[PPT] - 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 Presentation

SLIDE 1

Time accelerated 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

F P 7 P ro je ct F P 7 P r oje ct

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

P E R F O R M 6 0 P E R F O R M 6 0

SLIDE 2

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 2

Finite elements ab initio Molecular dynamics Mesoscopic

Multi-scale modelling + experimental validation

1nm3 0 - ps ns (10-30nm)3 cm3 µm3 h-year s - h (30-100nm)3 m3 40 years

Micro-macro Dislocation dynamics

Barbu, CEA Pareige, U. Rouen

EURATOM European Project PERFECT (FI6O-CT-2003-508840)

F P 7 P r o je ct F P 7 P r oje ct

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

P E R F O R M 6 0 P E R F O R M 6 0

KMC cohesive model & parameterisation

SLIDE 3

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 3

Material: Fe + alloying elements: Cu, Ni, Mn, Si, … + carbon, nitrogen + dislocations Irradiation: Electron: Frenkel pairs Ion and neutron: displacement cascades ( 10 - 100 keV) vacancies and interstitials: isolated and in clusters Microstructure evolution: point defect clusters: nanovoids, dislocation loops solute clusters (# or \# point defects)

TEM, Barbu, CEA TAP, Pareige, U. Rouen

neutron

displacement cascades vacancies interstitials PKA

PKA : primary knock-on atom

E

energy transfert Elastic interaction 15x15x50 nm Cu Mn Ni Si

0.08 dpa – Neutron irradiation

Radiation damage

SLIDE 4

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 4

surface surface cascades Paires de Frenkel surface surface

Cascades

Paires de Frenkel

Frenkel pairs Ageing (one single vacancy) PBC PBC

Electrons

Frenkel pairs

+ Annihilation

Interstitial loop Emission Interstitial cluster Vacancy cluster traps Vacancy loop

Neutrons

cascade

+

Emission Migration

+

Recombination

PBC

r

surface

sinks dislocation

Kinetic Monte Carlo simulation of irradiation

Atomic KMC Object KMC

[JNM 335 (2004) 121–145]

SLIDE 5

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 5

AKMC

Solute interactions (Cu, Ni, Mn, Si) (interface energies, mixing energies …)

Ab initio

Solute diffusion by

vacancy mechanisms
interstitial mechanisms

Parameterisation cohesive model Experimental data and Thermodynamical data Experimental validation: TAP, SANS, SAXS, PA, TEP

Fe-V_1nn Fe-Si_2nn

) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( ) (

3 4 6 8 3 4

X X X X X Fe X Fe Fe Fe Fe Fe mixing

E

     

            

) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( ) (

3 4 6 8 ) (

Z Z Z Z Z V Z V Z formation V

E

   

       

) 1 ( ) ( ) 1 ( ) ( ) 1 ( ) ( ) 1 ( ) ( ) 1 ( ) ( X V Fe Fe X Fe V Fe X V binding

E

    

       

Objective: Simulation formation of solute rich complexes (observed by TAP) under irradiation

TAP, Pareige, U. Rouen

15x15x50 nm Cu Mn Ni Si

Atomic Kinetic Monte Carlo of microstructure evolution

SLIDE 6

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 6

Atomistic Kinetic Monte Carlo (AKMC) Atomistic Kinetic Monte Carlo (AKMC)



Treatment of multi-component systems on a rigid lattice

 Substitutional elements  Interstitial elements



Diffusion by 1nn jumps

 Via vacancies  Via interstitials

Jump Probability:



Residence Time Algorithm applied to all events

 Vacancy and Interstitial jumps  Frenkel Pairs and Cascade flux for irradiation

Average time step:

        kT Ea

X X

exp 



 

k j jk

t

,

1

 Environment dependant form of activation energy Ea

X = attempt frequency



1,1



2,1



2,2



1,2

v1 v2 v

3 

3,1 3,2

 

1,1



2,1



1,8



2,7

 

3,2 3,7



1,1



2,1



2,2



1,2

v1 v2 v

3 

3,1 3,2

 

1,1



2,1



2,2



1,2

v1 v2 v

3 

3,1 3,2

 

1,1



2,1



1,8



2,7

 

3,2 3,7



1,1



2,1



1,8



2,7

 

3,2 3,7

2 ) ( Ei Ef X Ea Ea

i

  

Code: LAKIMOCA

Vincent et al. NIMB 255 (2007) 78 Vincent et al. JNM 382 (2008) 154

SLIDE 7

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 7

7

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

surface surface cascades Paires de Frenkel

Cascades

Paires de Frenkel

Frenkel pairs PBC PBC

Typical simulation box: 1.01  10-17 cm3 boxes 8.65 106 atoms

SLIDE 8

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 8

AKMC simulation of radiation damage accumulation

Target dose: 0.1 dpa Irradiation duration: 2 days (105 s) up to 40 years (109 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: ~1010 steps / month Very complex situation: many events with different time scale & long simulation required

SLIDE 9

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 9

9

Cohesive energy model Cohesive energy model

2 ) ( Ei Ef X Ea Ea

i

  

+

) (

1 j nnTens l

X E

+

) (

1 j i nnComp l

X dumb E 

dumbbell - dumbbell

Eb (dumb - dumb) 1nn & 2nn

SIA:

) (

k j mixed l

X X E 

Solute atoms Fe atom

Fe-V_1nn Fe-Si_2nn

Vacancy: FIA (C): FIA vacancy solute SIA

+ + +

solute - dumbbell

    

               

i j j j i l k j mixte l j nnTens l j i nnComp l f dumb

dumb dumb E X X E X E X dumb E E E

, 1 1

) ( ) ( ) ( ) (

     

     

     

p i Y X n i X V m i X Fe l i V Fe k i V V j i Fe Fe

E

) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (

      ~ 100 ab initio data considered in the model

RPV: 1nn and 2nn pair interactions
FeCr: 2BM potential

SLIDE 10

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 10

10

i = 1 or 2 X, Y = solute atoms

)

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( i Y X i Fe Fe i Y Fe i X Fe i Y X liaison

E

    

       

Binary alloys Ternary alloys…

Z = Fe or solute atom

) 1 ( ) ( ) 1 ( ) ( ) 1 ( ) ( ) 1 ( ) ( ) 1 ( ) ( X lac Fe Fe X Fe lac Fe X lac liaison

E

    

       

) 2 ( ) ( ) 1 ( ) (

3 4 ) (

Z Z Z Z cohésion Z

E

 

   

) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( ) (

3 4 6 8 ) (

Z Z Z Z Z lac Z lac Z formation lac

E

   

       

) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (

2

i lac lac i Fe Fe i lac Fe i lac lac liaison

E

   

     

) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( ) ( ) 100 ( int

2 2 4 2

X X X X X Fe X Fe Fe Fe Fe Fe erface

E

     

            

) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( ) (

3 4 6 8 3 4

X X X X X Fe X Fe Fe Fe Fe Fe mélange

E

     

            

Ab initio data Parameters

εFe-Cu_1nn εSi-Si_2nn Adjustment on thermal annealing experiment

Cohesive model: X-Y and V-X determination

SLIDE 11

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 11

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

SIA Cu Si Mn Cu Si Mn Cu Si Mn Ni Cu Si Mn Cu Si Mn Cu Si Mn Ni Ni V Point defect clusters = germs for precipitation

Neutron irradiation of FeCuNiMnSi alloys Medium term evolution by atomic Kinetic Monte Carlo [> 1 month on 1 CPU]

SLIDE 12

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 12 5 10 15 20 25 30 35 40 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 Cluster Number Number of species in clusters Cu Si Mn Ni P Vac SIA

 Distribution and composition of clusters:

 High Nd of PD clusters

Vacancy clusters are bigger and less numerous than SIA clusters

 Solute clusters form on PD clusters (induced segregation)

Clusters associated with SIA clusters are enriched in Mn Clusters associated with vacancy clusters are enriched in Si/Cu/Mn and Ni/P

 Cu enriched clusters observed (enhanced precipitation)

12

Fe – CuMnNiSiP (at.%) alloys Fe – CuMnNiSiP (at.%) alloys

10 20 30 40 Vacancy SIA Pure Solute Vacancy SIA Pure Solute Nd of Clusters Mean size of Clusters 5 10 15 20 25 Solute-Vacancy Solute-SIA Pure solute Mean composition of clusters SIA Vac P Ni Mn Si Cu

0.18Cu 1.38Mn 0.69Ni 0.43Si 0.01P (A533B plate) 5.79x10-4 dpa/s - 300°C - 9.03 mdpa

SLIDE 13

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 13

5 10 15 20 25 1 7 13 19 25 31 37 43 49 55 61 67 73 79 Répartition des espèces Numéro de l'amas

SIA Vac P Ni Mn Si Cu

The biggest solute clusters are associated with PD clusters

− In agreement with induced segregation mechanism to account for solute clusters formation

Clusters associated with interstitial clusters are enriched in Mn, and P/Ni
Clusters associated with vacancy clusters are enriched in Si/Cu/Mn (mostly) and Ni
I-Solute complexes  V-Solute complexes

Cluster ID

V-Solute SIA-Solute Pure solute

Fe – CuMnNiSiP (at.%) alloys

0.18Cu 1.38Mn 0.69Ni 0.43Si 0.01P 5.79x10-5 dpa/s - 300°C - 18.05 mdpa

SLIDE 14

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 14

80 100 120 140 160 180 200 220 T (K)

          n n dT d (%/K)

2 4 5.79 x 10-5 dpa 1.16 x 10-4 dpa 1.74 x 10-4 dpa 2.31 x 10-4 dpa 2.89 x 10-4 dpa IE peak shift II peak shift

80 100 120 140 160 180 200 220 T (K)

          n n dT d (%/K)

2 4 5.79 x 10-5 dpa 1.16 x 10-4 dpa 1.74 x 10-4 dpa 2.31 x 10-4 dpa 2.89 x 10-4 dpa IE peak shift II peak shift

80 100 120 140 160 180 200 220 T (K)

          n n dT d (%/K)

2 4 5.79 x 10-5 dpa 1.16 x 10-4 dpa 1.74 x 10-4 dpa 2.31 x 10-4 dpa 2.89 x 10-4 dpa IE peak shift II peak shift

[C. C. Fu et al., 2004]

Isochronal annealing: pure Fe

Triangle: Exp. Results: S. Takaki, et al., Radiat. Eff. 79, 87-122, 1983

Isochronal annealing in pure Fe DT/Dt = 2K/300s (T<30K) DT/TDt = 0.03K/300s (T>30K) Tirrad = 4.5 K

 (Resistivity) n (number of defects) Differential Fractional Recovery d/dT (D /D0)  d/dT (n/ni)

SLIDE 15

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 15

Experimental results:

H. Abe, E. Kuramoto, J. Nucl. Mater. 271 & 272 (1999) 209.

3K / 180s - 2.4 10-5 dpa/s

80 100 120 140 T (K) 80 100 120 140 T (K)

          n n dT d (%/K)

2 4 IE peak shift (SIA trapping by P atoms) No modification

bserved on ID peak

Fe – 0.07% P Fe – 0.009% P Fe – 0.0044% P Pure Fe Fe – 0.1% P

80 100 120 140 T (K) 80 100 120 140 T (K)

          n n dT d (%/K)

2 4 IE peak shift (SIA trapping by P atoms) No modification

bserved on ID peak

Fe – 0.07% P Fe – 0.009% P Fe – 0.0044% P Pure Fe Fe – 0.1% P

79 K 124 K 142 K

Solid line: sim / dash line: exp

Isochronal annealing FeP

110 Fe-P Eb = 1.02 eV

Psubs  110Fe-P

Eb = 2.0 eV

SLIDE 16

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 16

120 140 160 180 200 220 T (K) 120 140 160 180 200 220 T (K)

2 4

         

II

n n dT d (%/K)

Fe – 0.07% P Fe – 0.009% P Fe – 0.0044% P Pure Fe Fe – 0.1% P

120 140 160 180 200 220 T (K) 120 140 160 180 200 220 T (K)

2 4

         

II

n n dT d (%/K)

Fe – 0.07% P Fe – 0.009% P Fe – 0.0044% P Pure Fe Fe – 0.1% P

250 K 160 K

190 K

232 K

Solid line: sim / dash line: exp

110 Fe-P Eb = 1.02 eV

Isochronal annealing FeP

Psubs  110Fe-P

Eb = 2.0 eV

SLIDE 17

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 17

With solutes, vacancy clusters & interstitial clusters (SIA and carbon), many “trapping”

situations.

Associated time steps 10-10 s (other ones 10-5 s - 1 s)
Large number of SIAs and vacancies in the simulation box (>100)
Do not know a priori which object (point defect solute cluster) will be the usual

suspect

During irradiation simulation, several different kind objects can be “trapping”

situations

Adapted version of the TAD algorithm of Voter et al. In our AKMC.
Different from “pulsing algorithm” of Wirth & Odette (1998 & 2007).
Based on temperature increase.

Time Accelerated Dynamics in our AKMC

SLIDE 18

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 18

1/T

Jump “probability” (s-1) Attempt frequency are all similar

106

Tref TTAD tref = tTAD exp[ Em / (1 / kTref – 1 / kTTAD ) ]

Time Accelerated Dynamics in our AKMC

10

SLIDE 19

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 19

tref = tTAD exp[ Em / (1 / kTref – 1 / kTTAD ) ]

Time Accelerated Dynamics algorithm in our AKMC

1/T

106

Tref TTAD

10

Every N steps, determination each defect mean free path (MFP)
If all MFPs are very low
Search of the 5 largest jump probabilities (P1 > P2 > P3 > P4 > P5)
If (P5 / P1) > 10
Choose TTAD in order to have P5/P1 = 10
Perform 3 AKMC steps (with adjusted time step)
back to Tref

SLIDE 20

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 20

100 200 300 400 500 600 700 800 900 1000 50 100 150 200 250 300 350 400

Fe Fe 0.7Ni Fe 1.4Mn

TAD - AKMC: performance improvements

“Speed-up” = Nb steps AKMC / Nb steps TAD-AKMC T (K)

“speed-up” : 2 order of magnitude
Simulation with solutes (Ni, Mn) very long due to SIA-solute interactions

SLIDE 21

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 21 10 20 30 40 50 60 70 80 90 100 50 100 150 200 250 300 350 400

Fe Fe 0.7Ni Fe 1.4Mn

10 20 30 40 50 60 70 80 90 100 50 100 150 200 250 300 350 400

Fe Ni Mn

TAD - AKMC: preliminary results

Isochronal annealing: Fe, Fe

0.7%Ni, Fe 1.4%Mn

Good agreement with

experimental results

standard-AKMC: 1 week CPU
TAD-AKMC: 12 hours CPU
Similar physical results (some

statistics are required)

T (K) T (K) Standard AKMC TAD - AKMC

SLIDE 22

EDF R&D - Workshop BEMOD12 - Dresden - March 2012 22

Conclusions & perspectives

 AKMC of complex alloys (with simple cohesive models) under irradiation feasible

for low doses and high fluxes

 Massive Parallelisation is a difficult issue  TAD method allows to improve the performance of the AKMC tools.  TAD method validated on isochronal annealing simulation.  Perspectives:

 To use TAD for radiation damage simulation under flux.  To improve cohesive models