Multi–scale modeling of hydrogen isotope diffusion in graphite

Abstract

The importance of plasma-wall interaction processes for the edge plasma is well known: creation of impurities by different sputtering mechanisms or recycling properties of the walls are examples of processes determining the divertor characteristics and the edge plasma profiles. To be able to have a better understanding of the plasma-wall interaction process itself, a multi-scale procedure is followed: molecular dynamics calculations resolve the microscopic length scale and deliver quite precise input data for kinetic Monte Carlo calculations (jump frequencies, migration energies, jump step-sizes) used for meso-scale up to the macroscopic system length. To cover the whole length scale involved -from microscopic up to macroscopic -several subsequent levels of kinetic Monte Carlo are needed, each providing the necessary input data for the next level. With this procedure the corresponding time scales spanning from picoseconds atomic interaction times to wall equilibration times of at least milliseconds will be spanned. Inclusion of a realistic structure model is also important, like for porous graphite where the void structure and orientation of the microcrystallites have to be included. First results of such a multi-scale calculation are presented studying the diffusion of hydrogen isotopes in porous graphite and are compared with experimental results from the literature.

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

“…A 3d, porous, granule structure was constructed using statistical distributions for crystallite dimensions and crystallite orientations for a specified micro-void fraction. The KMC scheme was extended to include trapping and detrapping at the crystallite-micro-void interface in the 3d porous granule structure to simulate trans-granular-diffusion (TGD) in the meso-scales (10 −7 −10 −6 m, several ms) [18] using the results from our micro-scale modeling and from experiments ( [19] and references therein). Later, this concept was extended our simulations to the macroscales (1 cm, up to a few s), thereby having a truly multi-scale capability.…”

Kinetic Monte–Carlo modeling of hydrogen retention and re-emission from Tore Supra deposits

“…In the earlier work hydrogen isotope diffusion in porous graphite was modeled using a time dependent, 3-dimensional, multi-scale model [9][10][11]. The model used molecular dynamics (MD) at the micro-scales (2.5 nm, 10 −10 s) and consistently parametrized the MD results within a KMC scheme [10].…”

Dynamic Monte-Carlo modeling of hydrogen isotope diffusion in co-deposited layers

“…Multiple showers of methyl radicals were considered to grow films of thickness ∼ 70 − 100Å. In the earlier work hydrogen isotope diffusion in porous graphite was modeled using a time dependent, 3-dimensional, multi-scale model [14,19,20]. The porous geometry was constructed using statistical distributions for crystallite dimensions and crystallite orientations for a specified micro-void fraction.…”

“…The model used molecular dynamics (MD) at the micro-scales (2.5 nm, 10 −10 s) and consistently parametrized the MD results within a KMC scheme [19]. The KMC scheme was extended to include trapping and detrapping at the crystallite-micro-void interface to simulate trans-granular-diffusion (TGD) at the meso-scales (10 −7 − 10 −6 m, several ms) [20] using the results from our micro-scale modeling and from experiments ( [21] and references therein). This concept was then extended to the macro-scales (1 cm, up to a few seconds), by using the parametrized TGD diffusion co-efficient in a Monte Carlo diffusion model with transport in voids using a KMC model, thereby having a truly multi-scale capability [14].…”

“…Due to lack of data (experimental or MD simulation), the migration energy for surface diffusion has been chosen to be 0.5 eV, which is of the same order as the binding energy of hydrogen bonds and of hydrogen surface diffusion in graphite [24]. The jump lengths are taken to be of the order of surface diffusion jump lengths in graphite (∼ 30Å) [20], for a similar reason as above. This does not affect the results as the size of the jumps is actually limited by the pore size of the co-deposits which have a distribution as shown in Fig.2.…”