Atomistic Modeling of Segregation and Precipitation in Fe-Cr … · 2016. 3. 29. · 2nd Int. MINOS Workshop, Irradiation of Nuclear Materials: Flux and Dose Effects November 4-6,

2nd Int. MINOS Workshop, Irradiation of Nuclear Materials: Flux and Dose Effects

November 4-6, 2015, CEA – INSTN Cadarache, France

Atomistic Modeling of

Segregation and Precipitation

in Fe-Cr Alloys under

Irradiation

C.-C. Fu, T. Jourdan, M. Nastar, O. Senninger,

F. Soisson

SRMP, CEA Saclay

E. Martinez

Los Alamos National Laboratory

Y. Bréchet

SIMAP, Grenoble INP

CEA – DEN 2nd Int. MINOS Workshop - November 4-6, 2015, CEA – INSTN Cadarache, France 2

Fe-Cr alloys: nuclear applications

• Fe-Cr alloys : a model for ferritic and ferritic-martensitic steels (7-18%Cr) candidate materials for future nuclear reactors (Gen IV and fusion)

Potential problems under irradiation: - α’ precipitation hardening and embrittlement - Cr depletion at GBs corrosion, embrittlement

Due to: point defect supersaturation Acceleration of precipitation

Radiation Induced Segregation (RIS) Radiation Induced Precipitation (RIP)

• Main objectives: - quantify the acceleration of precipitation in supersaturated alloys - understand the mechanisms controlling RIS - study possible effects of equilibrium vs non-equilibrium segregation, ballistic mixing, carbon

atoms,… on the precipitation and segregation kinetics

• Our approach : Atomistic Kinetic Monte Carlo (AKMC) simulations

0.0 0.2 0.4 0.6 0.8 1.0

400

600

800

1000

1200

α'α

T (

K)

c

α+α'

σ

TC


Diffusion model - AKMC Simulations

Pair interactions on stable (bcc) and saddle-point positions

• Diffusion by jumps of : - Vacancies (V) - Self-interstitial atoms (SIA) : dumbbells - Direct interstitials (C)

• The migration barriers are computed with a broken-

bond model: - with composition and temperature dependent pair

interactions - with saddle-point pair interactions - fitted on DFT calculations

• Formation of isolated Frenkel with replacement collision

sequences or small replacement cascades

• Annihilation of V and SIA on a perfect sink

ΓBV

ΓAV

“grain boundary” = perfect pd sink

L = 36 to 104 nm

Sink strength 22 /12 Lktot


x

PWSCF, GGA-PAW Special Quasi-random structures (SQS) Ordered structures Pair interaction model

Thermodynamics: effective pair interactions

Concentration dependent pair interactions: fitted on DFT calculations of ΔHmix at 0K Magnetic and vibrational contributions: linear temperature dependence, fitted on Tα-α’ (exp) M. Levesque et al, Phys. Rev. B 84, 184205 (2011)

( ) ( ) ( ), , ( )n n nFeFe CrCr FeCrh h h x

( ) ( ) ( )

( ) (1 )

( ) 2 ( )2

mix

n n nnFeFe CrCr FeCr

n

H x x x

zx h h h x

( ) ( ) ( )( , ) ( ) (x) , with 1,2n n nFeCr FeCr FeCrg x T h x Ts n


Diffusion coefficients

~

0 10 20 30 40 50 60 70 80 90 10010

-17

10-16

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

Exp [1,2]

AKMC

850 K

1713 K [2]

1453 K [2]

D (

cm

2.s

-1)

% Cr

1124.2 K [1]

994.5 K [1]

914.8 K [1]

[1] Braun & Feller-Kniepmeier, 1985 [2] Jönsson 1995

Tracer diffusion coefficients (pure iron) Interdiffusion coefficients in Fe-Cr alloys

O. Senninger et al, Acta Mater. 73, 97–106 (2014)

- Acceleration of the diffusion at the F/P transition - The Curie temperature decreases with the Cr concentration

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.410

-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

10-15

10-14

DFe

Fe*

DFe

Cr*

D (

m2 s

-1)

1000/T (K -1)

TαγT

C 600°C 500°C

γ-Fe α-Fe α-Fe

para ferro

AKMC


Kinetics of α- α’ decomposition: isothermal annealing

Fe-20%Cr T = 500°C AKMC (E. Martinez et al, 2012) 3DAP (Novy et al, 2009)

0.0 0.2 0.4 0.6 0.8 1.0

400

600

800

1000

1200

'

'

T (

K)

xCr

E. Martinez et al, Phys. Rev. B 86, 224109 (2012) S. Novy et al, J. Nucl. Mater. 384 (2009) 96–102


Kinetics of α- α’ decomposition: isothermal annealing

500°C

540°C

SANS experiments AKMC simulations AKMC simulations without magnetic acceleration

Small-angle neutron scattering experiments (SANS) 500°C: Bley (1992) 540°C: Furusaka et al. (1986)

O. Senninger et al, Acta Mater. 73, 97–106 (2014)


Radiation Accelerated Precipitation: experiments

Experimental evidences (3DAP) in Fe-9% to 20%Cr alloys at 290-300°C - isothermal annealing: α’ precipitation is not observed due to slow kinetics - neutron irradiation: α’ precipitation Bachhav et al (Scripta Mater 2014) Fe-3%Cr to 18%Cr, T= 290°C 3.4 x 10-7 dpa/s, 1.82 dpa V. Kuksenko et al, JNM 432 (2013) 160 C. Pareige et al JNM 456 (2015) 471–476 Precipitation under neutron irradiation in Fe-9%Cr and Fe-12%Cr, but not under ion irradiation at higher flux

Cr rich clusters

• P • Si

3%Cr 6%Cr 9%Cr

12%Cr 15%Cr 18%Cr


3DAP Kuksenko et al

(2012) Fe-12%Cr

300°C – 0.6 dpa

Radiation Accelerated Precipitation: AKMC

AKMC simulations Point defect concentration profiles Fe-18%Cr @ 563 K, 3.4 x 10-7 dpa.s-1

104 nm

GB

Precipitate free zones near the GBs


Radiation Accelerated Precipitation: AKMC vs 3DAP

• AKMC simulations: one GB in the simulation box (constant sink strength: ) • Cluster Dynamics: evolution of the sink strength (in pure iron)

better estimation of the point defect concentration

rescaling of the Monte Carlo time scale

Strong acceleration by irradiation (x 106-107) Good agreement with the experiments of neutron irradiation (Bachhav et al, 2014)

F. Soisson, T. Jourdan, Acta Mater 2016.

2 212 /totk L

2, ,/ ( )i v tot i vc G k D

,

,

( )

( )i v

MC

i v

c AKMCt t

c CD

2totk

100

101

102

103

104

105

106

107

108

109

1010

1011

1012

1013

0.0

0.5

1.0

1.5

2.0

2.5

R (

nm

)

t (s)

100

101

102

103

104

105

106

107

108

109

1010

1011

1012

1013

1018

1019

1020

irradiation 3.4 x 10-7 dpa.s

-1

3DAP (Bachhav et al, 2014)

AKMC - k2

tot = 12/(L

2)

AKMC - k2

tot (CD)

dp (

cm

-3)

Fe-18%Cr @ 563 K

thermal ageing

10-1

100

101

102

103

104

105

106

107

108

109

1010

1011

1012

1013

0.0

0.5

1.0

1.5

2.0

2.5

thermal ageing

R (

nm

)

t (s)

1018

1019

1020

irradiation 3.4 x 10-7 dpa.s

-1

3DAP (Bachhav et al, 2014)

AKMC - k2

tot = C

te

AKMC - k2

tot (CD)

dp (

cm

-3)

Fe-15%Cr @ 563 K


Effect of ballistic mixing

• Experiments: Cr precipitation under neutron irradiation, but not under ion irradiation at higher flux A ballistic dissolution of α’ precipitates, in displacement cascades ?

• AKMC simulations - at different dose rates G (dpa.s-1) - with different numbers of replacements/displacement Nrep/Ndis = 0 (channeling) Nrep/Ndis = 10 (replacement collision sequences) Nrep/Ndis = 100 (cascades)

• At 290°C

- no dissolution of precipitates - no effect of Nrep/Ndis on the precipitation kinetics - dose rate effects: a simple acceleration due to the point defect supersaturation ballistic effects do not explain the difference between ion and neutron irradiations • Possible ballistic effects at lower temperatures (below 100°C)

10-3

10-2

10-1

100

101

102

103

104

105

106

0.5

0.6

0.7

0.8

0.9

1.0

R (

nm

)

t (s)

10-3

10-2

10-1

100

101

102

103

104

105

106

1018

1019

1020

3.4 x 10-7 dpa.s-1

10-3 dpa.s-1

dp (

cm

-3)

Fe-18%Cr @ 563 K

2, ,/ ( )i v tot i vc G k D

3 4balΓ

γ= 10 10Γ stth v v

G

c D


-40 -20 0 20 400.00

0.05

0.10

0.15

0.20

0.012 dpa

0.636 dpa

XCr

distance (nm)

-40 -20 0 20 4010

-14

10-13

10-12

10-11

10-10

10-9

vacancies

self-interstitials

Cd

Fe-10%Cr

950 K

10-3 dpa.s

-1

Radiation-Induced Segregation

CrV CrICr V

FeV FeI

L LC C

L L

Steady-state profile:

jj

μi ijJ L

-40 -20 0 20 400.00

0.05

0.10

0.15

0.20

0.007 dpa

0.294 dpa

XCr

distance (nm)

-40 -20 0 20 4010

-16

10-15

10-14

10-13

10-12

10-11

10-10

vacancies

self-interstitials

Cd

Fe-10%Cr

650 K

10-6 dpa.s

-1JV/JCr : negative coupling Cr depletion at sinks, dominant at high T JSIA/JCr : positive coupling Cr enrichment at sinks, dominant at low T

Fe-10%Cr

T = 650 K, 10-6 dpa.s-1

Fe-10%Cr

T = 950 K, 10-3 dpa.s-1

GB

GB

O. Senninger et al Acta Materialia 103, 1–11 (2016)


-40 -20 0 20 400.05

0.10

0.15

0.20

0.25

0.30

XCr

distance (nm)

0.06 dpa

-40 -20 0 20 400.05

0.10

0.15

0.20

XCr

distance (nm)

0.338 dpa

Radiation-Induced Segregation

CrV CrICr V

FeV FeI

L LC C

L L

Steady-state profile:

jj

μi ijJ L JV/JCr : negative coupling Cr depletion at sinks, dominant at high T JSIA/JCr : positive coupling Cr depletion at sinks, dominant at low T

Fe-10%Cr

T = 650 K, 10-6 dpa.s-1

Fe-10%Cr

T = 950 K, 10-3 dpa.s-1

GB

GB

W-shape profile

0.1eVsegCre

0.1eVsegCre


Radiation-Induced Precipitation (AKMC)

0.0 0.2 0.4 0.6 0.8 1.0

400

600

800

1000

1200

α'α

T (

K)

c

α+α'

σ

TC

Undersaturated alloys, at low T: strong Cr enrichment on sinks RIS radiation induced precipitation

T = 563 K Fe-9%Cr 10-6 dpa.s-1

0.20 dpa

-40 -20 0 20 400.05

0.10

0.15

0.20

CCr

d (nm)

-40 -20 0 20 4010

-17

10-16

10-15

10-14

10-13

10-12

10-11

10-10

vacancies

self-interstitials

d (nm)

Cd


CONCLUSIONS

AKMC simulations with thermodynamic and point defect parameters fitted on DFT calculations

Good description of driving forces, diffusion properties and nucleation

In Fe-Cr alloys • Magnetic effects are important (impact on thermodynamic and diffusion properties)

• Radiation Induced Segregation is controlled by a balance between opposite effects of V and SIA the Lij are very dependent of the details of migration barriers may explain the variability of experimental studies (≠ RIS in austenitic steels)

• Radiation accelerated precipitation

- a good agreement with neutron irradiations (with rescaling of the sink strength using CD) - no effect ballistic mixing in the experimental conditions (relatively high temperatures, high sink densities) does

not explain the difference between neutron an on irradiation - precipitation kinetics is less sensitive than Radiation Induced Segregation to the details of migration barriers

• Related work, perspectives

- Phase-Field model for RIS (J.B. Piochaud, L. Thunier, A. Legris – UMET, Lille)

- Precipitation under electron irradiation (O. Tissot, et al)

- Effects of C (or O, N) on the kinetics of precipitation and segregation

Documents

Atomistic Modeling of Segregation and Precipitation in Fe-Cr … · 2016. 3. 29. · 2nd Int. MINOS Workshop, Irradiation of Nuclear Materials: Flux and Dose Effects November 4-6,