Max-Planck-Institut für Plasmaphysik EURATOM Assoziation K. Schmid SEWG meeting on mixed materials...
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Transcript of Max-Planck-Institut für Plasmaphysik EURATOM Assoziation K. Schmid SEWG meeting on mixed materials...
Max-Planck-Institutfür PlasmaphysikEURATOM Assoziation
K. Schmid SEWG meeting on mixed materials
Parameter studies for the Be-W interaction
Klaus Schmid
K. Schmid, SEWG meeting on mixed materials
• Introduction
Outline
• Summary
• Modelling Be layer deposition on W
• Pure kinematics: TRIDYN
• Including diffusion and sublimation: ERODEPDIF
• Simple flux balance model
K. Schmid, SEWG meeting on mixed materials
Introduction
Deposition of mixed Be/W layers in ITER has been hyped during the past two years
Deposition of mixed Be/W layers in ITER has been hyped during the past two years
ITER Be erosion in main chamber
Be transported to Divertor
Potential Be layer deposition on C and W
ITER main plasma facing wall: Be, W, C
Depends on ratio of influx to Be loss mechanisms
Depends on ratio of influx to Be loss mechanisms Interdiffusion can lead to formation of
Be/W alloys
Interdiffusion can lead to formation of Be/W alloys
K. Schmid, SEWG meeting on mixed materials
Introduction
Higher W evaporation rate than pure W
Potential for large W influx into plasma due to melt layer ejection or evaporation Potential for large W influx into plasma due to melt layer ejection or evaporation
Lower melt temperature than pure W
Ch. Linsmeier
What are the issues with Be rich Be/W mixed layers ?
K. Schmid, SEWG meeting on mixed materials
IntroductionAvailable experimental data
PISCES-B plasma exposures
Polished W samples are exposed to a Be seeded D plasma
Vary temperature, Be flux fraction and ion energy
Non floating ion energies No Be layer growth
For temperatures > 1300K No Be layer growth No be rich alloys
ITER W baffles will operate in an ion energy and surface temp. range that will hinder Be layer formation
ITER W baffles will operate in an ion energy and surface temp. range that will hinder Be layer formation
K. Schmid, SEWG meeting on mixed materials
IntroductionAvailable experimental data
<Particle energy>
Sur
face
tem
pera
ture
fBea
fBeb
fBea < fBe
b
Be layer deposition region
Be deposition is limited by either sputtering, sublimation or both
? What is the parameter range (Te, TSurf, fBe) where Be layer deposition and alloy formation are possible
? What is the parameter range (Te, TSurf, fBe) where Be layer deposition and alloy formation are possible
Sublimation limit
Sputter limit
K. Schmid, SEWG meeting on mixed materials
0 100 200 300 400 5000.0
0.2
0.4
0.6
0.8
1.0
Total fluence x 1016 cm-2
FLC: 0.0 FLC: 1000.0 FLC: 2000.0 FLC: 3000.0 FLC: 6000.0 FLC: 14000.0
Be
co
nc
en
trat
ion
Depth (A)
10eV Ion energy, 0.4% Be
Modelling Be layer deposition on WPure kinematics: TRIDYN
Expected Be depth profile in PISCES-B experiments: Floating energies
No Be erosion Thick Be layer deposit
Agrees with PISCES-B results
Accumulated fraction of Be:PISCES-B 5x10-3 TRIDYN 4x10-3
K. Schmid, SEWG meeting on mixed materials
0 50 100 150 2000.0
0.2
0.4
0.6
0.8
1.0 Tot. fluence x 1016 cm-2
FLC: 5000.0 FLC: 10000.0 FLC: 20000.0 D-Range
Be
co
nce
ntr
atio
n
Depth [A]
75eV Ion energy, 0.15% Be
Modelling Be layer deposition on WPure kinematics: TRIDYN
Expected Be depth profile in PISCES-B experiments: Non floating energiesE
rosi
on
zone
Ero
sion
zo
ne
Deposition zone
Deposition zone
High re-erosion rate depletes surface from Be
Be implanted beyond erosion zone accumulates
TRIDYN partly explains low temp. non floating PISCES results
K. Schmid, SEWG meeting on mixed materials
ERODEPDIF Simulates Be deposition and re-erosion including:
• Diffusion
• Sputtering
• Sublimation
• Reflection
All these processes are considered to be dependent on the surface composition Very important for Be on W
TRIDYN won’t work for Be plasma fractions < 10-5 due to statisticsTRIDYN won’t work for Be plasma fractions < 10-5 due to statistics
TRIDYN can’t handle diffusion or sublimationTRIDYN can’t handle diffusion or sublimation
Modelling Be layer deposition on WIncluding diffusion and sublimation: ERODEPDIF
Fick’s second law
Predetermined reflection yield
Arrhenius temperature dependence
Predetermined sputter yield
K. Schmid, SEWG meeting on mixed materials
Modelling Be layer deposition on WIncluding diffusion and sublimation: ERODEPDIF
Erosion zone
Depos. zone
Diffusion zone
Thickness of Erosion and deposition zone are kept constant by moving material to and from the bulk Simulates layer growth
The resulting depth profile diffuses according to Fick’s second law with a concentration dependent diffusion coefficient
Erosion (sublimation and sputtering) occurs only in the erosion zone, deposition occurs in both the erosion and the deposition zone
ERODEPDIF Surface model
K. Schmid, SEWG meeting on mixed materials
Modelling Be layer deposition on WIncluding diffusion and sublimation: ERODEPDIF
Sputter and reflection yield as function of surface concentration
In a Be/W mixture Be is sputtered by D reflected in the bulk
ERODEPDIF uses linear functions to approximate Y(C) and R(C)
In a Be/W mixture the Be reflection & sputter yields depend on surface composition
BeBeBeBeBeBe CRRCYY and
0.0 0.2 0.4 0.6 0.8 1.00.00
0.05
0.10
0.15
0.20
Y0 and Y1 scale
relative to Bohdansky sputter formula:<Y1/YBohd> = 1.74
<Y0/YBohd> = 5.84
Total Be sputter yield for 75eV ion energy
Linear fit
To
tal B
e s
pu
tte
r y
ield
Be concentration
Y0
Y1
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
Calculated reflection yield 10eV to 200eV
Linear fit
Re
fle
cti
on
yie
ld
Be concentration
Reflection yield only shows little energy but strong composition dependence
Total sputter yield scales linearly with composition
Linear function parameters can be deduced from Bohdansky sputter formula
K. Schmid, SEWG meeting on mixed materials
Concentration and temperature dependent inter-diffusion coefficient for Be and W
0 1000 2000 30000.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
2.0x10-19
4.0x10-19
T = 1073K Initial 7200 s Calc 7200 s 36000 s Calc 36000 s
Be
-co
nc
en
tra
tio
n
Depth (A)
Be concentration
D(C
) (m
2 s
-1)
8.8x10-4 9.0x10-4 9.2x10-4 9.4x10-4 9.6x10-4 9.8x10-41.00x10-15
1.00x10-14
1.00x10-13
1.00x10-12
Ln
(D)
(m2
s-1 )
1/T (K-1)
D (cm2 s-1) Linear fit
Activation energy from linear slope 4.5eV
Concentration dependence Temperature dependence
TKEExpCDTCD
B
DBeBe ~
,
Modelling Be layer deposition on WIncluding diffusion and sublimation: ERODEPDIF
D(T) from reaction zone thicknesD(C) from modelling of depth profiles
K. Schmid, SEWG meeting on mixed materials
Modelling Be layer deposition on WIncluding diffusion and sublimation: ERODEPDIF
The sublimation rates and energies for pure Be or W are well known But what about mixed Be/W surface ?
Given the heat of formation UMIX for a given mixture the surface binding energy that has to be overcome during sublimation or sputtering can be calculated:
Given the heat of formation UMIX for a given mixture the surface binding energy that has to be overcome during sublimation or sputtering can be calculated:
ABBBAABAMIX VVVccZU
2
1
number onCoordinati Z
energy binding earHeteronucl
energy binding rHomonuclea,
AB
BBAA
V
VV
Solving for VAB yields:
The surface binding energy (SBE) then reads for the binary Be/W system:
BBAA
MIXBA
MIXBBAAAB VV
Z
UccZ
UVVV
2
1
12
1
BeWwWWWESBE
WBewBeBeBeBeSBE
VcVcE
VcVcE
,,,
,,,
Be SBE is increased W SBE is decreased
Be SBE is increased W SBE is decreasedeVV
eVV
WW
BeBe
68.8
2.3
,
,
Increased W sublimation Decreased Be sublimation
Increased W sublimation Decreased Be sublimation
K. Schmid, SEWG meeting on mixed materials
Modelling Be layer deposition on WIncluding diffusion and sublimation: ERODEPDIF
0 100 200 3000.0
0.2
0.4
0.6
0.8
1.0Fluence x1016 cm-2
TRIDYN 5400 18000 50000
ERODEPDIF 5400 18000 50000
Be
co
nc
en
tra
tio
n
Depth (A)
Comparison of TRIDYN and ERODEPDIF for PISCES-B conditions at low temperatures (No diffusion or Sublimation)
ERODEPDIF closely matches TRIDYN results at low temperatures
ERODEPDIF closely matches TRIDYN results at low temperatures
75eV Ion energy 0.15% Be plasma fraction
Simulate high temperature cases including sublimation & diffusion
K. Schmid, SEWG meeting on mixed materials
0 2000 4000 60000.0
0.2
0.4
0.6
0.8
1.0 1073K 1320K
Be
co
nc
en
tra
tio
n
Depth (A)
Ion energy: 10eV no sputteringBe flux fraction: 0.4%
Total fluence: 5.4x1024 m-2
Modelling Be layer deposition on WIncluding diffusion and sublimation: ERODEPDIF
Model high temperature PISCES-B exposures with ERODEPDIF: Low energies
Due to lack of sputtering surface concentration ~1
Be12W alloy comp.
At 1073K a thick pure Be layer forms + 200A Be12W
At 1320K strong diffusion & sublimation hinder alloy formation
Result agrees with PISCES-B data
K. Schmid, SEWG meeting on mixed materials
Modelling Be layer deposition on WIncluding diffusion and sublimation: ERODEPDIF
Model high temperature PISCES-B exposures with ERODEPDIF: High energies
0 500 1000 1500 20000.01
0.1
1 300K 1073K 1320K
Be
co
nc
en
tra
tio
n
Depth (A)
Ion energy: 75eVBe flux fraction: 0.4%
Total fluence: 5.4x1024 m-2
At 300K a thick Be layer forms but no Be/W alloying
At 1073K a thick Be12W layer forms
At 1320K a sublimation hinders Be layer formation
Due to high sputter and/or sublimation losses the Be surface
concentration is ~0 in all cases
Simple flux balance models are have difficulties predicting layer formation
Be12W alloy comp.
Sublimation and sputtering are diffusion limited Results depend on diffusion coefficient
Sublimation and sputtering are diffusion limited Results depend on diffusion coefficient
0 200 400 600 800 10000.001
0.01
0.1
1
1320K with varying diffusion coefficient From experimental diffusion data 100 times lower 10 times lower
Be
co
nc
en
tra
tio
n
Depth (A)
K. Schmid, SEWG meeting on mixed materials
Modelling Be layer deposition on WSimple flux balance model
Assumptions:
Implantation & Erosion (Sputtering, Sublimation) occur homogeneously in the same depth interval
Particle energies and temperatures are low enough such that no W erosion occurs
Be surface concentration is given by Be erosion/deposition flux balance alone
Be surface concentration is given by Be erosion/deposition flux balance alone
0Tt, SputImplSublDiff T
)(
),(Tt,
Subl0Subl
0Diff
TtCT
txErfctC
0e0Sput
00Impl
,TY
R1
CtC
CBe
tC0
K. Schmid, SEWG meeting on mixed materials
Modelling Be layer deposition on WSimple flux balance model
Surface and plasma temperature range where Be layer growth occurs
ITER divertor conditions Te ~ 20 – 40eVTSurf < 1000K
More than 5% Be plasma concentration needed for layer growth
PISCES-B Parameter range
K. Schmid, SEWG meeting on mixed materials
Summary/Outlook
Experiments at PISCES-B indicate the Be layers only form at low (~10eV) particle energies and temperatures (~1000K)
Modelling calculation can explain the PISCES-B results(quantitative comparison difficult due to lack of Be depth profiles)
Calculations suffer from lack of thermodynamic data for the Be/W system
Be / W interdiffusion
Be sublimation from Be / W alloys
Depth profiling of Be in PISCES-B exposed samples + Comparison with calculated depth profiles