COSIRES 2004, Helsinki, June 28 - July 2, 2004 1

E. Vincent*,**, C.S. Becquart*, C. Domain**

* 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

Ab initio calculations of point defect interactions with solute atoms in bcc Fe

EDFElectricitéde France

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

COSIRES 2004, Helsinki, June 28 - July 2, 2004 2

•Under neutron irradiation : point defect and complexes formation (MD and KMC)

•Role of Cu (modelled FeCu dilute alloy)

•Rate theory or kinetic Monte Carlo simulations (time evolution of primary damage) needs point defect properties

PRESSURE VESSEL EMBRITTLEMENT

•Radiation damage in pressure vessel steels (low Cu contents ~ 0.1%)

•Radiation damage simulation (REVE & PERFECT project)

COSIRES 2004, Helsinki, June 28 - July 2, 2004 3

PRESSURE VESSEL EMBRITTLEMENT

A. Barbu (CEA) TEM

15x15x50 nm

P. Pareige (Université Rouen)Tomographic atom probe

Cu Ni

MnSi

PCu

Under irradiation: point defect and complexes are formed

Hardening

Embrittlement

•Effect of solute atoms (Cu, Ni, Mn, Si, P)

•Effect of interstitial atoms (C, N)

C P Si Cr Mo Mn Ni Cu0.16 0.008 0.19 0.24 0.55 1.25 0.74 0.07

neutron

Displacement cascade

COSIRES 2004, Helsinki, June 28 - July 2, 2004 4

FORMATION OF THESE SOLUTE RICH CLUSTERS

X-Y Fe-Cu Fe-Ni Fe-Mn Cu-Ni Cu-Mn Mn-Ni

ij (kJ/mol) 44200 1400 14200 4200 0 -31000

[C.L. Liu, G.R. Odette, B.D. Wirth, G.E. Lucas, Materials Science and Engineering A 238 (1997) 202-209]

Kinetics ?

•Cohesive model (Fe-Cu, Fe-Ni, Fe-Si, ..., Ni-Mn, ...)

–phase diagram (thermodynamics)

–ab initio calculations

Metropolis Monte Carlo+

Cu Mn Ni0.2% 0.8% 1.6%

COSIRES 2004, Helsinki, June 28 - July 2, 2004 5

Density Functional Theory

VASP (Vienna Ab initio Simulation Package)

Plane wave (energy cutoff 240 eV)

Ultra soft pseudo potentials (Vanderbilt type pseudo potentials)

Exchange and correlation: GGA (PW91)

Spin polarised

54 atoms (555 k points) – 128 atoms (333 k points) – 240 eV

All atomic positions for defects calculation are relaxed

Constant volume calculation

METHODS & COHESIVE MODELS

Ab initioVASP:

[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)

COSIRES 2004, Helsinki, June 28 - July 2, 2004 6

E binding = E(# A & B non interacting) – E(# A & B interacting)

E binding = [ E(# A) + E(# B) ] – [ E(# A & B defect interacting) + E(without defect) ]

But only small system size tractable...

++

A A

BB

POINT DEFECT BINDING ENERGY CALCULATIONS

A A

B

B

COSIRES 2004, Helsinki, June 28 - July 2, 2004 7

Si Mn Ni Cu

Supercell size 54 at. 128 at. 54 at. 128 at. 54 at. 128 at. 54 at. 128 at.

Hsol (eV/at) –1.12 –1.08 –0.14 f –0.10 –0.22 –0.12 0.55 0.55

Eb (Solute–Solute 1nn) (eV) –0.29 –0.31 –0.19 –0.28 –0.15 –0.07 0.15 0.14

Eb (Solute–Solute 2nn) (eV) –0.20 –0.16 –0.21 –0.15 –0.06 –0.02 0.04 0.03

SUBSTITUTIONAL & SOLUTE BINDING ENERGY

Cu: verylow solubility

Si, Mn, Ni: soluble in Fe

Fe-Si

Fe-CuFe-Ni

Fe-Mn

COSIRES 2004, Helsinki, June 28 - July 2, 2004 8

RELAXATION FIELD AROUND DEFECTS

Si Mn Ni Cu

Ωsf (%) [King] –7.88 +4.89 +4.65 +17.53

1st nearest neighbour (%) 0.06 0.71 0.32 0.93

2nd nearest neighbour (%) –0.79 –0.28 0.02 –0.13

3rd nearest neighbour (%) –0.01 –0.04 0.03 0.05

H.W. King, J. Mater. Sci. 1 (1966) 79.

COSIRES 2004, Helsinki, June 28 - July 2, 2004 9

VACANCY - SOLUTE BINDING ENERGIES

1nn 2nn

[exp] Möslang, E. Albert, E. Recknagel, and A. Weidinger, Hyperfine Interact. 15/16, (1983) 409

Si Mn Ni Cu

Supercell size 54 at. 128 at. 54 at. 128 at. 54 at. 128 at. 54 at. 128 at.

Em (solute) (eV) 0.44 0.45 NC 1.03 f 0.5 af 1.2 f 0.70 0.69 0.56 0.55

Eb (V-Solute 1nn) (eV) 0.23 0.24 0.09 af –0.41 f 0.12 af –0.36 f 0.03 0.03 0.17 0.17

Eb (V-solute 2nn) (eV) 0.15 0.14 –0.08 af NC 0.07 af NC 0.19 0.18 0.21 0.19

Eb (V-Solute) (eV)

[exp]0.21 — — 0.21 0.11

Emig Fe : 0.65 eV

f µMn Ferro magn. af µMn AntiFerro magn.

w’3w2

w6

w

5

w4

w3

w’’3w’’4w’4

COSIRES 2004, Helsinki, June 28 - July 2, 2004 10

SOLUTE DIFFUSION COEFFICIENT IN Fe (vacancy mechanism)

)/66.2exp(2.2 kTeVDFeFe

)/44.2exp(2.2 kTeVDCuFe

cm2 s – 1

cm2 s – 1

9-frequency model (Le Claire)

Fe = Cu = 3.65 10 15s-1

Hypothesis

[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) C3-13.

[1]

[2]

(model I and II not valid)

w’3w2

w6

w5

w4

w3

w’’3w’’4

w’4

CuFe

FeFe DD

(cf. COSIRES 2002)

COSIRES 2004, Helsinki, June 28 - July 2, 2004 11

P. Moser, Mem. Scient. Revue Metall., 63 (1966) 431

(µB)

INTRINSIC POINT DEFECT FORMATION ENERGIES

C. Domain, C.S. Becquart, Phys. Rev B 65 (2002) 024103

LARGE E btw <110> / <111> configuration: 0.7 eV

Experimental (Moser): <110> most stable

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

System Ef vac Ef <100> Ef <110> Ef <111>E <110> <111>

27 atoms (vol rlx) 1.93 4.59 3.84 4.64 0.854 atoms (vol rlx) 1.95 4.37 3.41 4.11 0.7

54 atoms 1.93 5.07 3.96 4.75 0.79128 atoms 2.02 5.04 3.94 4.66 0.72

128 atoms SIESTA(C.C. Fu et al.)

2.07 4.64 3.64 4.34 0.70

EAM (Ludwig et al.) 4.57 3.67 3.54 -0.13FS ( Ackland et al.) - 4.87 5.00 0.13

EAM (Mendelev et al.) 1.84 4.34 3.53 4.02 0.5

COSIRES 2004, Helsinki, June 28 - July 2, 2004 12

3.835

3.7153.691 3.682 3.675 3.667

3.55

3.6

3.65

3.7

3.75

3.8

3.85

(eV)

54 128 250 432 1024 8192

Ef <110>

SELF INTERSTITIALS & SMALL SUPERCELLS

Fe potential: Ackland et al., Phil. Mag. 1997

MD convergence test

COSIRES 2004, Helsinki, June 28 - July 2, 2004 13

SELF INTERSTITIALS & SOLUTE INTERACTIONS

Solute in compression region Solute in tensile region

Mixed <110> dumbbell Mixed crowdion1nnCompression 1nnTension

COSIRES 2004, Helsinki, June 28 - July 2, 2004 14

<110> INTERSTITIAL – SOLUTE BINDING ENERGIES

Si Mn

Ni

Cu

0.33 0.27

-0.02 0.02

-0.17 -0.22

0.38 0.44

0.18 0.11

-0.27 -0.28

-0.04 -0.04

-0.12 -0.10

-0.36 -0.30

0.13 0.06

0.04 -0.02

-0.52 -0.46

sf – 7.9% sf +4.9%

sf +4.7%

sf +17.5%

Mos

t sta

ble

conf

igur

atio

nB

indi

ng e

nerg

y (e

V)

0.98 1.02

0.85 0.83

-0.36 -0.35

P

sf – 13.2%

COSIRES 2004, Helsinki, June 28 - July 2, 2004 15

INTERSTITIAL – SOLUTE INTERACTIONS: <110> – <111> ENERGY DIFFERENCES

Si Mn Ni Cu

0.33 0.27

-0.02 0.02

0.38 0.44

0.18 0.11

-0.04 -0.04

-0.12 -0.10

0.13 0.06

0.04 -0.02

sf – 7.9% sf +4.9% sf +4.7% sf +17.5%

Mos

t sta

ble

conf

igur

atio

nB

indi

ng e

nerg

y (e

V)

0.98 1.02

0.85 0.83

P

sf –13.2%

E (<110> – <111>) Fe: 0.79 eV

0.72 0.66 0.93 0.770.42

COSIRES 2004, Helsinki, June 28 - July 2, 2004 16

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 eV)

• Cu: site under tensile stress (~0.1 eV)

• P: strong interaction & mixed dumbbell (~ 1 eV)

• Si: significant interaction in 1nnCompression (~0.3 eV)

• Ni: no interaction with <110> SIA (~0 eV)

• Si, Mn, Ni: site(s) under compression

COSIRES 2004, Helsinki, June 28 - July 2, 2004 17

•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

CONCLUSIONS