NIM B Beam Interactions with Materials & Atoms Nuclear Instruments and Methods in Physics Research B 255 (2007) 32–36 www.elsevier.com/locate/nimb Formation of interstitial loops in tungsten under helium ion irradiation: Rate theory modeling and experiment Y. Watanabe b a,* , H. Iwakiri b, N. Yoshida b, K. Morishita c, A. Kohyama c a Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816-8580, Japan c Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan Available online 12 December 2006 Abstract Formation of interstitial loops in tungsten under helium ion irradiation has been evaluated by microstructural observation and numerical model calculation. In the model, two types of mechanisms of interstitial loop nucleation are employed in addition to introducing an eﬀect of trap mutation. When the binding energy of an SIA to a helium-vacancy complex is around 0.7 eV, the irradiation-time dependence of calculated interstitial loop density shows good agreement with the experiment. The energy value (0.7 eV) is consistent with molecular dynamics evaluations in the literature. 2006 Elsevier B.V. All rights reserved. PACS: 61.80.Az; 61.72.Ji; 61.72.Cc; 67.80.Mg Keywords: Rate theory; Interstitial loops; Tungsten 1. Introduction Tungsten is proposed as one of the candidates for plasma facing materials in nuclear fusion reactors because of the low sputtering yield, low hydrogen solubility and high-melting temperature [1,2]. Plasma facing materials are bombarded with plasma particles such as hydrogen and helium isotopes with the energy from 101 to 104 eV in addition to 14 MeV neutrons, which induces the production of athermal lattice defects (point defects and defect clusters). The concentration of helium and hydrogen atoms in plasma facing materials is much higher than those in blanket structural materials in nuclear fusion reactors. A high concentration of helium atoms in a material enhances radiation-induced microstructural changes such as the formation of interstitial loops and helium bubbles (Hebubbles) resulting from point defect production and * Corresponding author. Tel.: +81 774 38 3463; fax: +81 774 38 3467. E-mail address: [email protected] (Y. Watanabe). 0168-583X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.11.008 accumulation. He-bubbles cause void swelling, surface roughening and intergranular embrittlement, while interstitial loops cause transgranular embrittlement . However, the formation of interstitial loops enhanced by the existence of helium is not well understood. In the present work, the formation of interstitial loops under helium ion irradiation is investigated. For a quantitative analysis of radiation-induced microstructural evolution, focusing on the formation process of interstitial loops, an ‘‘in situ’’ observation experiment using transmission electron microscopy (TEM) is conducted. Then, the numerical analysis of defect accumulation using the kinetic rate theory based model is conducted. 2. Experimental The specimen used in the present work is high purity (99.995%) sintered tungsten (W) in the form of a circular disk with the thickness of 0.1 mm and the diameter of 3 mm. The specimen was annealed at 2273 K for 600 s in Y. Watanabe et al. / Nucl. Instr. and Meth. in Phys. Res. B 255 (2007) 32–36 a vacuum of about 5 · 104 Pa, was cleaned with twin-jet electro-polishing, then was bombarded with a helium ion beam in a 200-keV TEM equipped with a low energy ion accelerator . Fig. 1 shows the TEM image of microstructural changes in W bombarded at 300 K with an 8-keV helium ion beam, the dose rate of which is 2.6 · 1017 He+/m2/s. At ﬁrst interstitial loops appear, and the areal density and sizes of interstitial loops increase with increasing dose. At around a dose of 2.6 · 1019 He+/m2, the loop density saturates at the value of 3.5 · 1016 m2 with the average loop size of 5 nm. After that part of the interstitial loops pile up as tangled dislocations, as shown in Fig. 1(e). At a dose of 2.0 · 1021 He+/m2, as shown in Fig. 1(f), He-bubbles are observed, where the density of the bubbles is much higher than that of interstitial loops. 33 3. Model in the numerical calculation It is widely recognized that the formation of interstitial loops under high-energy electron irradiation at a low temperature of 300 K can be simulated using the conventional mechanism [5,6] of interstitial loop nucleation, where two freely-migrating self-interstitial atoms (SIAs) interact with each other and form a ‘‘di-interstitial’’ which can be the nucleus of an interstitial loop at that low temperature. This mechanism is hereafter called Type-I. However, experimental results of helium ion irradiation cannot be explained using only the Type-I mechanism. In experiments the saturated density of interstitial loops under helium ion irradiation is much higher than that under high-energy electron irradiation, even with a similar damage rate . It indicates that the nucleation of interstitial loops under helium ion irradiation is enhanced by the existence of helium. Helium atoms implanted in the matrix are trapped in radiationinduced vacancies and form helium-vacancy (He-vacancy) complexes of various sizes. Yoshida et al. proposed the diﬀerent mechanism  of interstitial loop nucleation, enhanced by He-vacancy complexes, where an SIA trapped in the stress ﬁeld of a He-vacancy complex interacts with a migrating SIA, and forms a di-interstitial. This mechanism is hereafter called Type-II. Using the kinetic rate theory based model where both the Type-I and Type-II mechanisms are employed, Yoshida et al. provided a better interpretation for experimental results of helium ion irradiation under similar experimental conditions (temperature, irradiating helium ion energy, and the ion dose) to those in the present work, although this model did not take into account an increase in freely-migrating SIAs produced by trap mutation . The trap mutation is deﬁned as the process during which a He-vacancy complex containing excess helium atoms creates additional vacancies by the emission of SIAs into its surrounding lattice. The trap-mutation ‘reaction’, for example, in molybdenum , can be expressed as follows: Hen V1 + He ! Henþ1 V2 + I, ð1Þ n P 6, as the ﬁrst of a series of reactions Hen Vm + He ! Henþ1 Vmþ1 + I, mP2 n = 7, 8, ... , ð2Þ Fig. 1. TEM images of microstructural changes in W bombarded at 300 K with an 8-keV helium ion beam, the dose rate of which is 2.6 · 1017 He+/ m2/s. Interstitial loops and He-bubbles are clearly observed. (a)–(e): Interstitial loops, (f): He-bubbles. where He, I and HenVm denote a helium atom, an SIA produced by trap mutation and a He-vacancy complex composed of n helium atoms trapped in a cluster of m vacancies, respectively. SIAs produced by the trap mutation of a He-vacancy complex can be trapped in the stress ﬁeld of the mutated He-vacancy complex ; however, the SIAs can be thermally dissociated from the stress ﬁled. As shown in our experimental result, a high concentration of He-bubbles is observed even at a low temperature of 300 K where vacancies cannot migrate due to a high migration energy of 1.7 eV . It indicates that He-vacancy complexes grow by a series of trap-mutation reactions. Assuming that SIAs 34 Y. Watanabe et al. / Nucl. Instr. and Meth. in Phys. Res. B 255 (2007) 32–36 produced by trap mutation of He-vacancy complexes become thermally dissociated from the complexes, then the concentration of migrating SIAs in the matrix will increase, leading to the enhancement of interstitial loop nucleation by the Type-I mechanism. Key assumptions of our model in the present work are both introducing the eﬀect of an increase in freely-migrating SIAs produced by trap mutation and incorporating the Type-I and Type-II mechanisms for interstitial loop nucleation. The model assumptions employed in the present work are as follows: (a) Vacancies and SIAs are produced in tungsten by atomic displacements under helium ion irradiation. The production rates (P) of vacancies and SIAs and the implantation rate (PHe) of helium atoms are estimated using the TRIM-91 code  as a function of depth (x) from the specimen surface. (b) Vacancies cannot freely migrate at a low temperature of 300 K due to the high migration energy of 1.7 eV  for vacancies. (c) SIAs and helium atoms can freely migrate because the migration energies are EIm ¼ 0:054 eV  and EHe m ¼ 0:28 eV , respectively. The corresponding mobilities at temperature (T) are M I ¼ m0 exp½ðEIm =kT Þ and M He ¼ m0 exp½ðEHe m =kT Þ for SIAs and helium atoms, respectively, where k is the Boltzmann constant and m0 is the jumping frequency assumed to be 1013 jumps/s. (d) The specimen with the thickness of 200 nm, which is the same value as that in the TEM observation, is divided into 40 meshes along the depth (x). Simultaneous rate equations representing defect interactions described here are applied to each mesh. Changes in the concentrations of SIAs and helium atoms per d2 C I unittime due to diﬀusion are given by DI dx2 and (j) (k) (l) (m) 2 (e) (f) (g) (h) (i) DHe d dxC2He , respectively, where CI and CHe are the concentrations of migrating SIAs and helium atoms, and DI and DHe are diﬀusion coeﬃcients for SIAs and helium atoms, respectively. Notice that concentration of defects is deﬁned as the fraction of defects to lattice points. The specimen surface is a perfect sink for SIAs and helium atoms. Vacancies and SIAs mutually annihilate: V + I ! 0. Two SIAs form a di-interstitial: I + I ! I2. A di-interstitial is thermally stable at this temperature, indicating the nucleus of an interstitial loop. Interstitial loops are immobile for simplicity. This simpliﬁcation may be valid, because the migration of interstitial loops can be eﬀectively prohibited by the existence of He-vacancy complexes that are produced much more than interstitial loops, as described in Section 4. An interstitial loop (In, n P 2) composed of n SIAs grows by absorbing SIAs: In + I ! In+1, n P 2. In order to compare calculation results to the experi- (n) (o) (p) (q) mental data, an interstitial loop larger than that composed of 44 SIAs is deﬁned as a TEM-visible loop. The diameter of an I44 loop is estimated to be 1 nm. A He-vacancy complex grows by absorbing helium atoms and causing trap mutation whenever conditions dictate. In our model, for simplicity, the ﬁnal growth stage of He-vacancy complexes (HenVm) is He12V3, where 1 6 m 6 3 and 0 6 n 6 12. It is noted that He0V1 corresponds to a single vacancy. A HenV1 (0 6 n 6 5) complex can absorb helium atoms to be a He6V1 complex: HenV1 + He ! Hen+1V1. A HenV1 (1 6 n 6 4) complex is annihilated with a migrating SIA, resulting in the production of n helium atoms : HenV1 + He ! n He, 1 6 n 6 4. A He6V1 complex with an additional helium atom mutates into a He7V2 complex with an SIA that is trapped in the stress ﬁeld of the mutated complex. He6V1 + He ! He7V2I, where He7V2I indicates a He7V2 complex trapping an SIA. The binding energy of an SIA to a He7V2 complex is denoted as Eb that is treated as an adjustable parameter in the calculations. The SIA trapped by a He7V2 complex can be thermally dissociated from the complex: He7V2I ! He7V2 + I, where I in the right hand side is a freely-migrating SIA. As a reverse reaction, a He7V2 complex traps a migrating SIA to form a He7V2I complex: He7V2 + I ! He7V2I. The rate for thermal dissociation of an SIA from a He7V2 complex is given by QHe7 V2 I ¼ m0 exp½ðEI m þ Eb Þ=kT . The SIA trapped by a He7V2 complex interacts with a migrating SIA, leading to the formation of a di-interstitial trapped by the complex: He7V2I + I ! He7V2I2. Such a di-interstitial is also regarded as the nucleus of an interstitial loop, which corresponds to the Type-II mechanism of interstitial loop nucleation. Interstitial loops produced by this mechanism are also immobile. Besides, a He7V2I2 complex cannot absorb additional helium atoms.Similar assumptions to (k)–(m) are as well applied to larger He-vacancy complexes than a He7V2 complex, as follows: A He7V2I complex can absorb helium atoms to be a He11V2I complex: HenV2I + He ! Hen+1V2I, 7 6 n 6 10. The SIA trapped by a HenV2 (7 6 n 6 11) complex can be thermally dissociated: HenV2I ! HenV2 + I, 7 6 n 6 11. The thermal dissociation rate of an SIA from a HenV2 (7 6 n 6 11) complex is given by QHen V2 I ¼ m0 exp½ðEIm þ Eb Þ=kT , 76n 6 11. The binding energy of an SIA to a HenV2 (7 6 n 6 11) complex takes the same value as that to a He7V2 complex, for simplicity. A HenV2 (7 6 n 6 10) complex can absorb helium atoms to be a He11V2 complex: HenV2 + He ! Hen+1V2, 7 6 n 6 10. A HenV2 (7 6 n 6 11) complex interacting with an additional migrating SIA becomes a HenV2I (7 6 n 6 11) complex: HenV2 + I ! HenV2I, 7 6 n 6 11. Y. Watanabe et al. / Nucl. Instr. and Meth. in Phys. Res. B 255 (2007) 32–36 (r) A migrating SIA can be trapped by a HenV2I complex (7 6 n 6 11), resulting in the formation of a di-interstitial in the stress ﬁeld of the complex: HenV2I + I ! HenV2I2, 7 6 n 6 11. (s) With additional helium atoms, He11V2 and He11V2I complexes mutate into He12V3I and He12V3I2 + 2 Dose of helium ions (He /m ) 14 18 -2 10 16 10 10 16 10 18 10 8-keV He + → W (300K) 2.6 × 1017 He +/m 2/s Specimen thickness = 200nm EmI = 0.054 eV EmHe = 0.28 eV Eb = 0.0 ~ 2.0 eV 20 10 0.8 ~ 2.0 eV 0.7 eV 0.6 eV 14 10 0.5 eV 12 0.4 eV 10 0.0 eV 10 Cal. Exp. 10 8 10 -4 10 -2 2 10 1 10 Irradiation time, t (s) 4 10 Fig. 2. The time dependence of areal density of interstitial loops obtained from the numerical calculations as a function of Eb. Each calculated loop density is evaluated by integrating the number of loops per unit area in each mesh of 5 nm. The loop density obtained from the TEM observation is also plotted. 35 complexes, respectively: He11V2 + He ! He12V3I; He11V2I + He ! He12V3I2. 4. Results and discussion Simultaneous rate equations derived from the above assumptions were solved using the Gear method , to evaluate defect accumulation in tungsten during helium ion irradiation. Eb was varied as an adjustable parameter from 0.0 to 2.0 eV. The time dependence of areal density of interstitial loops obtained from the numerical calculations is shown in Fig. 2, where the areal density is evaluated by integrating the number of loops per unit area in each mesh of 5 nm. The areal density obtained from the TEM observation is also plotted. The calculated loop density strongly depends on Eb. Consider the dependence of defect accumulation processes on Eb in detail. Fig. 3 shows the time dependence of calculated defect concentrations at the helium implantation peak (25 nm) under the following three conditions: (i) Eb = 0.0 eV, (ii) Eb = 2.0 eV and (iii) Eb = 0.7 eV. Note that C I2 in the ﬁgure indicates the concentration of di-interstitials (interstitial loop nuclei) produced by both the TypeI and Type-II mechanisms. The time evolution of defect accumulation until 102 s does not depend much on Eb values: CI almost remains constant until 102 s because most of the SIAs produced by atomic displacements diﬀuse to the specimen surface due to their high mobility Fig. 3. The time dependence of calculated defect concentrations at the helium implantation peak (25 nm) in the case of (i) Eb = 0.0 eV, (ii) Eb = 2.0 eV and (iii) Eb = 0.7 eV. 36 Y. Watanabe et al. / Nucl. Instr. and Meth. in Phys. Res. B 255 (2007) 32–36 (MI = 1.2 · 1012 jumps/s), and therefore, C I2 increases linearly with increasing time. It is noted that all di-interstitials are produced by the Type-I mechanism, where most of the He-vacancy complexes are still in the form of HenV1 (1 6 n 6 4) complexes. On the other hand, CHe increases linearly with increasing time at ﬁrst, and saturates after 104 s where implanted helium atoms freely diﬀuse, with the mobility of MHe = 2.0 · 108 jumps/s, to sinks such as vacancies, He-vacancy complexes and the specimen surface. The dependence of defect accumulation processes on Eb appears after 102 s. When Eb is 0.0 eV, after 102 s, CI decreases with increasing time because most of the migrating SIAs are consumed by mutual annihilation with a high concentration of vacancies, during which MVCV and MICI are balanced with each other, as deduced from Fig. 3(i). For example, from 102 to 1 s, CV increases in proportion to t0.5 while CI decreases in proportion to t0.5. Although CL is likely to saturate at around 1 s, it increases again after about 10 s. The re-increase in CL reﬂects the inﬂuence of an increase in freely-migrating SIAs produced by trap mutations. In fact, C He7 V2 is much higher than C He7 V2 I which is below the scale represented in the ﬁgure. It indicates that a large number of SIAs produced by trap mutation are dissociated from He7V2 complexes due to Eb = 0.0 eV, leading to the enhancement of interstitial loop nucleation by the Type-I mechanism. However, as shown in Fig. 2, the value of loop density at 102 s is about ﬁve orders of magnitude lower than that in the experiment. This is because most of the SIAs dissociated from He7V2 complexes are consumed by mutual annihilation with a high concentration of vacancies after 1 s, resulting in the suppression of an increase in CV. When Eb = 2.0 eV, C I2 begins to increase extremely again suddenly after 102 s. This sudden increase is related to the formation of a high concentration of HenV2I (7 6 n 6 11) complexes (i.e. HenV2 (7 6 n 6 11) complexes trapping SIAs), where the He-vacancy complexes play a role as nucleation sites for interstitial loops (the Type-II mechanism). Such a high concentration of the complexes is largely expected to provide enough evidence to us to understand the experimentally observed high density of loop formation. However, as shown in Fig. 2, the loop density increases in proportion to t1.1 for the experimental time zone (10 102 s), while the observed loop density increases in proportion to t0.5; besides, the loop density value at 2.5 · 102 s in the calculation is about one order of magnitude higher than that in the experiment. It indicates that too many HenV2I (7 6 n 6 11) complexes are produced as interstitial loop nucleation sites because most of the SIAs trapped by HenV2 (7 6 n 6 11) complexes cannot be dissociated due to the high binding energy of Eb = 2.0 eV. When Eb = 0.7 eV, in similar to the previous case (Eb = 2.0 eV), C I2 begins to increase extremely again suddenly after 102 s. In this case, the number of HenV2I (7 6 n 6 11) complexes is much less than that in the previous case, from which the number of interstitial loop nuclei is expected to be consistent with the experimental result. In fact, the loop density is proportional to t0.6 during the experimental time frame, which is in good agreement with the experimental data. This low value (0.7 eV) of binding energy is consistent with molecular dynamics evaluations in the literature [9,17–19]. 5. Conclusion The formation of interstitial loops in tungsten under helium ion irradiation has been analyzed by microstructural observation and numerical model calculation. In the model, two types of mechanism of interstitial loop nucleation are employed in addition to introducing the eﬀect of trap mutations. One mechanism is the so-called conventional di-interstitial model, and the other is associated with the formation of He-vacancy complexes. When the binding energy of an SIA to a He-vacancy complex is assumed to be around 0.7 eV, the irradiation-time dependence of interstitial loop density in the calculation shows good agreement with that in the experiment. This energy value (0.7 eV) is consistent with molecular dynamics evaluations in the literature. References  T. Tanabe, N. Noda, H. Nakamura, J. Nucl. Mater. 196–198 (1992) 11.  T. Tanabe, J. Nucl. Fus. 5 (Suppl.) (1994) 120.  H. Ullmaier, Radiat. Eﬀ. 78 (1983) 1.  T. Muroga, R. Sakamoto, M. Fukai, N. Yoshida, T. Tukamoto, J. Nucl. Mater. 196–198 (1992) 1013.  M. Kiritani, N. Yoshida, H. Takata, J. Phys. Soc. Jpn. 35 (1973) 95.  N. Yoshida, M. Kiritani, J. Phys. Soc. Jpn. 35 (1973) 1418.  N. Yoshida, E. Kuramoto, K. Kitajima, J. Nucl. Mater. 103–104 (1981) 373.  L.M. Caspers, R.H.J. Fastenau, A. Van Veen, W.F.W.M. Van Heugten, Phys. Stat. Sol. (a) 46 (1978) 541.  L.M. Caspers, M.R. Ypma, A. Van Veen, G.J. Vanderkorkolk, Phys. Stat. Sol. (a) 63 (1981) 183.  L.M. Caspers, A. Van Veen, T.J. Bullough, Radiat. Eﬀ. 78 (1983) 67.  R.W. Balluﬃ, J. Nucl. Mater. 69–70 (1978) 240.  J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985.  F. Dausinger, H. Schultz, Phys. Rev. Lett. 35 (1975) 1773.  A. Wagner, D.N. Seidman, Phys. Rev. Lett. 42 (1979) 515.  E.V. Kornelsen, A.A. Van Gorkum, J. Nucl. Mater. 92 (1980) 79.  S.D. Cohen, A.C. Hindmarsh, Comput. Phys. 10 (1996) 138.  W.D. Wilson, C.L. Bisson, M.I. Baskes, Phys. Rev. B 24 (1981) 5616.  K. Morishita, R. Sugano, B.D. Wirth, T. Diaz de la Rubia, Nucl. Instr. and Meth. B 202 (2003) 76.  K. Morishita, R. Sugano, B.D. Wirth, J. Nucl. Mater. 323 (2003) 243.