1. Olga Ogorodnikova, 2008, Salamanka, Spain Comments to modelling of hydrogen retention and permeation in tungsten O.V. Ogorodnikova Max-Planck-Institut für Plasmaphysik, EURATOM ASS., Garching, Germany Model Implantation + Diffusion + trapping + recombination

2. Olga Ogorodnikova, 2008, Salamanka, Spain Comments to modelling of hydrogen retention and permeation in tungsten O.V. Ogorodnikova Max-Planck-Institut für Plasmaphysik, EURATOM ASS., Garching, Germany Input parameters diffusivity, trapping energy & trapping density, recombination Model Implantation + Diffusion + trapping + recombination T inventory

3. Olga Ogorodnikova, 2008, Salamanka, Spain Diffusivity & solubility Serra E., Benamati G., Ogorodnikova O.V. J. Nucl. Mater., 1998, v. 255, p. 105 The recommended diffusivity and solubility are given by Frauenfelder. Frauenfelder’s experiment has been done at temperatures high enough (1173–2073 K) to negligible the effects of trapping.

4. Olga Ogorodnikova, 2008, Salamanka, Spain Recombination coefficient of deuterium on W Permeation data can be described well by both Anderl‘s parameters and our parameters (K r, E t, W t ) Anderl‘s model: K r =1.3x10 -17 exp(-0.84/kT), intrinsic (vacancies) defects: E t =1.34 eV, W t =2x10 -5 at.fr. Anderl-Longhurst‘s model W t =const 1. natural defects:

5. Olga Ogorodnikova, 2008, Salamanka, Spain Recombination coefficient of deuterium on W Permeation data can be described well by both Anderl‘s parameters and our parameters (K r, E t, W t ) Anderl‘s model: K r =1.3x10 -17 exp(-0.84/kT), intrinsic (vacancies) defects: E t =1.34 eV, W t =2x10 -5 at.fr. Anderl-Longhurst‘s model W t =const 1. natural defects: Present model 2. ion-induced defects: 1. natural defects:W t =const W t =f(W m,    Present model: K r clean =3x10 -25 /T 1/2 exp(2/kT), intrinsic (dislocations) traps + ion-induced defects: E t =0.85 eV; W t =8x10 -4 at.fr. + E t =1.45 eV; W t max =6x10 -2 at.fr. E t =1.8 eV; W t =1x10 -6 at.fr. + E t =2.1 eV; W t max =10 -3 at.fr.

6. Olga Ogorodnikova, 2008, Salamanka, Spain Recombination coefficient of deuterium on W Permeation data can be described well by both Anderl‘s parameters and our parameters (K r, E t, W t )

7. Olga Ogorodnikova, 2008, Salamanka, Spain Recombination coefficient of deuterium on W TDS calculated with Anderl‘s parameters resul in a disagreement with experiments at RT Permeation data can be described well by both Anderl‘s parameters and our parameters (K r, E t, W t ) Present model: K r clean =3x10 -25 /T 1/2 exp(2/kT), intrinsic (dislocations) + ion-induced defects: E t =0,85 eV, W t =8x10 -4 at.fr. + E t =1,45 eV, W t max =6x10 -2 at.fr. Anderl‘s model: K r =1,3x10 -17 exp(-0.84/kT), intrinsic (vacancies) defects: E t =1,34 eV, W t =2x10 -5 at.fr.

8. Olga Ogorodnikova, 2008, Salamanka, Spain Recombination coefficient of deuterium on W TDS calculated with Anderl‘s parameters resul in a disagreement with experiments at 773 K Permeation data can be described well by both Anderl‘s parameters and our parameters (K r, E t, W t ) Present model: K r clean =3x10 -25 /T 1/2 exp(2/kT), intrinsic (dislocations) + ion-induced defects: E t =1.8 eV; W t =1x10 -6 at.fr. + E t =2.1 eV; W t max =10 -3 at.fr. Anderl‘s model: K r =1,3x10 -17 exp(-0.84/kT), intrinsic (vacancies) defects: E t =1,34 eV, W t =2x10 -5 at.fr.

9. Olga Ogorodnikova, 2008, Salamanka, Spain Recombination coefficient of deuterium on W 1. E c =0 [P.W.Tamm & L.D.Schmidt, J. Chem. Phys. V.55, N9, 1971 ]. Using Fraunfelder’s solubility, recombination coefficient for a clean metal surface is extremely high 2. Recombination coefficient for a dirty surface increases with temperature. Franzen’s K r corresponds to contaminated surface with a surface barrier of E c =1.2 eV

10. Olga Ogorodnikova, 2008, Salamanka, Spain Recombination coefficient of deuterium on W 1. E c =0 [P.W.Tamm & L.D.Schmidt, J. Chem. Phys. V.55, N9, 1971 ]. Using Fraunfelder’s solubility, recombination coefficient for a clean metal surface is extremely high 2. Recombination coefficient for a dirty surface increases with temperature. Franzen’s K r corresponds to contaminated surface with a surface barrier of E c =1.2 eV Recombination coefficient for a clean metal surface is a function of - diffusion prefactor, - square of the jumping length, - heat of solution. K r clean =D 0 2 exp(2Q s /kT) (molecules m 4 /atoms 2 s)

11. Olga Ogorodnikova, 2008, Salamanka, Spain Recombination coefficient of deuterium on W 1. E c =0 [P.W.Tamm & L.D.Schmidt, J. Chem. Phys. V.55, N9, 1971 ]. Using Fraunfelder’s solubility, recombination coefficient for a clean metal surface is extremely high 2. Recombination coefficient for a dirty surface increases with temperature. Franzen’s K r corresponds to contaminated surface with a surface barrier of E c =1.2 eV H Me EcEc EsEs Impurity

12. Olga Ogorodnikova, 2008, Salamanka, Spain Recombination coefficient of deuterium on W Anderl’s recombination coefficient does not satisfy the analytical equation Recombination coefficient for a clean metal surface is a function of - diffusion prefactor, - square of the jumping length, - heat of solution. K r clean =D 0 2 exp(2Q s /kT) (molecules m 4 /atoms 2 s) Recombination coefficient : K r =s 0  exp(-2(E c -Q s )/kT)/K s0 2

13. Olga Ogorodnikova, 2008, Salamanka, Spain Conclusion N°1 - Anderl’s model does not describe any experimental TDS at T=300-800 K -Recombination of deuterium atoms on a clean W surface is very fast -Reliable set of parameters (K r, E t i, W t i ) should describe simultaneously permeation, depth profile and TDS experiments

14. Olga Ogorodnikova, 2008, Salamanka, Spain Trapping parameters: Implantation of D + 200 eV 3000 eV polycrystalline W (99.96%) W (99.999%) Linear temperature ramp -> TDS (L=0.5 mm) Sample preparation: -1300°C 3 hours heating at p=10 -6 Torr - outgasing at 1000°C 10 min. just before implantation Depth profile Thermal desorption spectroscopy

15. Olga Ogorodnikova, 2008, Salamanka, Spain Depth profile and TDS of D in polycrystalline W Model includes trap production, diffusion and recombination. Ion-induced traps Natural traps

16. Olga Ogorodnikova, 2008, Salamanka, Spain Depth profile and TDS of D in polycrystalline W Model includes trap production, diffusion and recombination. Ion-induced traps Natural traps 0.85 eV 1.45 eV

17. Olga Ogorodnikova, 2008, Salamanka, Spain PCW: Only natural traps Depth profiles cannot be modeled using only natural traps. TDS at RT can be described using only natural traps with energies of 0.9 eV and 1.2 eV and trapping densities of W=10 -3 at.fr. and W=6x10 -4 at.fr., respectively.

18. Olga Ogorodnikova, 2008, Salamanka, Spain Time delay between implantation and TDS decreases D inventory in low-energy defects such as dislocations and grain boundaries Trapping energies are 0.85 eV and 1.45 eV Depth profile of D in PCW

19. Olga Ogorodnikova, 2008, Salamanka, Spain Time delay D inventory in W increases as a square root of fluence at RT => diffusion-limited trapping. Most of D are trapped in the bulk at high fluences. Small variation in purity is not important. Time delay between implantation and TDS decreases D inventory

20. Olga Ogorodnikova, 2008, Salamanka, Spain PCW: Surface barrier effect: E c =1.12 eV 1.Change of the surface barrier up to E c =1 eV does not influence D retention. 2.Depth profiles can be described using recombination coefficient for a clean W surface as well as recombination coefficient for contaminated W surface with the surface barrier of E c =1.12 eV. TDS at RT can be described using low recombination coefficient for E c =1.12 eV with energies of 0.85 eV and 1.3 eV and trapping densities of W m =10 -3 at.fr. and W m =5x10 -2 at.fr., respectively.

21. Olga Ogorodnikova, 2008, Salamanka, Spain 500 eV D + in W, RT, F=10 24 D/m 2, TDS, SIMS D retention in SCW Poon/Haasz/Davis/, J. Nucl. Mater, 2007 SCW: UTIAS (Toronto) ion beam facility Poon et al. model: Modeling only TDS. No modeling of implantation stage - All D are in traps - D depth profile according to SIMS - Anderl’s recombination coefficient 1.07 eV1.34 eV

22. Olga Ogorodnikova, 2008, Salamanka, Spain Using a dynamic model including trap creation, diffusion and recombination: 1. the calculated depth profile after one day of time delay looks similar to SIMS depth profile, But! Modelling of D retention in SCW: Anderl‘s K r

23. Olga Ogorodnikova, 2008, Salamanka, Spain Using a dynamic model including trap creation, diffusion and recombination: 1.the calculated depth profile after one day of time delay looks similar to SIMS depth profile, But! 2.The D retention is much higher compared to experiment: 4.45x10 20 D/m 2 3. Total D retention decreases only by a factor of 4 after one day of time delay Modelling of D retention in SCW: Anderl‘s K r Poon/Haasz/Davis/, J. Nucl. Mater, 2007

24. Olga Ogorodnikova, 2008, Salamanka, Spain Using a dynamic model including trap creation, diffusion and recombination: 1.the calculated depth profile after one day of time delay looks similar to SIMS depth profile, But! 4.The suggestion about negligible amount of D in solution is wrong 5. Total D retention is mainly defined by D in solution Modelling of D retention in SCW: Anderl‘s K r

25. Olga Ogorodnikova, 2008, Salamanka, Spain Using a dynamic model including trap creation, diffusion and recombination: 1.the calculated depth profile after one day of time delay looks similar to SIMS depth profile, But! 4.The suggestion about negligible amount of D in solution is wrong 5. Total D retention is mainly defined by D in solution Modelling of D retention in SCW: Anderl‘s K r

26. Olga Ogorodnikova, 2008, Salamanka, Spain Using Poon/Haasz/Davis model with Anderl’s K r, calculations are in a disagreement with TDS experiments The suggestion of negligible amount of D in solution after several days of time delay is wrong using Anderl’s K r Post-irradiation time delays prior TDS is not sufficient to release most of D from solution Modelling of D retention in SCW: Anderl‘s K r

27. Olga Ogorodnikova, 2008, Salamanka, Spain Using Poon/Haasz/Davis model with Anderl’s K r, calculations are in a disagreement with TDS experiments The suggestion of negligible amount of D in solution after several days of time delay is wrong using Anderl’s K r Post-irradiation time delays prior TDS is not sufficient to release most of D from solution Modelling of D retention in SCW: Anderl‘s K r

28. Olga Ogorodnikova, 2008, Salamanka, Spain Conclusion N°2 Using a dynamic model including trap creation, diffusion and recombination: 1. Both the experimental depth profiles and TDS cannot be modeled using Poon/Haasz/Davis model with Anderl’s Kr 2. Post-irradiation time delays prior TDS is not sufficient to release most of D from solution The suggestion of negligible amount of D in solution after several days of time delay is wrong using Anderl’s Kr It is necessary to minimize the number of suggestions as less as possible =>

29. Olga Ogorodnikova, 2008, Salamanka, Spain Modelling of D retention in SCW: K r clean Total D retention is calculated after 1 day of time delay. H9: E t =1.55 eV,  =10 -2, W m =3x10 -2 at.fr. E t =1.3 eV,  =2x10 -3, W m =2x10 -2 at.fr. Using K r for a clean W surface, calculations are in a agreement with TDS experiments D2VD2VDV Poon/Haasz/Davis/, J. Nucl. Mater, 2007

30. Olga Ogorodnikova, 2008, Salamanka, Spain Modelling of D retention in SCW: K r clean Total D retention is calculated after 1 day of time delay. H9: E t =1.55 eV,  =10 -2, W m =3x10 -2 at.fr. E t =1.3 eV,  =2x10 -3, W m =2x10 -2 at.fr. Using K r for a clean W surface, calculations are in a agreement with depth profile experiments

31. Olga Ogorodnikova, 2008, Salamanka, Spain Calculated time delay between implantation and TDS D retention decreases after several days of post-irradiation time delay prior TDS Time delay effect D retention decreases with time delay between implantation and TDS

32. Olga Ogorodnikova, 2008, Salamanka, Spain Calculated time delay between implantation and TDS D retention decreases after several days of post-irradiation time delay prior TDS Time delay effect D retention decreases with time delay between implantation and TDS

33. Olga Ogorodnikova, 2008, Salamanka, Spain Recombination of D on a clean W surface is very fast Contaminations on W surface or the presence of a surface barrier (E c  1.2 eV) result only in a decrease of the trapping energy of atomic or molecular D with a vacancy from 1.45 eV to 1.3 eV. The trapping energies for molecular D and atomic D with a vacancy can be resolved for SCW: 1.3 eV for D 2 V and 1.55 eV for DV for a clean tungsten surface (see also Poon et al. J. Nucl. Mater, 2007). The trapping energies of atomic or molecular D with a vacancy are not resolved for PCW and are about 1.45 eV. The measurement of TDS after one or several days of post-irradiation time delay can decrease the D inventory by 2-4 times. Conclusion

34. Olga Ogorodnikova, 2008, Salamanka, Spain - E t 1 = 0.65 - 0.85 eV => dislocations, grain boundaries (T=400-450 K) - E t 2 = 1.3 - 1.6 eV => several D in vacancy (DxV), one D in vacancy (DV) and one D in several vacancies (DVx) (T=500-800 K) - E t 3 = 1.8 - 2.1 eV => chemisorption of D on bubble wall (900-1000 K) Dislocations 0.85 eV D 2 V 1.3 eV DV 1.5 eV Conclusion

35. Olga Ogorodnikova, 2008, Salamanka, Spain - E t 1 = 0.65 - 0.85 eV => dislocations, grain boundaries (T=400-450 K) - E t 2 = 1.3 - 1.6 eV => several D in vacancy (DxV), one D in vacancy (DV) and one D in several vacancies (DVx) (T=500-800 K) - E t 3 = 1.8 - 2.1 eV => chemisorption of D on bubble wall (900-1000 K) Conclusion All trapping sites can exist in W as intrinsic defect. The density of natural traps depends on W structure (SCW, PCW or PSW). The trapping sites can be ion-induced defects produced in W by stress field for low-energy ions and produced in W by both stress and atomic displacement damage for high-energy ions.

36. Olga Ogorodnikova, 2008, Salamanka, Spain Mechanism of deuterium behaviour in PCW ½ H 2 (g) 1.04 1.4 0.4 JdJd Solution 0.45 1.05 1.8 Chemi- sorption E b vacancy =(Q c +Q s )/2 0.5- 1.2 RecombinationDiffusionTrapping dislocations, grain boundaries bubbles, vacancies chemisorption on the internal wall of bubbles: He + -implantation

37. Olga Ogorodnikova, 2008, Salamanka, Spain Modelling of D retention in SCW: K r clean Total D retention is calculated after 1 day of time delay. H9: E t =1.55 eV,  =10 -2, W m =3x10 -2 at.fr. E t =1.3 eV,  =2x10 -3, W m =2x10 -2 at.fr. Using K r for a clean W surface, calculations are in a agreement with depth profile experiments