Modelling of radiation damage in tungsten including He production

Modelling of radiation damage in tungsten including He production C.S. Becquart 1, C. Domain 2 A. De Backer 1 M.F. Barthe 3 M. Hou 4, C. Ortiz 5 1 Unité Matériaux Et Techniques, UMET, UMR 8207, Villeneuve d Ascq, France 2 EDF R&D, MMC Centre des Renardières, Moret sur Loing, France 3 CEMHTI, UPR 3079, Orléans, France 4 Physique des Solides Irradiés et des Nanostructures CP234, Université Libre de Bruxelles, Bd du Triomphe, B-1050 Brussels, Belgium 5 Laboratorio Nacional de Fusión por Confinamiento Magnético, CIEMAT, E-28040 Madrid, Spain EUROPEAN FUSION TECHNOLOGY PROGRAMME: CEA Contrat V 3542.001 PROGRAMME INTERDISCIPLINAIRE ENERGIE DU CNRS 2006-2009 PFMC-13, Rosenheim, may 2011 C. S. Becquart 1

Object Kinetic Monte Carlo: LAKIMOCA Microstructure = objects defined by: type centre-of-mass position reaction radius possible reactions PBC or surface 200nm Recombination Emission + Traps Interstitial loop Emission dislocation Vacancy cluster Interstitial cluster Annihilation + Mixed He vacancy cluster He cluster Migration PFMC-13, Rosenheim, may 2011 C. S. Becquart 2

Object Kinetic Monte Carlo: LAKIMOCA Microstructure = objects defined by: type centre-of-mass position reaction radius possible reactions PBC or surface Recombination Emission + Traps Interstitial loop Emission dislocation Vacancy cluster Interstitial cluster Annihilation + 200nm He cluster Mixed He vacancy cluster Migration Properties of He (and H), interactions with vacancy and vacancy clusters, with SIAs and impurities (binding and migration energies): ab initio calculations. ===> Use He desorption experiments to check. PFMC-13, Rosenheim, may 2011 C. S. Becquart 3

Object Kinetic Monte Carlo: LAKIMOCA Microstructure = objects defined by: type centre-of-mass position reaction radius possible reactions PBC or surface 200nm Recombination Emission + Traps Interstitial loop Emission dislocation Vacancy cluster Interstitial cluster Annihilation + Mixed He vacancy cluster He cluster Migration He, H atoms Frenkel pairs + Neutrons, ions cascade PFMC-13, Rosenheim, may 2011 C. S. Becquart 4

Object Kinetic Monte Carlo: LAKIMOCA Microstructure = objects defined by: type centre-of-mass position reaction radius possible reactions PBC or surface Recombination Emission + Traps Interstitial loop Emission dislocation Vacancy cluster Interstitial cluster Annihilation + He, H atoms Frenkel pairs + Neutrons, ions 200nm Mixed He vacancy cluster He cluster cascade Migration Properties External events: of He He (and implantation, H), interactions damage with vacancy and vacancy clusters, with SIAs and impurities (binding and migration energies): ab initio calculations. ==> BCA code Marlowe adjusted on exp. results ===> Use He desorption experiments to check. PFMC-13, Rosenheim, may 2011 C. S. Becquart 5

DFT ab initio method PAW VASP (Vienna Ab initio Simulation Package) Exchange and correlation: GGA (PW91) All atomic positions relaxed Constant volume calculations Supercells with PBC. Cut off W: 350 ev. G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993); ibid. 49, 14 251 (1994) G. Kresse and J. Furthmüller, Comput. Mat. Sci. 6, 15 (1996) G. Kresse and J. Furthmüller, Phys. Rev. B 55, 11 169 (1996) Formation, binding and migration energies 54 atoms + 5x5x5 kpoints, 128 atoms + 3x3x3 kpoints, 250 atoms + 3x3x3 kpoints Ab initio BO MD: NVT ensemble, time step 1 fs, cutoff 350 ev and 1 kpt PFMC-13, Rosenheim, may 2011 C. S. Becquart 6

He desorption experiments He implantation at 5K Below threshold 1.2 1 R R R R 1 o o 0.8 0.6 0.4 0.2 0 250 ev, 2.3 ppm 250 ev, 39 ppm 400 ev, 13 ppm 400 ev, 17 ppm 400 ev, 350 ppm 1.69 kev, 4.7 ppm 3 kev, 0.28 ppm 3 kev, 3 ppm 3 kev, 12 ppm 1 10 100 1000 Above threshold T (K) A.S. Soltan, R. Vassen and P. Jung, J. Appl. Phys. 70(2) (1991) 793 PFMC-13, Rosenheim, may 2011 C. S. Becquart 7

He Ab initio Exp. (ev) Empirical potentials (ev) Octahedral 6.38 7.83 [HENR04] 5.47 [WILS72] Tetrahedral 6.16 5.71 [WILS72] Substitutional 4.70 Migration mig energy E He 0.06 0.28 ( 3 He [AMA84]) 0.24-0.32 ( 4 He [WAG79]) 0.29 [HENR04] 0.24 [WILS72] E mig (He) very low: discrepancy with exp. results. Consistent with tendency to form clusters [BEC06], agreement with Soltan [SOLT91] J. Amano and D. Seidman, J. Appl. Phys. 56 (1984) 983 A. Wagner and D.N.Seidman, Phys. Rev. Lett. 42 (1979) 515 C.S. Becquart & C. Domain, Phys. Rev. Lett. 97 (2006) 196402. A.S. Soltan, R. Vassen and P. Jung, J. Appl. Phys. 70(2) (1991) 793 PFMC-13, Rosenheim, may 2011 C. S. Becquart 8

He clusters Binding energy (ev) 3 2.5 2 1.5 1 0.5 0 Ab initio capillary approx. 0 5 10 15 20 25 n (total number of He in the resulting cluster) E = for for for. ( n ( n 1) + 1) = E ( n 1) + E ( 1) E ( n) b for 3 ( E ( 2) E ( 1) )( n) 2 3 ( n 1) 2 3 / 2 2 1 + E b [ ( )] for ( 1) PFMC-13, Rosenheim, may 2011 C. S. Becquart 9

He clusters Small clusters are mobile Ab initio MD at 1000 K, center of mass (CM) trajectories 44 ps 82 ps 5He 10He PFMC-13, Rosenheim, may 2011 C. S. Becquart 10

2He 150 K : 103 ps 300 K : 105 ps 300 K 1000 K : 103 ps 600 K : 107 ps PFMC-13, Rosenheim, may 2011 C. S. Becquart 11

8 MSD ( 2 ) 4 150 K 150 K 2He He MSD ( 2 ) 20 10 300 K 300 K 2He He 0 0 5 t (ps) 10 3He 0 0 5 t (ps) 10 Center of Mass MSD MSD ( 2 ) 60 30 0 t (ps) 600 K 2He He 3He 0 5 t (ps) 10 Emig He ~ 0.04 ev Emig 2He (1D) ~ 0.027 ev Emig 3He ~ 0.07 ev PFMC-13, Rosenheim, may 2011 C. S. Becquart 12

External events: MARLOWE parameterized on exp. results Number of pairs 3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 0 W -> W Poly 29/9/08 PAPA1:/home/mhou/W PSIPC6:mhou-FP7-He-Frenkel_pairs_and_ranges-WW-WNEW Seidman 1.18 a 0 0 1 2 3 Separation distance (lu) 5 KeV 10 KeV 20 KeV 30 KeV 40 KeV 50 KeV 60 KeV 70 KeV D. Pramanik and D. N. Seidman, Jour. Appl. Phys. 54 (1983) 6352; D. N. Seidman, R. S. Averback, and R. Benedek, Phys. Stat. Solidi (b) 144 (1987) 85. M. Hou, C. J. Ortiz, C.S. Becquart, C. Domain, U. Sarkar, A. Debacker, J. Nucl. Mater. 403 (2010) 89. PFMC-13, Rosenheim, may 2011 C. S. Becquart 13

Check parameterization: OKMC simulations of He desorption Two steps: -implantation in 399 400 1001 l.u. box Exp. rate = 10 15 s -1 m -2 ==> 16 He per s PBC in two directions: thin foil 317.3 nm thick. Surface perpendicular to 001 direction -isochronal annealing T increase of 2K every 60 s Monitor the total number of defects (not objects) in the box C.S. Becquart, C. Domain, U. Sarkar, A. DeBacker, M. Hou, accepted in J. Nucl. Mater. 403 (2010) 75. PFMC-13, Rosenheim, may 2011 C. S. Becquart 14

OKMC simulations of He desorption implanted «under threshold» Normalized number of He 1 0.9 0.8 0.7 0.6 Random He Experimental data Marlowe polycrystal 1 10 100 Temperature (K) Normalized number of He 1.1 1 0.9 0.8 0.7 Exp: 400 ev He, 13 ppm He and 350 ppm He Random He Marlowe polycrystal Experimental data 1 10 100 1000 Temperature (K) - Relevance of He distribution PFMC-13, Rosenheim, may 2011 C. S. Becquart 15

Mean spatial distribution of He at the end of implantation Number of He 20000 15000 10000 5000 Marlowe polycrystal Random He Number of He 20000 15000 10000 5000 Marlowe polycrystal Random He 0 0 50 100 150 200 Distance from the surface in lattice units 0 0 10 20 30 40 Number of He in the cluster Exp: 350 ppm 400 ev He PFMC-13, Rosenheim, may 2011 C. S. Becquart 16

Normalized number of He 1 0.9 0.8 0.7 Marlowe poly, previous Marlowe poly, new Experimental data 1 10 100 1000 Temperature (K) Migration of small He clusters Role of impurities Exp: 350 ppm 400 ev He PFMC-13, Rosenheim, may 2011 C. S. Becquart 17

Role of impurities (ab initio) E binding (ev 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 H He C Mo Re Fe Ni 2He 3He He v SIA Most impurities trap He and small He clusters ===> potential bubble nucleation centers 128 atoms 3x3x3 kpoints PFMC-13, Rosenheim, may 2011 C. S. Becquart 18

Role of impurities (ab initio) E binding (ev 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 H He C Mo Re Fe Ni 2He 3He He v SIA Most impurities trap He and small He clusters ===> potential bubble nucleation centers 128 atoms 3x3x3 kpoints PFMC-13, Rosenheim, may 2011 C. S. Becquart 19

Vacancy and voids VASP: divacancy unstable; not predicted by empirical potentials; agreement (now) between DFT calculations Exp: vacancy loops [BUSW70; HAUS72; RAU70] (TEM) and voids (FIM) [SEID78] formed under heavy particle irradiation. -2v stabilised by C and O [VASP] or H [Kato, ICFRM-15] -Cascade condition: all vacancies in narrow volume J.T. Buswell, Phil. Mag. 22 (1970) 391 and 787; F. Häussermann, Phil. Mag. 25 (1972) 561 and 583 ; R.C. Rau, Phil. Mag. 18 (1970) 1079. D. N. Seidman, Surf.Science 70 (1978) 532. BUT PFMC-13, Rosenheim, may 2011 C. S. Becquart 20 Binding energy (ev) 2 1.5 1 0.5 0-0.5 Ab initio capillary approx. 1 2 3 4 5 6 7 8 9 10 m (total number of vacancies in the resulting cluster)

He. 2v + He 2He. 2v Binding energy (ev) 7 6 5 4 8He.6v + He 9He. 6v Stability of nhe.mv clusters 3 2 15He + He 16He 1 0 1 3 5 7 9 Nbr of He nhe.mv clusters are very stable 11 13 15 S1 S3 0 2 4 S5 Not mobile 6 S7 Nbr of v Binding energy (ev) 14 12 10 0Binding energy (ev) 8 6 4 2 0-2 2 5He + v 5He. v 4 6 8 10 Nbr of He 12 14 8He.6v + 19He He.3v9 + He v. 6 v19 He. 4v 16 18 S5 7 S1 1 3 5 Nbr of v PFMC-13, Rosenheim, may 2011 C. S. Becquart 21

SIA and SIA clusters SIA very mobile: 0.013 ev ; 1D motion with Erot = 0.38 ev [DERL07] Binding energy (ev) 7 6 5 4 3 2 1 0 Ab initio capillary approx. 0 2 4 6 8 10 Number of SIAs in resulting cluster SIA clusters very stable and also very mobile [DUDA08] P.M. Derlet, D. Nguyen-Manh and S.L. Dudarev, Phys. Rev. B 76 (2007) 054107-1 S. L. Dudarev, C.R. Physique 9 (2008) 409. PFMC-13, Rosenheim, may 2011 C. S. Becquart 22

1 M-Polycrystal Normalized number of defects and He 0.9 0.8 0.7 M-Amorphous Experiment better reproduced when W is considered as a polycrystal 12 ppm 3 kev He 0.6 Experimental data 1 10 100 1000 Temperature (K) - Relevance of the choice of matrix structure on He and primary damage distribution and on longer term evolution. PFMC-13, Rosenheim, may 2011 C. S. Becquart 23

Influence of He atoms in the void formation of 800 kev 3 He implanted in tungsten Exp. results of P.E. Lhuilier PhD thesis CEMHTI Orléans: the higher the fluence, the smaller the voids in the track region 1/ Implantationstage done at 300 K with experimental flux and fluences (10 14, 10 15, 10 16 and 5 10 16 ions per cm 2 ). 2/ Isochronal annealing stage : T = 10 K every 3600 s up to 900 K.. PFMC-13, Rosenheim, may 2011 C. S. Becquart 24

a 800 kev 3 He atom produces on average 33 FP (Marlowe) Track region Box size: 195 203 2208 a 0 = 64 64 700 nm; track region: 3.75 % of the He atoms and 25.4 % of the point defects: 221 FP per He atom PFMC-13, Rosenheim, may 2011 C. S. Becquart 25

RT implantation ==> SIA and nhe clusters are mobile: annihilation, desorption... surface Fluence increases surface Defect population after implantation stage: v, mv, nhe.psia, He.v, nhe.v PFMC-13, Rosenheim, may 2011 C. S. Becquart 26

RT implantation ==> SIA and nhe clusters are mobile: annihilation, desorption... surface Fluence increases surface non mobile Defect population after implantation stage: v, mv, nhe.psia, He.v, nhe.v PFMC-13, Rosenheim, may 2011 C. S. Becquart 27

End of implantation sequence (PAS) Good agreement with exp. data PFMC-13, Rosenheim, may 2011 C. S. Becquart 28

During the isochronal annealing, v start moving, small mv clusters emit 10 16 ion/cm -2 concentration 10 19 cm -3 SIA He v v clusters (mv, nhe.mv) PFMC-13, Rosenheim, may 2011 C. S. Becquart 29

During the isochronal annealing, v start moving, small mv clusters emit Clustering phase 10 16 ion/cm -2 concentration 10 19 cm -3 SIA He v v clusters (mv, nhe.mv) PFMC-13, Rosenheim, may 2011 C. S. Becquart 30

Clustering T range depends on fluence. Amount of desorption, annihilation and clustering also At 900K PFMC-13, Rosenheim, may 2011 C. S. Becquart 31

Vacancy cluster distribution at 900 K Nbr of clusters 100 75 50 25 ion/cm -2 10 16 10 15 10 14 0 0 50 100 150 200 Nbr of v in cluster The higher the fluence, the smaller the v clusters as observed experimentally PFMC-13, Rosenheim, may 2011 C. S. Becquart 32

Cluster distribution at the end of the implantation PFMC-13, Rosenheim, may 2011 C. S. Becquart 33

Cluster distribution at the end of the implantation Free vacancies PFMC-13, Rosenheim, may 2011 C. S. Becquart 34

Cluster distribution at the end of the implantation Germs nhe.psia Free vacancies PFMC-13, Rosenheim, may 2011 C. S. Becquart 35

At high fluence, it is easier to form clusters because the vacancies have less distance to cover. Furthermore, there are more germs and less desorption. Free vacancies / «germs» 60 40 20 0 At the end of implantation sequence 1 2 3 4 5 10 13 10 14 10 16 10 15 5 10 16 Fluence (ions cm -2 ) «germs» = non mobile clusters = nv.mhe + nsia.mhe Without He, not the same trends anymore PFMC-13, Rosenheim, may 2011 C. S. Becquart 36

Conclusions ==> Ab initio calculations: - He is very mobile - small He clusters are mobile, 2He clusters perform 1D motion at low T. - He and He clusters bind to almost everything - di-vacancy is unstable - vacancies stabilise He clusters ==> OKMC model parameterized on ab initio data and exp.: - relevance of implantation model - need more information on mobility of He clusters; trap mutation OKMC model can help interpret experimental results and vice versa PFMC-13, Rosenheim, may 2011 C. S. Becquart 37