Kinetic Monte Carlo simulation of irradiation effects in bcc Fe-Cu alloys L. Malerba 1, C. Domain 2, C. S. Becquart 3 and D. Kulikov 1,4,5 COSIRES-7, Helsinki, 28 June – 2 July SCK-CEN, 2 EDF, 3 U. Lille 4 UL Bruxelles, 5 Ioffe Institute S. Petersburg Work performed in the framework of

2 Motivation  Reactor pressure vessel (RPV) steels harden and embrittle under irradiation during operation mainly as a consequence of Cu precipitation  Fe-Cu is the model alloy typically used to study the basic mechanisms of RPV steel embrittlement, both in modelling-oriented experiments and multiscale models  Object KMC methods are promising tools to simulate the long-term effects of irradiation, taking into account the inherent inhomogeneity of neutron radiation damage

3 Problem  The open question concerning OKMC methods is the elaboration of the parameter set describing interactions between radiation-produced defects  The elaboration of an adequate parameter set requires a delicate work of:  identification of key physical mechanisms  calculation of basic magnitudes, such as cluster binding and migration energies  feedback from experimental observations

4 Method: Object Kinetic Monte Carlo P1P1 P1P1 P2P2 P2P2 PiPi PiPi PNPN PNPN Random number extraction, R n  [0,1] ekek ekek  Each object defined by:  type  centre-of-mass position  reaction radius  possible reactions probabilities = frequencies residence time algorithm

5 Calculation of Cu-VC binding energies (see poster by D. Kulikov) Metropolis MC on rigid lattice N Cu N V Lowest energy configuration MD relaxation at 0 K E f (N V )=(N 0 -N V )[E coh (N V inFe)-E coh (bccFe)] E f (N Cu )=N 0 Ecoh(N Cu inFe)-[(N 0 -N Cu )E coh (bccFe)+N Cu E coh (fccCu)] E f (N V +N Cu )=(N 0 -N V )E coh (N V +N Cu inFe)-[(N 0 -N Cu -N V )E coh (bccFe)+N Cu E coh (fccCu)] E b (V) = E f (cluster) + E f (V) – E f (cluster+V) E b (Cu-Vpair) = E f (cluster) + E f( CuVpair) – E f (cluster+CuVpair) E b (Cu) = E f (cluster) + E f (Cu) – E f (cluster+Cu)

6 What do experiments say on Cu-VC ? Main reference:Nagai et al. Phys. Rev. B 63 (2001) Positron annihilation work on Fe-0.3%Cu, -0.15%Cu & -0.05%Cu Neutron irradiated at 100 & 300°C in JMTR 8.3e18 n/cm2 (~0.012 dpa), ~10 -8 dpa/s Specimens irradiated at 100°C annealed up to 700°C 100 °C Fe-0.3%Cu  1 =165 ps  ~Cu-V 1  2 =405 ps  ~ V 30/25 I 2 >50% 300 °C Fe-0.3%Cu  2 =300 ps  V 10 I 2 ~30% Cu-coated voids Ncu < 50 (?)

7 What do experiments say on Cu-VC ? Isochronal annealing From 100°C to 700°C, steps of 50°C 30 min at each temperature: Results: - Nanovoids anneal out at °C - Cu ppts anneal out at T > 650°C Fe-0.3%Cu Fe-0.05%Cu Nanovoids Cu ppts Pictures from: Nagai et al. Phys. Rev. B 63 (2001)

8 What experiments do NOT say  No measurements on reference pure Fe  No Cu-V cluster size distribution or number density  The positron signal is a function of cluster size, volume concentration AND specific trapping rate  The specific trapping rate of Cu-V clusters is not known  Only a complementary atom probe study could (partially) provide this information (but atom probe alone does not see vacancies …)  No information on pure Cu ppts size (not even indicative value)  Only information from positrons concerns saturation to pure Cu  No information on interstitial loops in these conditions  Even TEM study would not provide anything, because most likely loops would be too small in the considered irradiation conditions to be seen

9 Choice of the OKMC parameters  General (as in the past)  Dose-rate from 5, 10 and 20 keV MD cascades  All clusters mobile, but prefactors decrease with size  3nn distance reaction radius  SIA traps, V traps (impurities, elastic interactions, …)  Sinks: points (GB) & dislocation segments

10 Choice of the OKMC parameters SIA cluster size (n I ) (s -1 )E m (eV)Direction of motion 1 0 = 6· D /n I s s= D D Interstitial cluster mobility: recent picture Emission of vacancies and Cu-V pairs: Cu-coating effect Cluster size (n V, n Cu ) (s -1 )E a = E m + E b (eV) n V 2/3 -n Cu > 0 0 x(n V 2/3 -n Cu ) E m =0.7 ; E b =formulae (see D. Kulikov) n V 2/3 -n Cu < 0 0 x(n V 2/3 /n Cu )

11 Choice of the parameters Comparison with experiment of resistivity recovery during low temperature isochronal annealing for pure Fe using proposed parameters ( Abe & Kuramoto, JNM , 2002, 174 ): DefectExperimentSimulation Single SIA K88 K Di-SIA K148 K Single vacancy K188 K This is necessary condition for the acceptability of the parameter set (but not sufficient  ) Temperature (K) 88 K148 K188 K Number of defects

12 Results: Irradiation dpa, dpa/s 100a 0 side simulation box Mixed Cu-V complexes form, in larger number for larger Cu concentrations Ncu << 50 (not in disagreement with PAS) Size is fairly small (~1 nm maximum)

13 Results: Irradiation T (K)n (cm -3 )  sim (ps)  exp (ps) · · ~ · · ·10 16 //~300 Pure Fe dpa, dpa/s 100a 0 side simulation box Fe-0.3%Cu Density decreases with T

14 Results: Irradiation T (K)n (cm -3 )  sim (ps)  exp (ps) · · ~ · · · ~300 Pure Fe dpa, dpa/s 200a 0 side simulation box Fe-0.3%Cu

15 Results: Irradiation  In Fe slightly larger sizes than in Fe-0.3Cu around 100°C  In Fe-0.3Cu voids form up to 573 K - in Fe they start not to form earlier (right above stage V)  Calculated positron lifetime varies with temperature less or in a different way than in experiments  Better temperature regime reproduction with larger box Considering the many approximations and unknowns, the model is at least reasonable in the irradiation description

16 Results: Annealing ← Voids disappear during 30 min annealing at increasing T, but they do so ~ K above experiments ← Temperature is ~correct for much longer annealing than in experiment ← Little difference Fe-Cu/Fe Expected annealing Fe-Cu Expected annealing Fe Cu precipitate dissolution during thermal ageing according to the model takes too high temperatures or too long times compared to experiments Overall, the annealing description is not fully satisfactory

17 Summary  Positron annihilation experiments on Fe-Cu alloys provide useful information concerning features and (partially) size of Cu-V complexes formed in Fe-Cu under irradiation and their stability during annealing  A first attempt OKMC parameter set for the description of Fe-Cu alloys has been elaborated, based on:  Latest qualitative guess concerning SIA and SIA cluster mobility in Fe  Extensive MC/MD calculation of Cu-V cluster binding energies as a function of size  Biased prefactor for V and Cu-V pair emission from Cu-VC to account for effect of Cu-coating of voids  The application of this first attempt parameter set gives reasonable results for the reproduction of realistic irradiation conditions, but does not fully reproduce the correct temperature/time behaviour during annealing

18 Missing ingredients and open problems  Detailed mobility description of SIA clusters according to recent picture (migration energies, directionality, nature of clusters, …)  Actual law of pre-factor decrease for diffusivity of all clusters  Complex defect-defect interactions (trapping of SIA clusters by vacancies before recombination, …)  Detailed trap description (different behaviour for different impurities, mobile traps, elastic interactions, …)  Detailed description of migration and emission for V clusters and Cu-V clusters (energy barriers, size effect, effect of Cu coating, …)  Interaction between solute atoms and SIA clusters  Sink evolution (dislocation density) under irradiation  …  Importance of box size effect?

Acknowledgements This work was financed by the PERFECT IP, 6 th FP, Euratom, Contract no. F160-CT Special thanks to Jan Kuriplach (C. U. Prague) for his assistance in understanding positron results