1. Cosires 2004C.S. Becquart RPV steels microstructure evolution under irradiation: a multiscale approach Charlotte Becquart and... EDF Electricité de France A. Barbu: CEA, C. Domain: EDF, S. Jumel: EDF, M. Hou: U.L.B, A. Legris: LMPGM, L. Malerba: SCK-CEN,J-M. Raulot, J-C. Van Duysen: EDF, A. Souidi: U. Saida, D. Bacon: U. Liverpool, M. Perlado: Polytech., M. Hernández-mayoral, CIEMAT, R. Stoller: ORNL, B. Wirth: LLNL, B. Odette: UCSB... PhD and Master of Science students : P. Renuit, E. Vincent, S. Jumel, A. Marteel, P. Herrier, J-C. Turbatte, J-M Raulot, S. Pourchet, A. Tigeras, Z. Zhao

2. Cosires 2004C.S. Becquart Vessel 12 m 4.4 m 22 cm

3. Cosires 2004C.S. Becquart 0 50 100 150 200 250 -200-1000100200300 Temperature (°C) Energy (J) baseline irradiated DBTT shift (41 J level) USE drop yield increase D0D0D0D0 l0l0l0l0 Displacement ------ Baseline ------ Irradiated Under irradiation: modification of the mechanical properties ===> hardening and embrittlement T Dose Flux Composition Chemical composition (wt.%) of DAMPIERRE 2

4. Cosires 2004C.S. Becquart SIA-Loop Nanovoid Cu-rich ppt or atmospheres P-segregation Matrix Damage Precipitation Segregation at GBs Microstructural changes Tomographic atom probe Université de Rouen V = 4 x 4 x 4 nm 3 Fe-0.1%Cu, dose 5.5 10 19 n/cm 2

5. Cosires 2004C.S. Becquart SIA-Loops Nanovoid Cu-rich ppt P-segregation Matrix Damage Precipitation Segregation at GBs ? 0 50 100 150 200 250 -200-1000100200300 temperature (°C) energy (J) ? Necessary balance between simplifications and approximations versus completeness and physical detail

6. Cosires 2004C.S. Becquart  Rapid overview of the REVE ’s VTR  The primary damage : role of the cohesive model  The evolution of the primary damage : parameterisation of the Object Kinetic Monte Carlo Outline of the talk

7. Cosires 2004C.S. Becquart A. Seeger, Proc. 2nd UN Int. Conf. on Peaceful Usess of Atomic Energy, Geneva, 1958, vol.6 (United Nations, New York, 1958) p 250.

8. Cosires 2004C.S. Becquart - defect - dislocation interaction : Screw Dislocation Defect Hardening   V-Cu clusters (s to h) - Evolution - Primary damage vacancies & interstitials (15 ps) Microstructure Clusters and loops - PKA spectrum - neutron spectrum Simplified overview of the REVE ’s VTR Specter Incas Dymoka Lakimoca Dupair

9. Cosires 2004C.S. Becquart VASP (Vienna Ab initio Simulation Package) Density Functional Theory Plane wave & ultra soft pseudo potentials (Vanderbilt type pseudo potentials) Exchange and correlation: LDA and GGA (PW91) Spin polarised 54 atoms (5  5  5 k points) – 128 atoms (3  3  3 k points) all atomic positions for defects calculation are relaxed Methods and cohesive models Ab initio Semi-empirical potentials (FeCu) M. Ludwig, D. Farkas, D. Pedraza and S. Schmauder, Modelling Simul. Mater. Sci. Eng, 6 (1998) 19 G.J. Ackland, D.J. Bacon, A.F. Calder and T. Harry Phil. Mag. A, vol.75 (1997) 713 VASP: 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) Static calculations, molecular dynamics, atomic Kinetic Monte Carlo

10. Cosires 2004C.S. Becquart The primary damage : MD simulations

11. Cosires 2004C.S. Becquart The primary damage MD simulations Large systems ===> empirical potentials Embedded Atom Method Finnis Sinclair... M.W. Finnis and J.E. Sinclair, Phil. Mag. A 50 (1984) 45 R.J. Harrison, A.F. Voter and S.P. Chen, "Embedded Atom Potential for BCC Iron", Atomistic simulation of Materials- Beyond Pair Potentials, V. Vitek and D.J. Srolovitz (editors), 219, Plenum New York (1989) M.I. Haftel, T.D. Andreadis, J.V. Lill and J.M. Heridon, Phys. Rev. B 42 (1990) 11540 G. Simonelli, R. Pasianot and E.J. Savino, Mat. Res. Soc. Symp. Proc. 291 (1993) 567 R.A. Johnson and D.J. Oh. J. Mater. Res. 4 (1989)1195 Yu. N Osetsky and A. Serra, Phys. Rev. B 57 (1998) 755

12. Cosires 2004C.S. Becquart Fe I Not a T effect role of short range interaction of the potential Fe II RCS Role of the cohesive model (interatomic potential)

13. Cosires 2004C.S. Becquart Use BCA adjusted on MD results Molière potentialBorn Mayer potential range  = distance between atoms for which V(r ) = 30 eV stifness Statistics needed: Role of the cohesive model (interatomic potential)

14. Cosires 2004C.S. Becquart Distance (Å) Potential Energy (eV) 0-200 eV : formation range of RCS Role of the cohesive model (interatomic potential) Nombre moyen de RCS Température (K) Molière III BM III Mean number of RCS Temperature (K)

15. Cosires 2004C.S. Becquart Kinetic energy (eV) Fe I potential. The sequence is defocusing Role of the cohesive model (interatomic potential) Time (x10 -16 s) Kinetic energy (eV) MD Fe III potential. The sequence is defocusing, then focusing MD Fe I potential. The sequence is defocusing 50 eV PKA initiated at 0.3 deg. from Influence of potential on focusing

16. Cosires 2004C.S. Becquart The stiffer the BCA potential (the shorter ranged) the lower the focalisation threshold the less kinetic energy losses between successive collisions the more numerous the RCS and the longer. rayon d’écrantage (Å) Seuil de focalisation (eV) Molière I Molière III Influence of potential on focusing Role of the cohesive model (interatomic potential)

17. Cosires 2004C.S. Becquart The shorter the range for very high energies, the larger the cascade volume Molière III BM III Volume a o 3 Fréquency Distance (Å) Potential energy (eV) The more diluted the cascade Influence of potential on cascade expansion Role of the cohesive model (interatomic potential)

18. Cosires 2004C.S. Becquart Short potential range favours focusing in RCS Large potential range favours focusons on the expense of RCS One third of the energy given by PKA partitioned between replacement sequences and focusons. Role of the cohesive model (interatomic potential)

19. Cosires 2004C.S. Becquart During the cascade development, one third of the energy given by the PKA to the lattice is partitioned between replacement sequences and focusons. Short potential range favours focusing and energy transport in RCS on the expense of focusons. The shorter the range for very high energies, the larger the cascade volume, the more “diluted” the cascade. Main conclusions on the cohesive model Quantitative results have to be taken with care Better model for atomic interactions at small separations : ab initio calculations M. I. Mendelev, S. Han, D. J. Srolovitz, G. J. Ackland, D. Y. Sun and M. Asta, Phil. Mag. A 83 (2004) 3977. Threshold displacement energies not enough

20. Cosires 2004C.S. Becquart Cluster size (number of interstitials)

21. Cosires 2004C.S. Becquart Temperature (K) MSD (Å 3 ) Temperature (K) Lattice parameter (Å) Let’s not forget the thermal properties

22. Cosires 2004C.S. Becquart Evolution of the primary damage Object Kinetic Monte Carlo

23. Cosires 2004C.S. Becquart Annihilation Interstitial loop Emission Interstitial cluster Vacancy cluster traps Vacancy loop Electrons Neutrons Frenkel pairs cascade Object KMC: the events + Emission Migration Parameterisation + + Recombination G i =G i 0 exp( -E a / kT) >300nm PBC or surface sinks

24. Cosires 2004C.S. Becquart OKMC ageing of 20 keV cascade in Fe 0.2%Cu Absorbing boundary conditions

25. Cosires 2004C.S. Becquart Parameterisation : interaction with solute atoms Interstitials –No interaction with solute atoms Vacancies –V-Cu clusters: mobility decreases with size (# solute atoms and # V) –V and (V-Cu) emission depends on binding and formation energies diffusion / migration V emission V-Cu emission

26. Cosires 2004C.S. Becquart loops Reaction radii V-I recombination distance Exp 2.2 a 0 - 3.3a 0 MD 1.7 a 0 - 1.9 a 0 J. Dural, J. Ardonceau and J. C. Roussett, Le Journal de Physique 38 (1977) 1007 ‑ 1011. M. Biget, R. Rizk, P. Vajda and A. Bessis, Solid state comm. 16 (1975) 949-952. F. Gao, D. J. Bacon, A. V. Barashev and H. L. Heinisch, Mater. Res. Soc. Symp. Proc. 540 (1999) 703-708.

27. Cosires 2004C.S. Becquart Ab initio EAM Ludwig et al. 4.05 Å No recombination FS Ackland et al. Reaction radii

28. Cosires 2004C.S. Becquart Reaction radii Highly anisotropic

29. Cosires 2004C.S. Becquart Reaction radii Ageing of a 20 keV cascade Log(t) (s) Mean number of defect in clusters

30. Cosires 2004C.S. Becquart Log(t) (s) Mean number of V mixed Cu-V clusters Log(t) (s) Mean number of Cu in mixed Cu-V clusters Å Å Å Å Ageing of a 20 keV cascade containing 0.2 at.%Cu Reaction radii

31. Cosires 2004C.S. Becquart M. Eldrup, B.N. Singh, S.J. Zinkle, T.S. Byun and K. Farrell, Journ. Nucl. Mater. 307-311 (2002) 912-917]. Neutron irradiation (HFIR flux) Density of vacancy clusters Reaction radii HFIR : dose-rate  10 -6 dpa/s dpa Density (m -3 ) r = 1 nn/2 r = 1.9 a 0 /2 r = 3.3 a 0 /2 experimental * 70°C 3  10 16 FP  cm ‑ 3  s ‑ 1 4  10 14 10 keV and 2  10 14 20 keV cascade-debris  cm ‑ 3  s ‑ 1

32. Cosires 2004C.S. Becquart P. Auger, P. Pareige, S. Welzel, and J ‑ C. Van Duysen, J. Nucl. Mater. 280 (2000) 331. % of Cu precipitated dpa Neutron irradiation (HFIR flux) % of Cu precipitated Reaction radii

33. Cosires 2004C.S. Becquart dpa Density (m -3 ) M. Eldrup, B.N. Singh, S.J. Zinkle, T.S. Byun and K. Farrell, Journ. Nucl. Mater. 307-311 (2002) 912-917]. Neutron irradiation (HFIR flux) Density of vacancy clusters Mobilities dose-rate  10 -6 dpa/s 3  10 16 FP  cm ‑ 3  s ‑ 1 4  10 14 10 keV and 2  10 14 20 keV cascade-debris  cm ‑ 3  s ‑ 1

34. Cosires 2004C.S. Becquart Mobilities INTERSTITIALS –mono–interstitials: 3D random walk –clusters: 3D random walk or 1D along direction (cf. MD) I à 1000K I à 600K 2 I à 600K MD simulations clusters (size m >=2): attempt frequency E m = 0.04 eV, s = 0.51 Yu. N. Osetsky, D. J. Bacon, A. Serra, B. N. Singh and S. I. Golubov, J. Nucl. Mater. 276 (2000) 65. C.-C. Fu, F. Willaime, and P. Ordejón, Phys. Rev. Lett. 92, 175503 (2004) Exp and Ab initio E m = 0.3 eV for SIA

35. Cosires 2004C.S. Becquart A. Hardouin du parc, Ph. D. Thesis, Paris XI-Orsay University (1997), ISSN 0429 ‑ 3460, CEA report R ‑ 5791 Model experiment (A. Hardouin du parc, A. Barbu, CEA France) 1400 nm 1.5 10 -4 dpa/s 900 s TEM : interstitial dislocation loop density Mobilities

36. Cosires 2004C.S. Becquart Mobilities Set B, s = 10, large clusters almost immobile Loop density after 1200 s 1/T (K -1 ) Loop density (cm -3 ) * set A set B, r = 1nn/2 set B, r = 3.3 a 0 /2 experimental clusters (size m >=2): attempt frequency E m = 0.04 eV

37. Cosires 2004C.S. Becquart 0.28 eV 0.36 eV 0.70 eV Binding energies V-clusters 128 atoms, 3x3x3 kpoints 0.26 eV 0.36 eV

38. Cosires 2004C.S. Becquart Binding energies: larger clusters Turn to empirical potentials Need a clever way to find the most stable configuration See D. Kulivov poster

39. Cosires 2004C.S. Becquart Main conclusions on the OKMC Very powerful technique to simulate many experimental situations: electron irradiation, neutron irradiation, annealing, isochronal annealing... Combination of simulation techniques (AKMC, MD, MC, AB initio…) necessary Simple experiments necessary also Many unresolved questions, do we know enough physics?

40. Cosires 2004C.S. Becquart REVE VTR : a multiscale modelling of RPV vessel. Very simple models, lots of parameters : need to use combined techniques, simpler as well as more complicated ones. Simple modelling oriented experiments very useful. Need more physical insight (SIA loops). REVE continues in the PERFECT project (6th FP Euratom). CONCLUSIONS

41. Cosires 2004C.S. Becquart Log(t) (s) Mean number of V mixed Cu-V clusters

42. Cosires 2004C.S. Becquart Vacancy production rate Vacancy-SIA recombination rate Disappearance of vacancies at sinks Coupling with SIA concentration equation !

43. Cosires 2004C.S. Becquart P. Auger, P. Pareige, S. Welzel, and J ‑ C. Van Duysen, J. Nucl. Mater. 280 (2000) 331. % of Cu precipitated dpa Neutron irradiation (HFIR flux) % of Cu precipitated Reaction radii

44. Cosires 2004C.S. Becquart Ab initio (pure Fe: 0.64 eV) FS Ackland et al. (pure Fe: 0.77 eV) EAM Ludwig et al. (pure Fe: 0.69 eV) Mobilities And what about clusters ? J.R. Beeler Jr and R.A Johnson, Phys. Rev. 156 (1967) 677-684. Mobility decreases with vacancy cluster size (size > 2) Attempt frequency Migration energy constant

45. Cosires 2004C.S. Becquart Binding energies: Cu n clusters 0.26 eV(128 at. 2x2x2 kpts2) Most stable configurations0.15 eV (128 at. 3x3x3 kpts) -0.23 eV

46. Cosires 2004C.S. Becquart 0.26 eV 0.17 eV 0.28 eV 0.21 eV -0.03 eV 0.36 eV Cu-Cu 1 st nn - V 1nn V 1 st nn to both Cu atoms (no Cu interaction in 2 nd nn) 128 atom cells calculations Binding energies

47. Cosires 2004C.S. Becquart

48. Cosires 2004C.S. Becquart w’ 3 w2w2 w6w6 w5w5 w4w4 w3w3 w’’ 3 w’’ 4 w’ 4 cm 2 s – 1 9-frequency model (Le Claire) n Fe = n Cu = 3.65 10 15 s -1 Hypothesis [1] A.D. Le Claire, in Physical Chemistry: an advanced treatise, edited by H. Eyring, Academic Press, New York, 1970), vol. 10, chap. 5. [1] [2] [2] F. Soisson, G. Martin and A. Barbu, Annales de Physique, vol.20 (1995) C3-13.

49. Cosires 2004C.S. Becquart Influence of potential on vacancy-interstitial separation distances Frenkel Pair separation distance distributions. The frequencies are the largest when the energy carried by RCS is the largest and energy carried by focusons is the smallest frequency Vacancy-interstitial pair separation distance (a 0 ) Role of the cohesive model (interatomic potential)

50. Cosires 2004C.S. Becquart Fuel. Usually pellets of uranium oxide (UO 2 ) arranged in tubes to form fuel rods. The rods are arranged into fuel assemblies in the reactor core. Moderator. This is material which slows down the neutrons released from fission so that they cause more fission. It may be water, heavy water, or graphite. Control rods. These are made with neutron-absorbing material such as cadmium, hafnium or boron, and are inserted or withdrawn from the core to control the rate of reaction, or to halt it. (Secondary shutdown systems involve adding other neutron absorbers, usually as a fluid, to the system.) Coolant. A liquid or gas circulating through the core so as to transfer the heat from it. Pressure vessel or pressure tubes. Either a robust steel vessel containing the reactor core and moderator, or a series of tubes holding the fuel and conveying the coolant through the moderator. Steam generator. Part of the cooling system where the heat from the reactor is used to make steam for the turbine. Containment. The structure around the reactor core which is designed to protect it from outside intrusion and to protect those outside from the effects of radiation or any malfunction inside.Ý It is typically a metre-thick concrete and steel structure. There are several different types of reactors as indicated in the following table.

51. Cosires 2004C.S. Becquart  guide design and analysis of experimental irradiation programs  explore conditions outside existing databases (very long time and high fluences), important to lifetime extension  systematically evaluate individual and combined influence of multitude of material variables (composition and microstructure) and the irradiation service conditions (T, flux, spectrum,...)  help design advanced materials for future fission and fusion reactors. Virtual Test Reactors (VTRs)

52. Cosires 2004C.S. Becquart Reconstruction 3D acier VVER 440 irradié neutrons (20 ans) Volume de 15  15  50 nm 3 (serie1) Cu P Si FeNi Ni Mn Courtesy: Philippe Pareige

53. Cosires 2004C.S. Becquart Volume de 15  15  50 nm 3 (série 2) Cu + P Si FeNi Ni Mn

54. Cosires 2004C.S. Becquart Zoom sur un des amas 5  5  5 nm 3 Cu + P Si FeNiNi Mn