2014 Joint ICTP-IAEA Conference on Models and Data for Plasma-Material Interaction in Fusion Devices, 3 7 November 2014, International Centre for Theoretical Physics (ICTP), Trieste, Italy. Multiple hydrogen trapping by vacancies: Its impact on defect dynamics and hydrogen retention in tungsten D. Kato a,b, H. Iwakiri c, Y. Watanabe d, K. Morishita e, T. Muroga a,b, N. Fernandez f, A. Allouche f, and Y. Ferro f a National Institute for Fusion Science (NIFS), Toki, Gifu 509-5292, Japan b The Graduate University for Advanced Studies (SOKENDAI), Toki, Gifu 509-5292, Japan c University of the Ryukyus, Okinawa 903-0213, Japan d Japan Atomic Energy Agency (JAEA), Rokkasho, Aomori 039-3212, Japan e Institute of Advanced Energy, Kyoto University, Ui, Kyoto 611-0011, Japan f Aix-Marseille University, CNRS, PIIM UMR 7345, 13397 Marseille, France 2014/11/05 ICTP-IAEA@Trieste 1
Acknowledgments This work has been performed in the period of IAEA-CRP Data for Surface Composition Dynamics Relevant to Erosion Processes (2007-2011), and MEXT Grand-in-Aid Scientific Research in Priority Areas Tritium for Fusion (2007-2011) (Chair: Tetsuo Tanabe). DK is grateful to supports by KAKENHI (22560821), Joint Usage/Research Program on Zero-Emission Energy Research (Institute of Advanced Energy, Kyoto University, ZE26A-8), and NIFS/NINS under the proect of Formation of International Scientific Base and Network. 2014/11/05 ICTP-IAEA@Trieste 2
contents Introduction: Super-saturation of H in W under high-flux divertor plasma irradiation Di-vacancies formation in W under hydrogen rich condition [D. Kato et al., J. Nucl. Mater. 417 (2011) 1115] C impurity diffusion interacting with ambient H in W [D. Kato et al., Plasma and Fusion Research: Regular Article, Vol. 6 (2011) 2405062] Summary 2014/11/05 ICTP-IAEA@Trieste 3
D/T retention in W Fusion power output ~3GW DT fusion reaction ~ a few % FBR~0.1 1 dpa 100 D T microstructure codeposit n ~10 21 n/s blanket ~10 21 T/s TBR > 1 diffusion limit wall saturation (ITER divertor incident particles) ~10 24 T/s No experimental knowledge He 10 25 /m 2 fluence 10 31 /m 2 T invetory increase (Wall pumping) thermal diffusion deep and trapped inside (square root of incident fluence) codeposition with sputtered particles (low T, linearly increase with fluence) microstructure develop (T dependence?, fluence dependence?) Reemission character Optimal operation temperature window 2014/11/05 ICTP-IAEA@Trieste 4
ITER divertor ITER first-wall D trap concentration in damaged W Surrogate ion experiments Radiation effects depend on character of defects. Scaling with dpa has large uncertainty. PKA energy dependence 300 kev H 12 MeV Si DEMO:10 dpa Power plant:100 dpa Whyte, ITPA (2008) Ueda (Osaka Univ.) 2014/11/05 ICTP-IAEA@Trieste 5
Super-saturation of H concentration by high-flux plasma irradiation Fractional concentration of H at the surface is estimated in steady state of incident flux ϕ in = 10 24 /m 2 /s. in f in 2 k r C s C s f in k r Anderl s data (Fus. Tech. v.21, 745, 1992) for recombination coefficients k r, 1 kev D + ion, Frauenfelder s diffusivity is used. Reflection coefficient (TRIM.SP) 0.76~0.98@10 ev (f=1e-1~1e-2); t Hoen et al. PRL 111, 2013, f = 1e-5~1e-7@5 ev. H solubility in W under high H pressure calculated by Sugimoto&Fukai (Acta Metall. Mater. v.40, 2327, 1992) 2014/11/05 ICTP-IAEA@Trieste 6
Super-saturated D and blistering (D/C mixed irradiation) Temperature dependence of D/W fraction on surfaces Peng, Ueda, JNM 2013 D/C mixed irradiation increase D concentration 10-4 Zakharov Blistering on W surfaces by D/C mixed irradiation. (No blistering observed with D only) 10-6 Frauenfelder 2014/11/05 ICTP-IAEA@Trieste 7
New vacancy creation under super-saturated hydrogen condition Wright, 18 th PSI (May, 2008) Implanted D super-saturates The implantation zone. W atom is displaced and a vacancy is formed. Vacancy clustering and void/blister formation What experimental factors influence strength and formation of stress fields? Plasma flux density sets rate of implantation (source) Hydrogenic solubility sets saturation limit (boundary condition) Diffusion/surface recombination rate-limiting process removes D from implantation zone (sink). 82014/11/05 ICTP-IAEA@Trieste
Super abundant vacancy creation in the form of VH complex Statistical thermodynamics model proposed by Fukai extended to evaluate concentration of each complex. x xi xt N N exp f kt, f VH x N W x f ( T ) e (VH i f i t f f ( T ) e (H) f f i H l ) 6 N W, x, 3 l h l 2 3 (H) x x V0 V exp 0 x f V kt 06 f : formation free energies h l 2 (VH ) ktln 1 exp ktln 1 exp h (H) l h kt 1,6,3,4,12,6,1 (VH ) l kt Collaboration with Y.Ferro, N.Fernandez f 0 f 0 f f ( T 0) 0 f V 3.25 ev 2014/11/05 ICTP-IAEA@Trieste 9
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contents Introduction: Super-saturation of H in W under high-flux divertor plasma irradiation Di-vacancies formation in W under hydrogen rich condition [D. Kato et al., J. Nucl. Mater. 417 (2011) 1115] C impurity diffusion interacting with ambient H in W [D. Kato et al., Plasma and Fusion Research: Regular Article, Vol. 6 (2011) 2405062] Summary 2014/11/05 ICTP-IAEA@Trieste 11
In order to investigate influence of ambient hydrogen atoms on coalescence of vacancy clusters, di-vacancy formation associated with hydrogen trapping is studied from first-principles. 2 nd nearest-neighbor (2NN) V 1 st nearest-neighbor (1NN) 3 rd nearest-neighbor (3NN) 2014/11/05 ICTP-IAEA@Trieste 12
Equilibrium states of V 2 H complex Relaxation of ionic configuration and cell shape for constant volumes Blue: W Red: H Energy-volume curve Fitting to Birch-Murnaghan s equation of states Equilibrium total-energy, volume, bulk modulus y x z Image of equilibrium configuration of V 2 H cluster in bcc tungsten crystal GGA-PBE DFT calculation using VASP code. A reference bcc super-cell containing 128 tungsten atoms (periodic boundary condition). 8 8 8 shifted k-point grid of the Monkhorst-Pack scheme. Plane wave cut-off energy of 300 ev. Numerical convergence < 10 mev. Configuration (ion and cell-shape) relaxation using conugate gradient method (force per atom < 20 mev/å). 2014/11/05 ICTP-IAEA@Trieste 13
Surface-energy correction of vacancy formation energy in W 1NN Surface of electronic void 2NN 3NN Di-vacancies S Numerical data for ellium model [S. Kurth, J. P. Perdew, P. Blaha, Int. J. Quantum Chem. 75 (1999) 889.] are adopted; 1.77 10-2 ev/å 2 for Wigner- Seitz radius r s =1.62 corresponding to an electron density of bulk W. w/o surface-energy correction e f(3nn) 2 e f(v) < e f(1nn) < e f(2nn) Ω f(1nn) > Ω f(3nn) 2 Ω f(v) > Ω f(2nn) Surface-energy correction Δe f = S ε PBE-ellium (= + 1.77 10-2 ev/å 2 ) S 1NN S 2NN < S 3NN 2 S V Δe f(1nn) Δe f(2nn) < Δe f(3nn) 2 Δe f(v) TABLE: Vacancy formation energy (e f ), formation volume (Ω f ), and binding energy (e b ). V: mono-vacancy, V 2 (1NN): the first nearrestneighbor di-vacancy, V 2 (2NN): the second one, V 2 (3NN): the third one. Bold represents present results (numbers in parentheses are the results w/o correction). V V 2 (1NN) V 2 (2NN) V 2 (3NN) e f (ev) Ω f (Å 3 ) e b (ev) 3.68 (3.17) 10.5 3.5 4.1 a 3.56 b 3.6 c 12.4 c 3.95 e 3.54 7.31 (6.50) 6.71 b 7.06 c 7.32 e 7.63 (6.81) 6.93 b 6.42 c 7.36 e 7.48 (6.47) 7.32 c 21.4 25.4 c 20.1 23.6 c 20.8 24.8 c +0.05 (-0.16) +0.41 b +0.14 c +0.7 d +0.58 e +0.45 g -0.04 h -0.27 (-0.47) +0.19 b +0.78 c +0.54 e +0.29 g -0.44 h -0.12 (-0.13) -0.12 c a)landolt-börnstein data-book, b)dft-gga (PLATO), c)johnson s model potential, d)experimental (FIM), e)modified embedded atom model, f)kittle s text, g)tight-binding 2014/11/05 Δe b(1nn) Δe b(2nn) ICTP-IAEA@Trieste > Δe b(3nn) 0 methods, h)def-gga(pbe) by Ventelon et al. 14
Hydrogen trapping effect on di-vacancy formation in W V 2 H complex binds with H stronger than VH A nucleus of larger vacancy clusters 1NN 2V apparent binding energy ~0.7 ev 2NN DFT potential energy surface of H Binding energy of single hydrogen atom to V 2 1.8 ev for 1NN at an octahedral site. 2.1 ev for 2NN at the center of a line connecting two vacancies. (Binding energy to V is 1.4 ev) 2014/11/05 Hydrogen effect in formation energies of V 2 and V 2 H in tungsten for 1NN and 2NN configurations. Other DFT results (triangles, L.Ventelon 2012) using AM05 functional optimized to vacancy calculations are also plotted for comparison. Dotted line indicates an experimental value obtained by field ion microscopy (FIM, J.Y.Park 1983). ICTP-IAEA@Trieste 15
Multiple-hydrogen trapping of V 2 is not studied in present work. Theoretical studies on the multiple trapping by V 2 have been reported for C atoms in a bcc Fe [C.J. Först et al., Phys. Rev. Lett. 96 (2006) 175501.]; lower formation energies were obtained for V 2 trapping more C atoms. This suggests that the multiple-hydrogen trapping may also assist the V 2 formation more efficiently. C.J. Först et al., Phys. Rev. Lett. 96 (2006) 175501. 2014/11/05 ICTP-IAEA@Trieste 16
contents Introduction: Super-saturation of H in W under high-flux divertor plasma irradiation Di-vacancies formation in W under hydrogen rich condition [D. Kato et al., J. Nucl. Mater. 417 (2011) 1115] C impurity diffusion interacting with ambient H in W [D. Kato et al., Plasma and Fusion Research: Regular Article, Vol. 6 (2011) 2405062] Summary 2014/11/05 ICTP-IAEA@Trieste 17
SIMS yield C impurity level in SC-W surface increases significantly after D ion implantation. C impurity plays a primary role to explain D retention characteristics. Depth (nm) Depth profile indicates the impurity atoms diffuse into W as deep as D. Impurity levels are apparently increased into 90 nm deep (much longer than intrinsic diffusion lengths of the impurity atoms). Ion energy: 1.5 kev D 3 + (500 ev /D) Flux: 5-6x10 19 /m 2 s Poon et al., JNM (2003) 2014/11/05 ICTP-IAEA@Trieste 18
Strong repulsion with dissolved C atom W C H E B ( C-H) EF(C) EF(H) EF(C H) 2014/11/05 ICTP-IAEA@Trieste 19
Activation enthalpy, entropy of vibration, and hopping frequency. o-c: an isolated interstitial C, o- C/t-H: an interstitial C-H pair. ΔE (ev) ΔS vib /k B ν (THz) o-c 1.42-0.03 16.3 o-c/t-h 0.97-0.87 16.1 Jumping rate [/s]: Γ exp S k exp E k T, vib (D. Kato et al., PFR: Regular Article, 2011) B B 2014/11/05 ICTP-IAEA@Trieste 20
x Γ x Γ Γ 3 4 3 4 1 H 0, 2 3 2, 3 2 1 2 W * Γ a D x D D Theoretical evaluation of ambient hydrogen effect 21 2014/11/05 ICTP-IAEA@Trieste
Hydrogen effect on diffusion length of C Diffusion length ratio, L * /L 0 = (D * /D 0 ) 1/2, of an interstitial C in W crystal. L 0 is the diffusion length of an isolated C, L * with 5 at% ambient H concentration. 2014/11/05 ICTP-IAEA@Trieste (D. Kato et al., PFR, 2011) 22
Volume diffusion coefficients of C in W single-crystal Interstitial diffusion coefficients of C in the bulk W crystal. Two experimental values of volume diffusion coefficients, which were measured with single-crystal W samples, are also plotted for comparison. 2014/11/05 ICTP-IAEA@Trieste (D. Kato et al., PFR, 2011) 23
Summary Super-saturated H is anticipated in W under high-flux divertor plasma irradiation, and gives influence on defect dynamics and concurrently H/D/T retention. Multiscale modeling of the super-saturated H effects is important for a better characterization of defects in divertor of ITER and DEMO. Remarkable effects of H on di-vacancy formation and C impurity diffusion in W are predicted from first-principles based on DFT calculations. Di-vacancy formation is facilitated by trapping H. Calculated formation energy of V 2 H complex coincides to an experimental measurement. Interstitial diffusion of dissolved C in W is enhanced by repulsive interaction with ambient H. Diffusion length increases almost 10 times at low temperatures assuming 5 at% H in W. 2014/11/05 ICTP-IAEA@Trieste 24