Ab initio calculations of point defect interactions with
Ab initio calculations of point defect interactions with solute atoms in bcc Fe E. Vincent*, **, C. S. Becquart*, C. Domain** EDF 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 (FI 6 O-CT-2003 -508840) COSIRES 2004, Helsinki, June 28 - July 2, 2004 1
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 Fe. Cu dilute alloy) • Rate theory or kinetic Monte Carlo simulations (time evolution of primary damage) needs point defect properties COSIRES 2004, Helsinki, June 28 - July 2, 2004 2
PRESSURE VESSEL EMBRITTLEMENT 15 x 50 nm Cu Ni neutron Si Mn Displacement cascade A. Barbu (CEA) TEM P 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 COSIRES 2004, Helsinki, June 28 - July 2, 2004 3
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] Cu 0. 2% Kinetics ? COSIRES 2004, Helsinki, June 28 - July 2, 2004 Mn 0. 8% Ni 1. 6% 4
METHODS & COHESIVE MODELS Ab initio VASP: Density Functional Theory VASP (Vienna Ab initio Simulation Package) Plane wave (energy cutoff 240 e. V) Ultra soft pseudo potentials (Vanderbilt type pseudo potentials) Exchange and correlation: GGA (PW 91) Spin polarised 54 atoms (5 5 5 k points) – 128 atoms (3 3 3 k points) – 240 e. V [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) All atomic positions for defects calculation are relaxed Constant volume calculation COSIRES 2004, Helsinki, June 28 - July 2, 2004 5
POINT DEFECT BINDING ENERGY CALCULATIONS A A B B E binding = E(# A & B non interacting) – E(# A & B interacting) But only small system size tractable. . . A A B + + B E binding = [ E(# A) + E(# B) ] – [ E(# A & B defect interacting) + E(without defect) ] COSIRES 2004, Helsinki, June 28 - July 2, 2004 6
SUBSTITUTIONAL & SOLUTE BINDING ENERGY Si, Mn, Ni: soluble in Fe Fe-Mn Fe-Ni Cu: very low solubility Fe-Cu Fe-Si COSIRES 2004, Helsinki, June 28 - July 2, 2004 7
RELAXATION FIELD AROUND DEFECTS H. W. King, J. Mater. Sci. 1 (1966) 79. COSIRES 2004, Helsinki, June 28 - July 2, 2004 8
VACANCY - SOLUTE BINDING ENERGIES 1 nn 2 nn w 2 w’’ 4 w’’ 3 w’ 4 w’ 3 w 6 w 5 Emig Fe : 0. 65 e. V f µMn Ferro magn. af µMn Anti. Ferro magn. [exp] Möslang, E. Albert, E. Recknagel, and A. Weidinger, Hyperfine Interact. 15/16, (1983) 409 COSIRES 2004, Helsinki, June 28 - July 2, 2004 9
SOLUTE DIFFUSION COEFFICIENT IN Fe (vacancy mechanism) 9 -frequency model (Le Claire) [1] (model I and II not valid) Hypothesis n. Fe = n. Cu = 3. 65 10 15 s-1 w’’ 3 w’’ 4 [2] w’ 4 w 4 cm 2 s – 1 w 2 w 3 cm 2 s – 1 w’ 3 w 6 w 5 (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) C 3 -13. COSIRES 2004, Helsinki, June 28 - July 2, 2004 10
INTRINSIC POINT DEFECT FORMATION ENERGIES LARGE DE btw <110> / <111> configuration: 0. 7 e. V 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 COSIRES 2004, Helsinki, June 28 - July 2, 2004 (µB) 11
SELF INTERSTITIALS & SMALL SUPERCELLS MD convergence test Fe potential: Ackland et al. , Phil. Mag. 1997 COSIRES 2004, Helsinki, June 28 - July 2, 2004 12
SELF INTERSTITIALS & SOLUTE INTERACTIONS Mixed <110> dumbbell 1 nn. Compression Solute in compression region 1 nn. Tension Mixed crowdion Solute in tensile region COSIRES 2004, Helsinki, June 28 - July 2, 2004 13
Most stable configuration Binding energy (e. V) <110> INTERSTITIAL – SOLUTE BINDING ENERGIES Ni 0. 98 1. 02 0. 38 0. 44 Wsf +4. 7% 0. 13 0. 06 0. 33 0. 27 0. 85 0. 83 0. 18 0. 11 0. 04 -0. 02 -0. 04 -0. 27 -0. 28 -0. 36 -0. 35 -0. 52 -0. 46 -0. 17 -0. 22 -0. 12 -0. 10 P Wsf – 13. 2% Si Mn Cu Wsf – 7. 9% Wsf +4. 9% COSIRES 2004, Helsinki, June 28 - July 2, 2004 Wsf +17. 5% 14 -0. 36 -0. 30
Most stable configuration INTERSTITIAL – SOLUTE INTERACTIONS: <110> – <111> ENERGY DIFFERENCES 0. 98 1. 02 0. 33 0. 27 0. 38 0. 44 Binding energy (e. V) 0. 13 0. 06 -0. 04 0. 85 0. 83 -0. 02 0. 18 0. 11 0. 04 -0. 02 -0. 12 -0. 10 P Wsf – 13. 2% Si Mn Ni Cu Wsf – 7. 9% Wsf +4. 7% Wsf +17. 5% DE (<110> – <111>) Fe: 0. 79 e. V COSIRES 2004, Helsinki, June 28 - July 2, 2004 0. 42 0. 72 0. 66 15 0. 93 0. 77
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 e. V) • Cu: site under tensile stress (~0. 1 e. V) • P: strong interaction & mixed dumbbell (~ 1 e. V) • Si: significant interaction in 1 nn. Compression (~0. 3 e. V) • Ni: no interaction with <110> SIA (~0 e. V) • Si, Mn, Ni: site(s) under compression COSIRES 2004, Helsinki, June 28 - July 2, 2004 16
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 COSIRES 2004, Helsinki, June 28 - July 2, 2004 17
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