# Atomistic Mechanism from Vacancy Trapped H/He Atoms to Initiation of Bubble
in W under Low Energy Ions Irradiation

Yu-Wei Youa, Xiang-Shan Konga, Q. F. Fanga, Jun-Ling Chenb, G.-N. Luob, C. S.
Liua,∗, B. C. Panc,†, and Y. Daid,‡00footnotetext<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>aKey Laboratory of
Materials Physics, Institute of Solid State Physics, Chinese Academy of
Sciences, P. O. Box 1129, Hefei 230031, P. R. China bInstitute of Plasma
Physics, Chinese Academy of Sciences, Hefei 230031, P. R. China cHefei
National Laboratory for Physical Sciences at Microscale and Department of
Physics, University of Science and Technology of China, Hefei 230026, P. R.
China dSpallation Neutron Source Division, Paul Scherrer Institut, 5252
Villigen PSI, Switzerland

###### Abstract

With the first-principles calculations of H and He induced energetics change
we demonstrate that in W the accumulation of H (up to 9) and He (up to 4) in a
single vacancy (V) surprisingly reduce the formation energy of first and
second nearest vacancy (as low as $\sim$0 eV), which gives the direct evidence
of V-H(He) complex mutation mechanism from V-Hn(Hen) to V2-Hn(Hen) and with
the potential to lead to the growth of H/He-vacancy complexes: an initial step
to H and He bubble. This finding well explains the long-standing problem of
why H and He bubbles being produced on W surface exposed to low-energy (far
lower than displacement threshold energy) D or He ions irradiation. The
further identified repulsive (attractive) interaction between V-H12(V-He14)
and additional H(He) illustrates the experimentally observed big difference of
deposition depth of H (${\mu}m$) and He ($\sim$100Å) bubbles in W even the
migration rate of He is far larger than that of H.

††journal: Journal of Nuclear Materials

##  1 Introduction

Tungsten (W), a high-Z material, has been chosen to be the plasma facing
material (PFM) in the next step fusion device ITER [1] due to its excellent
properties of high melting point and low sputtering yield. However, as a PFM,
W must be exposed to extremely high fluxes of deuterium (D), tritium and
helium (He) ions and neutrons, which directly leads to the displacement
damage, bubble formation, and ultimate failure of the material [2, 3, 4, 5].
Therefore it is crucial to understand hydrogen (H)/He-metal-atoms and H/He-
defects interactions in the material.

Generally, defects in materials such as dislocations, grain boundaries and
vacancies can act as traps for H and He, and origins of H and He bubbles.
Among these defects, vacancy receives much more attention. A series of works
by Fukai _et al_. indicated that H can stabilize and increase the
concentration of vacancy because the vacancy formation energies in metals are
reduced substantially due to the insertion of H atoms [6, 7, 8, 9]. The role
of vacancy on trapping H to form the V-Hn complex and the maximum number of
$n$ in the complex were emphasized in the cases of many metals such as Pd [9,
10, 11], Al [12, 13, 14], Fe [10, 15, 16] and W [17, 18, 19, 20]. Nucleation
free energies evaluated with density function theory indicated that H trapping
assists the divacancy formation in bcc W crystal [21]. No doubt, these
contribute enormously to our understanding of H bubble formation and
blistering, but the microscopic atom-level relationship between H bubble
formation and H trapping in vacancies is far from understood, i.e., it is
still unclear that how the V-Hn complexes grow to form H bubbles.

Particularly, the minimum energy of D ions for producing displacement damage
in W is calculated to be 940 eV on the basis of the displacement threshold
energy of 40 eV [22], whereas the experimental results have shown that D
plasmas with energy of tens of eV definitely produce blisters [23, 24, 25, 26,
27]. In sharp contrast with the case of W, the experimental result [28]
reported no bubbles formation in Pd implanted by 10 keV D to a very high
supersaturation of about 1.7 D/Pd mole ratio. Shu thought that the lowered
vacancy formation energy by trapping H might be responsible for the bubble
formation in W when the incident H ion energy is greatly lower than the
threshold value for the displacement [27]. Ogorodnikova _et al._ proposed that
several D atoms in a single vacancy could cause the displacement of
neighboring lattice atoms due to stress-induced atomic diffusion, creating a
divacancy and thus initiate bubble growth [29]. It is also found
experimentally that the extent of blistering in W depends on the crystal
orientation [23, 24, 25, 26, 27]. Similar to H, He irradiation also often
leads to blister formation and subsequent degradation of the mechanical
properties of metals [30]. Experimental results showed that bubbles are formed
in W so far as the incident He ion energy is above 5 eV, which is the surface
barrier potential energy for He penetrating into the W and is much lower than
the threshold energy (500 eV) [31]. Empirical potential studies in $\alpha$-Fe
and Ni suggested that a spontaneous emission of a self-interstitial atom
nearby Hen, V-Hen and V2-Hen complexes is possible if $n$ is large enough [32,
33]. Using first-principles methods, Fu _et al_. investigated the energetics
of Vm-Hen complex in $\alpha$-Fe and predicted that the emission of a self-
interstitial atom close to Hen complex is energetically favorable for n$>$4
[34, 35]. Meanwhile, Henriksson _et al._ suggested a mechanism for the growth
of small He bubbles in low-energy He implanted W by performing molecular
dynamics simulations: displacements of W atom nearby Hen complex towards the
surface via the formation of (111) crowdion interstitials [36, 37].

Therefore, two crucial questions arise. The first question is how the
energetics of nearest neighboring metal atoms of the V-Hn and V-Hen complexes
change with the increase of $n$, in other words, what will happen to the
neighboring metal atoms of the vacancy as the number of trapped H or He atoms
increases? Does the creation of new vacancy become more easily at the
neighboring sites closest to the trapped H/He vacancy with the number of H or
He atoms? The second question is what are the similarity and difference in the
local structures and energetics between V-Hn and V-Hen complexes. Here, the
similarity should be related to the common feature that both H and He bubbles
can be formed under low energy ions irradiation; the difference should be
related to the different behaviors of H and He bubbles. The answers to the
first question should play a dominant role in atomic-level understanding the H
and He bubble formation mechanism; the answers to the second question will
help us understand the difference (for example, in deposition depth) between H
and He bubbles. In this paper, we have performed systematic first-principles
calculations mainly to examine the energetics of relevant V-H/Hen complexes in
bcc W in hope of shedding light on the formation mechanism of H and He
bubbles. In addition, some calculations in Pd (its stable H-site is octahedral
interstitial site) have been carried out to make a comparison and explore the
obvious difference mentioned above in H behaviors between W and Pd.

##  2 Computation method

The present calculations are performed within density functional theory as
implemented in the VASP code with the projector augmented wave potential
method [38]. The generalized gradient approximation and the Perdew-Wang
functional are used to describe the electronic exchange and correlation effect
[39]. The supercell composed of 128 lattice points ($4\times 4\times 4$) is
used. The relaxations of atomic position and optimizations of the shape and
size of the supecell are performed. The plane wave cutoff and k-point density,
obtained using the Monkhorst-Pack method [40], are both checked for
convergence for each system to be within 0.001 eV per atom. Following a series
of test calculations a plane wave cutoff of 500 eV is used and a k-point grid
density of $3\times 3\times 3$ is employed. The structural optimization is
truncated when the forces converge to less than 0.1 eV/nm. The vacancy, H(He)
interstitial and substitutional defect formation energies are computed by
following formula:

$E_{f}=E_{tot}^{nW,mF}-nE^{W}-mE^{F},$ (1)

where $F$ indicates foreign H or He, $E_{tot}^{nW,mF}$ is the total energy of
the system with n W atoms and m foreign atoms like H or He, $E^{W}$ is the
energy per atom of pure crystal W and $E^{F}$ is one half of the energy of H2
molecule (-3.40 eV) or the energy of an isolated He atom (0.00 eV). The
binding energies of interstitial H or He atoms are determined for different
configurations, which is expressed by:

$E_{b}^{F1,F2,\cdots,Fn}=\sum_{1}^{n}E_{tot}^{Fn}-E_{tot}^{F1+F2+\cdots+Fn}-(n-1)E_{tot}^{pure},$
(2)

where $E_{tot}^{Fn}$ is the energy of the W system with foreign atom $Fn$,
$E_{tot}^{F1+F2+\cdots+Fn}$ is the energy of the system with foreign atoms
from $F1$ to $Fn$, and $E_{tot}^{pure}$ is the total energy of pure crystal W.
In such a scheme a positive binding energy indicates attractive interaction
while a negative value means a repulsion. The trapping energy
$E_{tr}^{V-F_{n}}$, when the number of H(He) atoms is increased from $n-1$ to
$n$ in a vacancy, is defined as:

$E_{tr}^{V-F_{n}}=E_{tot}^{V-F_{n}}-E_{tot}^{V-F_{n-1}}-(E_{tot}^{F_{tet}}-E_{tot}^{pure}),$
(3)

where _n_ is the number of $F$ atoms and $E_{tot}^{V-F_{n}}$ is the total
energy of the system with $n$ $F$ atoms in a vacancy, $E_{tot}^{F_{tet}}$ is
the total energy of the W system with a H(He) tetrahedral interstitial defect.
A negative value of $E_{tr}^{V-F_{n}}$ indicates taking an interstitial H(He)
atom and adding it to a vacancy that already contains $n-1$ H(He) atoms is
energetically favorable, with $|E_{tr}^{V-F_{n}}|$ being the energy gained in
that process. Here, we specially calculate the new vacancy formation energy of
the W atom close to the Vm-1-Fn complex using the following equation:

$E_{f}^{V_{new}}=E_{tot}^{V_{m}-F_{n}}+E^{W}-E_{tot}^{V_{m-1}-F_{n}},$ (4)

where $E_{tot}^{V_{m}-F_{n}}$ is the total energy of the system with $m$
vacancies holding $n$ F atoms. Zero point energy corrections are not taken
into account, as it has very little influence (10-2 eV) on our results such as
binding energy, trapping energy and vacancy formation energy.

##  3 Results and discussion

###  3.1 Binding properties of interstitial H-H and He-He pairs

Our calculated defect formation energy results of H and He in the perfect W
system are in good agreement with that previously reported [41, 42]: both H
and He prefer to occupy tetrahedral interstitial site (TIS) rather than
octahedral interstitial site (OIS), and the energy difference of H(He) at OIS
and TIS is 0.39 eV(0.21 eV). So in the present work the interactions of two
H(He) atoms located at different TIS separated by a certain distance are
considered. The calculated binding energies as a function of the final
distances of the two H(He) atoms in the W system are shown in Fig. 1. The
results show that the binding energy increases with the increasing distance
between the two H atoms, and fluctuates around zero when the distance is
larger than 0.2 nm which agrees well with the results reported by Liu _et al_
[43]. The negative value of binding energy indicates the existence of
repulsive interactions between near interstitial H atoms. The minimum binding
energy is -0.46 eV in the W system, corresponding to the nearest distance of
the two H atoms (0.16 nm). Due to the repulsive interactions of H atoms in the
W system, H atoms can not form cluster easily but diffuse deeper into the bulk
from the H-implanted W surfaces. In contrast, the binding energy is positive
and decreases as the increase of the distance between the two He atoms, and
fluctuates around zero when the distance is larger than 0.30 nm. The maximum
binding energy is 1.08 eV when the two He atoms are separated apart by 0.15
nm, which is in good agreement with the results reported by Becquart _et al_
[30]. Moreover, it is noticeable that when the distance between the two He
atoms ranges from 0.16 to 0.30 nm, they will aggregate together spontaneously
to the distance of $\sim$0.15 nm. Therefore, He atoms can form cluster easily,
which hinders the diffusion of He into the deep bulk.

###  3.2 The effect of interstitial H/He atoms on the vacancy formation

According to the relationship of defect concentration with temperature and
defect formation energy [14], at 300 K the equilibrium concentration of
vacancy is relatively low ($\sim$10-54) due to the large vacancy formation
energy of 3.20 eV in the perfect W system. As pointed out above, under low-
energy D or He ion irradiation (below threshold energy) no W atom is displaced
to form a vacancy, however bubbles are observed at the W surface [23, 24, 25,
26, 27, 31]. It is natural to firstly ask whether interstitial H and He atoms
could result in substantial change in the vacancy formation energy. So, the
effects of tetrahedral interstitial H and He on the vacancy formation have
been studied. As shown in Table 1, the vacancy formation energies of the W
atoms surrounded by 1, 2, 3 and 4 nearest H atoms at TIS are 1.99 eV, 0.83 eV,
-0.35 eV and -1.39 eV, respectively. Meanwhile, the calculated binding
energies suggest that the occupancy of two H atoms (the distance between the
two H atoms is optimized to more than 0.2 nm) around the same W atom is
possible, however the occupancy of 3 and 4 H atoms around the same W atom is
difficult because of their repulsive interactions. In contrast, even one
interstitial He atom can reduce the vacancy formation energy to -1.36 eV,
suggesting the nearest W atom of interstitial He becomes unstable. The large
positive binding energy indicates that there exist strong attractive
interaction among the He atoms around the same W atom. Thus, both H and He
atoms at TIS do reduce the energy required for the nearby vacancy formation
considerably, especially He. Once the new vacancy is formed, it will change to
the V-Hn or V-Hen complex.

###  3.3 H/He-monovacancy interactions

H and He diffuse with the barriers of as small as 0.2 eV [44] and 0.06 eV [30,
44] in perfect W, respectively, indicating that H and He can migrate quickly
until they are tightly trapped by the defects to form H(He)-defect complex. In
this part, our main objective is to explore the energetics related to the
V-Hn(V-Hen) complex. We firstly calculate the trapping energy per H and He
atom displayed in Fig. 2 as a function of the number of H and He trapped
_sequentially_ in a single vacancy. For the case of H in single vacancy, with
increasing number of H atoms the trapping energy shows a generally increasing
trend, and its occasional fluctuations originate from the presence of H
configurations with high symmetry. The atomic configurations of one to twelve
H in the vacancy are in good agreement with the results reported by Ohsawa
[19]. The side length of the unit cell of having trapped 12 H atoms inside the
vacancy expands by $\sim$5% compared to the perfect unit cell. And the
formation of a H2 molecule inside a vacancy is not observed. The Bader’s
charge analysis [45] proves that H gains charge from surrounding W, and the
averaged charge around H changes from $\sim$-0.54 $\mid$$e$$\mid$ to
$\sim$-0.62 $\mid$$e$$\mid$, which results in the repulsive interactions among
the H atoms inside the vacancy, and that is why H2 molecule is not observed.
It is energetically favorable for a W monovacancy to trap as many as 12 H
atoms. The further calculation has been carried out of the binding energy
between an additional H atom and the V-H12 complex, which is shown in the
inset of Fig. 2. The calculated binding energy clearly indicates that the
presence of monotonically increasingly repulsive interaction with decrease of
the distance between additional H atom and the V-H12 complex. And when their
distance is increased to at least 0.44 nm the binding energy approaches zero,
suggesting that H atoms can not aggregate around the V-H12 complex to grow and
form H bubbles only based on the trapping H role of vacancy.

In contrast, the trapping energy of He in single vacancy is more negative than
that of H in vacancy, indicating that He atoms are more strongly trapped in W
vacancy than H atoms, which is consistent with the previously reported results
that the binding of He and the vacancy is much stronger than that of H and the
vacancy [44]. As displayed in Fig. 2, the trapping energy of He firstly
increases rapidly from about -5 eV to about -3 eV and then fluctuates around
-2.7 eV, being always far below zero energy even if He atoms is added up to
16. That is, He is extremely more favorable to aggregate in the vacancy rather
than sit at the TIS far away from vacancy. Why can the vacancy trap so many He
atoms? The optimized structure configurations from one to sixteen He atoms
trapped in the vacancy are shown _on the same scale_ in Fig. 3. Obviously,
with increasing He atoms the systems expand and distort more and more strongly
but the nearest distance of He-He keeps about 0.16 nm. And 15th and 16th He
atoms indeed move out of the original unit cell with the vacancy, indicating
that the vacancy can trap up to 14 He atoms and additional He atoms prefer to
cluster round the V-He14 complex, which is in agreement with the tendency to
form He clusters confirmed in Ref. [30]. Here it should be stressed that the
binding energy of V-He14 complex with additional He atom is more than one eV
larger than the strongest binding energy between two interstitial He atoms.
Therefore He atoms may aggregate persistently inside/around vacancy to grow
and form He bubbles. The unit cell of having trapped 14 He atoms expands by
$\sim$26% in length compared to the perfect unit cell, indicating that the
swelling from He atoms is very heavy. There exist high symmetry configurations
for the cases of 1, 2, 3, 4, 6 and 8 He atoms, which are partially responsible
for the fluctuation in the trapping energy with the number of He atoms.

Based on the above obtained results: the existence of respective repulsion-
and attraction-interactions of interstitial H pairs and interstitial He pairs
in bulk W, single interstitial He atom yielding the negative vacancy formation
energy while single interstitial H atom leading to the reduced but still
positive vacancy formation energy, and the appearance of repulsive interaction
between additional H and V-H12 complex and strongly attractive interaction of
additional He with V-He14 complex, we may draw the following conclusions.
During He atom diffuses into the bulk it can be easily attracted to the V-Hen
complex or the other He atoms. Whereas during H atoms diffuse into the bulk,
because of the absence of the attractive force from the V-H12 complex or the
other H atoms, H atoms can diffuse deeper into the bulk than He atoms. Thus it
could be understandable that even at temperatures where the migration rate of
He is far larger than that of H at 500 K, He will form bubbles right at
$\sim$10nm to the W surface, while H bubbles are found at micrometer depths
[46, 47, 48, 49, 50, 51, 52].

###  3.4 Mutation from V-H/Hen complex into V2-H/Hen to lead to the growth of
H/He-vacancy complex

Although the above obtained results clearly reveal that a single vacancy in W
can trap as many as 12 H or 14 He atoms, it remains unclear how the V-Hn and
V-Hen complexes grow to form H and He bubbles specially due to the saturation
of H trapped inside vacancy. Using Eq. (4), we systematically calculate the
new (second) neighboring vacancy formation energy of the W atom closest to the
vacancy trapped $n$ H or He atoms (i.e., V-Hn or V-Hen complex). Note that the
first nearest neighbor ($1nn$), second nearest neighbor ($2nn$) and third
nearest neighbor ($3nn$) (see the inset of Fig. 4) vacancy formation energies
around the already existed vacancy are 3.16 eV, 3.52 eV and 3.22 eV,
respectively. Thus, it is much difficult that the vacancy grows to form large
vacancy clusters spontaneously under low energy ions irradiation. However, to
our surprise, after the already existed vacancy having trapped H or He atoms
the situation will be very different. As shown in Fig. 4, the $1nn$ and $2nn$
vacancy formation energies are displayed as a function of the number of
trapped H or He atoms inside the vacancy. The $1nn$ and $2nn$ vacancy
formation energies of the V-Hn complex reduce in a steplike way, slowly at the
first (i.e., when the number of H is between 1-5) and then decrease very
rapidly to $\sim$0 eV when the trapped H number increases from 6 to 9. It
should be stressed that the substantial reduction in $1nn$ and $2nn$ vacancy
formation energies presently observed is quite different from the previously
reported vacancy formation energies in metals due to the insertion of H [9,
53], where the energy of a vacancy is lowered mainly by the sum of binding
energies of H atoms with vacancy. In general, the $1nn$ vacancy formation
energy is smaller than the $2nn$ vacancy formation energy. Compared to the
remarkably change in the $1nn$ and $2nn$ vacancy formation energies, the $3nn$
vacancy formation energy decreases very weakly, here which is not presented in
Fig. 4 for clarity.

In sharp contrast, as shown in Fig. 5 we have not observed much strong
decrease in the $1nn$ and $2nn$ new vacancy formation energies of H-vacancy
complex in Pd. It is found that the maximum of 6 H atoms can be held in a
vacancy in Pd and the configurations of the H atoms are in good agreement with
previous results [11]. The resulting neighboring vacancy formation energy due
to the trapped 6 H atoms is still larger than 1.2 eV, therefore, it is
reasonable that as pointed out previously no bubbles form in Pd implanted by
10 keV D ions [28].

For the case of V-Hen complex as shown in Fig. 4, the $1nn$ and $2nn$ vacancy
formation energies decrease sharply and almost linearly before He inside
vacancy adds up to 10 and then do not change obviously. It should be pointed
out that both $1nn$ and $2nn$ vacancy formation energies are lower than 0 eV
when the number of trapped He is beyond 4. The $3nn$ vacancy formation energy
closest to the V-Hen complex behaves like that of the V-Hn complex, being
unsensitive to the trapped He atom number. The great difference in energetics
between H and He trapped in a single vacancy is in that the $1nn$ and $2nn$
vacancy formation energies decease to $\sim$0 eV when the trapped atom number
is up to 9 for H whereas the trapped number is larger than 4 for He. The
reasons for the substantial reduction of new vacancy formation energy near the
V-Hn and V-Hen complexes can be understood by the weakened W-W metal bond
which originates from two parts: the increased W-W bond length and the
decrease of electron density between W-W atoms around the corresponding
complex. The averaged nearest-neighbor distances of both the $1nn$ and $2nn$ W
atoms increase by $\sim$0.005 nm for the V-Hn complex and $\sim$0.012 nm for
the V-Hen complex when $n$ changes from 1 to 12. The increase of the W-W bond
length weakens the W-W interactions, causing the reduction of vacancy
formation energies nearby V-Hn and V-Hen complexes. The electron density
around $1nn$ and $2nn$ W atoms is obviously reduced. The electron densities of
(110) plane across $1nn$, $2nn$ and $3nn$ atoms (named by 1, 2 and 3 in Fig.
4) of the vacancy are calculated and displayed in Fig. 6. Specially, we take
two different cases of the V-H10 and V-He6 complexes for example, and they are
compared with the ‘empty’ vacancy (Fig. 6(a)). As shown in Fig. 6(b), the
accommodation of 10 H atoms in the single vacancy directly results in the
extension of the light blue region, and the shrinking of the dark green region
around the $1nn$ and $2nn$ W atoms, while the various color regions around the
$3nn$ W atoms do not show evident changes. These indicate that the electron
density around $1nn$ and $2nn$ W atoms reduces obviously, whereas the electron
density around the $3nn$ W atoms shows little change. Similar phenomena are
found for the V-He6 complex that the electron density round the $1nn$ and
$2nn$ W atoms decreases obviously (shown in Fig. 6(c)), and some dark green
regions even disappear, but the electron density around the $3nn$ W atoms of
the V-He6 complex changes little. The reduction of the electron density could
further weaken the interactions of W-W, leading to the decrease of the $1nn$
and $2nn$ vacancy formation energies nearby both V-H10 and V-He6 complexes.

From above results and discussion, we can conclude that the new vacancy is
much easily produced in the region closest to the V-Hn and V-Hen complexes
when the number of H or He inside the vacancy is beyond a certain number. This
means that the V-Hn and V-Hen complexes can easily (even spontaneously) mutate
into the V2-Hn and V2-Hen complexes when $n$ is large enough, respectively.
The further calculations have been performed about the energetics of closest W
atoms (nearby V2-H10 (V2-He10) complex) which are removed in a stepwise
fashion to create V3-H10(V3-He10) and V4-H10(V4-He10) complexes, we find that
the successive vacancy formation energies to form these complexes are 1.87
eV(-2.26 eV) and 2.42 eV(-0.43 eV), respectively. If the trapped H or He atoms
are larger than 10, these new vacancy formation energies will be further
reduced. This finding suggests a cascade mechanism, as recently reported in
the large variation of vacancy formation energies in the surface of
crystalline ice [54], whereby once a vacancy is created and when this vacancy
traps certain numbers of H or He atoms, neighboring W atoms become very weakly
bound and thus easily to be removed to form a new vacancy, and with the
potential to lead to the growth of H/He-vacancy complexes.

A V-He-complex mutation growth mechanism for He bubble has been mentioned by
Caspers et al. in 1978 [55], which works as follows. Assuming the He atoms are
trapped in a single vacancy and form V-Hen complex due to the strong He-
vacancy bonding energy. Some fraction of the V-Hen complexes, which reach a
critical size, mutate into a complex with two vacancies (V2-Hen) by ejecting
an interstitial into the metal matrix. By absorbing He atoms and further
ejecting interstitial metal atoms, the complexes become larger and larger and
finally lead to He bubble formation. Our results indicate that the mechanism
is also suitable for H. The presently observed substantial reduction of the
$1nn$ and $2nn$ vacancy formation energies close to the V-Hn and V-Hen
complexes, to our best knowledge, not only gives the direct evidence for this
mechanism, but also gives the reasonable explanation of the experimental
results: Why H and He bubbles with diameters of a few to hundreds of microns
could form on W surface even if the ion energy is so low that no displacement
damage is created [23, 26, 47, 48, 49, 50].

##  4 Conclusions

In summary, based on the first-principles method we have investigated the
energetics of H/He-vacancy complex in W by calculating the trapping energy of
H/He and the new nearby vacancy formation energy. We find that a monovacancy
can accommodate up to 12 H and 14 He to form V-H12 and V-He14 complexes,
respectively. And the V-H12 exhibits strong repulsive role with the approach
of additional H atoms, but the V-He14 shows great attraction to the nearby He
atoms. The aggregation of H and He in W vacancy remarkably favors the creation
of new vacancy around the H/He-vacancy complexes: the first-nearest-neighbor
and second-nearest-neighbor formation energies of vacancy close to the H/He-
vacancy complex decrease to about 0 eV when the trapped atom number is up to 9
for H and larger than 4 for He. These results, not only provide the direct
evidence of the He-vacancy complex mutation mechanism proposed by Caspers for
the He bubble formation, but also suggest a cascade mechanism, as recently
reported in the large variation of vacancy formation energies in the surface
of crystalline ice by Watkins et al, whereby once a vacancy is created and
when this vacancy traps certain numbers of H or He atoms, neighboring W atoms
become very weakly bound and thus easily to be removed to form a new vacancy,
and with the potential to lead to the growth of H/He-vacancy complexes.
Besides, the results well explain the experimental phenomena — the huge
discrepancy of deposition depth of H and He in W, and the formation of H/He
bubble with diameters of a few to hundreds of microns on W surface even if the
ion energy is so low that no displacement damage is created. However, there is
no quite large decrease in the new neighboring vacancy formation energy nearby
a vacancy having trapped H atoms in Pd, leading to the neighboring vacancy
formation energy still being larger than 1.2 eV, thus no bubbles formation in
Pd even implanted by 10 keV D ions.

## Acknowledgement

This work was supported by the National Magnetic Confinement Fusion Program
(Grant Nos.: 2011GB108004 and 2009GB106005), the National Natural Science
Foundation of China (Nos.: 91026002, 91126002) and the Strategic Priority
Research Program of Chinese Academy of Sciences (Grant Nos.: KJCX2-YW-N35 and
XDA03010303), and by the Center for Computation Science, Hefei Institutes of
Physical Sciences.

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Figure caption:

Fig. 1. The binding energy as a function of the final distance of interstitial
H-H(He-He) pair in the perfect W system. The diatomic He will aggregate
together to a distance of $\sim$0.15 nm when the two He atoms are separated by
from 0.16 to 0.30 nm. The inset is the enlargement of the binding energy of
two He atoms separated by from 0.143 to 0.154 nm.

Fig. 2. Trapping energy per H and He in a single W vacancy as a function of
the number of trapped H and He atoms, here the zero point is the energy of H
or He at the TIS far away from the vacancy. Inset: the binding energy between
additional H atom with the V-H12 complex as a function of the distance between
additional H atom and the center of the V-H12 complex.

Fig. 3. The lowest-energy configurations of 1 to 16 He atoms inside (or
around) a single W vacancy, note that here all configurations are shown using
the same scale. Big and small balls indicate W and He atoms, respectively.

Fig. 4. The $1nn$ and $2nn$ vacancy formation energy of the V-Hn and V-Hen
complexes as a function of the number of trapped H or He atoms. Lines are
guides to the eyes.

Fig. 5. The $1nn$ and $2nn$ vacancy formation energy of the V-Hn complex as a
function of the number of trapped H atoms in Pd. Lines are guides to the eyes.
Inset: trapping energy per H in a single Pd vacancy as a function of the
number of H atoms, here the zero point is the energy of H at the OIS far away
from the vacancy. From the inset, a maximum of 6 H atoms could be held in a
vacancy in Pd.

Fig. 6. The electron density maps (electron/Å3) of three different cases: the
empty vacancy (a), the V-H10 (b) and V-He6 (c) complexes. In all cases, the
slices are cut through the same (110) plane of the supercell considered. 1, 2
and 3 denote the first, second and third nearest neighbor W atoms of the
vacancy. ‘x’ and ‘y’ represent the directions of $\langle$1̄01$\rangle$ and
$\langle$01̄0$\rangle$.

Table 1 The vacancy formation energy $E_{f}^{V}$ (eV) of W atom that has
multiple (1-4) neighboring interstitial H(He) atoms are calculated. Meanwhile,
the binding energy $E_{b}$(eV) of these H(He) atoms are also calculated using
Eq. 2.

| 1H | 2H | 3H | 4H | 1He | 2He | 3He | 4He
---|---|---|---|---|---|---|---|---
$E_{b}$(eV) | – | 0.00 | -0.06 | -0.22 | – | 1.08 | 2.18 | 3.61
$E_{f}^{V}$(eV) | 1.99 | 0.83 | -0.35 | -1.39 | -1.36 | -3.38 | -5.31 | -6.64