Instituto Fusión Nuclear (DENIM) ----------- Universidad Politécnica de Madrid (UPM)

1. Instituto Fusión Nuclear (DENIM) ----------- Universidad Politécnica de Madrid (UPM) Microstructure characterization of Radiation Damage of SiC, and metals under pulse irradiation, by using Multiscale Modeling J.M. Perlado1, D. Lodi1,2, M. Salvador1, M. J. Caturla3, T. Díaz de la Rubia3, L. Colombo4 1Instituto de Fusión Nuclear (DENIM) / Universidad Politécnica de Madrid (UPM) 2 SCK-CEN, Boeretang 200, 2400 Mol, Belgium. 3 Lawrence Livermore National Laboratory, Livermore, CA94550, USA 4Universitá degli Studi Cagliari, Monserrato, Cagliari, Italy IEA_WS Fusion Neutronics

2. Instituto de fusión nuclear ----------- Universidad Politécnica de Madrid Contents of the work • Pulsed Irradiation of -Fe • Study in more realistic environment for IFE: - Pulse Frequency1 - 10 Hz - Dose rate0.1- 0.01 dpa/s • Comparison between pulsed and continuous irradiation • New Tight- Binding Molecular Dynamics model for assessing defect energetics in SiC. IEA_WS Fusion Neutronics

3. Instituto de fusión nuclear ----------- Universidad Politécnica de Madrid Neutron Environment conditions • Target neutron emission:Intensity~ 10 21 n.s-1 (<> 600 MJ – 3 Hz) • Target neutron Energy spectra <E> = 10-12 MeV • Frequency choice : From considerations among - Driver energy - Target energy - Requested Power 1 - 10 Hz IEA_WS Fusion Neutronics

4. Structural Material HT9 (assued Fe) HT9 (assumed Fe) HT9 (assumed Fe) HT9 (assumed Fe) Neutron Source Spectral <10 MeV> Spectral <10 MeV> Spectral <10 MeV> Monoenergetic 14 MeV Effective Thickness (Li17 Pb83) 66 cm 0 (Bare Wall) 133 cm 66 cm Peak (dpa/s) 0.013 25 0.0014 0.018 Peak (appm He/s) 0.17 220 0.00012 0.24 Neutron Damage in Structural Wall Here we calculate the damage dose rates Dose rates in the Wall 66cm of LiPb Iron Pellets 7 m IEA_WS Fusion Neutronics

5. Duration of the pulse in the wall According to transport calculation 130 ns from 14 MeV unscattered neutron - ASSUMING TARGET SPECTRAL CONDITIONS - PROTECTED (66 CM) WALL 1  Sec 170 ns from neutrons scattered in the blanket IEA_WS Fusion Neutronics

6. PKA Energy Spectra FOR 14 MeV NEUTRONS 45 % of recoils have energies larger than 200 keV, producing 75% of displacements 60 % of recoils have energies larger than 100 keV producing 90% of displacements 150keV FOR SLOWED-DOWN NEUTRONS Only 11% of recoils with energies larger than 100 keV producing 70% of displacements IEA_WS Fusion Neutronics

7. Unprotected Wall Corresponding PKA spectra Here we calculate the neutron flux Iron Pellets 7 m IEA_WS Fusion Neutronics

8. Why Computational Simulation The Absence of an appropriate Pulsed neutron source make Computational Simulation an important tool for microscopic interpretation of macroscopic effects and for predicting the response of materials to irradiation Some proposal appear in the last few years making use of laser technology (Perkins et al. Nuclear Fusion 40/N.1 (2000) 1-19). IEA_WS Fusion Neutronics

9. Computational tools • SPECTER code to determine the PKA spectrum • TRIM to determine the PKA damage Energy • MDCASK (LLNL-DENIM) to study the primary damage state (cascade), and defects energetics • BIGMAC (LLNL) to study the evolution of the microstructure IEA_WS Fusion Neutronics

10. Multiscale Modeling up to Microscopic Computational tools Informations provided Transport + Kinematic codes How many PKAs and with which energy To determine PKA spectrum Energy transfered to the atom and geometrical distribution of the subcascades Binary collision code To determine PKA damage Energy and Collisional Cascade description Molecular Dynamics code Nº and characteristics of defects per cascade and defects energetics To study the primary damage state and defects energetics Kinetic Montecarlocode Defects type and concentration To study the evolution of the micro structure IEA_WS Fusion Neutronics

11. Multiscale approach for Pulsed Irradiation Cascade data base Program that builds a PKA PKA spectrum Transport code Molecular Dynamics Code PKA KMC box KMC box Annealing PULSE New Pulse The Nº of PKAs forming the pulse depends on the dose rate, the Pulse deposition Time and the dimension of the box Kinetic Montecarlo code Kinetic Montecarlo code Input parameters of the KMC simulation are : temperature, dose rate, dose The pulse has a deposition time which must be previously calculated Annealing time = Pulse rate (sec) - Pulse deposition time O.1 - 1 s IEA_WS Fusion Neutronics

12. KMC code BIGMAC Migration energy, Binding energy. Diffusion parameters Read Input Considered events • Diffusion • Clustering of defects of the same type • Dissociation from a cluster • Annihilation of defects of the opposite type • Annihilation in sink • Trapping • New cascade Inizialize variables Create events File Choose an event Choose a particle Spontaneous events Update time Execute event All done IEA_WS Fusion Neutronics

13. Vacancies Migration energies (Em) V: Em= 0.90 eV V2: Em= 0.75 eV Pre-factor (Do) V: Do= 5.0 x10-2 V2: Do= 2.5x10-2 Binding Energies (Eb) V2: Eb= 0.22 eV V3: Eb= 0.33 eV Vn: Eb(n) = 1.70-2-59 [n2/3-(n-1)2/3] Interstitial Migration Energies (Em) I: Em= 0.12 eV In: Eb= 0.10 eV In N > 5 undergo 1D migration Pre-factor (Do) I: Do= 2.0 x 10-3 cm2/s In : Do = 2.0 x10-3/ n cm2/s Binding Energies (Eb) I2: Eb = 0.97 eV ; I3: Eb=1.45eV In : Eb(n) = 4.33-5.76 [n2/3- (n-1)2/3] Defects Energetic Immobile Impurities Defect-Impurities reactions : Ix+ S = trapped Ix with Eb= 1.0 Ev IEA_WS Fusion Neutronics

14. Trapped Interstitials IEA_WS Fusion Neutronics

15. Vacancy Concentration IEA_WS Fusion Neutronics

16. Vacancy clusters average size IEA_WS Fusion Neutronics

17. Vacancy clusters Concentrationvs. Pulse frequency IEA_WS Fusion Neutronics

18. Vacancy clusters Concentration during 1 Hz pulse Peak After relaxation IEA_WS Fusion Neutronics

19. Continuous vs Pulsed Comparison between Pulsed and Continuous irradiation leads to the conclusion that damage accumulation is almost identical as regard to vacancy clusters density IEA_WS Fusion Neutronics

20. Tight Binding Molecular Dynamics for SiC • We develop a semiempirical tight binding molecular dynamics scheme to study the defects energetics in SiC. • We justify the need of this scheme: • The classical interatomic potentials used in large scale simulations are poor in SiC due to its empirical nature • The computational cost of the Tight Binding methods is less expensive in comparison with the ¨ ab initio ¨ method, With TBMD we can obtain results of complex systems with a great friability and with more atoms in our simulations IEA_WS Fusion Neutronics

21. Tight Binding Molecular Dynamics for SiC • The TBMD semiempirical method consist in to solve the Schröndinger equation where some operators are substituted by experimental results. • The TB model, is a semiempiric version of the Linear Combination of Atomic Orbital (LCAO) method, with a minimum basis functions; basically, the analysis is reduced to the problem of one particle moving in an average field. • The total electronic energy of the system, depends on an attractive and repulsive term: • Etot = Ebs + Urep • Where Ebsis the structure energy band obtained by the Fermi-Dirac Distribution IEA_WS Fusion Neutronics

22. Tight Binding Molecular Dynamics for SiC We use a simple average for the interaction of the Hamiltonian matrix elements. The on-site energies are those of Weissmann and Fu, and in the pair interaction between Silicon and Carbon, we use a weighted average suggested by the same authors. In our TB scheme we can manage different atomic coordination number, chemical bonding and equilibrium distances. We use a short-ranged repulsive term Urep, for which we adopt the functional form, suggested by Goodwin, Skinner and Pettifor for the scaling function s ( r ) and the pairwise potential Φ ( r ). IEA_WS Fusion Neutronics

23. Tight Binding Molecular Dynamics for SiC For computing the attractive force we implement the Hellmann - Feynman theorem, using the linear combination and exploiting the analytical dependence of the TB hopping upon the interatomic distances. We use for the development of the TB model, the LAPACK library for the diagonalization of the Hamiltonian Matrix. IEA_WS Fusion Neutronics

24. Tight Binding Molecular Dynamics for SiC We can reproduce efficiently the cohesive energies of different SiC crystalline structure. IEA_WS Fusion Neutronics

25. Tight Binding Molecular Dynamics for SiC Here we shown the Energy Band Structure in a SiC Molecule in dependence of its interatomic distance IEA_WS Fusion Neutronics

26. Conclusions • Multiscale Modeling proved by Experiments • Pulse Radiation Damage • Time between pulses is the variable that control vacancy clusters density and size • Frequency has no effect on Interstitials accumulation • No significant differences between average pulsed and continuous irradiation in the range studied • New Model for Defect Energetic in SiC using Tight Binding Molecular Dynamics is starting to be succesfully proved IEA_WS Fusion Neutronics

27. Programs link-up TRIM Damage Energy and Collisional Cascade description SPECTER FromNeutronSpectrum ToPKA spectrum IEA_WS Fusion Neutronics

28. Programs link-up Damage Energy and Collisional Cascade description BIGMAC MDCASK To the primary Damage State From the Damage Energy To the Evolution of the Microstructure IEA_WS Fusion Neutronics

29. Vacancies For a given dose rate, frequency control vacancy cluster size Lower frequency = larger average size IEA_WS Fusion Neutronics

30. Vacancies For a given dose rate frequency control vacancy clusters density Higher frequency = more accumulation IEA_WS Fusion Neutronics

31. Trapped Interstitials We considered 5 appm of impurities The migration of interstitial clusters is so fast that frequency shows no effect on cluster density No sessile custer accumulation has been recorded in any of the simulations IEA_WS Fusion Neutronics