Transcript Design and Assembly of the Movable Limiter System and Proposals

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Study on C-W interactions
by Molecular Dynamics Simulations
Zhongshi Yang , Q. Xu, G. -N. Luo
Institute of Plasma Physics, Chinese Academy of Sciences,
Hefei 230031, China
G. -H. Lu
Department of Physics, Beihang University, Beijing 100083, China
Outline
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 Background
 Simulation Method
 Range distribution
 Points defects
 Conclusion
W as PFM
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W: A suitable candidate plasma facing material for
limiters and divertors of thermalnuclear fusion reactors
 good thermal conductivity
 high temperature strength
 high energy threshold for physical sputtering
 high melting point
 low vapour pressure
C- W Mixing
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carbon based materials: widely used in fusion devices as PFM.
 The divertor PFM of ITER: a combination of C and W
mixing with C on the W surface:
 carbon based materials are easy to be eroded and the
eroded C atoms will generally migrate to other locations due to
long range plasma transport processes and interact with the W
surface.
 it is necessary to understand and predict the W surface
properties and performance in the presence of C impurities.
 further understanding co-depostion of carbon and hydrogen
on W surface and the hydrogen inventory in W.
Summary of C-W interactions
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experimental data:
confined in the C projectiles with high energy of keV interacting with
W
Simulations:
based on the binary collision approximation and adopted amorphous
target materials
this work:
the molecular dynamics (MD) simulations
bond-order interatomic potential*: for modeling the ternary W–C–H
system
Focus on:
surface effect, projected range distribution of C atoms with different
incident energy on W surface.
point defects in W: vacancy and interstitial C atoms as well as their
mutual interactions
*N. Juslin, et al, J. Appl. Phys. 98 (2005) 123520
Simulation Method
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The initial computational cell:
 (001) plane normal to the incidence direction,
 dimension of 63.31 Å × 63.31 Å × 31.65 Å, consisting of 8000 atoms.
 Periodic boundary conditions imposed in the x and y directions. the atoms in the
lowest three atomic layers kept fixed .
MD steps are changed according to the kinetic energy of the incident C atoms.
The BOP is used to describe the W-W and W-C interactions.
C projectiles:
a series of kinetic energies from 0.5 eV to 200 eV,
z0 greater than the potential cutoff radius, initial x0 and y0 randomly selected
above the cell.
overall 200 runs performed to obtain significant statistics For a given incident
energy
Amorphous W cell
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simulated annealing process:
The initial structure: random cell consisting of 8000 W atoms, a density of 19.25 g/cm3, periodic
boundary conditions applied along the three directions
The system was first heated to 4000 K. Once molten, the sample was equilibrated at 4000 K for 200
ps. The liquid sample was then cooled to 300 K with a linear cooling rate of 40 Kps-1. Finally, the
system was equilibrated at 300 K for an additional 50 ps to anneal away any transient structures
(a)
W-W (amorphous W)
g(r)
5
4
3
2
1
0
20
g(r)
15
(b)
W-W (crystalline W)
10
5
0
2
4
r (Å)
6
8
10
The W-W pair distribution function g(r) for the
simulated amorphous cell in comparison with
the crystalline sample.
The first-neighbor peak is
corresponding to the first-neighbor peak
in the crystalline tungsten cell indicating
the short-range order in the amorphous
cell.
 The second peak shifts along the
distance and more high-order peaks
become broader and less well defined
with increasing distance meaning the
absence of long-range order.
Surface damage
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Snapshots of the simulation cells
after successive 50 incident energetic
projectiles’ bombardment at
1 eV (b) 5 eV (c) 10 eV
(d) 50 eV (e) 100 eV (f)200 eV
*red balls represent the C atoms
*black ones represent W atoms.
The amorphization in the top few layers is pronounced with increasing
incident energy.
The kinetic energy of the projectiles is released through fast collisions
with contiguous lattice atoms hence the increase of temperature in the
impact area and vibration amplitude of lattice atoms.
Reflection
1.0
Particle Reflection Coefficinet
0.9
0.8
(a)
0.7
0.5
0.4
0.3
0.2
0.1
1.0
0.9
0.8
1
crystalline-W
amorphous-W
Eckstein
10
100
(b)
Above 10 eV, the RC decreases monotonically
with increasing incident energy because the
energetic projectile has larger probability to be
implanted into the tungsten bulk.
Below 10 eV, the RC decreases with incident
energy and the projectiles have a larger
probability to stick on the tungsten surface.
0.7
0.6
0.5
0.4
The energy reflection upon incident energy has
a similar trend to the particle reflection.
0.3
0.2
0.1
0.0
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At 10 eV incident energy, the reflection
coefficient (RC) has a largest value near to unity.
0.6
0.0
Energy Reflection Coefficinet
crystalline-W
amorphous-W
Eckstein
1
10
Incident Energy (eV)
100
(a) Particle and (b) energy reflection coefficients of normal
incident carbon atoms on two types of tungsten surfaces,
bcc tungsten (001) surface and amorphous tungsten surface,
as a function of incident energy. Eckstein’s results*
calculated by TRIM.SP are also displayed. The statistical
* W. Eckstein, Calculated Sputtering, Reflection and Range
uncertainties are covered by the graphical markers.
Values, IPP 9/132, 2002
Fraction of counts (%) Fraction of counts (%)
1eV
14
12
10
8
6
4
2
0
5eV
14
12
10
8
6
4
2
0
10eV
15
-2
-2
0
2
4
6
8
10
12
0
2
14
(b)
D epth ( Å )
4
6
8
D epth ( Å )
10
12
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20
(a)
14
12
10
8
6
4
2
0
Average depth (Å)
Fraction of counts (%) Fraction of counts (%) Fraction of counts (%)
Projected range distribution
crystalline-W
amorphous-W
Eckstein
10
5
14
(c)
0
1
-2
0
14
12
10
8
6
4
2
0
50eV
14
12
10
8
6
4
2
0
100eV
-2
-2
2
4
6
8
10
12
0
0
2
4
6
8
10
12
4
6
8
14
(e)
Depth (Å )
2
14
(d)
D e pth ( Å )
10
12
Average depth (mean range) of atomic
carbons implanted in crystalline
tungsten at normal incidence on (001)
tungsten surface and amorphous cell
surface as a function of incident energy.
The results calculated by Eckstein using
TRIM.SP code are also shown.
14
D e p th ( Å )
The projected range
distribution of atomic C with
different incident energy on W
(001) surface: (a) 1eV, (b) 5 eV,
(c) 10 eV, (d) 50 eV,(e) 100 eV.
10
Incident Energy (eV)
100
Below 10 eV, the un-scattered C atoms are absorbed on the top layer and
can not penetrate into the bulk.
Near 10 eV, the incident atoms have largest probability to be backscattered from the surface.
Above 10 eV, the energetic projectile has larger probability to be implanted
into the W bulk and the range mean range increases as well as the range
straggling.
Around the energy of 50 eV, the mean range for the crystalline surface
exceeds the result for the amorphous surface which may be attributed to the
channeling effect.
Channeling
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160
140
50
40
120
KE (eV)
80
20
60
40
Depth (Å)
Kinetic Energy
30
Depth from the surface
100
Time variation of the kinetic
energy and projected range
of the channeled projectile with
incident kinetic energy 150eV in
W bulk
10
20
0
0
0
20
40
60 80 100 120 140 160 180
Time (fs)
In the range of incident energy of 50-200 eV, channeling occurs
along the <001> crystallographic axis.
Before 50 fs, the atom does not make close-impact collisions with
lattice atoms and has a very low rate of kinetic energy loss, dE/dx, and
slight vibration with small amplitude.
Channeled trajectory of
C atom at Ein=150eV
in the W bulk
When the ion penetrates beyond 20th atomic layers after 50 fs, the
incident ion is subjected to intense nuclear stopping. The kinetic
energy decreases dramatically and starts to vibrate with great
amplitude through successive collisions with lattice atoms and in the
end the ion comes to rest in the bulk.
Point defects calculation
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 Bombardment of crystalline W surface with energetic
atoms produces regions of lattice disorder
the defects of vacancy and interstitial C atom in bcc
W are investigated using MD calculations
BOP (eV)
Exp.- Ab. (eV)
Ef-v
1.69
2.8--5.38
mono-vacancy
Em-v
1.3
1.7--2.02→1.5
vacancy-migration
Ef-Oh
2.57
---
octahedral interstitial
Ef-Th
2.91
---
tetrahedral interstitial
Ef-sub
3.39
---
substitutional
Eb1
2.35
2.01
vacancy-- 1st Oh
Eb2
0.041
--vacancy- -2nd Oh
 Ev = E((N-1)W) - (N-1)Eref(W)
 Eint = E(NW + C) - NEref (W) - Eref (C)
 Esub = E((N-1)W + C) - (N-1)Eref (W) - Eref (C)
 Eb(V-C) = Ef (V) + Ef (C) – Ef (V-C)
Interstitial configuration
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The formation energies for the octahedral site:
2.57 eV
The formation energies for the tetrahedral site:
2.91eV
The migration energy for the interstitial C atom
from octahedral to neighboring octahedral site
through the tetrahedral saddle point
0.34 eV
(A) the octahedral and (B) the
tetrahedral interstitial sites in bcc W
lattice
the C atoms prefer occupying the octahedral to
the tetrahedral interstitial sites
in agreement with previous study based on the
concept of elastic dipole *
* Gmelin Handbook of Inorganic Chemistry, 8 ed., Syst. No. 54, Tungsten, Suppl. Vol.
A2, Spring-Verlag, Berlin, Heidelberg, New York, Tokyo, 1987.
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Structural response of the W lattice
to the presence of interstitial C atom
 The relative distance of the first
neighbors of C increases by a factor
⊿d1/d1 = 0.236 along the <100> direction
 The second neighbors are slightly
decreased by a factor ⊿d2/d2 = 0.015
along the <110> direction
The lattice distortion
around the C atom in Oh configuration
*the dash balls denoted the original positions of the
lattice W atoms and octahedral interstitial C atom
*the solid balls represent the ultimate configuration
after sufficient structure relaxation
 These deformations are attributed to
energy difference during the system
relaxation
Conclusions
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The interaction between low-energy atomic C with W surface has
been studied by MD simulations using a bond-order potential.
Both particle and energy reflection coefficients are calculated as a
function of incidentenergy in the in the range from 0.5eV to 200eV.
Mean range and projected range distribution of C with different
incident energy on tungsten surface are discussed.
Vacancy formation energy and the migration energy, C interstitial
and substitutional formation energies have been calculated.
Most stable configuration of an interstitial C atom in W is in Oh
position;Lattice distortion around the C atom in Oh configuration
occurs along <100> and <110> directions
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