E. Vincent* , **, C.S. Becquart*, C. Domain **
description
Transcript of E. Vincent* , **, C.S. Becquart*, C. Domain **
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)
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•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)
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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
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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%
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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)
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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
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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
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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.
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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
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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)
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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
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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
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SELF INTERSTITIALS & SOLUTE INTERACTIONS
Solute in compression region Solute in tensile region
Mixed <110> dumbbell Mixed crowdion1nnCompression 1nnTension
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<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%
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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
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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
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•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