Time accelerated P E R F O R M 6 0 P E R F O R M 6 0 P E R F O R - PowerPoint PPT Presentation

Time accelerated P E R F O R M 6 0 P E R F O R M 6 0 P E R F O R M 6 0 P E R F O R M 6 0 F P 7 P ro je ct F P 7 P r oje ct F P 7 P ro je ct F P 7 P r oje ct Atomic Kinetic Monte Carlo for radiation damage modelling C. Domain, C.S. Becquart, R. Ngayam-Happy EDF R&D Dpt Matériaux & Mécanique des Composants Les Renardieres, Moret sur Loing, France UMET, Université de Lille 1 Villeneuve d’Ascq, France

1nm 3 0 - ps (10-30nm) 3 ns m 3 ab initio 40 years Molecular dynamics Multi-scale modelling Finite elements s - h cm 3 Barbu, CEA + experimental validation Pareige, U. Rouen KMC P E R F O R M 6 0 P E R F O R M 6 0 cohesive model P E R F O R M 6 0 P E R F O R M 6 0 F P 7 P r o je ct F P 7 P r oje ct F P 7 P r o je ct F P 7 P r oje ct & parameterisation Micro-macro (30-100nm) 3 µm 3 h-year Dislocation Mesoscopic dynamics 2 EDF R&D - Workshop BEMOD12 - Dresden - March 2012 EURATOM European Project PERFECT ( FI6O-CT-2003-508840)

Radiation damage Irradiation: Material: Electron: Fe Frenkel pairs + alloying elements: Cu, Ni, Mn, Si, … Ion and neutron: + carbon, nitrogen displacement cascades ( 10 - 100 keV) vacancies and interstitials: + dislocations isolated and in clusters 0.08 dpa – Neutron irradiation vacancies Ni Si displacement cascades neutron Mn PKA Cu interstitials  E Elastic interaction PKA : primary knock-on atom energy transfert 15x15x50 nm TAP, Pareige, U. Rouen Microstructure evolution: point defect clusters: nanovoids, dislocation loops solute clusters (# or \# point defects) TEM, Barbu, CEA 3 EDF R&D - Workshop BEMOD12 - Dresden - March 2012

Kinetic Monte Carlo simulation of irradiation Atomic KMC Object KMC Recombination Electrons + Emission + traps Frenkel Interstitial loop pairs PBC dislocation Emission or surface Vacancy cluster Interstitial cluster Neutrons surface surface Cascades cascades sinks + Annihilation Vacancy loop PBC cascade Migration PBC Frenkel pairs Paires de Frenkel Paires de Frenkel surface surface Ageing (one single vacancy) [JNM 335 (2004) 121–145] 4 EDF R&D - Workshop BEMOD12 - Dresden - March 2012

Atomic Kinetic Monte Carlo of microstructure evolution Ni Si Objective: Simulation formation of solute rich complexes (observed by TAP) under irradiation Mn Cu TAP, Pareige, U. Rouen 15x15x50 nm Ab initio AKMC  Fe-V_1nn Solute interactions (Cu, Ni, Mn, Si) (interface energies, Solute diffusion by  Fe-Si_2nn mixing energies …) - vacancy mechanisms - interstitial mechanisms Parameterisation cohesive model Experimental data and Thermodynamical data    ( 1 )   ( 2 )   ( 1 )   ( 2 )   ( 1 )   ( 2 ) 4 3 8 6 4 3 E       ( ) ( ) ( ) ( ) ( ) ( ) mixing Fe Fe Fe Fe Fe X Fe X X X X X   ( 1 )   ( 2 )   ( 1 )   ( 2 ) ( ) 8 6 4 3 Z E formation V     ( ) ( ) ( ) ( ) V Z V Z Z Z Z Z         ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) E      ( ) ( ) ( ) ( ) ( ) binding V X Fe V Fe X Fe Fe V X Experimental validation: TAP, SANS, SAXS, PA, TEP 5 EDF R&D - Workshop BEMOD12 - Dresden - March 2012

Atomistic Kinetic Monte Carlo (AKMC) Atomistic Kinetic Monte Carlo (AKMC) Vincent et al. NIMB 255 (2007) 78  Treatment of multi-component systems on a rigid lattice Vincent et al. JNM 382 (2008) 154  Substitutional elements  Interstitial elements Code: LAKIMOCA  Diffusion by 1nn jumps  Via vacancies  Via interstitials   Ea    Jump Probability: exp    X = attempt frequency X X   kT  Residence Time Algorithm applied to all events  Vacancy and Interstitial jumps          3,1 3,1 3,1 1,2 1,2 1,2 2,2 2,2 2,2  Frenkel Pairs and Cascade flux for irradiation v 2 v 2 v 2 v 1 v 1 v 1 v v v 1 3 3 3   t    Average time step:         2,1 2,1 2,1 3,2 3,2 3,2 1,1 1,1 1,1 jk    , j k 3,2 3,2 3,2                1,1 1,1 1,1 1,8 1,8 1,8 2,1 2,1 2,1 2,7 2,7 2,7 3,7 3,7 3,7  Environment dependant form of activation energy Ea  Ef Ei   ( ) Ea Ea X i 2 6 EDF R&D - Workshop BEMOD12 - Dresden - March 2012

AKMC irradiation simulation conditions AKMC irradiation simulation conditions For electron irradiation: Frenkel Pair (FP) flux For neutron irradiation: flux of • 20 keV and 100 keV cascades debris obtained by Molecular Dynamics (R. Stoller, J. Nucl. Mater. 307-311 (2002) 935) • Frenkel Pairs cascades surface Cascades PBC PBC Typical simulation box: 1.01  10 -17 cm 3 boxes 8.65 10 6 atoms Frenkel pairs Paires de Paires de Frenkel Frenkel surface 7 EDF R&D - Workshop BEMOD12 - Dresden - March 2012 7

AKMC simulation of radiation damage accumulation Target dose: 0.1 dpa Irradiation duration: 2 days (10 5 s) up to 40 years (10 9 s) Irradiation temperature: 573 K Defect accumulation: > 100 point defects in the simulation box Events: Self interstitial migration (0.3 eV) : time step : 10 -10 s Vacancy migration (0.65 eV) : time step : 10 -7 s Rapidly: annihilation or formation point defect clusters Point defect migration within point defect - solute clusters or trapping with solutes Very large number of jumps required to have “significant event” (ie emission or diffusion) Other jumps with high migration energies (1 eV) : time step : 10 -4 s Computational limitation: ~10 10 steps / month Very complex situation: many events with different time scale & long simulation required 8 EDF R&D - Workshop BEMOD12 - Dresden - March 2012

 Cohesive energy model Cohesive energy model Ef Ei   ( ) Ea Ea X i 2  Fe-V_1nn         ( )   ( )   ( )   ( )   ( )   ( ) i i i i i i E Vacancy:       ( ) ( ) ( ) ( ) ( ) ( ) Fe Fe V V Fe V Fe X V X X Y j k l m n p  Fe-Si_2nn • RPV: 1nn and 2nn pair interactions • FeCr: 2BM potential 1 nnComp  ( ) 1 E dumb X nnTens ( )  ( ) E X mixed i j E X X l l j • solute - dumbbell l j k + + SIA: E b (dumb - dumb) • dumbbell - dumbbell 1nn & 2nn Solute atoms Fe atom            1   1     ( ) ( ) ( ) ( ) nnComp nnTens mixte E E E dumb X E X E X X E dumb dumb   dumb f l i j l j l j k l   , i j j i j + + + FIA (C): FIA vacancy solute SIA ~ 100 ab initio data considered in the model 9 EDF R&D - Workshop BEMOD12 - Dresden - March 2012 9

Cohesive model:  X-Y and  V-X determination Binary alloys ( 1 ) ( 2 ) ( 1 ) ( 2 ) ( 1 ) ( 2 )              4 3 8 6 4 3 • E       ( ) ( ) ( ) ( ) ( ) ( ) mélange Fe Fe Fe Fe Fe X Fe X X X X X • ( 1 ) ( 2 ) ( 1 ) ( 2 ) ( 1 ) ( 2 )              2 4 2 2 E       int ( 100 ) ( ) ( ) ( ) ( ) ( ) ( ) erface Fe Fe Fe Fe Fe X Fe X X X X X • ( 1 ) ( 2 )     ( ) 4 3 i = 1 or 2 E cohésion Z   ( ) ( ) • Z Z Z Z X, Y = solute atoms ( 1 ) ( 2 ) ( 1 ) ( 2 )         Z ( ) 8 6 4 3 • E formation lac     ( ) ( ) ( ) ( ) lac Z lac Z Z Z Z Z Z = Fe or solute atom • ( ) ( ) ( ) ( )       i i i i 2 E     ( ) ( ) ( ) ( ) liaison lac lac Fe lac Fe Fe lac lac ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 1 )         E      ( ) ( ) ( ) ( ) ( ) liaison lac X Fe lac Fe X Fe Fe lac X ε Fe-Cu_1nn Ternary alloys… ε Si-Si_2nn ( ) ( ) ( ) ( ) ( )         i i i i i E      ( ) ( ) ( ) ( ) ( ) liaison X Y Fe X Fe Y Fe Fe X Y Parameters Ab initio data Adjustment on thermal annealing experiment 10 EDF R&D - Workshop BEMOD12 - Dresden - March 2012 10

Neutron irradiation of FeCuNiMnSi alloys Medium term evolution by atomic Kinetic Monte Carlo Fe-0.2Cu-0.53Ni-1.26Mn-0.63Si (at.%) at 300°C Flux: 6.5 10 -5 dpa.s -1 Dose: 1.3 10 -3 dpa V-solute complex SIA-solute complexes Small solute clusters Cu Cu Cu Cu Cu Cu Ni Ni Ni Point defect clusters = germs for precipitation V Si Si Si Si Si Si Mn Mn Mn Mn Mn Mn SIA [> 1 month on 1 CPU] 11 EDF R&D - Workshop BEMOD12 - Dresden - March 2012