through the target lattice is limited by volumetric diffusion and trapping/de-trapping
processes, so that it is possible to assume that the free hydrogen density at the
“surface” is zero. Nonetheless, it is plausible that the presence of hydrogen at the
surface along with a rather high hydrogen surface potential barrier E b can significantly alter the penetration and accumulation of the low energy hydrogen species in
the target (e.g. [52]). Therefore, the issue of hydrogen absorption at the surface
requires further thorough investigation.
Although the RD equations look similar and independent of both the target
material and the species transported through its lattice, in practice, the mechanisms
of the formation of the traps and, therefore, the overall dynamics of transport and the
characteristic processes associated with it are sensitive to both the target material and
the species transported.
Therefore, to be more specific in what follows, we consider the main features of
hydrogen and helium behavior in tungsten, which is chosen as the material for the
divertor targets in ITER and, therefore, has been studied very extensively in last
decade. In addition, tungsten, being irradiated by hydrogen and helium, exhibits
interesting physical phenomena, somewhat similar to those observed in other metals
(e.g. molybdenum, tantalum, etc. [24]).
Numerous DFT and MD simulations show a very different character of the
interactions of few hydrogen and helium atoms with tungsten (e.g. see [24] and
the references therein). Unlike hydrogen, the interstitial helium atoms in the tungsten
lattice exhibit a strong trend to clustering (formation of binaries, triplets, etc.) even in
the absence of lattice defects. For example, in Fig. 3.8 one can see an increase of the
helium binding energy to the interstitial cluster containing N helium atoms with
increasing N, whereas the binding energy for a hydrogen atom to a vacancy
decreases along with increasing the number of hydrogen atoms.
The formation of the interstitial helium cluster imposes large localized stress on
the lattice, which finally results in the creation of the Frenkel pair. This reduces the
–7
2 2.5 3 3.5 4 4.5 5 5.5 6
–6
–5
–4
–3
–2
–1
N
E
N –E
N–1 –E
1 (eV)
E N –E N–1 –E 1
Hydrogen Binding Energy (eV)
Liu et al. [87]
Johnson et al. [64]
Heinola et al. [88]
Ohsawa et al. [90]
Number of Hydrogen
1.4
1.2
1.0
0.8
0.6
0.2
0.0
–0.2
0
2
4
6
8 10 12 14 16
Tetrahedral interstitial H
E N –N E 1
E
N –N E
1 (eV)
–1.7
–1.6
–1.5
–1.4
–1.3
–1.2
–1.1
–1
–0.9
–0.8
Fig. 3.8 On the left, the He binding energy in an interstitial He cluster as a function of N (red
curve), reproduced with permission from [53], © American Physical Society 2014; On the right, the
H binding energy with a mono-vacancy as a function of the number of hydrogen atoms.
(Reproduced with permission from [54], © IAEA 2014)
3.2 Basic Features of Hydrogen/Helium Transport in Plasma-Facing Materials
59
processes, so that it is possible to assume that the free hydrogen density at the
“surface” is zero. Nonetheless, it is plausible that the presence of hydrogen at the
surface along with a rather high hydrogen surface potential barrier E b can significantly alter the penetration and accumulation of the low energy hydrogen species in
the target (e.g. [52]). Therefore, the issue of hydrogen absorption at the surface
requires further thorough investigation.
Although the RD equations look similar and independent of both the target
material and the species transported through its lattice, in practice, the mechanisms
of the formation of the traps and, therefore, the overall dynamics of transport and the
characteristic processes associated with it are sensitive to both the target material and
the species transported.
Therefore, to be more specific in what follows, we consider the main features of
hydrogen and helium behavior in tungsten, which is chosen as the material for the
divertor targets in ITER and, therefore, has been studied very extensively in last
decade. In addition, tungsten, being irradiated by hydrogen and helium, exhibits
interesting physical phenomena, somewhat similar to those observed in other metals
(e.g. molybdenum, tantalum, etc. [24]).
Numerous DFT and MD simulations show a very different character of the
interactions of few hydrogen and helium atoms with tungsten (e.g. see [24] and
the references therein). Unlike hydrogen, the interstitial helium atoms in the tungsten
lattice exhibit a strong trend to clustering (formation of binaries, triplets, etc.) even in
the absence of lattice defects. For example, in Fig. 3.8 one can see an increase of the
helium binding energy to the interstitial cluster containing N helium atoms with
increasing N, whereas the binding energy for a hydrogen atom to a vacancy
decreases along with increasing the number of hydrogen atoms.
The formation of the interstitial helium cluster imposes large localized stress on
the lattice, which finally results in the creation of the Frenkel pair. This reduces the
–7
2 2.5 3 3.5 4 4.5 5 5.5 6
–6
–5
–4
–3
–2
–1
N
E
N –E
N–1 –E
1 (eV)
E N –E N–1 –E 1
Hydrogen Binding Energy (eV)
Liu et al. [87]
Johnson et al. [64]
Heinola et al. [88]
Ohsawa et al. [90]
Number of Hydrogen
1.4
1.2
1.0
0.8
0.6
0.2
0.0
–0.2
0
2
4
6
8 10 12 14 16
Tetrahedral interstitial H
E N –N E 1
E
N –N E
1 (eV)
–1.7
–1.6
–1.5
–1.4
–1.3
–1.2
–1.1
–1
–0.9
–0.8
Fig. 3.8 On the left, the He binding energy in an interstitial He cluster as a function of N (red
curve), reproduced with permission from [53], © American Physical Society 2014; On the right, the
H binding energy with a mono-vacancy as a function of the number of hydrogen atoms.
(Reproduced with permission from [54], © IAEA 2014)
3.2 Basic Features of Hydrogen/Helium Transport in Plasma-Facing Materials
59