe
clusters in Tungsten
Temperature spike for IFE bare-wall reference
case lasts a few microseconds, with a maximum
temperature of lt2700oC gtHe emission rate needs
to be 105 higher than He ion irradiation/anneal
tests due to short duration of IFE temperature
spike (estimated increase in He emission
rate is lt104)
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Conclusions

• He-vacancy cluster evolution takes place in the
  area of high He generation regardless of He
  release into another part of the crystal
• He is released from tungsten already during
  irradiation at 850 C. However the effect is only
  significant at small implantation doses (ltlt1016
  He/m2)
• He is fully released from tungsten during each
  annealing step in the case of 1000 cycles (1016
  He/m2 per cycle)
• He practically retained in the crystal in the
  cases of 100, 10 and 1 cycles (1017 to 1019 He/m2
  per cycle)
• Main effect is related to fast increase of
  cluster sink strength.
• The results obtained would not be changed if
  Brownian motion of the clusters or higher values
  of He dissociation energy will be used in the
  calculations

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Size distribution function evolution in the case
of 1000 steps in tungsten
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At room temp. growth of He bubbles beneath the
surface causes blistering at 3 x 1021/m2 and
surface exfoliation at 1022/m2. For IFE power
plant, MeV He dose gtgtgt 1022/m2 .

First Wall Armor
MeV Helium
vacancy
MeV Helium
0 1 2 3 4 5 6
7 8 9 10
Time of microseconds
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Experimental observationsby Hashimoto et al.)
Proton spectra for single crystal tungsten
implanted at 850oC and flash Annealed at 2000oC
in 1, 10, 100, and 1000 cycles to a total dose of
1019 He/m2
) Fusion Science and Technology 47 (2005) 881
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Methods used to describe He-vacancy cluster
evolution

• Homogeneous approach
• Analytical analysis (nodal line method,
  di-atomic nucleation, ..)
• Discrete rate equations (Master Equation)
• Fokker-Plank equation (continuous variables
  -system of ordinary differential equations is
  approximated by a partial differential equation)
• Momentum method
• Hybrid approach (discrete equations for small
  size clusters and F-P/MM equations for large
  cluster size)
• Non Homogeneous approach
• Monte-Carlo
• Master Equation- basic method for homogeneous
  approach

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The code was originally benchmarked with with
experimental stainless steel results

• Observed and predicted size distribution
  functions in isochronal annealing study on
  stainless steel

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Comparison with experimental isochronal annealing
results on He-implanted stainless steel

• Bubble size and density in isochronal annealing
  study