Atomic scale understandings on hydrogen behavior in Li 2 O - toward a multi-scale modeling - Satoru Tanaka, Takuji Oda and Yasuhisa Oya The University of Tokyo

Background To establish a secure and efficient fuel cycle in a fusion reactor, produced tritium must be recovered rapidly from the breeding blanket. In the case of a solid breeding material (Li 2 O, Li 2 TiO 3 etc), radiation defects created in the severe radiation conditions affect the tritium behavior strongly. Hence, behaviors of tritium and defects in Li 2 O have been extensively studied. However, ….  The evaluated tritium diffusivities are scattered.  The concrete influence of each defect is not understood sufficiently. 6 Li + n → 4 He (2.1 MeV) + T (2.7 MeV) Our aim is to model the hydrogen isotope behavior precisely, based on the atomic-scale understandings (= multi-scale modeling).

Multi-scale modeling (i) Quantitative analysis by the ab initio calculation (ii) Quantitative analysis by the molecular dynamics (iii) Integration in mesoscale by the kinetic Monte Carlo simulation (iv) Extrapolation into the real scale by theoretical modeling (iv) Extrapolation into the real scale by theoretical modeling (v) Model validation by referring to experimental results (a) In the bulk (b) On the surface (c) At the grain boundary (a) (c) (b)

Subjects T+T+ surface bulk V Li T+T+ OT - T-T- H2H2 H2OH2O (LiOT) n n Li (1) (2) (3) O T+T+ F Tritium in defective Li 2 O (1) Radiation behavior (MD simulation) (2) Interaction with Li vacancy (FT-IR exp. & DFT calculation) (3) Interaction with O vacancy (DFT calculation) (4) Surface processes (XPS/UPS exp. & MC) *not a topic today (4)

Method-1 (experiment) : FT-IR under ion irradiation OD stretching vibrations shows multiple peaks by interaction with a specific defect. Sample ： Li 2 O s.c. φ10mm, 1mm The behaviors of hydrogen isotopes in various chemical states can be analyzed individually. IR absorption experimental system

Method-2 (ab initio calculation) : plane-wave pseudopotential DFT 2x2x2 Li : O : Conventional cell (Li 8 O 4 ) 2x2x2 supercell (Li 64 O 32 ) Software: CASTEP code Functional: GGA-PBE K-point grid: 3x3x3 Energy cutoff: 380 eV Calculation cost was reduced by use of plane- wave basis and pseudopotential technique (O 1s).

Method-3 (molecular dynamics) : MD for cascade simulation (i) Coulombic interaction (ii) Short range interaction (10 Å cutoff) q 1 q 2 /r + A × exp(-r/ρ) - C/r 6 Inter-ionic potential (Li-O) Software: DL-POLY System: 5x5x5 or 10x10x10 supercell (Li 1000 O 500 or Li 8000 O 4000 ) Ensemble: NpT or NEV Time step: 1 fs or variable step Simulation time: ~5 ns or ~4 ps In the classical MD, electrons are not described explicitly. As a result, the calculation cost is enough reduced to perform the dynamics simulation. In the case of radiation simulation, the Buckingham potential was connected to the ZBL potential by polynomial at around Å.

Subject-1 ; (1) Radiation behavior of Li 2 O T+T+ surface bulk V Li T+T+ OT - T-T- H2H2 H2OH2O (LiOT) n n Li (1) (2) (3) O T+T+ F Tritium in defective Li 2 O (1) Radiation behavior (MD simulation) (2) Interaction with Li vacancy (FT-IR exp. & DFT calculation) (3) Interaction with O vacancy (DFT calculation)

(1) Radiation behavior of Li 2 O ; eV Li PKA along (MD) Movie 1. Li PKA along [110] (PKA energy: eV, NEV with 0K initial temp.)

(1) Radiation behavior of Li 2 O ; threshold displacement energy (MD) Li O Vacant Li 2 O crystal [555] [550] [500] [505] ( 0 eV80 eV ) O displacement Li displacement (left: vac., right: O) Threshold displacement energies Angle dependence of the threshold displacement energy was obtained: angular resolution of 6x6=36 for each under NEV ensemble (0 K initial temp.)  O requires much more high energy for displacement than Li.  The threshold energy can be ordered as [111] ＞ [110] ＞ [100].

(1) Radiation behavior of Li 2 O ; key points for the modeling (MD)  Number of stable defects are sensitively dependent on the PKA energy. (due to the self-annealing effect, etc) Number of Li vac. survived after 4 ps Variation of the maximum energy The threshold energy is not enough to describe the radiation event.  The PKA energy is immediately spread into the system. * [relaxation time] ∝ [PKA energy] 2  The self-annealing is occurred within the relaxation time.

Subject-2 ; (2) Interaction with Li vacancy T+T+ surface bulk V Li T+T+ OT - T-T- H2H2 H2OH2O (LiOT) n n Li (1) (2) (3) O T+T+ F Tritium in defective Li 2 O (1) Radiation behavior (2) Interaction with Li vacancy (FT-IR exp. & DFT calculation) (3) Interaction with O vac. (DFT calculation)  The threshold displacement energy: O > Li, [111] ＞ [110] ＞ [100].  The PKA energy is rapidly spread into the system.

(2) Interaction with Li vac. ; FT-IR during 3keV D 2 + irradiation O-D peaks during 3keV D 2 + irradiation Intensity variation of each peak O-D is stabilized in the bulk by interaction with a defect (2605 cm -1 ) or by mutual aggregation (LiOD phase: 2710 cm -1 )  2710 cm -1 is LiOD phase.  2660 cm -1 is mainly the surface O-D.  2605 cm -1 is not attributed..  [Low fluence] Only the surface O-D.  [High] The LiOD phase becomes dominant. What is the “defect” ??

(2) Interaction with Li vacancy ; FT-IR during heating after the D 2 + irradiation increase decrease By the heating, the 2605 cm -1 peak decreased, while the 2710 cm -1 peak increased. Variation in O-D peaks during heating O-D aggregated each other: (LiO - -D + ) n [2605 cm -1 ] → LiOD phase [2710 cm -1 ] By the aggregation, (LiO - -D + ) can be really stabilized ??

(2) Interaction with Li vacancy ; stabilization by aggregation (DFT) Li : O : H : A: 1 isolated (LiO - - H + ) B: 2 isolated (LiO - - H + ) C: (LiO - - H + ) 2 ⊿ E ＝ E C － E B ＝ eV Stabilization by aggregation is confirmed ! Electronic density How many (LiO - - H + ) for the 2605 cm -1 peak ? >> Frequency analysis

(2) O-D stretching frequency in LiOD (as a validation of frequency analysis) Table Calculated O-D frequency Peak sift of O-D vibration in LiOD (FT-IR experiment) A potential energy curve near the equilibrium position was obtained by ab initio calculation, and the Schrodinger equation of anharmonic oscillator is solved to analyze the O-D stretching frequency. The plane-wave pseudopotential DFT with PBE/PW91 can provide good predictions.

(2) O-D stretching frequency for O-D of sub./int. D + in Li 63 O 32 D Substitutional D + ; 2440 cm -1, Interstitial D + ; 2493 cm -1 O-D in Li 2 O at high temperatures (LiO - -D + ) n [2605 cm -1 ] → LiOD phase [2710 cm -1 ] → int. or sub. D + [2510 cm -1 ] O-D of a substitutional D + for Li + in Li 63 O 32 D supercell

Subject-3 ; (3) Interaction of H + with F centers T+T+ surface bulk V Li T+T+ OT - T-T- H2H2 H2OH2O (LiOT) n n Li (1) (2) (3) O T+T+ F Tritium in defective Li 2 O (1) Radiation behavior (2) Interaction with Li vacancy (3) Interaction with O vacancy (DFT calculation)  The threshold displacement energy: O > Li, [111] ＞ [110] ＞ [100].  The PKA energy is rapidly spread into the system.  Li vacancy heightens the stability of D + (formation of subs. D + ).  (LiO - - H + ) becomes more stable by aggregation.

(3) Interaction with F centers ; locally stable positions near F centers (DFT) Li:, O:, H:, F centers: *By controlling the system charge, O vac., F +, and F 0 are modeled. Sub. H + neighboring F center in Li 2 O

(3) Interaction with F centers ; stability around F centers (DFT) Stability of sub. H + near F center F centers trap H strongly, and reduce it to H -.

Summary T+T+ surface bulk V Li T+T+ OT - T-T- H2H2 H2OH2O (LiOT) n n Li (1) (2) (3) O T+T+ F Tritium in defective Li 2 O (1) Radiation behavior (2) Interaction with Li vacancy (3) Interaction with O vacancy (3) Interaction with O vacancy  The threshold displacement energy: O > Li, [111] ＞ [110] ＞ [100].  The PKA energy is rapidly spread into the system.  F centers trap T + and reduce it to T -.  Capturing force depends on the charge state of F centers: F 0 > F + > O vacancy  Li vac. heightens the stability of D + (formation of subs. D + ).  (LiO - - H + ) becomes more stable by aggregation.