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

2. 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

3. K. Schmid, SEWG meeting on mixed materials Introduction 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 Interdiffusion can lead to formation of Be/W alloys

4. 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 Lower melt temperature than pure W Ch. Linsmeier What are the issues with Be rich Be/W mixed layers ?

5. K. Schmid, SEWG meeting on mixed materials Introduction Available 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

6. K. Schmid, SEWG meeting on mixed materials Introduction Available experimental data Surface temperature f Be a f Be b f Be a < f Be b Be layer deposition region Be deposition is limited by either sputtering, sublimation or both ? What is the parameter range (T e, T Surf, f Be ) where Be layer deposition and alloy formation are possible Sublimation limit Sputter limit

7. K. Schmid, SEWG meeting on mixed materials Modelling Be layer deposition on W Pure 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

8. K. Schmid, SEWG meeting on mixed materials Modelling Be layer deposition on W Pure kinematics: TRIDYN Expected Be depth profile in PISCES-B experiments: Non floating energies Erosion 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

9. 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 wont work for Be plasma fractions < 10 -5 due to statistics TRIDYN cant handle diffusion or sublimation Modelling Be layer deposition on W Including diffusion and sublimation: ERODEPDIF Ficks second law Predetermined reflection yield Arrhenius temperature dependence Predetermined sputter yield

10. K. Schmid, SEWG meeting on mixed materials Modelling Be layer deposition on W Including 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 Ficks 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

11. K. Schmid, SEWG meeting on mixed materials Modelling Be layer deposition on W Including 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 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

12. K. Schmid, SEWG meeting on mixed materials Concentration and temperature dependent inter-diffusion coefficient for Be and W Concentration dependence Temperature dependence Modelling Be layer deposition on W Including diffusion and sublimation: ERODEPDIF D(T) from reaction zone thicknes D(C) from modelling of depth profiles

13. K. Schmid, SEWG meeting on mixed materials Modelling Be layer deposition on W Including 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 U MIX for a given mixture the surface binding energy that has to be overcome during sublimation or sputtering can be calculated: Solving for V AB yields: The surface binding energy (SBE) then reads for the binary Be/W system: Be SBE is increased W SBE is decreased Be SBE is increased W SBE is decreased Increased W sublimation Decreased Be sublimation Increased W sublimation Decreased Be sublimation

14. K. Schmid, SEWG meeting on mixed materials Modelling Be layer deposition on W Including diffusion and sublimation: ERODEPDIF Comparison of TRIDYN and ERODEPDIF for PISCES-B conditions at low temperatures (No diffusion or Sublimation) ERODEPDIF closely matches TRIDYN results at low temperatures 75eV Ion energy 0.15% Be plasma fraction Simulate high temperature cases including sublimation & diffusion

15. K. Schmid, SEWG meeting on mixed materials Modelling Be layer deposition on W Including diffusion and sublimation: ERODEPDIF Model high temperature PISCES-B exposures with ERODEPDIF: Low energies Due to lack of sputtering surface concentration ~1 Be 12 W alloy comp. At 1073K a thick pure Be layer forms + 200A Be 12 W At 1320K strong diffusion & sublimation hinder alloy formation Result agrees with PISCES-B data

16. K. Schmid, SEWG meeting on mixed materials Modelling Be layer deposition on W Including diffusion and sublimation: ERODEPDIF Model high temperature PISCES-B exposures with ERODEPDIF: High energies At 300K a thick Be layer forms but no Be/W alloying At 1073K a thick Be 12 W 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 Be 12 W alloy comp. Sublimation and sputtering are diffusion limited Results depend on diffusion coefficient Sublimation and sputtering are diffusion limited Results depend on diffusion coefficient

17. K. Schmid, SEWG meeting on mixed materials Modelling Be layer deposition on W Simple 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

18. K. Schmid, SEWG meeting on mixed materials Modelling Be layer deposition on W Simple flux balance model Surface and plasma temperature range where Be layer growth occurs ITER divertor conditions T e ~ 20 – 40eV T Surf < 1000K More than 5% Be plasma concentration needed for layer growth PISCES-B Parameter range

19. 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