Modeling Carbon Diffusion in W

1
Modeling Carbon Diffusion in W Armor and
SiC Shahram Sharafat and N. Ghoniem University
of California Los Angeles, CA.
HAPL Materials Working Group Meeting UCLAMay
15 and 16, 2006
2
OUTLINE

• Current Capabilities (7 slides)
• Since 14th HAPL (2 slides)
• Planned Improvements (1 slide)

3
Current Capabilities

• Model the Carbon buildup using multi-physics PDE
• (1) Carbon mass diffusion combined and
• (2) temperature evolution
• Use spatial Carbon implantation profile at time
  t0
• Use end of shot temperature profile at time t0
• Determine Carbon buildup in tungsten armor

Carbon Implantation Profile
4
Carbon Diffusion Model

• Consider only Carbon Diffusion with R 0
• No WC or W2C formation

Carbon Diffusion in Tungsten ?
http//FusionNET.seas.ucla.edu
(Eckstein, 1999)
5
Carbon Concentration Profile
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Carbon Concentration Profile
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Quasi Steady State Diffusion Approximation

• Quasi Steady State Parameters
• Carbons per shot 1.07 ? 1019 ions
• Avg. Carbon Flux (r10.1 m, 10 Hz) 8.35 ?
  1016 m-2 s-1
• Avg. W-Temperature (50 um) 500 oC
• Diffusion Pre-exponential (Do) 3.15 ?107 m2 s-1
  
• Activation Energy (Q) 1.78 eV

8
Current Capabilities

• Model the Carbon buildup using multi-physics PDE
• (1) Carbon mass diffusion combined and
• (2) temperature evolution
• Use spatial Carbon implantation profile at time
  t0
• Use end of shot temperature profile at time t0
• Determine Carbon buildup in tungsten armor

Carbon Buildup Profile
Carbon Implantation Profile
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Carbon Diffusion Observations

• The high W-surface layer temperatures facilitate
  C diffusion in W.
• Carbon does not preferentially diffuse out from
  surface but also spreads inwards (towards F82H).
• C-to-W ratio of 1 can be reached in lt10 days (2
  mm at 10 Hz r 10.1 m, 405 MJ).
• Quasi Steady State Analysis shows that F82H steel
  wall is protected from C pickup (C reaches 20
  um lt 1 year).
• Formation of W2C and WC was not considered
  (would slow C-diffusion until C/W ratio gt 1).
• Evaporation of C from WC surface was not
  considered It would increase C loss from
  surface WC?W2C above 2000 oC(1).

1Yamada, JNM 2000
10
Since 14th HAPL

• Accumulated thermodynamic properties of WC and
  W2C (formation energies and solubility limits)
• Set up model to include reactions between W and
  C.
• Based on solubility limits of C in W (at 2000 oC
  0.05 at. ) all Carbon is consumed in
  reactions.
• Revisited C diffusion in SiC

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WC and W2C Formation
Solubility of C in W

• Need Experiments with WC including the effects of
  H and He implantation on
• Mechanical Properties of WC
• Helium and Hydrogen Release

UCLA FusionNETWORK fusionNET.seas.ucla.edu

• At 2000 oC solubility of C in Tungsten is of the
  order of 0.05 at.

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Carbon Implantation in SiC
Implantation of 12C per shot

• Carbon Implantation range 1.75 mm
• Number of C per shot 6.8x1019 C/shot

• After 1x106 shots (1.2 days) C/SiC ratio
  approaches unity (or SiC2) assuming no diffusion

• Concerns Regarding Excess Carbon in SiC
• Carbon diffuses readily (int.
  substit./detrapping)
• Carbon can bond chemically with H, D, and T
• Formation of Hydro-carbons CxHy ?T retention?

Huanchen, Ghoniem 1994

• Chemical Trapping of H, D, T slows down proton
  diffusion, defect annealing, and may interact
  synergistically with He
• Pursuing rate of Hydro-Carbon formation

13
Planned Improvements

• Complete modeling of WC and W2C formation in
  multi-physics analysis of C-diffusion
• Expecting less of a spread of Carbon ? highly
  localized WC formation (implantation profile may
  be maintained until W/C 1)
• Investigate effects of simultaneous H
  implantation ? will H compete with W for Carbon
  ??
• Model C diffusion in SiC using Multi-physics PDE
  solver.

14
WC-W2C Thermo-Mechanical Impact

• Concerns
• Lower KIC , s affects mechanical response (crack
  nucl. growth).
• Lower k, Tm may impacts thermal performance of
  FW.
• High C-content might impact Tritium release rates
  
• W2C forms at 800 oC and WC forms(1) at 1000 oC
• Helium release from WC above 1200 oC is similar
  to W(2).

2 SiC-B4C data Hino-JNM-1999
1Hatano 2005 Roth 2001