1. Baden-Beden, October 2001 IEA_WS Fusion Neutronics 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. Perlado 1, D. Lodi 1,2, M. Salvador 1, M. J. Caturla 3, T. Díaz de la Rubia 3, L. Colombo 4 1 Instituto 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 4 Universitá degli Studi Cagliari, Monserrato, Cagliari, Italy

2. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Instituto de fusión nuclear ----------- Universidad Politécnica de Madrid Contents of the work Pulsed Irradiation of  -FePulsed Irradiation of  -Fe Study in more realistic environment for IFE: Frequency1 - 10 Hz - Pulse Frequency 1 - 10 Hz Dose rate0.1- 0.01 dpa/s - Dose rate 0.1- 0.01 dpa/s Comparison between pulsed and continuous irradiation New Tight- Binding Molecular Dynamics model for assessing defect energetics in SiC.New Tight- Binding Molecular Dynamics model for assessing defect energetics in SiC.

3. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Instituto de fusión nuclear ----------- Universidad Politécnica de Madrid Neutron Environment conditions IntensityTarget neutron emission: Intensity ~ 10 21 n.s -1 (<> 600 MJ – 3 Hz) Energy spectraTarget neutron Energy spectra = 10-12 MeV FrequencyFrequency choice : From considerations among - Driver energy - Target energy -Requested Power 1 - 10 Hz

4. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Neutron Damage in Structural Wall Pellets 7 m 66cm of LiPb Iron Here we calculate the dose rates damage dose rates Dose rates in the Wall Structural Material HT9 (assued Fe) HT9 (assume d Fe) HT9 (assume d Fe) HT9 (assumed Fe) Neutron SourceSpectral Spectral Spectral Monoener getic 14 MeV Effective Thickness (Li 17 Pb 83 ) 66 cm0 (Bare Wall) 133 cm66 cm Peak (dpa/s)0.013250.00140.018 Peak (appm He/s)0.172200.000120.24

5. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Duration of the pulse in the wall According to transport calculation 1  Sec 130 ns 130 ns from 14 MeV unscattered neutron 170 ns 170 ns from neutrons scattered in the blanket ASSUMING TARGET SPECTRAL - ASSUMING TARGET SPECTRAL CONDITIONS CONDITIONS PROTECTED (66 CM) WALL - PROTECTED (66 CM) WALL

6. Baden-Beden, October 2001 IEA_WS Fusion Neutronics PKA Energy Spectra FOR 14 MeV NEUTRONS 45 %75% 45 % of recoils have energies larger than 200 keV, producing 75% of displacements 60 %90% 60 % of recoils have energies larger than 100 keV producing 90% of displacements FOR SLOWED-DOWN NEUTRONS 11%70% Only 11% of recoils with energies larger than 100 keV producing 70% of displacements 150 keV

7. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Unprotected Wall Pellets 7 m Iron Here we calculate the neutron flux Corresponding PKA spectra

8. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Why Computational Simulation 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).

9. Baden-Beden, October 2001 IEA_WS Fusion Neutronics 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

10. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Multiscale Modeling up to Microscopic Computational tools Transport + Kinematic codes Binary collision code Molecular Dynamics code Kinetic Montecarlo code To determine PKA damage Energy and Collisional Cascade description To study the primary damage state and defects energetics To study the evolution of the micro structure To determine PKA spectrum Informations provided How many PKAs and with which energy Energy transfered to the atom and geometrical distribution of the subcascades Nº and characteristics of defects per cascade and defects energetics Defects type and concentration

11. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Multiscale approach for Pulsed Irradiation PKA spectrum Program that builds a PKA Cascade data base PKA PULSE The pulse has a deposition time which must be previously calculated KMC box Pulse rate (sec Pulse deposition time Annealing time = Pulse rate (sec) - Pulse deposition time Annealing New Pulse KMC box dose rate Pulse deposition Time dimension of the box The Nº of PKAs forming the pulse depends on the dose rate, the Pulse deposition Time and the dimension of the box Transport code Molecular Dynamics Code Kinetic Montecarlo code Input parameters of the KMC simulation are : temperature, dose rate, dose O.1 - 1  s

12. Baden-Beden, October 2001 IEA_WS Fusion Neutronics KMC code BIGMAC Considered events 1)Diffusion 2) Clustering of defects of the same type 3)Dissociation from a cluster 4)Annihilation of defects of the opposite type 5)Annihilation in sink 6)Trapping 7)New cascade 8) 9) Read Input Inizialize variables Create events File Choose an event Choose a particle Update time Execute event All done Spontaneous events Migration energy, Binding energy. Diffusion parameters

13. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Defects Energetic Vacancies Migration energies (E m ) V: E m = 0.90 eV V2: E m = 0.75 eV Pre-factor (D o ) V: D o = 5.0 x10 -2 V2: D o = 2.5x10 -2 Binding Energies (E b ) V2: E b = 0.22 eV V3: E b = 0.33 eV Vn: E b (n) = 1.70-2-59 [n 2/3 -(n-1) 2/3 ] Interstitial Migration Energies (E m ) I: E m = 0.12 eV In: E b = 0.10 eV In N > 5 undergo 1D migration Pre-factor (D o ) I: D o = 2.0 x 10 -3 cm 2 /s In : D o = 2.0 x10 -3 / n cm 2 /s Binding Energies (E b ) I2: E b = 0.97 eV ; I3: E b =1.45eV In : E b (n) = 4.33-5.76 [n 2/3 - (n-1) 2/3 ] Immobile Impurities Defect-Impurities reactions : I x + S = trapped I x with E b = 1.0 E v

14. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Trapped Interstitials

15. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Vacancy Concentration

16. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Vacancy clusters average size Vacancy clusters average size

17. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Vacancy clusters Concentration vs. Pulse frequency

18. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Vacancy clusters Concentration during 1 Hz pulse Peak After relaxation

19. Baden-Beden, October 2001 IEA_WS Fusion Neutronics 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

20. Baden-Beden, October 2001 IEA_WS Fusion Neutronics 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 We justify the need of this scheme: The classical interatomic potentials used in large scale simulations are poor in SiC due to its empirical natureThe 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 ¨ methodThe 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

21. Baden-Beden, October 2001 IEA_WS Fusion Neutronics 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 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: The total electronic energy of the system, depends on an attractive and repulsive term: E tot = E bs + U rep E tot = E bs + U rep Where E bs is the structure energy band obtained by the Fermi-Dirac Distribution

22. Baden-Beden, October 2001 IEA_WS Fusion Neutronics 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 ).

23. Baden-Beden, October 2001 IEA_WS Fusion Neutronics 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 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.

24. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Tight Binding Molecular Dynamics for SiC We can reproduce efficiently the cohesive energies of different SiC crystalline structure.

25. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Tight Binding Molecular Dynamics for SiC Here we shown the Energy Band Structure in a SiC Molecule in dependence of its interatomic distance

26. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Conclusions Multiscale Modeling proved by ExperimentsMultiscale Modeling proved by Experiments Pulse Radiation DamagePulse 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 studiedNo 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 provedNew Model for Defect Energetic in SiC using Tight Binding Molecular Dynamics is starting to be succesfully proved

27. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Programs link-up From Neutron Spectrum To PKA spectrum Damage Energy and Collisional Cascade description

28. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Programs link-up Damage Energy and Collisional Cascade description From the Damage Energy To the primary Damage State To the Evolution of the Microstructure

29. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Vacancies Lower frequency = larger average size For a given dose rate, frequency control vacancy cluster size

30. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Vacancies For a given dose rate frequency control vacancy clusters density Higher frequency = more accumulation

31. Baden-Beden, October 2001 IEA_WS Fusion Neutronics Trapped Interstitials The migration of interstitial clusters is so fast that frequency shows no effect on cluster density We considered 5 appm of impurities No sessile custer accumulation has been recorded in any of the simulations