E. Vincent* , **, C.S. Becquart*, C. Domain **

1. Ab initio calculations of point defect interactions with solute atoms in bcc Fe EDF E. Vincent*,**, C.S. Becquart*, C. Domain** Electricité de France * LMPGM, UMR 8517, Université de Lille I, F-59655 Villeneuve d'Ascq Cédex, France ** EDF-R&D, Dept MMC, Les Renardières, F-77250 Moret sur Loing, France EURATOM European Project (FI6O-CT-2003-508840)

2. PRESSURE VESSEL EMBRITTLEMENT • Radiation damage in pressure vessel steels (low Cu contents ~ 0.1%) • Radiation damage simulation (REVE & PERFECT project) • Under neutron irradiation : point defect and complexes formation (MD and KMC) • Role of Cu (modelled FeCu dilute alloy) • Rate theory or kinetic Monte Carlo simulations (time evolution of primary damage) needs point defect properties

3. PRESSURE VESSEL EMBRITTLEMENT 15x15x50 nm Cu Ni neutron Si Mn Displacement cascade P A. Barbu (CEA) TEM Cu Under irradiation: point defect and complexes are formed • Effect of solute atoms (Cu, Ni, Mn, Si, P) • Effect of interstitial atoms (C, N) P. Pareige (Université Rouen) Tomographic atom probe  Hardening  Embrittlement

4. Cu Mn Ni 0.2% 0.8% 1.6% FORMATION OF THESE SOLUTE RICH CLUSTERS • Cohesive model (Fe-Cu, Fe-Ni, Fe-Si, ..., Ni-Mn, ...) • phase diagram (thermodynamics) • ab initio calculations Metropolis Monte Carlo + [C.L. Liu, G.R. Odette, B.D. Wirth, G.E. Lucas, Materials Science and Engineering A 238 (1997) 202-209] Kinetics ?

5. METHODS & COHESIVE MODELS Ab initio VASP: [1] G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993); ibid. 49, 14 251 (1994) [2] G. Kresse and J. Furthmüller, Comput. Mat. Sci. 6, 15 (1996) [3] G. Kresse and J. Furthmüller, Phys. Rev. B 55, 11 169 (1996) Density Functional Theory VASP (Vienna Ab initio Simulation Package) Plane wave (energy cutoff 240 eV) Ultra soft pseudo potentials (Vanderbilt type pseudo potentials) Exchange and correlation: GGA (PW91) Spin polarised 54 atoms (555 k points) – 128 atoms (333k points) – 240 eV All atomic positions for defects calculation are relaxed Constant volume calculation

6. A A B B A A + + B B POINT DEFECT BINDING ENERGY CALCULATIONS E binding = E(# A & B non interacting) – E(# A & B interacting) But only small system size tractable... E binding = [ E(# A) + E(# B) ] – [ E(# A & B defect interacting) + E(without defect) ]

7. SUBSTITUTIONAL & SOLUTE BINDING ENERGY Cu: very low solubility Si, Mn, Ni: soluble in Fe Fe-Mn Fe-Cu Fe-Ni Fe-Si

8. RELAXATION FIELD AROUND DEFECTS H.W. King, J. Mater. Sci. 1 (1966) 79.

9. w’’3 w’’4 w’4 Emig Fe : 0.65 eV w4 w’3 w2 w3 w6 w5 f µMn Ferro magn. af µMn AntiFerro magn. [exp] Möslang, E. Albert, E. Recknagel, and A. Weidinger, Hyperfine Interact. 15/16, (1983) 409 VACANCY - SOLUTE BINDING ENERGIES 2nn 1nn

10. w’’3 w’’4 w’4 w4 w’3 w2 w3 w6 w5 SOLUTE DIFFUSION COEFFICIENT IN Fe (vacancy mechanism) (model I and II not valid) 9-frequency model (Le Claire) [1] Hypothesis nFe = nCu = 3.65 10 15s-1 [2] cm2 s – 1 cm2 s – 1 (cf. COSIRES 2002) [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.

11. (µB) INTRINSIC POINT DEFECT FORMATION ENERGIES LARGE DE btw <110> / <111> configuration: 0.7 eV Experimental (Moser): <110> most stable P. Moser, Mem. Scient. Revue Metall., 63 (1966) 431 C. Domain, C.S. Becquart, Phys. Rev B 65 (2002) 024103 C. C. Fu, F. Willaime, P. Ordejon, Phys. Rev. Lett. 92 (2004) 175503 M.I. Mendelev, S. Han, D.J. Srolovitz, G.J. Ackland, D.Y. Sun, and M. Asta, Phil. Mag. 83 (2003) 3977-3994

12. SELF INTERSTITIALS & SMALL SUPERCELLS MD convergence test Fe potential: Ackland et al., Phil. Mag. 1997

13. SELF INTERSTITIALS & SOLUTE INTERACTIONS Mixed crowdion 1nnCompression 1nnTension Mixed <110> dumbbell Solute in tensile region Solute in compression region

14. 0.98 1.02 0.38 0.44 0.13 0.06 0.33 0.27 0.85 0.83 0.18 0.11 0.04 -0.02 -0.02 0.02 -0.04 -0.04 -0.27 -0.28 -0.52 -0.46 -0.17 -0.22 -0.36 -0.35 -0.12 -0.10 -0.36 -0.30 <110> INTERSTITIAL – SOLUTE BINDING ENERGIES Most stable configuration Ni Wsf +4.7% Binding energy (eV) P Si Mn Cu Wsf – 13.2% Wsf – 7.9% Wsf +4.9% Wsf +17.5%

15. DE (<110> – <111>) Fe: 0.79 eV 0.66 0.42 0.72 0.93 0.77 INTERSTITIAL – SOLUTE INTERACTIONS: <110> – <111> ENERGY DIFFERENCES Most stable configuration 0.98 1.02 0.38 0.44 0.33 0.27 0.13 0.06 -0.04 -0.04 0.85 0.83 -0.02 0.02 0.18 0.11 Binding energy (eV) 0.04 -0.02 -0.12 -0.10 P Si Mn Ni Cu Wsf +4.7% Wsf –13.2% Wsf – 7.9% Wsf +4.9% Wsf +17.5%

16. INTERSTITIAL - SOLUTE BINDING ENERGIES • No change of the relative stability between <110> and <111> interstitial orientation • Mn: mixed <110> dumbbell (significant interaction with SIA ~0.4 eV) • Cu: site under tensile stress (~0.1 eV) • P: strong interaction & mixed dumbbell (~ 1 eV) • Si: significant interaction in 1nnCompression (~0.3 eV) • Ni: no interaction with <110> SIA (~0 eV) • Si, Mn, Ni: site(s) under compression

17. CONCLUSIONS • Ab initio calculations can be useful in the study of radiation damage: chemical interaction between solute and point defects • Chemical interactions with point defect important: relative size criteria not sufficient • Perspectives: introduction of these data in kinetic Monte Carlo