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Comments to modelling of hydrogen retention and permeation in tungsten O.V. Ogorodnikova

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. Comments to modelling of hydrogen retention and permeation in tungsten

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Comments to modelling of hydrogen retention and permeation in tungsten O.V. Ogorodnikova

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  1. 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. 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. Diffusivity & solubility 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. Serra E., Benamati G., Ogorodnikova O.V. J. Nucl. Mater., 1998, v. 255, p. 105

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

  5. Recombination coefficient of deuterium on W Anderl-Longhurst‘s model 1. natural defects: Wt=const Anderl‘s model: Kr=1.3x10-17exp(-0.84/kT), intrinsic (vacancies) defects: Et=1.34 eV, Wt=2x10-5 at.fr. Present model 1. natural defects: Wt=const 2. ion-induced defects: Wt=f(Wm, h, I0) Permeation data can be described well by both Anderl‘s parameters and our parameters (Kr, Et, Wt) Present model: Krclean=3x10-25/T1/2exp(2/kT), intrinsic (dislocations) traps + ion-induced defects: Et=0.85 eV; Wt=8x10-4 at.fr. + Et=1.45 eV; Wtmax=6x10-2 at.fr. Et=1.8 eV; Wt=1x10-6 at.fr. + Et=2.1 eV; Wtmax=10-3 at.fr.

  6. Recombination coefficient of deuterium on W Permeation data can be described well by both Anderl‘s parameters and our parameters (Kr, Et, Wt)

  7. Recombination coefficient of deuterium on W Permeation data can be described well by both Anderl‘s parameters and our parameters (Kr, Et, Wt) TDS calculated with Anderl‘s parameters resul in a disagreement with experiments at RT Anderl‘s model: Kr=1,3x10-17exp(-0.84/kT), intrinsic (vacancies) defects: Et=1,34 eV, Wt=2x10-5 at.fr. Present model: Krclean=3x10-25/T1/2exp(2/kT), intrinsic (dislocations) + ion-induced defects: Et=0,85 eV, Wt=8x10-4 at.fr. + Et=1,45 eV, Wtmax=6x10-2 at.fr.

  8. Recombination coefficient of deuterium on W Permeation data can be described well by both Anderl‘s parameters and our parameters (Kr, Et, Wt) TDS calculated with Anderl‘s parameters resul in a disagreement with experiments at 773 K Anderl‘s model: Kr=1,3x10-17exp(-0.84/kT), intrinsic (vacancies) defects: Et=1,34 eV, Wt=2x10-5 at.fr. Present model: Krclean=3x10-25/T1/2exp(2/kT), intrinsic (dislocations) + ion-induced defects: Et=1.8 eV; Wt=1x10-6 at.fr. + Et=2.1 eV; Wtmax=10-3 at.fr.

  9. Recombination coefficient of deuterium on W 1. Ec=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 Kr corresponds to contaminated surface with a surface barrier of Ec=1.2 eV

  10. Recombination coefficient of deuterium on W Recombination coefficient for a clean metal surface is a function of - diffusion prefactor, - square of the jumping length, - heat of solution. Krclean=D0l2exp(2Qs/kT) (molecules m4/atoms2 s) 1. Ec=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 Kr corresponds to contaminated surface with a surface barrier of Ec=1.2 eV

  11. Me Impurity H Es Ec Recombination coefficient of deuterium on W 1. Ec=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 Kr corresponds to contaminated surface with a surface barrier of Ec=1.2 eV

  12. Recombination coefficient of deuterium on W Recombination coefficient for a clean metal surface is a function of - diffusion prefactor, - square of the jumping length, - heat of solution. Krclean=D0l2exp(2Qs/kT) (molecules m4/atoms2 s) Recombination coefficient: Kr=s0mexp(-2(Ec-Qs)/kT)/Ks02 Anderl’s recombination coefficient does not satisfy the analytical equation

  13. 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 (Kr, Eti, Wti) should describe simultaneously permeation, depth profile and TDS experiments

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

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

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

  17. 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. Depth profile of D in PCW 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

  19. 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. PCW: Surface barrier effect: Ec=1.12 eV • Change of the surface barrier up to Ec=1 eV does not influence D retention. • 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 Ec=1.12 eV. TDS at RT can be described using low recombination coefficient for Ec=1.12 eV with energies of 0.85 eV and 1.3 eV and trapping densities of Wm =10-3 at.fr. and Wm=5x10-2 at.fr., respectively.

  21. D retention in SCW 1.07 eV 1.34 eV SCW: UTIAS (Toronto) ion beam facility 500 eV D+ in W, RT, F=1024 D/m2 , TDS, SIMS • 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 Poon/Haasz/Davis/, J. Nucl. Mater, 2007

  22. Modelling of D retention in SCW: Anderl‘s Kr 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!

  23. Modelling of D retention in SCW: Anderl‘s Kr • Using a dynamic model including trap creation, diffusion and recombination: • the calculated depth profile after one day of time delay looks similar to SIMS depth profile, But! • The D retention is much higher compared to experiment: 4.45x1020 D/m2 • 3. Total D retention decreases only by a factor of 4 after one day of time delay Poon/Haasz/Davis/, J. Nucl. Mater, 2007

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

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

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

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

  28. 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. Modelling of D retention in SCW: Krclean D2V DV Total D retention is calculated after 1 day of time delay. H9: Et=1.55 eV, h=10-2, Wm =3x10-2 at.fr. Et=1.3 eV, h=2x10-3, Wm =2x10-2 at.fr. Using Kr for a clean W surface, calculations are in a agreement with TDS experiments Poon/Haasz/Davis/, J. Nucl. Mater, 2007

  30. Modelling of D retention in SCW: Krclean Total D retention is calculated after 1 day of time delay. H9: Et=1.55 eV, h=10-2, Wm =3x10-2 at.fr. Et=1.3 eV, h=2x10-3, Wm =2x10-2 at.fr. Using Kr for a clean W surface, calculations are in a agreement with depth profile experiments

  31. Time delay effect D retention decreases after several days of post-irradiation time delay prior TDS Calculated time delay between implantation and TDS D retention decreases with time delay between implantation and TDS

  32. Time delay effect D retention decreases after several days of post-irradiation time delay prior TDS Calculated time delay between implantation and TDS D retention decreases with time delay between implantation and TDS

  33. Conclusion • Recombination of D on a clean W surface is very fast • Contaminations on W surface or the presence of a surface barrier • (Ec<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 D2V 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.

  34. Conclusion • - Et1 = 0.65 - 0.85 eV => dislocations, grain boundaries (T=400-450 K) • Et2 = 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) • Et3 = 1.8 - 2.1 eV => chemisorption of D on bubble wall (900-1000 K) Dislocations 0.85 eV D2V 1.3 eV DV 1.5 eV

  35. Conclusion • - Et1 = 0.65 - 0.85 eV => dislocations, grain boundaries (T=400-450 K) • Et2 = 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) • Et3 = 1.8 - 2.1 eV => chemisorption of D on bubble wall (900-1000 K) • 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. Mechanism of deuterium behaviour in PCW Recombination Diffusion Trapping Jd Chemi- sorption 0.4 1.4 0.45 1.04 ½ H2(g) 1.05 1.8 Solution 0.5- 1.2 dislocations, grain boundaries bubbles, vacancies chemisorption on the internal wall of bubbles: He+-implantation Ebvacancy=(Qc+Qs)/2

  37. Modelling of D retention in SCW: Krclean Total D retention is calculated after 1 day of time delay. H9: Et=1.55 eV, h=10-2, Wm =3x10-2 at.fr. Et=1.3 eV, h=2x10-3, Wm =2x10-2 at.fr. Using Kr for a clean W surface, calculations are in a agreement with depth profile experiments

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