Dynamic Monte-Carlo modeling of hydrogen isotope reactive-diffusive transport in porous graphite

1. Max-Planck Institute for Plasma Physics, EURATOM Association Dynamic Monte-Carlo modeling of hydrogen isotope reactive-diffusive transport in porous graphite Abha Rai PhD work within IMPRS since 17 March, 2005 Computational Material Science Group Stellarator Theory Division Max-Planck-Institut für Plasmaphysik, EURATOM Association

2. Max-Planck Institute for Plasma Physics, EURATOM AssociationOutline • Plasma Wall Interaction and Motivation • Multi-scale approach • Results • Summary • Future Plans

3. Max-Planck Institute for Plasma Physics, EURATOM AssociationPlasma Wall Interaction in Fusion • Challenge: Extremely high power loads (radiation losses needed) • Requirement: Pure plasma core (impurities pollute plasma) • Physical and chemical erosion from carbon tiles due to H, D, T (charged and neutrals)

4. Max-Planck Institute for Plasma Physics, EURATOM AssociationDiffusion in Graphite Carbon deposition in divertor regions of JET and ASDEX UPGRADE JET Major topics: tritium co-deposition chemical erosion Paul Coad (JET) ASDEX UPGRADE Achim von Keudell (IPP, Garching) V. Rohde (IPP, Garching)

5. Chemical Erosion of carbon by hydrogen produces hydrocarbon species (CxHy) Dissociation & Recombination's leads to amorphous hydrocarbon layer formation Carbon acts as sponge for hydrogen Tritium is retained by co-deposition with carbon, on the plasma facing sides or on remote areas. G F Counsell, Plasma Sources Sci. Technol. 11 (2002) A80–A85 Max-Planck Institute for Plasma Physics, EURATOM AssociationHydrocarbon - Codeposition Hydrogen

6. Max-Planck Institute for Plasma Physics, EURATOM AssociationGraphite as a PFM But !! • Chemical sputtering • Hydrogen isotope inventory • Good thermal conductivity • High sublimation energy • Low atomic number

7. Max-Planck Institute for Plasma Physics, EURATOM AssociationOther Options • Problems with Carbon have motivated to opt for other materials • Tungsten • Beryllium • W erosion and interaction with H and He is still a challenge • Mixed materials! ASDEX-Upgrade ITER

8. Max-Planck Institute for Plasma Physics, EURATOM AssociationPorous structure of graphite Real structure of the material needs to be included Internal Structure of Graphite Granule sizes ~ microns Void sizes ~ 0.1 microns Crystallite sizes ~ 50-100 Angstroms Micro-void sizes ~ 5-10 Angstroms Multi-scale problem in space (1cm to Angstroms) and time (pico-seconds to seconds)

9. Material science:

10. Max-Planck Institute for Plasma Physics, EURATOM AssociationMulti – Scale approach ´Intelligent´ coupling necessary Source distribution: Thermalized atoms (TRIM) Macroscales KMC and Monte Carlo Diffusion (MCD) Mesoscales Kinetic Monte Carlo (KMC) Microscales Molecular Dynamics (MD)

11. Max-Planck Institute for Plasma Physics, EURATOM AssociationKinetic Monte Carlo- Basic idea 0 = jump attempt frequency (s-1) Em = migration energy (eV) T = trapped species temperature (K) Poisson process (assigns real time to the jumps) Jumps are independent (no memory)

12. Fitting Parameters (0 ,Em ,L ) Hydrogen atoms Diff. channel 1 Diff. channel 2 Detrapping ω = 1013 (s-1) Em=2.6 eV L = 1 Å ω = 1013 (s-1) Em=2.67 eV L = 3 Å Going into crystallite ω = 1013 (s-1) Em=0.9 eV L = 2 Å Desorption Max-Planck Institute for Plasma Physics, EURATOM AssociationParametrization of processes

13. Large variation in observed diffusion coefficients Diffusion coefficients without knowledge of structure are meaningless Max-Planck Institute for Plasma Physics, EURATOM AssociationKMC – Comparison with experiments standard graphites highly saturated graphite • Diffusion in voids dominates • Strong dependence on void sizes and not void fraction

14. Max-Planck Institute for Plasma Physics, EURATOM AssociationEffect of voids B: 20 % voids C: 20 % voids A: 10 % voids Larger voids Longer jumps Higher diffusion Inner porous structure is important, not just void fraction!!

15. Max-Planck Institute for Plasma Physics, EURATOM AssociationParametrization of processes Fitting Parameters (0 ,Em ,L ) Hydrogen atoms Diff. channel 1 Diff. channel 2 Detrapping ω = 1013 (s-1) Em=2.6 eV L = 1 Å ω = 1013 (s-1) Em=2.67 eV L = 3 Å Going into crystallite ω = 1013 (s-1) Em=0.9 eV L = 2 Å Desorption My work starts here !! Hydrogen molecules Simple jump ω = 2.74 × 1013 (s-1) Em=2.0 eV L = 3 Å ω = 2.74 × 1013 (s-1) Dissociation Em=4.45 eV L = 2 Å ω = 1.0 × 1013 (s-1) Em=0.06 eV L = 10 Å Desorption Recombination

16. H2 9% H2 5% Re-emitted Flux (Fraction) H2 8% Re-emitted Flux (%) H 8% H 5% H 9% Temperature(Kelvin) Temperature (K) Max-Planck Institute for Plasma Physics, EURATOM AssociationHydrogen re-emission Experiment: P. Franzen, E. Vietzke, J. Vac. Sci. Technology A12(3), 1994 Simulation: • H-atom release is limited by detrapping process,not by diffusion • Simulation matches very well with experiment

17. Max-Planck Institute for Plasma Physics, EURATOM AssociationHydrogen re-emission Simulation - Result 2 Increasing void fraction (same element size) : large number of voids trapping probability decreases recombination increases more molecules, fewer atoms H Atom Re-emitted Flux (Fraction) H2 molecule Void Fraction

18. Max-Planck Institute for Plasma Physics, EURATOM AssociationHydrogen re-emission Simulation - Result 3 Increasing internal porosity (element size): large voids trapping probability decreases recombination increases more molecules, fewer atoms H Atom Re-emitted Flux (Fraction) H2 molecule Element size (meters)

19. H2Standard Graphite Re-emittedFlux (Fraction) H2Tore-Supra H Tore-Supra Temperature (Kelvin) H Standard Graphite Max-Planck Institute for Plasma Physics, EURATOM AssociationHydrogen re-emission Tore-Supra Samples • Standard Graphite : • Void Frac 5 % with 5 nm • cubical voids • Tore-Supra Samples: • Void Frac 8% with 20-50 nm • size dome like voids • Onset of H emission starts at Lower temperature

20. Max-Planck Institute for Plasma Physics, EURATOM AssociationIsotope Exchange Experiment: S. Chiu, A.A. Haasz, Journal of Nuclear Materials 196-198 (1992) 972 • Simultaneous bombardment • with H and D ions: • maximum overlapping • ion ranges • (b) completely separated • ion ranges • Hydrogen molecule emission insensitive to ion range separation

21. Max-Planck Institute for Plasma Physics, EURATOM AssociationIsotope Exchange Benchmark: ideal mixing case HD Re-emitted particles H2 D2 Time (s) • Ideal mixing (H2:HD:D2 is 1:2:1) case very well reproduced !!

22. Max-Planck Institute for Plasma Physics, EURATOM AssociationIsotope Exchange Experiment: Simulation: HD Re-emitted flux (arb. units) Re-emitted particles H2 D2 Time (s) ΓH2 > ΓD2 > ΓHD ΓHD > ΓH2 > ΓD2

23. Max-Planck Institute for Plasma Physics, EURATOM AssociationIsotope Exchange Simulation: completely separated ion ranges rise in re-emission level when ion beams are switched on (change of void fraction) ion-induced de-trapping dominates Re-emitted particles Time (s)

24. D2 DdeeperthanH Re-emitted Flux (Arbt. Units) H2 HdeeperthanD D2 HdeeperthanD H2 DdeeperthanH Time (sec) HDHdeeperthanD HDDdeeperthanH Max-Planck Institute for Plasma Physics, EURATOM AssociationIsotope Exchange Experiment: Simulation: H(10KeV) deeper than D(700eV) H(3KeV) deeper than D(1KeV) Deeply distributed specie have higher re-emitted flux

25. Max-Planck Institute for Plasma Physics, EURATOM AssociationIsotope Exchange Possible Reasons for the Discrepancy : • Different Range of Penetration for the two hydrogen isotopes • Effect of temperature rise due to impinging ion beam • Graphite sample may contain a surface layer pre – saturated with hydrogen

26. Max-Planck Institute for Plasma Physics, EURATOM AssociationIsotope Exchange Deuterium TRIDYN Simulation: Effect of ion – beam fluence on range of penetration of hydrogen isotopes is negligible Depth (Å) Hydrogen Particle density (Atoms / Å3) Effect of temperature rise (for 10 keV ion beam, max. temperature rise for a surface layer ~ 200K): too small Depth (Å) Particle density (Atoms / Å3)

27. H2 Re-emitted Flux (Arbt. Units) HD D2 Time (sec) Max-Planck Institute for Plasma Physics, EURATOM AssociationIsotope Exchange Graphite sample may contain a surface layer pre – saturated with hydrogen: Totally Overlapping ion Ranges • The relative re-emitted signal of D2 and HD is similar • Reemission level of H2 • increases, expected due to • large content of hydrogen near the surface

28. HD With H SatLayer HD Virgin Sample Re-emitted Flux (Arbt. Units) D2 With H SatLayer H2 With H SatLayer Time (sec) Max-Planck Institute for Plasma Physics, EURATOM AssociationIsotope Exchange Tore-Supra Samples: Totally Overlapping ion Ranges • Relative re-emission levels are same as the ideal mixing • Large pores connected to the surface, H re-emitted • mainly in atomic form Extent of isotope mixing depends very strongly on inner porous structure and Temperature!!

29. Max-Planck Institute for Plasma Physics, EURATOM AssociationSummary Multi-scale model developed including molecular processes Model reproduces experimental results: H atom and molecule desorption, isotope exchange Ralf Schneider, Abha Rai et. al. ‘Dynamic Monte-Carlo modeling of hydrogen isotope reactive-diffusive transport in porous graphite’. Presented in 12th International Conference on Fusion Reactor Materials (ICFRM), Santa Barbara, Dec. 4 – 9, 2005. More experimental data base is required and question of the interpretation of experimental results remains Inner porous structure is important not just void fraction!!

30. Max-Planck Institute for Plasma Physics, EURATOM AssociationFuture Plans Swift chemical sputtering Küppers – Hopf cycle • Study of chemical erosion • Effect of porosity of graphite

31. Thank you for your kind attention !!