Multiscale modeling of hydrogen isotope transport in porous graphite Max-Planck-Institut für Plasmaphysik, EURATOM Association Multiscale modeling of hydrogen isotope transport in porous graphite Manoj Warrier Thesis advisor: Ralf Schneider PhD work within IMPRS since January, 2002 Max-Planck Institut für Plasmaphysik Stellarator Theory Division, Edge Modeling Group

Max-Planck-Institut für Plasmaphysik, EURATOM Association 2. Outline Plasma Wall Interaction and motivation Multi-scale approach and results Summary and conclusions

3. Plasma Wall Interaction in Fusion Max-Planck-Institut für Plasmaphysik, EURATOM Association 3. Plasma Wall Interaction in Fusion Challenge: Extremely high power loads Requirement: Pure plasma core

Good thermal conductivity, high sublimation energy, low atomic number Max-Planck-Institut für Plasmaphysik, EURATOM Association 4. Graphite as a PFM Good thermal conductivity, high sublimation energy, low atomic number V. Rohde (IPP, Garching) But: chemical sputtering, hydrogen isotope inventory

5. Porous Structure of Graphite Max-Planck-Institut für Plasmaphysik, EURATOM Association 5. Porous Structure of Graphite Granule sizes ~ microns Void sizes ~ 0.1 microns Crystallite sizes ~ 50-100 Å Micro-void sizes ~ 5-10 Å Multi-scale problem in space (1 cm to 1 Å) and time (ps to s) H transport in complex, 3D, porous graphite structure

6. Multi-scale approach Macroscales Mesoscales Microscales Max-Planck-Institut für Plasmaphysik, EURATOM Association 6. Multi-scale approach Macroscales KMC and Monte Carlo Diffusion (MCD) Mesoscales Kinetic Monte Carlo (KMC) Microscales Molecular Dynamics (MD)

7. Molecular dynamics at microscales Max-Planck-Institut für Plasmaphysik, EURATOM Association 7. Molecular dynamics at microscales Hydrogen in crystal graphite (960 atoms) Brenner potential, Nordlund long range interaction HCParcas: Developed by Kai Nordlund Berendsen thermostat (150K - 900K for 100 ps) Reactive Empirical Bond Order (REBO) potential allows simulation of hydrocarbon reactions Periodic boundary conditions

8. MD simulation at 150K and 900K 150K 900K Max-Planck-Institut für Plasmaphysik, EURATOM Association 8. MD simulation at 150K and 900K 150K 900K Large jumps at high temperatures > 450K No diffusion across graphene layers

9. MD simulation results Two diffusion channels Max-Planck-Institut für Plasmaphysik, EURATOM Association 9. MD simulation results Two diffusion channels Non-Arrhenius temperature dependence for hydrogen isotope diffusion in crystal graphite

10. Kinetic Monte Carlo - basic idea Max-Planck-Institut für Plasmaphysik, EURATOM Association 10. Kinetic Monte Carlo - basic idea Poisson process (assigns real time to the jumps) Jumps are independent (no memory)

11. Mesoscales - Comparison with experiments Max-Planck-Institut für Plasmaphysik, EURATOM Association 11. Mesoscales - Comparison with experiments standard graphites highly saturated graphite Large variation in observed diffusion coefficients Strong dependence on void sizes and not void fraction Saturated H: 0~105s-1 and step sizes ~1Å (QM?)

12. Effect of voids A: 10 % voids B: 20 % voids C: 20 % voids Max-Planck-Institut für Plasmaphysik, EURATOM Association 12. Effect of voids A: 10 % voids B: 20 % voids C: 20 % voids Larger voids Longer jumps Higher diffusion

13. KMC and MCD at macroscales Max-Planck-Institut für Plasmaphysik, EURATOM Association 13. KMC and MCD at macroscales Trapping - detrapping (2.7 eV) Desorption (1.9 eV) Surface diffusion (0.9 eV) KMC with Jump lengths depend on the process Monte Carlo Diffusion (MCD) used to simulate TGD ζ

14. Results at macroscales Max-Planck-Institut für Plasmaphysik, EURATOM Association 14. Results at macroscales variation of 3D structure surface diffusion 0.9 eV adsorption- desorption 1.9 eV Different processes dominate at different temperatures Diffusion in voids dominates Diffusion coefficients without knowledge of structure are meaningless

15. Further results at macroscales Max-Planck-Institut für Plasmaphysik, EURATOM Association 15. Further results at macroscales Interpretation of diffusion? Subdiffusion Superdiffusion H atom desorption begins above 1200 K Closed pores efficiently supress hydrogen diffusion

Max-Planck-Institut für Plasmaphysik, EURATOM Association 16. Defect agglomeration Graphite surface during hydrogen bombardment (STM analysis from T. Angot et al., Univ. of Provence, Marseille)

Defect agglomeration on graphite surface reproduced by simulation Max-Planck-Institut für Plasmaphysik, EURATOM Association 17. Defect agglomeration Defect agglomeration on graphite surface reproduced by simulation

Defect agglomeration on graphite surface reproduced by simulation Max-Planck-Institut für Plasmaphysik, EURATOM Association 17. Defect agglomeration Defect agglomeration on graphite surface reproduced by simulation

Diffusion coefficients without knowledge of structure are meaningless Max-Planck-Institut für Plasmaphysik, EURATOM Association Summary Multi-scale model developed M. Warrier, R. Schneider, E. Salonen, K. Nordlund, Physica Scripta, T108 (2004) 85. M. Warrier, R. Schneider, X Bonnin, Computer Physics Communications, 160, 1 (2004) 46 R. Schneider, et. al., Computer Physics Communications 164 (2004) 9. Model reproduces experimental results: H atom desorption, diffusion coefficients, defect agglomeration M. Warrier, R. Schneider, E. Salonen, K. Nordlund, J. Nucl. Mater (In press). M. Warrier, R. Schneider, E. Salonen, K. Nordlund, Contrib. Plasma Phys., 44, 1-3 (2004) 307 Model suited for predictions: diffusion coefficients, isotope exchange, chemical sputtering Diffusion coefficients without knowledge of structure are meaningless