1. Nuclear Data and Materials Irradiation Effects - Analysis of irradiation damage structures and multiscale modeling - Toshimasa Yoshiie Research Reactor Institute, Kyoto University

2. Comparison of irradiation effects between different facilities Power reactors  Research reactors Neutron irradiation  Ion irradiation  Electron irradiation DPA (Displacement per atom) The number of displacement of one atom during irradiation DPA dose not represent the effect of cascades

3. Estimation of irradiation damage Ion irradiation 100MeV He,10 18 ions/cm 2 Neutron irradiation 10 18 n/cm 2 ( ＞ 1MeV or ＞ 0.1MeV) Displacement par atom (dpa) α ｘ deposited energy in crystal lattice 2 ｘ threshold energy of atomic displacement Kinchin-Pease model E P E T DPA is the number of displacement for 1 atom during irradiation =

4. Cascade Frenkel pair formation Cascade formation

5. Example of MD Simulation 40keV cascade of iron at 100K

6. Clustering of Point Defects Stress field

7. Interstitial Type Dislocation Loops in FCC Interstitial type dislocation loops in Al

8. Embrittlement Materials with no voids Materials with voids Voids

9. Stacking Fault Tetrahedra

11. High energy Particle Cascade Vacancy rich area Subcascades Nucleation of defect Interstitial rich area clusters Cascade Damage

12. 14MeV neutrons at 300K. Neutron PKA Comparison of Subcascade Structures by Thin Foil Irradiation

13. Au, KENS irradiation and 14 MeV irradiation at room temperature 14MeV neutrons 13 KENS neutrons

14. 14MeV neutron irradiated Cu

18. Temperature Effects of Cascade Damage Subcascades Subcascades fuse into a large cluster Lower temperature Higher temperature

19. Thin foil Irradiated Au by Fusion Neutrons A group of SFTs A large SFT Subcascade Cascade fuses structures into one SFT

20. Fission-fusion Correlation of SFT in Au Fusion neutrons Fission neutrons 563K 573K 0.017dpa Large SFTs High number density of SFTs 0.044dpa Small SFTs Low number density of SFTs

21. PKA Energy Spectrum Analysis α= 0.05 E TH = 80keV N SFT : the concentration of SFTs observed α: the SFT formation efficiency ： the neutron fluence ： the differential cross- section for PKA E TH :threshold energy for SFT formation

22. MULTI-SCALE MODELING OF IRRADIATION EFFECTS IN SPALLATION NEUTRON SOURCE MATERIALS Toshimasa Yoshiie 1, Takahiro Ito 2, Hiroshi Iwase 3, Yoshihisa Kaneko 4, Masayoshi Kawai 3, Ippei Kishida 4, Satoshi Kunieda 5, Koichi Sato 1, Satoshi Shimakawa 5, Futoshi Shimizu 5, Satoshi Hashimoto 4, Naoyuki Hashimoto 6, Tokio Fukahori 5, Yukinobu Watanabe 7, Qiu Xu 1, Shiori Ishino 8 1 Research Reactor Institute, Kyoto University 2 Department of Mechanical Engineering, Toyohashi University of Technology High Energy Accelerator Research Organization Osaka City University 5 Japan Atomic Energy Agency 6 Hokkaido University 7 Kyushu University 8 Univerity of Tokyo

23. Motivation Spallation neutron source and Accelerator Driven System (ADS) are a coupling of a target and a proton accelerator. High energy protons of GeV order irradiated in the target produce a large number of neutrons. The beam window and the target materials thus subjected to a very high irradiation load by source protons and spallation neutrons generated inside the target. At present, there are no materials that enable the window to be operational for the desired period of time without deterioration of mechanical properties.

24. Importance of GeV Order Proton Irradiation Effects in Materials Spallation neutron source J-PARC (Japan) SNS (USA) Accelerator driven system (in the planning stage ) 800MW ADS (Minor Actinide transmutation, Japan Atomic Energy Agency) 5MW Accelerator driven subcritical reactor (Kyoto University, neutron source)

26. Purpose and outline In this paper, mechanical property changes of nickel by 3 GeV protons were calculated by multi-scale modeling of irradiation effects. Nickel is considered to be a most simple model material of austenitic stainless steels used in beam window. The code consists of four parts. Nuclear reaction, the interaction between high energy protons and nuclei in the target is calculated by PHITS code from 10 -22 s. Atomic collision by particles which do not cause nuclear reactions is calculated by molecular dynamics and k-Monte Carlo. As the energy of particles is high, subcascade analysis is employed. In each subcascade, the direct formation of clusters and the number of mobile defects are estimated. Damage structure evolution is estimated by reaction kinetic analysis. Mechanical property change is calculated by using 3D discrete dislocation dynamics (DDD). Stress-strain curves of high energy proton irradiated nickel are obtained.

27. Size (m) Vacancy High energy particle 10 -20 10 -15 10 -10 10 -5 10 0 10 5 10 10 PHITS

28. Data flow between each code Nuclear reactions （ PHITS code ） Primary knock-on energy spectrum Atomic collisions （ Molecular dynamics) Point defect distribution Damage structural evolutions (Reaction kinetic analysis) Concentration of defect clusters Mechanical property change (Three-dimensional discrete dislocation dynamics) Stress-strain curve

29. 1. Nuclear Reaction Nucleation rate of neutrons, photons, charged particles and PKA energy spectrum by them

30. Number of PKA energy (left) and energy deposition by PKA (right) in 3 GeV proton irradiated Ni of 3 mm in thickness. Result of PHITS Simulation Ni 3GeV protons

31. Subcascade Analysis Large cascades are divided into subcascades. In the case of Ni, subcascade formation energy is calculated to be 10 keV. Cascade The number of subcascasdes are obtained from the result of PHITS.

32. Number of subcascades by deposition of energy T T SC : Subcascade formation energy Total number of subcascades

33. Calculation Condition  Potential model by Daw and Baskes (1984)  NVE ensemble ( i.e., number of the atoms, cell volume and energy were kept constant)  35x35x35 lattices (171500 atoms) in a simulation cell  Periodic boundary condition for the three directions  Initial condition : equilibrium for 50 ps at 300 K, 0MPa  PKA energy：10keV  MD runs with different initial directions of PKA ( none of which were parallel to the lattice vector.) 35a 0 a 0 : lattice constant at 300 K x y z 2. Atomic Collision Simulation by MD

34. 0.006ps 0.025ps1.132ps 7.395ps 96.38ps 18.40ps Marble : interstitial atoms ， Violet ： Vacancy cites Typical Distribution of Point Defects

35.  Cascades terminated within 10~20ps  On average17 vacancies, 17 interstitials were produced.  Formation of defect clusters is calculated by k-Monte Carlo. Clusters of three point defects are formed. Number of vacancies Results of MD Calculation

36. 3. Damage Structure Evolution by Reaction Kinetic Analysis In order to estimate damage structural evolution, the reaction kinetic analysis is used. Assumptions used in the calculation are as follows: (1) Mobile defects are interstitials, di-interstitials, tri-interstitials, vacancies and di- vacancies. (2) Thermal dissociation is considered for di-interstitials, tri-interstitials di-vacancies and tri-vacancies, and point defect clusters larger than 4 are set for stable clusters. (3) Time dependence of 10 variables, concentration of interstitials, di-interstitials, tri- interstitials, interstitial clusters (interstitial type dislocation loops), vacancies, di- vacancies, tri-vacancies, vacancy clusters (voids), total interstitials in interstitial clusters and total vacancies in vacancy clusters are calculated to 10 dpa. (4) Interstitial clusters (three interstitials) and vacancy clusters (three vacancies) are also formed directly in subcascades. (5) Materials temperature is 423 K during irradiation. The result is as follows, Formation of vacancy clusters of four vacancies, concentration: 0.59x10 -3, Dislocation density: 1.1x10 -9 cm/cm 3.

37. Reaction Kinetic Analysis damage production I-I recombination mutual annihilation absorption by loops absorption by voids C I : Interstitial concentration (fractional unit). C V : Vacancy concentration Z : Cross section of reaction M: Mobility annihilation of interstitials at sink

38. 4. Estimation of Mechanical Property Changes (Plastic Deformation of Metals)   Plastic Deformation of Metals Work Hardening ↓ Motions of Dislocation Lines Dislocation Glide along Slip Planes  

39. Calculation of Dislocation Motions Motions of Curved Dislocations  External Stress  Elastic Interaction between Dislocations  Line Tension Very Complicated ! Division of a Dislocation Line ↓ Discrete Dislocation Dynamics (DDD) Simulation

40. 3D-Discrete Dislocation Dynamics Mixed Dislocation Model Zbib, et al (1998 ～ ) Schwarz et al Fivel et al ， Cai et al Connection of Dislocation Segments with Mixed Characters Connection of Dislocation Segments with Mixed Characters b Peach-Koehler Force Dislocation Velocity External Stress Stresses from another segment Line tension Edge+Screw Dislocation Model Devincre (1992 ～ )

41. Stress axis ＝ [1 0 0] slip plane ＝ (1 1 1) slip vector ＝ [1 0 1] Mobile dislocation Obstacles （ void ） 0.593×10 -3 void/ atom the density along the slip plane : 1.10x10 4 void / μm 2 0.14μm Model Crystal and Mobile Dislocation Ni: shear modulus = 76.9 Gpa Poisson’s ratio = 0.31 Burgers vector = 0.24916 nm

42. Interaction between Dislocation and void Detrapping angle

43. [ Ī Ī 2] [ Ī l 0] [ l l l ] (Ī Ī 2) (Ī l 0) ( l l l) void Stress Size and orientation of model lattice used for Static energy calculation of dislocation movement. b is the Burgers vector. Stable atomic position is determined by an effective medium theory (EMT) potential for Ni fitted by Jacobsen et al. [K. W. Jacobsen, P. Stoltze, J. K. Norskov, Surf. Sci. 366 (1996) 394]. Determination of Detrapping Angle (Statistic Energy Calculation Method)

44. Motion of dislocation near the slip plane under shear stress. X axis and Y axis are by atomic distance. In the left figure, a dislocation is separated into two partials. Four vacancies are at (16.0, 0.722, -0.408), (15.5, -0.144, -0.408), (16.0, 0.144, 0.408) and (15.5, 1.01, 0.408). Other figures indicate only right partial. 65 ° Determination of Detrapping Angle between Edge Dislocations and 4 Vacancies

45. Dislocation Motion by DDD Simulation (no void) 400MPa600MPa 700MPa

46. 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa Normal stress Dislocation motion in the crystal with randomly-distributed voids 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa 0MPa 200MPa 300MPa 400MPa 500MPa 600MPa 650MPa 700MPa 750MPa 800MPa 820MPa 840MPa 860MPa 880MPa 900MPa 920MPa 930MPa 935MPa

47. Stress-Strain Curves Calculated with DDD Simulation Plastic shear strain  p = A b / V Plastic strain  p =  p S f A: area swept by a dislocation b: Burgers vector V: volume of model crystal S f : Schmid factor (x10 -6 )

48. Summary Importance of nuclear data for materials irradiation effects was shown. DPA is not good measure of irradiation damage. PKA energy spectrum is more useful to analyze damage structures. As an example of the analysis, the mechanical property change in Ni by 3 GeV proton irradiation was calculated and preliminary results were obtained. Nuclear reactions : PHITS PKA energy spectrum Atomic collision : MD, k-Monte Carlo, Subcascade analysis. The number of point defects and clusters in the subcascade Damage structure evolution : Reaction kinetic analysis Void density, Dislocation density Mechanical properties : Discrete dislocation dynamics Statistic energy calculation Stress strain curve

49. Important data for materials irradiation effects High energy particles High energy particle energy spectrum Primary knock on atom energy spectrum Formation rate of atoms by nuclear reactions