Hydrogen trapping and erosion of W crystal

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Hydrogen trapping and erosion of W crystal

• Daiji Kato
• National Institute for Fusion Science, Toki
  509-5292, Japan
• Collaboration with H. Iwakiri1, K. Morishita2, K.
  Ohya3, T. Tanabe4
• 1Univ. of the Ryukyu, 2Kyoto Univ., 3Tokushima
  Univ., 4Kyushu Univ.

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OUTLINE

• Hydrogen trapping by mono-vacancy in W (bcc)
  crystals
• Case study statistical mechanics of W crystals
  eroded with hydrogen atoms and mono-vacancies
• Research plan
• Introduction of MD study on reflection and
  sputtering of hydrogenated C and W/C mixed layers
  (K. Ohya)

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Multiple hydrogen trapping by mono-vacancy,
pointed out by Myers et al. (1986)
Besenbacher et al., J. Appl. Phys. 61 (1987)
Binding energies of hydrogen atoms trapped at
octahedral sites around a mono-vacancy in
ferritic iron (bcc). Dotted lines are the binding
energies deduced from experimentally observed
hydrogen retention. Solid line stands for
solution energy of interstitial hydrogen atom
(tetrahedral-site). ? effective medium theory
(EMT).
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Binding energies deduced from ion-beam experiment
and calculations by effective medium theory
Myers et al., JNM 165 (1989)
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Hydrogen cluster at mono-vacancy in W crystal
DFT, PBE version of GGA (VASP code) Energy
cut-off350 eV 6x6x6 Monkhorst-pack k-point
grids 54 atom bcc super cell
Cell shape and lattice configuration were relaxed
until the lowest total energy was obtained for a
given cell volume.
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Energy level variation, molecular hydrogen is not
stable inside mono-vacancy (?)
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What determines the stability of VHn complexes in
W
Strong hybridization of H-1s and W-5d orbital,
indicating covalent bonding character.
H atoms being embedded in high density conduction
electrons of W.
Partial densities of states (DOS) projected to
the hydrogen atom and its nearest-neighbor
tungsten atom for two cases a VH complex and an
interstitial hydrogen atom in the tungsten
super-cell, respectively.
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Zero-point vibration energy of VH in W
Assuming harmonic oscillation around an
equilibrium point, Hessian matrix is evaluated
and diagonalized.
3 normal modes
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Zero-point vibration energy of VH2
In-phase
Anti-phase
6 normal modes
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Zero-point vibration energy of VH3
9 normal modes
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Binding energy of VHn complex
The 3rd and 5th hydrogen atoms have binding
energies insensitive to zero-point vibration
effects. Cancelation of zero-point energies
between interstitials and hydrogen clusters.
4th and 6th show drops in the binding energies,
which may be ascribed to higher symmetries of
their whole configurations of super
cells. Perturbation from some impurities in W may
break their symmetric configurations, and
increase the binding energies. It is a sort of
the Jahn-Teller effect.
The first and second hydrogen atoms influence
little each other. Vacancies dressed with three
or more hydrogen atoms would be less abundant at
ambient condition of hydrogen pressure.
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Experimental values for W

• Perturbed angular correlation technique using
  111In probe dissociation energies of VHn are
  1st 1.55 eV, 2nd 1.38 eV, 3rd 1.1 eV (Fransens
  1991). Binding energies are obtained by
  subtracting H migration energies.
• Inferred from TDS peaks binding energies are 1st
  1.4 eV (associated with 850 K peak), 2nd 0.85 eV
  (475 K peak) (Garcia-Rosales 1996).

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Statistical mechanics of eroded W bcc crystal

• N0 tungsten atoms, NH hydrogen atoms, and n
  mono-vacancies.
• rn hydrogen atoms are trapped among 6n
  octahedral sites of the mono-vacancies.
• NH rn hydrogen atoms are distributed over 6N0
  interstitial (tetrahedral) sites.

Partition functions
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Thermo-statistic properties of eroded W bcc
crystal
Free energy
Average number of trapped hydrogen atoms
Formation energy of VHn complex
Concentration of VHn complex
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Superabundant vacancy induced by H-rich condition
Mobile H atoms
Rapid increase of vacancy concentration is
associated with increase in the average number of
hydrogen atoms trapped by the vacancy. At higher
temperatures, larger amount of hydrogen atoms can
be accommodated in the interstitial sites (mobile
hydrogen atoms), which suppresses
vacancy-hydrogen complex formation and keeps the
vacancy concentration at lower levels.
Average number of trapped H atoms
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Summary (I)

• Mono-vacancy in W bcc crystal can trap multiple
  hydrogen atoms with appreciable binding energies.
  (first-principle calculations)
• Stability of VH complexes in W is described in
  terms of covalent bonding via hybridization of
  H-1s and W-5d orbital.
• Equilibrium thermo-statistic model gives
  enhanced vacancy (hydrogen trap) concentration in
  an eroded W crystal under hydrogen-rich
  conditions.

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Enhanced D-retention in Mo induced by high-flux
low-energy ion implantation
Wright, 18th PSI (Toledo, Spain, May, 2008)
?D 1021 m-2s-1 High rate of low-energy ion
implantation into a target with very low natural
hydrogenic solubility (lt10-7 D/Mo for conditions
in DIONISOS)
TMo 500 K Vbias 100 V
rimplant 10 nm
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New vacancy creation under super-saturated
hydrogen condition
Accommodation of background matrix under
hydrogen-rich condition. Equilibrium of V/H/W
mixed materials
Implanted D super-saturates The implantation zone.
W atom is displaced and a vacancy is formed.

• What experimental factors influence strength and
  formation of stress fields?
• Plasma flux density sets rate of implantation
  (source)
• Hydrogenic solubility sets saturation limit
  (boundary condition)
• Diffusion/surface recombination rate-limiting
  process removes D from implantation zone (sink).

Wright, 18th PSI (May, 2008)
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Summary (II)

• The present model does not conflict with a
  speculation suggested from the DIONISOS
  experiments 18th PSI (2008), that new hydrogen
  traps may be created by super-saturated
  low-energy hydrogen implantation.
• In low hydrogen solution, large uncertainties in
  transport coefficients may be ascribed to
  different abundance of natural traps inherent in
  low-solubility materials. However, in the present
  work we showed that at elevated hydrogen
  concentrations, the vacancy concentration itself
  could depend on the hydrogen concentration
  strongly.

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Research plan in the next few years

• Present study is extended involving larger VH
  complexes.
• Vacancy cluster (bubble) formation is studied
  with Fokker-Plank equation (and Monte-Carlo
  simulation).
• Influence of VH complexes to effective H
  transport coefficients (heat of solution,
  diffusion coefficient etc) in W (and Be)
  crystals.
• (Comparison with experiments of hydrogen
  solubility, diffusivity and micro structure
  change for mono-crystal W as functions of
  hydrogen concentration, material temperature,
  etc.)

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Theory and Code Development for Evaluation of
Tritium Retention Exhaust in Fusion Reactor
Grant in Aid for Scientific Research for Priority
Areas (2007-2011) Tritium Science and Technology
for Fusion Reactor
RESEARCH PROJECT A02
K. Ohya Institute of Technology and Science, The
University of Tokushima,

• Members
• JAPANESE SCIENTISTS
• K.Shimizu1), T.Takizuka1), H.Kawashima1),
  K.Hoshino1), Y.Tomita2),
• H.Nakamura2), D.Kato2), N.Ashikawa2),
  G.Kawamura2), A.Ito2,3), Y.Tanaka4),
• A.Hatayama5), M. Toma5), T.Ono6), T.Muramoto6),
  M.Wada7), T.Kenmotsu7),
• K.Yamazaki3), J. Kawata8), H. Kawazome8), K.
  Nishimura9), K. Inai 10)
• 1)JAEA, 2)NIFS, 3)Nagoya Univ., 4)Kanazawa Univ.,
  5)Keio Univ., 6)Okayama Univ.Sci.,
• 7)Doshisha Univ., 8)Takuma College Tech, 9)Numazu
  College Tech., 10)Univ. Tokushima
• OVERSEAS SCIENTISTS
• Kirschner1), D. Tskhakaya2), R. Schneider3)
• 1)Forschungszentrum Juelich, 2)Innsbruck Univ.,
  3)Max-Planck Institut fuer Plasmaphysik

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Preparation of Plasma Facing Walls Using
Molecular Dynamics Simulation
To prepare the fusion-relevant wall surface
W crystal

H-H, H-C, C-C Brenner potential
H-W, C-W, W-W Juslin et al., JAP (2005)
?Hydrogen concentration in the layer can be
varied with impact energy of H.
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Molecular Dynamics Simulation of Hydrocarbon
Reflection from Plasma Facing Walls
For hydrogenated amorphous C layer
?With increasing H content (x of CHx),
reflection coefficient increases. ?With
increasing energy, the coefficient
decreases. ?Heavy hydrocarbons (C2Hx) are
reflected more.
? Amount of H implanted in hydrogenated and
amorphized C is one order of magnitude
greater than other materials. (for CH4
incidence, maximum value of
implantation is 4)
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?Mixed amorphous layers decreases the
coefficient.
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Molecular Dynamics Simulation of Chemical
Sputtering of Fusion-Related Materials
(1) Redeposited carbon layer
? 200 H atoms bombard each surface of amorphized
carbon with different H/C.
?Instantaneous yield of chemical sputtering is
strongly dependent on H/C of redeposited carbon.
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