Atomistic modeling of segregation and precipitation in ferritic steels under irradiation

Transcription

1 Atomistic modeling of segregation and precipitation in ferritic steels under irradiation Frédéric Soisson CEA Saclay, Service de Recherches de Métallurgie Physique

2 Motivations Fe-Cr alloys : a model for ferritic and ferritic-martensitic steels (7-14%Cr), candidate materials for future nuclear reactors (Gen IV and fusion) Potential problems : - α precipitation, strongly accelerated by irradiation hardening and embrittlement - radiation induced segregation, e.g. Cr depletion at GBs corrosion, embrittlement ASTRID Sodium cooled fast reactor Gen IV (fuel cladding, wrapper tubes) ITER Fusion reactor (Test Blanket Modules) A model system for spinodal decomposition (decomposition in unstable solid solution) PAGE 2

3 Fe-Cr alloys Potential technological problems: coherent α - α decomposition (accelerated by irradiation) in alloys with 9-14%Cr hardening and embrittlement Cr depletion at grain boundaries (radiation induced segregation - RIS) loss of corrosion resistance, embrittlement Special thermodynamic and diffusion properties magnetic properties 5 DÉCEMBRE 2016 PAGE 3

4 From jump frequencies to the kinetics of phase transformations The precipitation kinetic pathways depend on point defect diffusion properties key points : the dependence of the migration barriers and the defect concentrations with the local configuration A multiscale Approach Ab initio calculations (thermodynamics and diffusion) Diffusion model on a rigid lattice Applications to Fe-Cr alloys Atomistic Kinetic Monte Carlo simulations (AKMC) decomposition during thermal ageing decomposition under irradiation radiation induced segregation comparison with experiments (3D atom probe and SANS)

5 D (m 2 s -1 ) DFT calculations of point defect properties Vacancies weak Cr-V interactions a low ΔH 2 migration barrier Cr Self-Interstitials (SIAs) V Fe-Cr alloys: <110> dumbbells mixed dumbbell is stable (E b = ev) With a low migration barrier 0 DFT (SIESTA) AKMC ΔH0 ΔH2 ΔH3 ΔH3' ΔH3" ΔH4 ΔH4' ΔH4" ΔH5 ΔH6 A rapid diffusion of Cr, both by vacancies and SIAs AKMC D T T C 600 C 500 C exp. Fe- Fe- Fe- para ferro D Cr* Fe* Fe Fe D Fe Fe* D Fe Cr* /T (K -1 ) 0.34 ev 0.23 ev PAGE 5

6 Diffusion and interaction model Pair interactions on a rigid BCC lattice: free energy of one atomic configuration FeCr alloys : - temperature dependent and composition dependent interactions effects of vibrational entropies and magnetic transitions. G conf ij g ( n) ij Diffusion by thermally activated point defects jumps - jump frequency : depend on the local environments mig ΔG AV Γ AV νa exp kt b - migration barriers: broken-bond models mig SP n Δ G G ( SP) G ( ini) g g Ai Aj ( ) ( n) AV sys sys kv i j, n k, n saddle-point interactions broken-bonds fitted on DFT calculations (0K) g Γ AV Γ BV AKMC: residence time algorithm - thermal ageing: simulations with atoms, PBC and 1 vacancy time scale : MC eq physical time: t t ( c / c ) MC V V - under irradiation: point defect formation and elimination mechanisms real time scale t MC 1 Г i i PAGE 6

7 THERMODYNAMICS AND DIFFUSION IREMEV monitoring meeting, Alicante, 7 9 June, 2016 F. Soisson, DMN/SRMP, CEA 10 AVRIL 2012 PAGE 7 5 DÉCEMBRE 2016

8 H mix (mev) Thermodynamics: the Fe-Cr phase diagram Short range ordering below approximately 10%Cr, unmixing tendency above Pair interactions on a rigid BCC lattice V g g g ( i) ( i) ( i) i FeFe CrCr FeCr - 1 st and 2 nd nn interactions, composition dependence fitted on DFT calculations of H mix (SQS, PWSCF, GGA-PAW) - temperature dependence fitted on the experimental c p and the α-α critical temperature Phase diagram : good agreement with the modified CALPHAD diagram (Bonny et al, 2010) asymmetrical miscibility gap, non-vanishing Cr solubility at low T PAGE 8

9 D (m 2 s -1 ) Fe-Cr alloys: Tracer Diffusion Coefficients for mig Δ S ( Fe) 4.1 k and Δ S ( Fe) 2.1k V B V B T αγ T C 600 C C 500 C 500 C AKMC exp. D Fe Cr* D Fe Fe* D Fe Fe* D Fe Cr* γ-fe Fe- Fe- α-fe α-fe Fe- para ferro /T (K -1 ) PAGE 9

10 D (cm 2.s -1 ) Fe-Cr alloys: Interdiffusion Coefficients ~ Exp [1,2] AKMC 850 K K [1] K [1] K [1] 1713 K [2] 1453 K [2] % Cr No experimental data below 900K The interdiffusion coefficients strongly decrease with the Cr content Its important to take into account the evolution of the vacancy concentration [1] Braun et al, 1985 [2] Jönsson th International Conference on Multiscale Materials Modeling 9 14 October 2016 Dijon, France PAGE 10

11 PRECIPITATION KINETICS: THERMAL AGEING (NO IRRADIATION) IREMEV monitoring meeting, Alicante, 7 9 June, 2016 F. Soisson, DMN/SRMP, CEA 10 AVRIL 2012 PAGE 11 5 DÉCEMBRE 2016

12 Kinetics of α-α decomposition : AKMC vs 3DAP Fe-20%Cr T = 500 C AKMC (E. Martinez, O. Senninger, CEA) 3D atom probe (Novy et al, GPM Rouen, 2009) PAGE 12

13 Kinetics of α-α decomposition : AKMC vs SANS Small Angle Neutron Scattering experiments : 500 C: Bley (1992) 540 C: Furusaka et al. (1986) 500 C 540 C SANS experiments AKMC simulations AKMC simulations without magnetic correction - F/P transition : strong acceleration of the decomposition between above 35% Cr (lower T C ) - better agreement with experimental kinetics PAGE 13

14 PRECIPITATION UNDER IRRADIATION IREMEV monitoring meeting, Alicante, 7 9 June, 2016 F. Soisson, DMN/SRMP, CEA 10 AVRIL 2012 PAGE 14 5 DÉCEMBRE 2016

15 Irradiation damage: short term evolution Ion and neutron irradiations: displacement cascades Molecular dynamics in α-fe (E PKA = 20 kev, 20 ps) E.A. Calder (2010) EAM potential Molecular Dynamics Displacements: creation of vacancies (V), self-interstitials (I) and point defect clusters radiation damage in dpa (displacement pet atom) dose rate in dpa.s -1 Replacements: change of the lattice sites ballistic mixing Long term evolution - acceleration of diffusion thermodynamic equilibrium - elimination of excess point defect solute fluxes radiation induced segregation - ballistic mixing (in alloys: homogenization, disordering) PAGE 15

16 Cr precipitation in iron under irradiation: Experimental Observations Fe-Cr based alloys, with 9-20%Cr at 300 C the precipitation α (Cr-rich) is too slow to be observed during isotheral annealing α precipitates have been observed after: - neutrons irradiation Fe-9% and 12%Cr at 300 C 7 x 10-7 dpa.s -1, 0.6 dpa V. Kuksenko et al, JNM 2013 Fe-9 to 18% Cr 290 C 3.4 x 10-7 dpa.s -1, 1.82 dpa M. Bachhav et al, SM electron irradiation Fe-15%Cr at 300 C 3.9 x 10-5 dpa.s -1, 0.7 dpa O. Tissot et al, SM ion irradiation Fe-15%Cr at 300 C 5.2 x 10-5 dpa.s -1, 0.7 dpa O. Tissot et al, MRL 2016 α precipitates have not been observed after: - ion irradiation Fe-12%Cr at 300 C 2 x 10-4 dpa.s -1, 0.5 dpa C. Pareige et al, JNM Ion irradiation Fe-15%Cr at 300 C 2.8 x 10-3 dpa.s -1, 120 dpa O. Tissot et al electron irradiation Fe-15%Cr at 300 C and 40 C 2.5 x dpa.s -1, 10-4 dpa O. Tissot et al General trend: strong acceleration od the precipitation at low/moderate dose rates no precipitation at high dose rates DECEMBER 5, 2016 PAGE 16

17 k 2 tot (cm-2 ) Point defect concentrations under irradiation Rate theory dci dt dcv dt 2 G Rc c k D c 2 G Rc c k D c c i v tot i i i v tot v v c eq v, i v, i G σφ creation 2 tot rec R 4πd D D / V k i v at dose rate (dpa.s-1) recombination I-V : total sink strenght, elimination at sinks (grain boundaries, dislocations, point defect clusters,...) Cluster Dynamics: evolution of point defect clusters v w ( nv, v) w ( nv, v) nv electrons, 300 C, 2.5 x dpa.s -1 (GB 141 m) electrons, 300 C, 2.5 x dpa.s -1 (thin film 5m) neutrons, 290 C, 3.4 x 10-7 dpa.s electrons, 300 C, 3.9 x 10-5 dpa.s -1 electrons, 400 C, 3.9 x 10-5 dpa.s -1 ions, 300 C, 5.2 x 10-5 dpa.s mi w ( nv, i) 10 9 Depending on the irradiation conditions, sink strengths vary between k 2 tot = 10 8 to cm -2 i t (s) Small vacancy clusters are usually the dominant sink, except at very low doses and under e- irradiations 8th International Conference on Multiscale Materials Modeling 9 14 October 2016 Dijon, France PAGE 17

18 k 2 tot (cm-2 ) Irradiation mechanisms in AKMC simulations Formation of Frenkel pairs Replacement collision Displacement cascades Sequences SIA (ion and neutron irradiation) (electron irradiation) random 1 st and 2 nd nn 1st nn replacements replacements in 111 directions n rep = 100 n rep = 10 V within a sphere R = 5 n SIA V SIA-V recombination (d rec = 3a) Point defect eliminations on perfect sinks Cluster dynamics k 2 () t tot k 2 () t tot AKMC simulations with random distribution of individual pd sinks with the same strength c d VAC c i =G/(D i k 2 tot ) AKMC rate theory SIA c v =G/(D v k 2 tot ) k 2 ( t) increases tot c i and c decrease favors ballistic mixing v t (s) PAGE 18

19 k 2 tot (cm-2 ) k 2 tot (cm-2 ) R (nm) R (nm) d p (cm -3 ) d p (cm -3 ) Electron irradiations Experiments O. Tissot et al Scripta Materialia 122, (2016) Fe-Cr alloys electron irradiations 300 and 400 C, 3.9 x 10-5 dpa.s -1 One dose: 1.82 dpa Fe-15%Cr 300 C 3.9 x 10-5 dpa.s Exp. (O.Tissot et al) electron irradiation thermal ageing Fe-15%Cr 400 C 3.9 x 10-5 dpa.s Exp. (O.Tissot et al) electron irradiation thermal ageing AKMC simulations good agreement with experiments coarsening regime No significant effect of ballistic mixing k tot 10 cm t (s) t (s) PAGE 19

20 k 2 tot (cm-2 ) R (nm) d p (cm -3 ) Ion irradiations high dose rate Experiments O. Tissot et al Materials Research Letters, 1-7 (2016) Fe-15%Cr alloys ion irradiations 300 C, 2.8 x 10-3 dpa.s -1 One dose: 120 dpa, no precipitate thermal ageing ion irradiation exp. (O. Tissot et al.) no precipitates AKMC simulations No precipitates at 120 dpa k tot 510 cm Suggest precipitates at low doses (R > 1nm between approx. 0.1 and 10 dpa) exp. (O. Tissot et al.) no precipitates t (s) PAGE 20

21 Precipitation under irradiation 3D Atom Probe of α precipitation, neutron irradiation in supersaturated alloys Bachhav et al Scripta Mater. 74 (2014) 48 V. Kuksenko et al, JNM 432 (2013) 160 AKMC simulations 563 K, 3.4 x 10-7 dpa.s -1 Kuksenko et al (2012) 3DAP Fe-12%Cr 300 C 0.6 dpa 104 nm GB PAGE 21

22 Conclusions on ballistic mixing G. Martin, P. Bellon (e.g. Driven alloys, Solid State Physics, Vol. 50, pp , 1997) Ballistic mixing effects inverse coarsening, dissolution of precipitates, disordering Thermally activated diffusion accelerated precipitation (in a supersaturated alloy) Ballistic mixing is dominant at high irradiation intensity: Dbal γ 1 irr D high sink strength low point defect concentration ballistic dissolution 2 2 D a Γ a n G bal bal rep irr irr irr G Dth 2 cv Dv with cv when elimination at sinks is dominant 2 Dk v tot γ a 2 n 2 repktot th - for a given sink density (or sink strength), the irradiation intensity is independent of the dose rate G 2 - depends on the dose rates k tot The ballistic mixing effects are mainly controlled by the sink density PAGE 22

23 RADIATION INDUCED SEGREGATION 8th International Conference on Multiscale Materials Modeling 9 14 October 2016 Dijon, France PAGE 23

24 Radiation Induced Segregation A-B alloy under irradiation: annihilation of excess point defects at GBs, dislocations, surfaces, etc vacancies sink C B J vac J J vac B vac A C V 1 interstitials sink C B J int int J Bint J 1 A C I vac J B vac J A int J B int J A Onsager equations : the off-diagonal terms control the coupling between solute and point defects fluxes For example: if L BV /L BB > 0 fluxes of V and B in the same direction otherwise in opposite directions Fe-Cr alloys (E. Marquis, Oxford) ODS steel - 12% Cr after thermal ageing J i j L μ ij j under irradiation (Fe ions) 500 C 500 C 300 C 5 DÉCEMBRE nm

25 AKMC: Radiation Induced vs equilibrium Segregation Fe-10%Cr T = 650 K, 10-6 dpa.s GB seg e Cr 0.1eV 0.06 dpa X Cr Fe-10%Cr T = 950 K, 10-3 dpa.s distance (nm) GB seg e Cr dpa 0.1eV X Cr Steady-state profiles : L CrV CrI CCr LFeV LFeI L C V one expects an enrichment of Cr at sinks at low T, a depletion at high T distance (nm) PAGE 25

26 Conclusions AKMC simulations with effective interactions fitted on DFT calculation advantages: good description of driving forces, diffusion properties (correlations) and nucleation drawbacks: rigid lattice approximation, time consuming (-> coupling with cluster dynamics, phase field) In Fe-Cr alloys Magnetic effects are important (impact on thermodynamic and diffusion properties) Radiation accelerated precipitation ballistic disordering at high dose rates, controlled by the evolution of the sink density important for the comparison between ion and neutron irradiation Radiation Induced Segregation is controlled by a balance between opposite effects of V and SIA -> may explain the variability of experimental studies ( RIS in austenitic steels) Related work, perspectives - large scale models - evolution of the mechanical properties - Austetinic steels (Fe-Ni-Cr, γ-cfc): paramagnetic -> a challenge for DFT calculations PAGE 26

27 Aknowledgments Chu-Chun Fu, Thomas Jourdan, Estelle Meslin, Maylise Nastar, Orianne Senninger CEA Saclay, SRMP Enrique Martinez Los Alamos National Laboratory Jean Henry, Olivier Tissot CEA Saclay, SRMA Cristelle Pareige, GPM, Université de Rouen PAGE 27