Properties of Point Defects in Fe-Cr Alloys
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This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48 UCRL 336674
Properties of Point Defects in Fe-Cr Alloys Harun Đogo
Faculty of Mechanical Engineering, Sarajevo, Bosnia and Herzegovina
French-Serbian European Summer UniversityVrnjačka Banja, October 23rd, 2006
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Source: U.S. Department of Energy, Office of Nuclear Energy
Energy from Nuclear Fission
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Source: U.S. Department of Energy, Office of Nuclear Energy
Generation IV Reactor Design – The SSTAR Project
•Global Nuclear Energy Partnership concept initiated at 2006 State of the Union Address
•Small, Sealed, Transportable Autonomous Reactor (SSTAR) currently under development at LLNL
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Advanced Reactor Material Operating Environment
Source: SJ Zinkle, ORNL, Application of Computational Materials Science Multiscale Modeling to Fission Reactors, LLNL Workshop, December 14-16, 2005
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Effects of Radiation Damage on Materials
Irradiation creep3
Radiation hardening and embrittlement4
High temperature He embrittlement2
Volumetric swelling from
void formation1
Vacancy – a vacant site in the crystal
lattice
Interstitial – an excess atom in the
crystal lattice5
Sources : 1. Computational Material Sciences Network, Basic Energy Sciences, U.S. DOE, 2. SJ Zinkle, ORNL, SJ Zinkle, ORNL, 4. JOM,53 (7) (2001), pp. 18-22., 5. S Domain & Becquart, PRB, 2001
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Multi Scale Materials Modeling
Source: Wirth Research Group, Dept. of Nuclear Engineering, UC Berkeley
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Research Methodology
Computational Materials Science
Source: Farrell and Byun, J. Nucl. Mater. 318 (2003) 274, A. Caro, D. A. Crowson, and M. Caro, Phys. Rev. Lett. 95, 075702 (2005).
Concentrated solution
• Positive heat of solution
• Magnetic frustration when Cr are nearest neighbors
neighbouring Cr's in Fe
??
Dilute solution
• Negative heat of solution
• Dilute Cr aligns anti-ferromagnetically in Fe
single Cr's in Fe
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Research Objectives
1. Using the EAM potential, define the formation energy of a single crystal lattice vacancy in:
• Pure Fe
• Pure Cr
• As a function of Cr concentration
2. Define the formation energy for interstitials in all possible configurations and orientations in:
•Pure Fe
•Pure Cr
•As a function of Cr concentration
Possible Configurations:
•Fe-Fe – “self interstitial”
•Fe-Cr – “mixed interstitial”
•Cr-Cr – “self-interstital”
Possible Orientations:
•Interstitial pair displaced in X and Y axes, or the <110> interstitial
•Interstitial pair displaced in the X, Y and Z axes, or the <111> interstitial
Only 4 possible configurations examined as a function of Cr concentration. Cr-Cr self interstitials and interstitials oriented in <100> not examined as their formation energies are too high for them to have any measurable longevity.
Source: Domain & Becquart, Phys. Rev. B, 2001
Vacancy – a vacant site in the crystal lattice
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Vacancy Formation Energy in Pure Elements
Vacancy in Iron Vacancy in Chromium
Linear Interpolation
1.721.84 1.85
2.041.89
1.63
1.95 2.02 2.071.86
0
0.5
1
1.5
2
2.5
This W
ork
Men
delev
#2, E
AM, F
ree V
, Rela
xed
Men
delev
#5, E
AM, F
ree V
, Rela
xed
Wall
enius
- EAM
, Free
V, R
elaxe
d
Acklan
d, DFT, F
ree V
, Unr
elaxe
d
Becqu
art E
AM, F
ree V
, Rela
xed
Becqu
art D
FT, Free
V, R
elaxe
d
Becqu
art -
DFT, Con
st. V
, Unr
elaxe
d
Dudare
v, DFT, C
onst.
V, U
nrela
xed
Experi
ment
[eV
]
2.56
2.14
2.64 2.56
2.1
0
0.5
1
1.5
2
2.5
3
This Work Wallenius - EAM,Free V, Relaxed
Dudarev, DFT,Const. V, Unrelaxed
Olsson, DFT, ConstV, Unrelaxed
Experiment
[eV
]
2.14
2.64
2.1
2.56
2.04
2.07
1.86
1.72
1.5
1.7
1.9
2.1
2.3
2.5
2.7
0 0.2 0.4 0.6 0.8 1
Cr Fraction
eV
Wallenius - EAM, Free V, Relaxed
Dudarev, DFT, Const. V,Unrelaxed
Experiment
This Work
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Vacancy as a Function of Cr Concentration
HT-9 Steel
Vacancy – a vacant site in the crystal lattice
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Interstitial Formation Energy in Pure Elements
3.443.61
3.52
3.95
3.56
3.96 3.94
4.66
3.88
4.28
4.03
4.72
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Formation Energy MixedInterstitial <110>
Formation Energy MixedInterstitial <111>
Formation Energy SelfInterstitial <110>
Formation Energy SelfInterstitial <111>
This WorkUSPP (Olsson)PAW (Olsson)
5.53
5.61
5.67 5.69
5.29
5.39
5.65
5.84
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Cr self-interstitial <110> Cr self-interstitial <111>
[eV
]
This Work
Dudarev
USPP (Olsson)
PAW (Olsson)
Interstitials in Iron Interstitials in Chromium
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3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
0 0.05 0.1 0.15 0.2
xCr
eV
<110>
<111>
HT-9 Steel
Self Interstitial (Fe-Fe) Formation Energies
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Conversion Function for Fe-Fe Self Interstitials
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3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Cr Concentration
eV
MIXED INTERSTITIAL <110>
MIXED INTERSTITIAL <111>
Mixed Interstitial (Fe-Cr) Formation Energies
HT-9 Steel
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
0 0.05 0.1 0.15 0.2
Cr Concentration
eV
SELF INTERSTITIAL <110>
MIXED INTERSTITIAL <110>
MIXED INTERSTITIAL <111>
SELF INTERSTITIAL <111>
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Application of Results
MCCASK is a hybrid Monte Carlo-molecular dynamics code developed by A. Caro and B. Sadigh in 2005. MCCASK code performs sequences of Monte Carlo events and Molecular Dynamics time steps. In this way, the equilibrium concentrations in the alloy are obtained, enabling precipitation and defect
studies on 106 atom scale. Shown is the performance of the EAM potential characterized in this work in simulating homogeneous Cr precipitation in a 20 % Cr sample, and the relationship of that precipitation
with a screw-type dislocation
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Conclusions• The designed EAM potential approximates available
ab-initio data very well and performs well in simulations depicting defect interaction.
• It is possible to use the potential with the MCCASK code and kinetic Monte Carlo to project time evolution of defects and their mutual interaction
• The modeling continues…
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Questions?