Properties of Point Defects in Fe-Cr Alloys

1. Properties of Point Defects in Fe-Cr Alloys Harun Đogo Faculty of Mechanical Engineering, Sarajevo, Bosnia and Herzegovina French-Serbian European Summer University Vrnjačka Banja, October 23rd, 2006

2. Energy from Nuclear Fission Source: U.S. Department of Energy, Office of Nuclear Energy

3. 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 Source: U.S. Department of Energy, Office of Nuclear Energy

4. 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

5. Effects of Radiation Damage on Materials Volumetric swelling from void formation1 High temperature He embrittlement2 Irradiation creep3 Interstitial – an excess atom in the crystal lattice5 Vacancy – a vacant site in the crystal lattice Radiation hardening and embrittlement4 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

6. Multi Scale Materials Modeling Source: Wirth Research Group, Dept. of Nuclear Engineering, UC Berkeley

7. Research Methodology • Positive heat of solution • Magnetic frustration when Cr are nearest neighbors • Negative heat of solution • Dilute Cr aligns anti-ferromagnetically in Fe Concentrated solution Dilute solution 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).

8. Research Objectives • 2. Define the formation energy for interstitials in all possible configurations and orientations in: • Pure Fe • Pure Cr • As a function of Cr concentration • 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 • 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 Vacancy – a vacant site in the crystal lattice 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

9. 3 2.5 2.07 2.04 2.64 2.02 1.95 1.89 2.56 2.56 1.86 1.85 1.84 2 1.72 1.63 2.5 1.5 2.14 2.1 [eV] 1 2 0.5 [eV] 1.5 0 Experiment This Work 1 Becquart DFT, Free V, Relaxed Becquart EAM, Free V, Relaxed Wallenius - EAM, Free V, Relaxed Ackland, DFT, Free V, Unrelaxed Dudarev, DFT, Const. V, Unrelaxed Mendelev #2, EAM, Free V, Relaxed Mendelev #5, EAM, Free V, Relaxed Becquart - DFT, Const. V, Unrelaxed 0.5 0 This Work Wallenius - EAM, Dudarev, DFT, Olsson, DFT, Const Experiment Free V, Relaxed Const. V, Unrelaxed V, Unrelaxed Vacancy Formation Energy in Pure Elements Vacancy in Iron Vacancy in Chromium Linear Interpolation

10. Vacancy as a Function of Cr Concentration HT-9 Steel Vacancy – a vacant site in the crystal lattice

11. 5.9 5.0 5.84 4.72 4.66 5.8 4.5 4.28 4.03 3.96 3.95 3.94 3.88 4.0 5.69 5.7 5.67 5.65 3.61 3.56 3.52 3.44 5.61 3.5 5.6 3.0 5.53 This Work This Work 5.5 Dudarev 2.5 USPP (Olsson) [eV] PAW (Olsson) USPP (Olsson) 5.39 5.4 PAW (Olsson) 2.0 5.29 1.5 5.3 1.0 5.2 0.5 5.1 0.0 Formation Energy Mixed Formation Energy Mixed Formation Energy Self Formation Energy Self 5 Interstitial <110> Interstitial <111> Interstitial <110> Interstitial <111> Cr self-interstitial <110> Cr self-interstitial <111> Interstitial Formation Energy in Pure Elements Interstitials in Iron Interstitials in Chromium

12. Self Interstitial (Fe-Fe) Formation Energies HT-9 Steel

13. Conversion Function for Fe-Fe Self Interstitials

14. Mixed Interstitial (Fe-Cr) Formation Energies HT-9 Steel

15. 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

16. 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…

17. Questions?