self-trapping reactions, one can find that ℓ He / 1=
ffiffiffiffiffi ffi
j He
p
[67]. Recalling that in Ref.
[62] j He has varied by four orders of magnitude, the helium self-trapping mechanism
should result in a two orders of magnitude difference in ℓ He , which contradicts the
experimental observations. A possible reconciliation of the experimental data with
their theoretical interpretation could be related to the following effects, which are not
allowed for in the simple analysis based on the form of the RD equations. First, one
can assume that the seeds for helium nano-bubble nucleation are formed by the
pre-existing lattice defects. In this case, ℓ He would be inversely proportional to the
defect density. The second one takes into account the MD simulation results
showing that the growth of the helium nano-bubbles on its own produces lattice
defects [15, 58, 68], which could serve as the helium trapping and nano-bubble
nucleation sites [51]. As a result, an avalanche effect occurs (a growing nano-bubble
produces seeds for nucleation of another nano-bubble), which makes the final
evolution of the formation of the helium nano-bubble layer very weakly dependent
on the particular initial helium trapping mechanism that provides the initial seed for
the helium bubbles, and, therefore, on the magnitude of j He [51] (although the time
needed to form such a layer is inversely proportional to j He , which implies, in
agreement with the experimental data, a fixed helium fluence).
Finally, it is conceivable that the formation of a large amount of helium clusters
very close to the surface, which is observed in MD simulations at some orientations
of the tungsten crystal [69], inhibits deeper penetration of helium.
At the target temperatures below 1000 K, the helium-reach layer does not exhibit
visible macroscopic change at helium fluence, Φ He , above Φ layer . It is plausible that
this is due to the so-called “bursting” of the nano-bubbles situated just beneath the
surface, which is observed in the MD simulations (e.g. see [70]). As a result of such
bursting, the very first layer of the nano-bubbles becomes actually open voids that
stop penetration of low-energetic helium deeper into the target and effectively
“freeze” the whole nano-bubble layer.
However, the situation becomes very different for the tungsten temperatures in
the range between 1000 and 2000 K. Instead of having a “freezed” layer of the nanobubbles at the fluence Φ He > Φ layer , nano-tendrils with diameter ~10 nm with some
embedded helium nano-bubbles start to grow from the surface (see Fig. 3.10),
forming the so-called “fuzz” and individual trees of nano-tendrils (e.g. see [5, 72–
74]). According to the experimental data, the thickness of the fuzz is proportional to
(Φ He À Φ layer )
1/2 [62]. We notice that similar growth of nano-tendrils under helium
irradiation was observed on many metals including Mo, Ta, Fe, Ni, Ti, etc., which
indicates that fuzz formation exhibits very general features of helium interaction
with metals (see corresponding references in [24]).
Although few mechanisms of nano-tendrils growth have been suggested (see
related references in [24] for details), neither of them can explain the whole set of the
available experimental data. Most probably, the fuzz growth is related to large
stresses imposed in the bulk material by continuously growing helium bubbles,
which results in plastic deformation of the lattice. Recent experimental observations
3.2 Basic Features of Hydrogen/Helium Transport in Plasma-Facing Materials
61
ffiffiffiffiffi ffi
j He
p
[67]. Recalling that in Ref.
[62] j He has varied by four orders of magnitude, the helium self-trapping mechanism
should result in a two orders of magnitude difference in ℓ He , which contradicts the
experimental observations. A possible reconciliation of the experimental data with
their theoretical interpretation could be related to the following effects, which are not
allowed for in the simple analysis based on the form of the RD equations. First, one
can assume that the seeds for helium nano-bubble nucleation are formed by the
pre-existing lattice defects. In this case, ℓ He would be inversely proportional to the
defect density. The second one takes into account the MD simulation results
showing that the growth of the helium nano-bubbles on its own produces lattice
defects [15, 58, 68], which could serve as the helium trapping and nano-bubble
nucleation sites [51]. As a result, an avalanche effect occurs (a growing nano-bubble
produces seeds for nucleation of another nano-bubble), which makes the final
evolution of the formation of the helium nano-bubble layer very weakly dependent
on the particular initial helium trapping mechanism that provides the initial seed for
the helium bubbles, and, therefore, on the magnitude of j He [51] (although the time
needed to form such a layer is inversely proportional to j He , which implies, in
agreement with the experimental data, a fixed helium fluence).
Finally, it is conceivable that the formation of a large amount of helium clusters
very close to the surface, which is observed in MD simulations at some orientations
of the tungsten crystal [69], inhibits deeper penetration of helium.
At the target temperatures below 1000 K, the helium-reach layer does not exhibit
visible macroscopic change at helium fluence, Φ He , above Φ layer . It is plausible that
this is due to the so-called “bursting” of the nano-bubbles situated just beneath the
surface, which is observed in the MD simulations (e.g. see [70]). As a result of such
bursting, the very first layer of the nano-bubbles becomes actually open voids that
stop penetration of low-energetic helium deeper into the target and effectively
“freeze” the whole nano-bubble layer.
However, the situation becomes very different for the tungsten temperatures in
the range between 1000 and 2000 K. Instead of having a “freezed” layer of the nanobubbles at the fluence Φ He > Φ layer , nano-tendrils with diameter ~10 nm with some
embedded helium nano-bubbles start to grow from the surface (see Fig. 3.10),
forming the so-called “fuzz” and individual trees of nano-tendrils (e.g. see [5, 72–
74]). According to the experimental data, the thickness of the fuzz is proportional to
(Φ He À Φ layer )
1/2 [62]. We notice that similar growth of nano-tendrils under helium
irradiation was observed on many metals including Mo, Ta, Fe, Ni, Ti, etc., which
indicates that fuzz formation exhibits very general features of helium interaction
with metals (see corresponding references in [24]).
Although few mechanisms of nano-tendrils growth have been suggested (see
related references in [24] for details), neither of them can explain the whole set of the
available experimental data. Most probably, the fuzz growth is related to large
stresses imposed in the bulk material by continuously growing helium bubbles,
which results in plastic deformation of the lattice. Recent experimental observations
3.2 Basic Features of Hydrogen/Helium Transport in Plasma-Facing Materials
61