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

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

Flash annealing regime used in the calculations

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

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

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

Transitions of x, m cluster via point defect reaction kinetics

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

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

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)

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

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

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

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

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

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

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

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

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)

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

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

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 0 1 2 3 4 5 6 7 8 9 10 Time of microseconds

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

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

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

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