1. S.I. Golubov, S.J. Zinkle and R.E. Stoller
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

2. 1.3 MeV He implanted & annealed tungsten
Critical incremental He fluence for nearly complete annealing is ~1016/m2
Tirr=850 C
Ramp anneal to 2000 C
Fusion Science and Technology 47 (2005) 881

3. Flash annealing regime used in the calculations

4. 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 =2.5*10-7 dpa/s and GHe =2.5*10-9 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

5. Sink strength of foil boundaries
where
is sink strength of foil interior defects
is a good approximation in the case
At l=0.7 μm

6. Absorption of newly created, injected or re-dissolved He atoms
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

7. Transitions of x, m cluster via point defect reaction kinetics

8. Two dimensional Master Equation
(x- number of vacancies and m- number of He atoms in a cluster)

9. Scheme of new Grouping Method (S.I. Golubov et al.)+
mean x,m fluxes
10 fluxes for each group are
required only

10. Parameters used in the W-He calculations
He-vacancy dissociation energies, Edis,
for mHe+1V 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 ,
Ω=1.585*10-29 m-3 ,
γ=2.8 J/m2,
Dislocation capture efficiencies:
Zv=1.00, Zi =1.25
He2Vm
HeVm
Edis are taken to be equal to 4.5 eV at x>1
Calculated dissociation energies
Vs size of He-V clusters (Van Veen)

11. Evolution of calculated 1-D cluster size distribution function, f(x), during 1 step irradiation of He
0.25 appm = 1x1016/m2 He

12. 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

13. 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

14. 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

15. 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

16. 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 % 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

17. 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

18. 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

19. Temperature dependence of He emission from V+nHe clusters in Tungsten
Temperature spike for IFE bare-wall reference case lasts a few microseconds, with a maximum temperature of <2700oC
=>He 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 <104)

20. Main effect is related to fast increase of cluster sink strength.
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 (<<1016 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

21. Size distribution function evolution in the case of 1000 steps in tungsten

22. For IFE power plant, MeV He dose >>> 1022/m2 .
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 >>> 1022/m2 .
First Wall Armor
MeV Helium
vacancy
MeV Helium
Time of microseconds

23. Experimental observations by 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

24. 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

25. The code was originally benchmarked with with experimental stainless steel results
Observed and predicted size distribution functions in isochronal annealing study on stainless steel
Predicted
TEM measurements

26. Bubble size and density in isochronal annealing study
Comparison with experimental isochronal annealing results on He-implanted stainless steel
Bubble size and density in isochronal annealing study