Max-Planck-Institut für Plasmaphysik EURATOM Assoziation K. Schmid SEWG meeting on mixed materials Parameter studies for the Be-W interaction Klaus Schmid.

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


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


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 ?


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


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


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


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


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



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



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


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 ~

,


D(T) from reaction zone thicknesD(C) from modelling of depth profiles



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



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


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


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



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)


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


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


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

Max-Planck-Institut für Plasmaphysik EURATOM Assoziation K. Schmid SEWG meeting on mixed materials Parameter studies for the Be-W interaction Klaus Schmid.

Documents

schmid sewg meeting

mixed materials modelling

mixed materials erodepdif

layer deposition region

mixed materials concentration

sublimation modelling

mixed bew surface

layer formation