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Watanabe2007-Loops-W-He.pdf
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 [3]. 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 [4].
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 [7]. 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 [7] 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 [8]. 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 [9], 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 [10]; 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 [11]. 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 [12] 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
[11] for vacancies.
(c) SIAs and helium atoms can freely migrate because the
migration energies are EIm ¼ 0:054 eV [13] and EHe
m ¼
0:28 eV [14], 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 [15]: 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 [16], 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.
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