1. 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 University Vrnjačka Banja, October 23 rd, 2006

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

3. 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

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 Irradiation creep 3 Radiation hardening and embrittlement 4 High temperature He embrittlement 2 Volumetric swelling from void formation 1 Vacancy – a vacant site in the crystal lattice Interstitial – an excess atom in the crystal lattice 5 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 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 Dilute solution Negative heat of solution Dilute Cr aligns anti- ferromagnetically in Fe

8. 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 interstitial Interstitial pair displaced in the X, Y and Z axes, or the interstitial Only 4 possible configurations examined as a function of Cr concentration. Cr-Cr self interstitials and interstitials oriented in 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

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

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

11. Interstitial Formation Energy in Pure Elements 3.44 3.61 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 Mixed Interstitial Formation Energy Mixed Interstitial Formation Energy Self Interstitial Formation Energy Self Interstitial This Work USPP (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 [eV] This Work Dudarev USPP (Olsson) PAW (Olsson) Interstitials in IronInterstitials in Chromium

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

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 10 6 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?