J. Boisse 1,2, A. De Backer 1,3, C. Domain 4,5, C.S. Becquart 1,4

Transcription

1 MODELLING SELF TRAPPING AND TRAP MUTATION IN TUNGSTEN USING DFT AND MOLECULAR DYNAMICS WITH AN EMPIRICAL POTENTIAL BASED ON DFT J. Boisse 1,2, A. De Backer 1,3, C. Domain 4,5, C.S. Becquart 1,4 1 Unité Matériaux et Transformations, UMET, UMR 8207, Villeneuve d Ascq, France 2 Laboratoire d Energétique et de Mécanique Théorique et appliquée, LEMTA, UMR 7563, Vandoeuvre-lès-Nancy, France 3 CCFE, Culham Science Centre, Abington, Oxon OX14 3DB, United Kingdom 4 Laboratoire commun EDF-CNRS Etude et Modélisation des Microstructures pour le Vieillissement des Matériaux (EM2VM), France 5 EDF R&D, MMC Centre des Renardières, Moret sur Loing, France EUROPEAN FUSION TECHNOLOGY PROGRAMME: CEA Contract V

2 Vacancies Context : Plasma facing Materials in Fusion Interstitials Helium - very low solubility in solids -(n,α) reactions -implantation -tritium decay - moves very quickly (mobile below 5 K in W [Soltan]) - can be trapped by many objects of the microstructure: vacancies, dislocations, GBs... - forms platelets and bubbles... - contributes to swelling, causes intergranular embrittlement, produces roughening and blistering at metal surfaces - SIA LOOPS H. Iwakiri, K. Yasunaga, K. A.S. Soltan, R. Vassen, P. Jung, J. Appl. Phys. 70 (1991) 793. Morishita, N. Yoshida, J. Nucl. Mater (2000)

3 Context: PFCs in Fusion Reactors Vacuum vessel : 20 x 10 m Divertor plate subject to irradiation, He, H etc... Microstructure evolution? Behavior of He in W W Combination of experiments (collaboration with M.F. Barthe CEMHTI) + multiscale modeling (Object Kinetic Monte Carlo (OKMC) + DFT calculations + MD + BCA to bridge to atomic scale + modeling of PA signal) 54 x 13 tons = 700 tons: divertor 3

4 First principles calculations and MD DFT (VASP, PAW, PW91): find ground state configurations of W containing: - m Vacancy (V) - n Helium (He) - p SIA (W) Constant volume calculations to relax atomic position Supercells with Periodic Boundary Conditions 1024 W atoms + 2x2x2 k-points MD to explore as many W-nHe.mV.pSIA configurations as possible! W-He very new interatomic potential E mig (He) very low: ~0.06 ev, He migration for T < 5K Agreement with Soltan results Eb He-He high: ~1 ev Consistent with tendency to form clusters! C.S. Becquart and C. Domain, Phys. Rev. Lett. 97 (2006) N. Juslin, B.D. Wirth, J. Nucl. Mater. 432 (2013) 61. A.S. Soltan, R. Vassen, P. Jung, J. Appl. Phys. 70 (1991)

5 He binding energy to pure He clusters en ergy (ev) (MD) nhe --> He + (n-1)he (DFT) nhe --> He + (n-1)he nu mber of He - n He binding energy to pure He clusters 5

6 Self Trapping / Trap Mutation - He clusters can self trap: nhe + He ---> (n+1) He.v.I - nhe.mv.mi clusters can emit more FP: trap mutation DFT results Many self interstitial atoms ==> dislocation loop: loop punching Greenwood (1959): G.W. Greenwood, A.J. E. Foreman, D.E. Rimmer, J. Nucl. Mater. 4 (1959) 305 6

7 Ground state config. + activation energies Self trapping Trap mutation Trap mutation Growing process 5He 5He.v SIA 10He.v 10He.2v SIA GS: 1- MD simulations with Juslin s potential (8 8 8 BCC cells = 1024 W atoms) 2 - DFT (1024 atoms 8kpts) calculations 3 - binding energies / ST or TM energies AE: MD simulations with Juslin s potential ( BCC cells ) at different T + NEB calculations 7

8 Self trapping energies 4 3 / 2 1 en nergy (ev) (MD) nhe --> He + (n-1)he (MD) nhe --> nhe.1v.sia (DFT) nhe --> He + (n-1)he (DFT) nhe --> nhe.1v.sia number of He - n Self trapping will take place when n > 6 8

9 Self Trapping (ST) for 8He cluster / 9

10 Self trapping and trap mutation energies DFT results SIA far SIA close 10

11 SIA cluster binding energy DFT results (2kpts) nhe.sia --> nhe + SIA (2kpts) nhe.1v.sia --> nhe.1v + SIA (2kpts) nhe.2v.sia --> nhe.2v + SIA (2kpts) nhe.3v.sia --> nhe.3v + SIA energy (ev) number of He - n The SIA is strongly bound to the nhe.mv cluster: confirmed in MD 11

12 SIA strongly bound to the nhe.mv cluster: MD number of defects ns vacancies dumbbells SIA-V distance (cells) 1 SIA + 1 v during 3 ns e-09 4e-09 6e-09 8e-09 1e-08 number of defects µs time (s) vacancies dumbbells SIA-V distance (cells) 1000 K; 5 He atoms e-08 4e-08 6e-08 8e-08 1e-07 time (s) 12

13 SIA strongly bound to the nhe.mv cluster: MD number of defects vacancies dumbbells SIA-V distance (cells) e-09 4e-09 6e-09 8e-09 1e-08 time (s) 1800 K: 4 He atoms The SIA unbinds from the He cluster 13

14 MD simulations at 300K MD simulations at 300 K, 1023 atoms + 8 He in one vacancy + one SIA SIA most of the time 111 sometimes 110 The SIA is trapped by the He cluster. No recombination so far 14

15 SIA clusters bound to nhe.mv cluster: DFT DFT results 15 He cluster 15 He atoms + 2v + 2SIA 15 He atoms + 3v + 3SIA 15 He atoms + 4v + 4SIA 15

16 v emission / He emission vs trap mutation energy (ev) Vac emission He.v-->He + v (2kpts) nhe.1v --> He + (n-1)he.1v (2kpts) nhe.2v --> He + (n-1)he.2v (2kpts) nhe.3v --> He + (n-1)he.3v (2kpts) nhe.4v --> He + (n-1)he.4v (2kpts) nhe.5v --> He + (n-1)he.5v (2kpts) nhe.1v --> v + nhe (2kpts) nhe.2v --> v + nhe.1v (2kpts) nhe.3v --> v + nhe.2v (2kpts) nhe.4v --> v + nhe.3v (2kpts) nhe.5v --> v + nhe.4v (2kpts) nhe.6v --> v + nhe.5v (2kpts) nhe.1v --> nhe.2v.sia (2kpts) nhe.2v --> nhe.3v.sia (2kpts) nhe.3v --> nhe.4v.sia 2He.2v -->2He.v + v number of He/number of V = n/m TM He emission 16

17 energy (ev) v emission / He emission vs trap Mutation Vac emission 2He.2v-->He.2v + He (2kpts) nhe.1v --> He + (n-1)he.1v (2kpts) nhe.2v --> He + (n-1)he.2v (2kpts) nhe.3v --> He + (n-1)he.3v (2kpts) nhe.4v --> He + (n-1)he.4v (2kpts) nhe.5v --> He + (n-1)he.5v (2kpts) nhe.1v --> v + nhe (2kpts) nhe.2v --> v + nhe.1v (2kpts) nhe.3v --> v + nhe.2v (2kpts) nhe.4v --> v + nhe.3v (2kpts) nhe.5v --> v + nhe.4v (2kpts) nhe.6v --> v + nhe.5v (2kpts) nhe.1v --> nhe.2v.sia (2kpts) nhe.2v --> nhe.3v.sia (2kpts) nhe.3v --> nhe.4v.sia 3He.v-->2He.v + He number of He/number of V = n/m TM He emission 17

18 v emission / He emission vs trap mutation energy (ev) Vac emission (2kpts) nhe.1v --> He + (n-1)he.1v (2kpts) nhe.2v --> He + (n-1)he.2v (2kpts) nhe.3v --> He + (n-1)he.3v (2kpts) nhe.4v --> He + (n-1)he.4v (2kpts) nhe.5v --> He + (n-1)he.5v (2kpts) nhe.1v --> v + nhe (2kpts) nhe.2v --> v + nhe.1v (2kpts) nhe.3v --> v + nhe.2v (2kpts) nhe.4v --> v + nhe.3v (2kpts) nhe.5v --> v + nhe.4v (2kpts) nhe.6v --> v + nhe.5v (2kpts) nhe.1v --> nhe.2v.sia (2kpts) nhe.2v --> nhe.3v.sia (2kpts) nhe.3v --> nhe.4v.sia number of He/number of V = n/m 10He.v-->10He.2v.I 20He.2v-->20He.3v.I TM 30He.3v-->30He.4v.I 18

19 Dissociation energies for the 3 processes E mig vac = 1.7 ev E mig SIA = ev E mig He = 0.06 ev TM, v and He emission, depend on bubble density (n/m) AND size (m) 19

20 Comparison with experimental results E.V. Kornelsen, A.A. Van Gorkum: A study of bubble nucleation in tungsten using thermal desorption spectrometry: clusters of 2 to 100 helium atoms. Jour. Nucl. Mater. 92 (1980)

21 100 ns MD simulations: a 0 S: 10 ns simulations vs: 1 ns simulations. -ST is a thermally activated event -The higher the T, the easier the ST -The more He, the easier the ST Activation energy calculations for ST 21

22 Activation energy for ST MD simulations in 1024 atom cells at different T for 5 to 8 pure He clusters. More than 1000 simulations per T and He cluster size 7 He cluster ==> geometric law. Fit provides the characteristic time for ST event 22

23 Activation energy for ST Delta E (ev) NEB_3He NEB_4He NEB_5He NEB_6He NEB_7He NEB_8He NEB (Lammps) τ (fs) /T (K -1 ) 8 He 6 He 7 He 5 He reduced coordinates Number of He atoms E a (ev) NEB E a (ev) MD * * *

24 Activation energy / Recovering phenomena Ex: 5 He Ex: 8 He 24

25 Conclusions -ST and TM are thermally activated events. -ST takes place for 6 He (and above) according to thermodynamics -TM takes place for ~15, ~21 and ~28 He atoms depending on amount of v. -TM, and to a lesser extent v and He emission, depend not only on He density in bubble (He/v ratio) but also on bubble size (number of v). -The SIA emitted is strongly bound to the He cluster (and other SIAs) - The dissociation model is not appropriate for ST and TM: we need to determine Ea and ν J. Boisse, A. De Backer, C. Domain, C.S. Becquart, JMR 29 (2014) 2374 Perspectives: Data implemented in our OKMC code. Soon: test the model on new experimental data obtained at CEMHTI: 300 ev He implanted at RT (work in progress) 25

26 First principles calculations DFT to find ground state configurations of bcc-w containing : - m Vacancy (V) - n Helium (He) - p SIA (W) VASP (Vienna Ab initio Simulation Package) Blo chl s Projector Augmented-Wave (PAW) Exchange and correlation: Generalised Gradiant Approximation (Perdew and Wang 1991) All atomic positions relaxed Constant volume calculations Supercells with Periodic Boundary Conditions Plane wave Cut off W: 350 ev. Box : 250 and 1024 W atoms + 2x2x2 k-points 26