dynamic monte-carlo modeling of hydrogen isotope reactive-diffusive transport in porous graphite

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

Max-Planck Institute for Plasma Physics, EURATOM Association


Outline

• Plasma Wall Interaction and Motivation

• Multi-scale approach

• Results

• Summary

• Future Plans


Plasma 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)

Carbon deposition in divertor regions of JET and ASDEX UPGRADE

Carbon deposition in divertor regions of JET and ASDEX UPGRADE

JET JET

ASDEX UPGRADE

ASDEX UPGRADE

Achim von Keudell (IPP, Garching)

V. Rohde (IPP, Garching)

Paul Coad (JET)

Major topics: tritium co-deposition

chemical erosion


Diffusion in Graphite


Hydrocarbon - Codeposition

Hydrogen

• 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

Good thermal conductivityHigh sublimation energyLow atomic number

But !!

• Chemical sputtering• Hydrogen isotope inventory


Graphite as a PFM


Other Options

ITER ASDEX-Upgrade

• 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!

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)

Real structure of the material needs to be included


Porous structure of graphite

Material science:

Microscales

Molecular Dynamics (MD)

Mesoscales

Kinetic Monte Carlo (KMC)

Macroscales

KMC and Monte Carlo Diffusion (MCD)

´Intelligent´ coupling necessary


Multi – Scale approach

Source distribution:

Thermalized atoms (TRIM)

Poisson process (assigns real time to the jumps)

Jumps are independent (no memory)


Kinetic Monte Carlo- Basic idea

0 = jump attempt frequency (s-1)Em = migration energy (eV)T = trapped species temperature (K)


Parametrization of processes

Fitting Parameters (0 ,Em , L )

Hydrogen atoms

Diff. channel 1

Diff. channel 2

ω = 1013 ( s-1) Em=2.6 eV L = 1 Å Detrapping

ω = 1013 ( s-1) Em=2.67 eV L = 3 Å Going into crystallite

ω = 1013 ( s-1) Em=0.9 eV L = 2 ÅDesorption

Large variation in observed diffusion coefficients

standardgraphites

highly saturatedgraphite

Diffusion coefficients without knowledge of structure are meaningless

Diffusion in voids dominates

Strong dependence on void sizes and not void fraction


KMC – Comparison with experiments

T1000 /

)s/cm(D 2


Effect of voids

A: 10 % voids B: 20 % voids C: 20 % voids

Larger voids Longer jumps Higher diffusion

Inner porous structure is important, not just void fraction!!


Parametrization of processes

Fitting Parameters (0 ,Em , L )

Hydrogen atoms

Diff. channel 1

Diff. channel 2

ω = 1013 ( s-1) Em=2.6 eV L = 1 Å Detrapping

Hydrogen molecules

ω = 2.74 × 1013 ( s-1) Em=2.0 eV L = 3 ÅSimple jump

ω = 2.74 × 1013 ( s-1) Em=4.45 eV L = 2 Å Dissociation

ω = 1.0 × 1013 ( s-1) Em=0.06 eV L = 10 Å Desorption

ω = 1013 ( s-1) Em=2.67 eV L = 3 Å Going into crystalliteω = 1013 ( s-1) Em=0.9 eV L = 2 Å Desorption

My work starts here !!

Recombination

Experiment: P. Franzen, E. Vietzke, J. Vac. Sci. Technology A12(3), 1994

H-atom release is limited by detrapping process,not by diffusion


Hydrogen re-emission

Simulation:

Simulation matches very well with experiment

Temperature (K)

Re

-em

itte

d F

lux

(%)

Re

-em

itte

d F

lux

(Fra

ctio

n)

Temperature(Kelvin)

H2 9%H2 5%

H2 8%

H 5%

H 9%

H 8%



Simulation - Result 2

Re-

emit

ted

Flu

x (F

ract

ion

)

Void Fraction

Increasing void fraction (same element size) : large number of voids trapping probability decreases recombination increases more molecules, fewer atoms

H Atom

H2 molecule



Simulation - Result 3

Re-

emit

ted

Flu

x (F

ract

ion

)

Element size (meters)

Increasing internal porosity (element size): large voids trapping probability decreases recombination increases more molecules, fewer atoms

H Atom

H2 molecule



Re-

emitt

ed F

lux

(Fra

ctio

n)

Temperature (Kelvin)

H Tore-Supra

H2 Standard Graphite

H2 Tore-Supra

H Standard Graphite

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

Experiment: S. Chiu, A.A. Haasz, Journal of Nuclear Materials 196-198 (1992) 972

Simultaneous bombardment with H and D ions:(a)maximum overlapping ion ranges(b) completely separated ion ranges

Hydrogen molecule emission insensitive to ion range separation


Isotope Exchange

Benchmark:

Ideal mixing (H2:HD:D2 is 1:2:1) case very well reproduced !!


Isotope Exchange

Time (s)

Re-

emitt

ed p

artic

les

ideal mixing case

HD

H2

D2

Simulation:


Isotope Exchange

Re-

emitt

ed fl

ux (

arb.

uni

ts)

Time (s)

Re-

emitt

ed p

artic

les

Experiment:

ΓH2 > ΓD2 > ΓHD

HD

H2

D2

ΓHD > ΓH2 > ΓD2

Simulation:


Isotope Exchange

Time (s)

Re-

emitt

ed p

artic

les

completely separated ion ranges

rise in re-emission level when ion beams are switched on (change of void fraction)

ion-induced de-trapping dominates

Simulation:


Isotope Exchange

Experiment:

H(10KeV) deeper than D(700eV)

Time (sec)

Re

-em

itte

d F

lux

(Arb

t.

Un

its) H2 DdeeperthanH

H2 HdeeperthanD

HD HdeeperthanDHD DdeeperthanH

D2 HdeeperthanD

D2 DdeeperthanH

H(3KeV) deeper than D(1KeV)

Deeply distributed specie have higher re-emitted flux

Possible Reasons for the Discrepancy :


Isotope Exchange

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


Isotope Exchange

Deuterium

Dep

th (

Å)

Particle density (Atoms / Å3)

Hydrogen

Particle density (Atoms / Å3)

Dep

th (

Å)

TRIDYN Simulation:Effect of ion – beam fluence on range of penetration of hydrogen isotopes isnegligible

Effect of temperature rise (for 10 keV ion beam, max. temperaturerise for a surface layer ~ 200K): too small


Isotope Exchange

Graphite sample may contain a surface layer pre – saturated with hydrogen:

The relative re-emitted signal of D2 and HD is similar Reemission level of H2 increases, expected due tolarge content of hydrogen near the surface

Time (sec)

Re

-em

itte

d F

lux

(Arb

t. U

nits

) H2

D2

HD

Totally Overlapping ion Ranges


Isotope Exchange

Tore-Supra Samples:

Relative re-emission levels are same as the ideal mixingLarge pores connected to the surface, H re-emittedmainly in atomic form

Totally Overlapping ion RangesHD With H SatLayer

HD Virgin Sample

H2 With H SatLayerD2 With H SatLayer

Time (sec)

Re

-em

itte

d F

lux

(Arb

t. U

nits

)

Extent of isotope mixing depends very strongly on inner porous structure and Temperature!!


Summary

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.

Inner porous structure is important not just void fraction!!

More experimental data base is required and question ofthe interpretation of experimental results remains


Future Plans

Study of chemical erosion

Effect of porosity of graphite

Swift chemical sputteringKüppers – Hopf cycle

Thank you for your kind attention !!

dynamic monte-carlo modeling of hydrogen isotope reactive-diffusive transport in porous graphite

Documents

plasma physics

graphite maxplanck institute

necessary maxplanck

pfm maxplanck institute

memory maxplanck institute

euratom association

euratom associationgraphite

pure plasma core impurities