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RPV steels microstructure evolution under irradiation: a multiscale approach

EDF. Electricité de France. RPV steels microstructure evolution under irradiation: a multiscale approach. Charlotte Becquart and.

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RPV steels microstructure evolution under irradiation: a multiscale approach

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  1. EDF Electricité de France RPV steels microstructure evolution under irradiation: a multiscale approach Charlotte Becquart and... 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 C.S. Becquart

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

  3. 250 baseline USE drop yield increase irradiated 200 Energy (J) 150 100 ------ Baseline ------ Irradiated D0 50 DBTT shift (41 J level) l0 0 -200 -100 0 100 200 300 Temperature (°C) Displacement Under irradiation: modification of the mechanical properties T Dose Flux Composition ===> hardening and embrittlement Chemical composition (wt.%) of DAMPIERRE 2 C.S. Becquart

  4. Fe-0.1%Cu , dose 5.5 1019n/cm2 Precipitation SIA-Loop Cu-rich ppt or atmospheres Nanovoid V = 4 x 4 x 4 nm3 Tomographic atom probe Université de Rouen Matrix Damage Segregation at GBs P-segregation Microstructural changes C.S. Becquart

  5. Precipitation SIA-Loops Cu-rich ppt Nanovoid Matrix Damage Segregation at GBs P-segregation ? ? 250 200 150 energy (J) Necessary balance between simplifications and approximations versus completeness and physical detail 100 50 0 -200 -100 0 100 200 300 temperature (°C) C.S. Becquart

  6. Outline of the talk • 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 C.S. Becquart

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

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

  9. Methods and cohesive models Ab initio VASP: 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3k points) all atomic positions for defects calculation are relaxed 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) Semi-empirical potentials (FeCu) Static calculations, molecular dynamics, atomic Kinetic Monte Carlo • 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 C.S. Becquart

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

  11. 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 C.S. Becquart

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

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

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

  15. Role of the cohesive model (interatomic potential) 50 eV PKA initiated at 0.3 deg. from <111> Time (x10-16s) MD Fe III potential. The sequence is defocusing, then focusing Kinetic energy (eV) Time (x10-16s) MD Fe I potential. The sequence is defocusing Influence of potential on focusing Kinetic energy (eV) C.S. Becquart Fe I potential. The sequence is defocusing

  16. Seuil de focalisation (eV) Molière I Molière III rayon d’écrantage (Å) Role of the cohesive model (interatomic potential) Influence of potential on focusing • 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. C.S. Becquart

  17. Potential energy (eV) Molière III BM III Fréquency Distance (Å) Volume ao3 Role of the cohesive model (interatomic potential) Influence of potential on cascade expansion The shorter the range for very high energies, the larger the cascade volume The more diluted the cascade C.S. Becquart

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

  19. Main conclusions on the cohesive model • Theshorterthe range for very high energies, thelargerthe cascade volume, the more“diluted” the cascade. • 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 theexpense of focusons. Threshold displacement energies not enough Better model for atomic interactions at small separations : ab initio calculations Quantitative results have to be taken with care M. I. Mendelev, S. Han, D. J. Srolovitz, G. J. Ackland, D. Y. Sun and M. Asta, Phil. Mag. A 83 (2004) 3977. C.S. Becquart

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

  21. MSD (Å3) Lattice parameter (Å) Temperature (K) Temperature (K) Let’s not forget the thermal properties C.S. Becquart

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

  23. Object KMC: the events Recombination Electrons + Emission + traps Frenkel pairs Interstitial loop PBC or surface Emission Vacancy cluster Neutrons Interstitial cluster sinks + >300nm Annihilation Vacancy loop cascade Migration Parameterisation • Gi =Gi0 exp( -Ea / kT) C.S. Becquart

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

  25. V emission V-Cu emission diffusion / migration 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 C.S. Becquart

  26. Reaction radii V-I recombination distance Exp 2.2 a0 - 3.3a0 MD 1.7 a0 - 1.9 a0 loops 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. C.S. Becquart

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

  28. Reaction radii Highly anisotropic C.S. Becquart

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

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

  31. Density (m-3) dpa Reaction radii Neutron irradiation (HFIR flux) Density of vacancy clusters 31016 FPcm‑3s‑1 41014 10 keV and 21014 20 keV cascade-debriscm‑3s‑1 HFIR : dose-rate 10-6 dpa/s r = 1 nn/2 r = 1.9 a0/2 r = 3.3 a0/2 experimental * 70°C M. Eldrup, B.N. Singh, S.J. Zinkle, T.S. Byun and K. Farrell, Journ. Nucl. Mater. 307-311 (2002) 912-917]. C.S. Becquart

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

  33. Density (m-3) dpa Mobilities Neutron irradiation (HFIR flux) Density of vacancy clusters 31016 FPcm‑3s‑1 41014 10 keV and 21014 20 keV cascade-debriscm‑3s‑1 dose-rate 10-6 dpa/s M. Eldrup, B.N. Singh, S.J. Zinkle, T.S. Byun and K. Farrell, Journ. Nucl. Mater. 307-311 (2002) 912-917]. C.S. Becquart

  34. clusters (size m >=2): attempt frequency Em = 0.04 eV, s = 0.51 Mobilities • INTERSTITIALS • mono–interstitials: 3D random walk • clusters: 3D random walk or 1D • along <111> direction (cf. MD) I à 1000K MD simulations Exp and Ab initio Em = 0.3 eV for SIA I à 600K 2 I à 600K 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) C.S. Becquart

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

  36. set A set B, r = 1nn/2 set B, r = 3.3 a0/2 experimental * Loop density (cm-3) 1/T (K-1) Em = 0.04 eV clusters (size m >=2): attempt frequency Mobilities Loop density after 1200 s Set B, s = 10, large clusters almost immobile C.S. Becquart

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

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

  39. 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? C.S. Becquart

  40. CONCLUSIONS 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). C.S. Becquart

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

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

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

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

  45. 0.15 eV (128 at. 3x3x3 kpts) 0.26 eV (128 at. 2x2x2 kpts2) Binding energies: Cun clusters Most stable configurations -0.23 eV C.S. Becquart

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

  47. C.S. Becquart

  48. w’’3 w’’4 w’4 w4 w’3 w2 w3 w6 w5 9-frequency model (Le Claire) [1] Hypothesis nFe = nCu = 3.65 10 15s-1 [2] cm2 s – 1 cm2 s – 1 [1] A.D. Le Claire, in Physical Chemistry: an advanced treatise, edited by H. Eyring, Academic Press, New York, 1970), vol. 10, chap. 5. • [2] F. Soisson, G. Martin and A. Barbu, Annales de Physique, vol.20 (1995) C3-13. C.S. Becquart

  49. Role of the cohesive model (interatomic potential) 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 (a0) C.S. Becquart

  50. Fuel. Usually pellets of uranium oxide (UO2) 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. C.S. Becquart

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