Simulations of atomic deuterium exposure in self-damaged tungsten

TLDR: In this article, simulations of deuterium (D) atom exposure in self-damaged polycrystalline tungsten at 500 and 600 K were performed using an evolution of the MHIMS (migration of hydrogen isotopes in materials) code in which a model to describe the interaction of D with the surface is implemented.

Abstract: Simulations of deuterium (D) atom exposure in self-damaged polycrystalline tungsten at 500 K and 600 K are performed using an evolution of the MHIMS (migration of hydrogen isotopes in materials) code in which a model to describe the interaction of D with the surface is implemented. The surface-energy barriers for both temperatures are determined analytically with a steady-state analysis. The desorption energy per D atom from the surface is 0.69  ±  0.02 eV at 500 K and 0.87  ±  0.03 eV at 600 K. These values are in good agreement with ab initio calculations as well as experimental determination of desorption energies. The absorption energy (from the surface to the bulk) is 1.33  ±  0.04 eV at 500 K, 1.55  ±  0.02 eV at 600 K when assuming that the resurfacing energy (from the bulk to the surface) is 0.2 eV. Thermal-desorption spectrometry data after D atom exposure at 500 K and isothermal desorption at 600 K after D atom exposure at 600 K can be reproduced quantitatively with three bulk-detrapping energies, namely 1.65  ±  0.01 eV, 1.85  ±  0.03 eV and 2.06  ±  0.04 eV, in addition to the intrinsic detrapping energies known for undamaged tungsten (0.85 eV and 1.00 eV). Thanks to analyses of the amount of traps during annealing at different temperatures and ab initio calculations, the 1.65 eV detrapping energy is attributed to jogged dislocations and the 1.85 eV detrapping energy is attributed to dislocation loops. Finally, the 2.06 eV detrapping energy is attributed to D trapping in cavities based on literature reporting observations on the growth of cavities, even though this could also be understood as D desorbing from the C-D bond in the case of hydrocarbon contamination in the experimental sample.

Figures

Figure 7. Comparison between simulated and experimental evolutions of the D total amounts with time during a 48 h atomic exposure at 600 K, flux of × ⋅ ⋅− −5.8 10  D m s18 2 1 followed by an isothermal desorption at 600 K for 43 h.

Table 1. Summary of the parameters used in the bulk and surface models.

Figure 3. (a) Evolution of mobile particle during atomic exposure at three times t1, t2 and t3 using the approximated model. (b) Evolution of the concentration of trapped particles in trap i using the approximated model.

Figure 6. (a) Comparison between experimental and simulated D depth profiles during atomic exposure at 600 K (maximum exposure time = 48 h). (b) Comparison between experimental and simulated D depth profiles during the isothermal desorption at 600 K.

Figure 9. Integrated trap amount between 0 and 2.4 µm as function of the annealing temperature for the simulation of D atom exposure at 500 K. The point at 500 K corresponds to the unannealed case.

Figure 8. Evolution of detrapping energies calculated by DFT with the number of H trapped inside different defects. For the H trapped in mono-vacancy, DFT data from Fernandez et al [15] and from You et al [53]. For H trapped by dislocations, DFT data from Terentyev et al [55] for dislocation line without and with jog and DFT data from Xiao et al [54] for dislocation loop. For H trapped by SIAs, DFT data from Heinola et al [56]. The detrapping energies are calculated by adding the migration energies calculated by DFT (0.2 eV) to the binding energies calculated by DFT for these defects. In this figure we also report the detrapping energies of intrinsic traps previously determined in [9], and detrapping energies of the self-damaged-induced trap determined in the MRE simulation from Ogorodnikova et al [49, 52] and in the present study. Detrapping energies from other MRE models are not presented on this plot for the sake of clarity.

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Simulations of atomic deuterium exposure in
self-damaged tungsten
E.A. Hodille, A Založnik, S Markelj, T. Schwarz-Selinger, C.S. Becquart,
Régis Bisson, Christian Grisolia
To cite this version:
E.A. Hodille, A Založnik, S Markelj, T. Schwarz-Selinger, C.S. Becquart, et al.. Simulations of
atomic deuterium exposure in self-damaged tungsten. Nuclear Fusion, IOP Publishing, 2017, 57
(5), pp.056002. �10.1088/1741-4326/aa5aa5�. �hal-01528018�

1 © 2017 CEA Printed in the UK
1. Introduction
Due to its good mechanical and thermal properties, tung-
sten (W) has been chosen to be the material constituting the
divertor region in ITER. This region is the part of the tokamak
which experiences the highest particle ux (10
24
m
−2
s
−1
)
making hydrogen isotope (HI) retention and outgassing from
W a key consideration for safety and plasma control issues.
During the deuterium/tritium phase in ITER, fast neutrons
(14.1 MeV) will be created. They can transmute the elements
present in plasma-facing components (PFCs) [1] and they will
also induce crystallographic defects that can change the HI
trapping and release properties of all the materials facing the
plasma. 14.1 MeV neutron sources are scarce and a hot cell
facility is required to deal with neutron-irradiated samples. A
good proxy to simulate the damage induced during neutron
irradiations has been found in MeV heavy-ion implantations
and especially MeV W ions [2], the latter irradiation resulting
Nuclear Fusion
Simulations of atomic deuterium exposure
in self-damaged tungsten
E.A.Hodille
1
, A.Založnik
2
, S.Markelj
2
, T.Schwarz-Selinger
3
,
C.S.Becquart
4
, R.Bisson
5
and C.Grisolia
1
1
CEA, IRFM, F-13108 Saint-Paul-lèz-Durance, France
2
Jožef Stefan Institute, Jamova cesta 39, 1000, Ljubljana, Slovenia
3
Max-Planck-Institut für Plasmaphysik, Boltzmannstrasse 2, D-85748 Garching, Germany
4
Université Lille I, UMET, UMR 8207, ENSCL, 59655 Villeneuve d’Ascq Cedex, France
5
Aix-Marseille Université, CNRS, PIIM, Marseille, France
E-mail: christian.grisolia@cea.fr
Received 1 September 2016, revised 12 December 2016
Accepted for publication 4 January 2017
Published 14 March 2017
Abstract
Simulations of deuterium (D) atom exposure in self-damaged polycrystalline tungsten at
500 K and 600 K are performed using an evolution of the MHIMS (migration of hydrogen
isotopes in materials) code in which a model to describe the interaction of D with the
surface is implemented. The surface-energy barriers for both temperatures are determined
analytically with a steady-state analysis. The desorption energy per D atom from the surface
is 0.69 ± 0.02 eV at 500 K and 0.87 ± 0.03 eV at 600 K. These values are in good agreement
with ab initio calculations as well as experimental determination of desorption energies. The
absorption energy (from the surface to the bulk) is 1.33 ± 0.04 eV at 500 K, 1.55 ± 0.02 eV
at 600 K when assuming that the resurfacing energy (from the bulk to the surface) is 0.2 eV.
Thermal-desorption spectrometry data after D atom exposure at 500 K and isothermal
desorption at 600 K after D atom exposure at 600 K can be reproduced quantitatively with
three bulk-detrapping energies, namely 1.65 ± 0.01 eV, 1.85 ± 0.03 eV and 2.06 ± 0.04 eV,
in addition to the intrinsic detrapping energies known for undamaged tungsten (0.85 eV and
1.00 eV). Thanks to analyses of the amount of traps during annealing at different temperatures
and ab initio calculations, the 1.65 eV detrapping energy is attributed to jogged dislocations and
the 1.85 eV detrapping energy is attributed to dislocation loops. Finally, the 2.06 eV detrapping
energy is attributed to D trapping in cavities based on literature reporting observations on the
growth of cavities, even though this could also be understood as D desorbing from the C-D
bond in the case of hydrocarbon contamination in the experimental sample.
Keywords: tungsten, damaged material, rate-equation modeling, deuterium atoms,
fuel retention
(Some guresmay appear in colour only in the online journal)
E.A. Hodille etal
Printed in the UK
056002
NUFUAU
© 2017 CEA
57
Nucl. Fusion
NF
10.1088/1741-4326/aa5aa5
Paper
5
Nuclear Fusion
IOP
International Atomic Energy Agency
2017
1741-4326
1741-4326/17/056002+15$33.00
https://doi.org/10.1088/1741-4326/aa5aa5
Nucl. Fusion 57 (2017) 056002 (15pp)

E.A. Hodille etal
2
in so-called self-damaged W samples. The interaction of HIs
with self-damaged W has been extensively studied exper-
imentally, particularly in relation to their retention properties
[3–8]. These studies show that the D retention in such mat-
erials is signicantly higher than in undamaged W. In addi-
tion, by analyzing thermal-desorption spectrometry (TDS)
results, it has been observed that D is released at a far higher
temper ature in the case of self-damaged W than in the case of
undamaged W [8].
In this study, the MHIMS (migration of hydrogen isotopes
in metals) [9] code, which is based on a macroscopic rate-
equation (MRE) model that couples both diffusion and trap-
ping of HIs, has been upgraded to simulate the experimental
results presented in [6, 7]. In these two experimental studies,
self-damaged polycrystalline W (PCW) samples were exposed
to a beam of deuterium (D) atoms with a low kinetic energy
of ~0.3 eV. With such a low kinetic energy, D atoms may not
directly reach the bulk and be implanted as they would be in
the case of energetic D ions. Instead, they are rst adsorbed on
the W surface [10, 11]. In order to include this kind of events
in simulations, a surface model needs to be built, and one of
the goals of this paper is to describe the implementation of
such a model in the MHIMS code. The article is organized as
follows. First, the model and its main features are described,
and then the procedure adopted to determine the different
energy barriers at the surface is detailed. Finally, the simula-
tion results obtained using the upgraded version of MHIMS
are compared to the experimental studies and discussed.
2. Simulation of the experimental results
2.1. Model description
In this paper, the MHIMS code that was previously used to
determine the trapping parameters of HIs in undamaged PCW
irradiated with D ions [9] was upgraded to simulate the two
experiments presented in [6, 7]. In the version of the code pre-
sented in [9], no surface effects were taken into account since
TDS experiments showed that surface recombination was not
the rate-limiting process in the desorption from undamaged
PCW implanted with 250 eV/D ions [12]. However, exper-
imental results by ‘t Hoen et al [10] showed that the inser-
tion of low energetic ions (<5 eV/D) is limited by the surface
process. Such results were conrmed by molecular dynamics
(MD) simulations of D on the W surface by Maya [11]. In
these simulations, it was shown that atoms with energy below
1 eV/D do not penetrate beneath the surface, but are instead
stuck on it. Thus, the 0.3 eV/D atoms used in [6, 7] should
not be directly implanted into the bulk, but instead should be
rst adsorbed on the surface. To simulate such exposure con-
ditions, a model describing the different surface processes has
been added to the standard version of the MHIMS code.
The model for surface and bulk interaction between HIs
and W can be described with the idealized interaction potential
diagram drawn in gure1 [13, 14]. Here, E
1
2
diss
is the energy
barrier per D atom associated to the dissociative adsorp-
tion of D
2
molecules impinging from the energy level
D
1
2
2
.
The upper-vacuum energy-level D corresponds to the one of
impinging D atoms. Noth these energy levels are thus sepa-
rated by half the D
2
dissociation energy
1
2
−
E
DD
. The activa-
tion energy for desorption
E
des
represents the energy needed to
form a desorbing D
2
molecule from two chemisorbed D atoms
and can be written as
=⋅E E2
desD
where E
D
is the desorption
energy per D atom [14]. This quantity should not be mistaken
with the chemisorption energy (E
chem
) or the isosteric heat of
adsorption (q
st
) which are equal to
−E E
desdiss
, nor the bond
energy of D atoms on the surface (E
W–D
), which is dened
as the energy difference between the vacuum energy level of
the impinging D and the energy level of D at the bottom of
the surface chemisorption well. According to Pick etal [14],
the solution energy is dened as the difference between the
molecular vacuum energy level and the atomic-bulk adsorp-
tion well, i.e.
=−+⋅ −
E
EE
EE
SAD
1
2
diss
R
(gure 1), where
E
A
is the energy needed for an adsorbed D to enter the bulk
(absorption energy) and
E
R
is the energy needed for an
absorbed D to go from the bulk to the surface (resurfacing
energy). Finally,
E
diff
is the energy barrier for D diffusion in
the bulk and
E
iB,
is the binding energy of D with a trap of type
ii (in gure1,
=i 1, 2
).
To build the model, three kinds of particles (i.e. HIs) are
considered:
1. Particles adsorbed on the surface: concentration
c
surf
.
(m
−2
).
2. Mobile particles that can diffuse in the bulk: concentration
c
m
. (m
−3
).
3. Particles trapped in the bulk: concentration
c
it,
. (m
−3
).
Several types of traps exist, characterized by their index i.
The nite amount of sites that can accommodate HIs are
of three kinds:
1. Adsorption sites on the surface: concentration
n
surf
(m
−2
).
2. Interstitial sites in the bulk: concentration
n
TIS
(m
−3
).
Indeed, density functional theory (DFT) calculations
show that interstitial HIs diffuse from tetrahedral intersti-
tial sites (TIS) [15] to nearest-neighbor TIS.
3. Trapping sites in the bulk: concentration
n
i
(m
−3
).
As shown above, all bulk concentrations are in m
−3
in
the model. However, in experimental results these are often
expressed in terms of percentage of atomic fraction (at.%)
by normalizing concentrations to the W atomic density
ρ ≈×
−
6.310m
W
28 3
. Thus, in the simulation results shown
here, the concentration will also sometimes be expressed in
at.%.
In the following, it is supposed that the amount of traps
is small compared to the amount of possible sites for the
mobile particles (
n n
iTIS
). Thus, each trap site is surrounded
by only TIS and a HI leaving a trap cannot be immediately
retrapped in another trap. In addition, it is considered that the
concentration of mobile particles is much smaller than the
concentration of TIS (
c n
mTIS
). Thus, among all the TIS that
surround a trapping site, there is at least one of them that is
empty. This hypothesis is always valid for the parameter range
encountered in laboratory experiments. Following these two
Nucl. Fusion 57 (2017) 056002

E.A. Hodille etal
3
hypotheses, the evolution of the concentration of trapped and
mobile particles in the bulk can be dened by the following
commonly used set of equations[16]:
()
∂
∂
=⋅
∂
∂
−Σ
∂
∂
c
t
DT
c
x
c
t
i
m
2
m
2
t,
(1)
() ()()
νν
∂
∂
=⋅⋅−
−⋅
c
t
Tc nc
Tc.
i
ii
t,
mmit,i t,
(2)
The rst term on the right-hand side of equation(1) is derived
from Fick’s law of diffusion and is characterized by the dif-
fusion coefcient of HIs in W,
()=⋅
−
⋅
DT
D e
0
E
kT
diff
B
, (m
2
s
−1
)
where
=× ⋅
−−
k 8.610eV K
B
51
is the Boltzmann constant, T
(K) is the sample temperature and
E
diff
(eV) is the energy
barrier for diffusion (gure 1). For this study, the diffusion
coefcient for hydrogen calculated using DFT by Fernandez
etal [15] is used:
()=× ⋅⋅
−
−
−
⋅
DT 1.910e m s
H
721
kT
0.2eV
B
. The
diffusion coefcient of D is equal to
()DT
H
divided by
2
,
the square root of the atomic mass ratio between D and H.
The second term on the right-hand side of equation(1) cor-
responds to the exchange (trapping and detrapping) between
mobile and trapped particles that is described by equation(2)
for trap type i. In equation (2), the rst term of the right-
hand side corresponds to the trapping of mobile particles into
an empty trap site (
−n c
iit,
). This process is characterized
by the rate
()
()
ν
=
λ
⋅
T
DT
n
m
TIS
2
(m
3
s
−1
) where
λ
is the distance
between 2 TIS or the jumping distance. This can be estimated
to be
λ ≈×
−
110 10 m
12
from ab initio calculations [15]. The
second term of equation(2) corresponds to the detrapping of
a trapped particle. This process is characterized by the rate
()ν ν=⋅
−
⋅
T e
i0
E
i
kT
t,
B
(s
−1
) where
=+E EE
iit, B, diff
. (eV) is the
detrapping energy of trap site i and
ν
0
is a pre-exponential
factor. The value of the pre-exponential factor is important
to know (at least its order of magnitude). Indeed, a change
of one order of magnitude on this pre-exponential factor will
lead to a change of
()≈⋅⋅kTln 10
B
on the determination of
the detrapping energy. For the simulation of a TDS experi-
ment done between 300 K and 1300 K, the corresponding
error would be between 0.05 and 0.25 eV. According to rst-
principles calculations [15], the pre-exponential factor for
detrapping of H from a W mono-vacancy is
ν ≈
−
10 s
0
13 1
and
this is the order of magnitude which is used for several MRE
simulations [5, 9] and which is used for this work too.
The model for the surface, acting as boundary conditions
for the global MRE model, is described by the evolution of
()=c x 0
m
and
c
surf
. The surface coverage is
θ =
c
n
surf
surf
. This
denes the amount of adsorption sites that are occupied: (
θ−1
)
is the probability that an adsorption site is empty. The evolutions
of the two quantities
()=c x 0
m
and
c
surf
are driven by different
uxes (m
−2
s
−1
) which are described hereafter (see gure2):
Figure 1. Idealized potential diagram describing the interaction of HIs with W at the surface (interface between the vacuum and the metal)
and in the bulk.
Figure 2. Explicative scheme of the ux balance on the surface.
Blue solid arrows correspond to ux of atoms and green dashed
arrows correspond to ux of molecules.
Nucl. Fusion 57 (2017) 056002

E.A. Hodille etal
4
–
() ()φ θ=− ⋅Γ ⋅−P11
atom
ratom
. This corresponds to the
part of the incident ux of atoms
Γ
atom
(m
−2
s
−1
) adsorbed
on the surface. The term
θ−1
implies that a fully cov-
ered surface prevents any incoming D atoms from being
adsorbed.
( )− P1
r
is the sticking probability. According
to MD simulations [17, 18] the sticking coefcient of a
0.3 eV D atom on a pristine W surface is
( )−=P10.19
r
which is the value used in the equation(
P
r
is not a free
parameter) and is also in good agreement with the value
determined experimentally [6].
–
φ σ=Γ ⋅⋅c
exc
atom ex
cs
urf
. This corresponds to direct
abstraction of a chemisorbed D, i.e. the recombination of
an incident D atom with an adsorbed atom on the sur-
face [6] which is characterized by the cross-section
σ
exc
(m
2
). The value of
σ
exc
. that is used in this work is the
one determined in [6] to reproduce an isotopic exchange
experiment on the surface:
σ ≈
−
10 m
exc
21 2
(
σ
exc
is not a
free parameter).
–
()φ ν=⋅ ⋅Tc
2
desorb
d
surf
2
. This corresponds to desorption
of D atoms from the surface as molecules. The desorption
rate constant is
() ν
νλ=⋅ ⋅
−
⋅
⋅
T e
d
0
d
des
2
E
kT
2
D
B
(m
2
s
−1
) where
ν
0
d
is the frequency associated to desorption and
λ
des
(m)
is the jumping distance between two surface-adsorption
sites. This can be estimated to be
λ
=
n
des
1
surf
.
–
→
()φ ν=⋅Tc
bulksurf
sb
surf
. This corresponds to the
absorption of a D adatom from the surface to the bulk
(with the assumption of low mobile concentration). The
absorption rate constant is
()ν ν=⋅
−
⋅
T e
sb
0
sb
E
kT
A
B
(s
−1
) with
ν
0
sb
the frequency associated to absorption.
–
→
() ()()φ νθ=⋅=⋅−Tcx 01
bulksurf
bs m
. This corre-
sponds to the release of a D atom from the bulk to the
surface (resurfacing). The surface becomes inactive once
it is fully covered by D atoms (
θ−=10
). The rate con-
stant for this process is
()ν
νλ=⋅ ⋅
−
⋅
T e
bs
0
bs
abs
E
kT
R
B
(m
1
s
−1
)
with
ν
0
bs
the frequency associated to resurfacing and
λ
abs
(m) the jumping distance between the rst TIS that the HI
encounters in the bulk and the adsorption site. It can be
estimated to be
λ =
n
n
abs
surf
TIS
.
–
()
()
φ
=− ⋅
∂
∂
=
DT
c
x
x
diff
0
m
. This corresponds to the diffu-
sion of the absorbed D atom from the rst bulk TIS below
the surface (
=x 0
) to deeper in the bulk (
>x 0
).
Regarding the pre-exponential factor, the same remark as for
the detrapping process applies here: a change of one order of
magnitude can affect the value of the different energies (
E
A
,
E
D
and
E
R
) by about 0.1 eV for exposure at 500 K and 600 K.
According to different authors [6, 19, 20], the pre-exponential
factor for desorption used to reproduce experimental measure-
ments is
λν⋅> ⋅> ⋅
−−
0
.01cm
s0
.001 cm s
21
des
2
0
d
21
. A value
of
λ
des
of the order of 0.2 nm (~interatomic distance in the W
lattice) and
ν =
−
10 s
0
d
13 1
leads to
λ ν⋅= ⋅
−
0.004cm s
des
2
0
d
21
. As
a consequence, it is assumed
ν =
−
10 s
0
d
13 1
. It is also assumed
that
ν ν==
−
10 s
0
sb
0
bs
13 1
, which is the order of magnitude of
what is calculated with the harmonic transition-state theory
for these adsorption and resurfacing processes [21].
The evolution of
()=c x 0
m
and
c
surf
is then described by the
balance of uxes (gure 2) as follows:
→→
φφφφ φ
∂
∂
=−−− +
t
c
surf
atom excdesorbsurf bulk bul
ks
ur
f
(3)
→→
⎜⎟
⎛
⎝
⎞
⎠
λ
φφφ⋅
∂
∂
=−−
=
c
t
.
x
m
0
surf bulk bulksur
fd
iff
(4)
The different parameters of the surface and bulk models
are summarized in table1. The values used for the non-free
parameters are also given in table1. The parameters that need
to be determined are called ‘free’ parameters.
2.2. Steady-state analysis and determination
of surface-energy barriers
Equations (1) and (2) give a general description of the model
in the bulk and equations(3) and (4) describe the model for
the surface. This set of equationsare solved numerically using
the code to simulate the experimental results (sections 2.3 and
2.4). Before going into the details of the simulations, a steady-
state analysis and a simplied model is presented in this sec-
tionthat intends to dene a strategy which will allow us to
determine the surface-energy barriers.
In order to understand the main features of the model, the
steady states of equations(3) and (4) are investigated when
=
∂
∂
0
c
t
surf
and
()

=
∂
∂
=
0
c
t
x 0
m
. In addition, it is considered that
the diffusive ux of particles from the sub-surface to the bulk
φ
diff
is negligible (i.e.
( )
=
∂
∂
=
0
c
x
x 0
m
) in order to simplify
the approach. It can be shown by simulation that this ux
is, indeed, not dominant. The steady-state regime is charac-
terized by constant values of
()=c x 0
m
and
c
surf
(and so
θ
.)
written as
c
m
eq
,
c
surf
eq
and
θ
eq
.
Following this assumption, a relation between
()=c x 0
m
and
c
surf
can be derived from equation(4) in the steady state:
()
()
()
ν
νθ
== ⋅
−
c
x
T
T
c
0
1
.
m
eq
sb
bs
surf
eq
eq
(5)
Using this relation in equation (3) in the steady state, with
θ
=
c
n
eq
surf
eq
surf
and assuming

=
∂
∂
0
c
t
surf
, we have the following
relation:
()()ωω− ⋅⋅ −⋅ +=vT cc20
d
surf
eq
2
1
surf
eq
2
(6)
with
()
()
ω
σ=Γ
⋅+
− P
n
1atom
1
exc
r
surf
and
()ω =− ⋅ΓP1
2ratom
.
These quantities are introduced only to simplify the notations.
By solving equation(6), the value of
c
surf
eq
can be calculated:
ων
ωω
ν
=
+⋅
⋅−
⋅
c
T
T
8
4
.
surf
eq
1
2
d2
1
d
()
()
(7)
If
()→vT 0
d
(no desorption of molecules) or
→Γ ∞
atom
(high ux), the surface concentration is
→ =
∞
c c
surf
eq
surf
=⋅
ω
ωσ
−
−+ ⋅
n
P
Pn
surf
1
1
2
1
r
rexc surf
. If
σ = 0
exc
(no abstraction), this con-
centration is
n
surf
. In the case of a non-negligible abstraction,
Nucl. Fusion 57 (2017) 056002

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Simulations of atomic deuterium exposure in self-damaged tungsten" ?

Finally, the 2. 06 eV detrapping energy is attributed to D trapping in cavities based on literature reporting observations on the growth of cavities, even though this could also be understood as D desorbing from the C-D bond in the case of hydrocarbon contamination in the experimental sample. 

Q2. Why is tungsten chosen as the divertor material in ITER?

Due to its good mechanical and thermal properties, tungsten (W) has been chosen to be the material constituting the divertor region in ITER. 

Q3. How much dislocation density decreases upon annealing?

upon annealing up to 1200 K, the total amount of dislocations (trap 4 and 5) decreases by 70% in the simulations, similarly to the experimental analysis of STEM images [7], which showed a decrease of 66% in the dislocation density. 

Q4. Why does the retention in the traps affect the results?

Due to their low detrapping energies, the retention in those traps does not influence the results considering that the exposure temperature is 600 K. – 

Q5. Why is trap 3 necessary in the simulations?

The presence of trap 3, however, is necessary in their simulations because otherwise the low-temperature shoulder (observed experimentally) would not appear in the simulations. 

Q6. What is the kinetic stability of a cavity in self-damaged W?

In order to be conclusive in relation to the presence of cavities in selfdamaged W, further experimental and theoretical studies are needed to characterize the energetic and the kinetic stability of W vacancy clusters in self-damaged W.It must also be noted that the detrapping energy of 2.06 eV could also be related to the desorption of D from the D–C bond in the case where the sample surface would be contaminated with an amorphous hydrocarbon layer. 

Q7. How did Oda describe the GB effect on hydrogen solubility?

using a thermodynamic model to describe the GB effect on hydrogen solubility, Oda [44] showed that the GBs decrease (respectively increase) the value of the solution energy (respectively the solubility) significantly below 1000 K. 

Q8. What is the important issue related to the recombination coefficient?

In addition, it has already been pointed out [30–32] that the most important issue related to the recombination coefficient is the large scattering of the different values used in the literature. 

Q9. What is the diffusion coefficient for hydrogen calculated using DFT?

For this study, the diffusion coefficient for hydrogen calculated using DFT by Fernandez et al [15] is used: ( ) = × ⋅ ⋅− − −⋅D T 1.9 10 e  m sH 7 2 1k T 0.2 eV B . 

Q10. What is the main dissipation process of the H atoms on a?

In the case of the H atoms on a clean W surface, the dissipation by electron–hole excitation seems to be the main dissipation process although, as explained earlier, the surface of the materials used in the experiments simulated in this paper may not be clean W surfaces, which may change the relative efficiency of the different dissipation processes. 

Q11. How does the evolution of the profile of mobile particles be described?

In this model, the evolution of the profile of mobile particles for three different times < <t t t1 2 3 can be described as a gradient from the source to the migration depth ( )R td at each time =ti 1,2,3 (figure 3(a)). 

Q12. What is the detrapping energy of H bound with a mono-vacancy?

It has been shown by DFT calculations [15, 53] that the detrapping energy of H bound with a mono-vacancy is 1.2 eV−1.1 eV if the mono-vacancy is filled with 3–5 H and it becomes 1.5−1.3 eV if the mono-vacancy is filled with 1–2 H, as shown figure 8. 

Q13. what is the order of magnitude of what is calculated with the harmonic transition-state theory?

It is also assumed that ν ν= = −10 s0 sb 0 bs 13 1, which is the order of magnitude of what is calculated with the harmonic transition-state theory for these adsorption and resurfacing processes [21]. 

Q14. What is the effect of the surface on the insertion of low energetic ions?

experimental results by ‘t Hoen et al [10] showed that the insertion of low energetic ions (<5 eV/D) is limited by the surface process. 

Q15. What is the proxy for neutron damage?

A good proxy to simulate the damage induced during neutron irradiations has been found in MeV heavy-ion implantations and especially MeV W ions [2], the latter irradiation resultingKeywords: tungsten, damaged material, rate-equation modeling, deuterium atoms, fuel retention(Some figures may appear in colour only in the online journal)NF10. 

Q16. what is the pre-exponential factor for desorption used to reproduce experimental measurements?

According to different authors [6, 19, 20], the pre-exponential factor for desorption used to reproduce experimental measurements is    λ ν⋅ > ⋅ > ⋅− −0.01 cm s 0.001 cm s2 1 des 2 0 d 2 1. A value of λdes of the order of 0.2 nm (~interatomic distance in the W lattice) and ν = −10 s0 d 13 1 leads to λ ν⋅ = ⋅ −0.004 cm sdes 2 0 d 2 1. 

Q17. How can the authors characterize the migration of mobile particles into the bulk?

To characterize the migration of mobile particles into the bulk from a surface source of mobile particles (described by cm MAX) a simple analytical model can be used, as firstNucl. 

Q18. How is the energy barrier to go from bulk to surface ER calculated?

It is assumed that the energy barrier to go from bulk to surface ER is roughly the migration energy of H in the bulk, as shown by several DFT calcul ations [26, 27], i.e. =E 0.2 eVR .