1. 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

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

3. 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

4. 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. 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 ~ 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

16. 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)

17. 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

18. 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

19. 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