1. Modeling Carbon Diffusion in W-Armor
Shahram Sharafat and Nasr Ghoniem
Graduate Students:
Jaafar El-Awady
Michael Andersen
Qyiang Hu
Jennifer Quan
Andrew Chen
Wen Guo (Alice Ying)
University of California Los Angeles, CA.
The High Average Power Laser (HAPL) Program Workshop Rochester, New York November 8 and 9, 2005

2. OUTLINE Brief Summary of UCLA Activities: Ion Implantation:
Roughening Modeling
Interface Bond Strength Measurements
Ion Implantation:
Carbon Implantation Profile
Multi-physics Simulation
Buildup ?

3. Modeling Surface Roughening
POSTER
Grooving patterns can appear in long rows, but crosshatch ends the valleys from continuing indefinitely.
TOOLS:
(1) Sharp Interface Approach (2) Phase-Field Modeling:
Solution is a summation of free energies from elastic (fe), gravity (fgravity), double well potential (fdw), and an equilibrium control (fc).
L.O. Eastgate Phys.Rev.E,65
Simulated phase field solution of a crack.
Michael Andersen, (Ph.D. Thesis)
Goal: Predict crack formation by modeling surface roughening
Surfaces ROUGHEN to alleviate stresses.
Solid buildup decreases elastic energy by growing tips (low stress).
“Deepening valleys” (material with high elastic energy is removed).
Sources of Stress:
Thermo-mechanical (Biaxial)
J. Blanchard HAPL Nov.’05

4. Measurement of W - F82H Bond Strength Using Laser Spallation Interferometry
POSTER
Jaafar El-Awady, Jennifer Qua, et. al.
Goal: Quantify the Interface bond strength between tungsten and F82H
Approach: Laser Spallation interferometry measurements
Experiment: ITER (JAERI) HIP’d W/F82H samples were tested. Used 6 different laser fluence energies to determine the critical energy.
50 mm W
F82H
D = 20 mm
Laser Fluence: 1065 mJ
Interfacial stress history
Laser Fluence (mJ):
613
1065
1329
1577
1708
1737
Failure:
No Failure
Some Cracks generates at the interface
Severe interfacial damage
Severe interfacial Damage
F82H W
100mm
Laser Fluence: 1708 mJ
Delamination
Interface Crack
Results Severe interfacial damage occurred above 1577 mJ. Analysis results in a bond strength between 300 and 450 MPa (depending on Young’s Modulus of W; 390 and 195 GPa, respectively)

5. Ion Implantation: (1) Helium (2) Carbon

6. Carbon Implantation Profile (SRIM)
Threat Spectra (405 MJ):
C = 1.07x1019 /shot
Peak: ~0.4 um
Avg. C/ W Ratio: ~ 2.5x10-7 (apa)
Pellet Geometry:
CH layer 3 mm
r = mm
C/ W~4.1x10-7 (apa)
DT gas
DT fuel
1 .734mm
2.264mm
DT ablator
(+ low density CH foam)
2.059mm
3mm solid CH shell
148mm
empty foam
100mg/cc
2.415mm
(Perkins, HAPL Oct’04)

7. C-Buildup: No Carbon Diffusion (SRIM 2003)
HAPL June ’05
154 MJ Target

8. Carbon Diffusion Model
Multi-physics problem
Consider Carbon Diffusion with R = 0: No WC or W2C
Future work will consider carbide formation (R ≠ 0)
Carbon Diffusion in Tungsten ?
(Eckstein, 1999)
(Eckstein, 1999)

9. Multi-physics Diffusion Solution
Used ANSYS to solve the diffusion equation:
it worked
Needed to couple temperature with diffusion in ANSYS:
did not work
Briefly considered:
Neutron Transport
Use COMSOL (PDE Solver) to solve the coupled thermal & diffusion model
Temperature: T(x,t)
IC: Implantation Profile C(to)
Range (um)
C / W (apa)
( fit SRIM data )

10. Carbon Concentration Profiles
IC Profile C(to)
Range (um)
C / W (apa)
14 mm
1 mm

11. Carbon Concentration Profile

12. Carbon Concentration Profile

13. Quasi Steady State Diffusion Approximation
Quasi Steady State Parameters:
Carbons per shot  1019 ions
Avg. Carbon Flux (r=10.1 m, 10 Hz) 8.35  1016 m-2 s-1
Avg. W-Temperature (50 um) oC
Diffusion Pre-exponential (Do) 107 m2 s-1
Activation Energy (Q) eV
Quasi Steady State Carbon Concentration:
The F82H cooling structure remains protected from Carbon (50 um W-armor)
T = 500 oC

14. 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 <10 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; < 1 year).
Formation of W2C and WC was not considered (would slow C-diffusion until C/W ratio > 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

15. 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).
1Hatano 2005; Roth 2001
2 SiC-B4C data: Hino-JNM-1999